Note: Descriptions are shown in the official language in which they were submitted.
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TITLE: FUSION POWER BASED ON A SYMMETRICAL PLASMA BEAM
CONFIGURATION
FIELD
[0001] The described embodiments relate to applied physics and, more
particularly,
to a system and method for thermonuclear fusion due to energy concentration
through
focusing of converging fuel particle plasma beams.
INTRODUCTION
[0002] Fusion power may generally refer to the power generated by nuclear
fusion
reactions. In one kind of fusion reaction that naturally occurs in many stars,
such as the
sun, two light atomic nuclei fuse together to form a heavier nucleus and, in
doing so,
release a large amount of energy. In some contexts, fusion power may also
refer to the
production of net usable power from a fusion source, similar to the usage of
the term
"hydroelectric power" to describe the production of net usable power from
water driven
turbines.
[0003] Fusion power may be generated from reactions using deuterium
from water
as fuel, without the need to use radioactive tritium as fuel. The amount of
deuterium in one
gallon of ordinary water contains the energy equivalent of three hundred
gallons of
gasoline. It should be understood that these numbers are illustrative only.
SUMMARY
[0004] The following introduction is provided to introduce the reader
to the more
detailed discussion to follow. The introduction is not intended to limit or
define any claimed
or as yet unclaimed invention. One or more inventions may reside in any
combination or
sub-combination of the elements or process steps disclosed in any part of this
document
including its claims and figures.
[0005] Fusion reaction rate
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[0006] As presently understood, fusion reactions are achieved by
bringing two or
more nuclei close enough to one another that their residual strong force
(i.e., nuclear force)
will act to pull the two or more nuclei together and form one larger nucleus.
When two
"light" nuclei fuse, the usual result is the formation of a single nucleus
having a slightly
smaller mass than the sum of the masses of the original two nuclei. In this
case, the
difference in mass between the single fused nucleus and the original two
nuclei is released
as energy according to the well-known mass-energy equivalence formula:
E=mc2 (1)
[0007] However, if two "heavy" nuclei of sufficient mass fuse together,
the mass of
the resulting single nucleus may be greater than the sum of the reactants'
original masses.
In this case, according to equation (1), a net input of energy from an
external source will be
required to drive such fusion reasons. Generally speaking, the dividing line
between "light"
and "heavy" nuclei is iron-56. Above this atomic mass, energy will generally
be released by
nuclear fission reactions; below it, by fusion.
[0008] The fusion of two nuclei is generally opposed by the repulsive
electrostatic
force created between the shared electrical charges of the two nuclei,
specifically the net
positive charge of the protons contained in the nuclei. To overcome this
electrostatic force
(referred to sometimes as a "Coulomb barrier"), some external source of energy
is
generally required. One way to provide an external source of energy is to heat
the reactant
atoms. This approach also has the additional benefit of stripping the atoms of
electrons
leaving the atoms as bare nuclei. Typically, the nuclei and electrons are
formed into
plasma.
[0009] As the temperature required to provide the nuclei with enough
energy to
overcome the repulsive electrostatic force varies as a function of the total
charge,
hydrogen, the atom having the smallest nuclear charge, tends to react at the
lowest
temperatures. Helium also has an extremely low mass per nucleon and is
therefore also
energetically favourable as a potential fusion product. Consequently, most
fusion reactions
are based on combining isotopes of hydrogen (protium, deuterium, or tritium)
to form
isotopes of helium, such as 3He or 4He.
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[0010] Reaction cross section, denoted cr, is a measure of the
probability of a fusion
reaction as a function of the relative velocity of the two reactant nuclei. If
the reactant nuclei
have a distribution of velocities, as would be expected for a thermal
distribution within
plasma, then an average over the distributions of the product of cross section
and velocity
may be performed. Reaction rate, in terms of fusion per volume per unit of
time, may then
be defined as (ov) times the product of the number density of reactant atoms.
Accordingly,
the reaction rate may equal:
f =(-n .f)v) (2a)
for one reactant, where n represents the number density of atoms of the single
reactant,
and:
f = n,n,(ov) (2b)
for two different reactants, where n1 represents the number density of atoms
of a first
reactant and n2 represents the number density of atoms of a second reactant
distinct from
the first reactant.
[0011] The product (ov) increases from near zero at room temperatures
up to
significant magnitudes at temperatures in the range of 10-100 keV (2.2-22 fJ).
For similar
plasma densities, deuterium-tritium (D-T) fusion tends to benefit from the
lowest ignition
temperature. Other possible fusions cycles include the proton-proton (p-p)
fusion cycle,
which provides the primary fusion power for stars like the Sun, the
deuterium¨deuterium
(D-D) fusion cycle, the proton-boron (p-11B), the deuterium-helium (D-3He),
and the helium-
helium (3He-3He) cycle. However, these other fusion cycles typically require
larger ignition
energies and, in some cases, depend on 3He (which is relatively scarce on
Earth).
[0012] Deuterium-Triti urn fuel cycle
[0013] One nuclear reaction presently used in fusion power is the
deuterium-tritium
fuel cycle, which may be expressed as:
2,D+3,7,24He oin
(3)
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where 2,D represented a Deuterium atom, 3,7' represents a tritium atom, ;He
represents a
helium atom, and oin represents a free neutron. Deuterium (also referred to as
"Hydrogen-
2") is a naturally occurring isotope of hydrogen and, as such, is universally
available.
Tritium (also referred to as "Hydrogen-3") is another isotope of hydrogen, but
occurs
naturally in small or negligible amounts due to its relatively brief
radioactive half-life of
approximately 12.32 years. Consequently, the deuterium-tritium fuel cycle
requires
synthesis of an ample supply of tritium atoms to be used in the fusion
reaction. Two
possible reactions to synthesize tritium from atoms of lithium include:
oin+36Li_.> T + 24He (4)
or alternatively:
1 7 = 4 r 1
0 n+1,13-IT+n
2 e+On (5)
[0014]
The 6Li reaction is exothermic, providing a small energy gain for the reactor
in
the form of the released heat. On the other hand, the 7Li reaction is
endothermic, thereby
requiring energy, but does not consume the reactant neutron. At least some 7Li
reactions
may be used to replace neutrons lost due to reactions with other elements. In
either lithium
reaction, the reactant neutron may be supplied by the D-T fusion reaction
shown above in
equation (3). Most reactor designs take advantage of the naturally occurring
mix of 6Li and
7Li lithium isotopes.
[0015]
Several limitations are commonly associated with the D-T fuel cycle. For
example, the D-T fuel cycle tends to produce substantial amounts of neutrons
that induce
radioactivity within the reactor structure and impose significant constraints
on material
design. Only about 20% of the fusion energy yield appears in the form of
charged particles
with the rest of the fusion energy being provided as neutron, which tends to
limit the extent
to which direct energy conversion techniques might be applied. The use of D-T
fusion
power also depends on available lithium resources, which are less abundant
than
deuterium resources and in growing demand due to increased production of
Lithium based
batteries and other related technologies. Yet another limitation of the D-T
fuel cycle is that it
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requires handling of the radioisotope tritium. Similar to hydrogen, tritium
may be difficult to
contain and may leak from reactors in some quantity.
[0016] Proton-proton chain reaction occurring within stars
[0017] As an alternative to the D-T fuel cycle, the proton-proton
chain reaction is a
naturally occurring process within stars of approximately the same size as the
Sun or
smaller. The proton¨proton chain reaction is one of several fusion reactions
by which stars
of equal or lesser size as the Sun convert hydrogen to helium. However, unlike
the D-T-fuel
cycle, the proton-proton chain reaction does not induce radioactivity through
neutron
production.
[0018] In general, proton¨proton fusion will occur when the temperature
(i.e., kinetic
energy) of the reactant protons is high enough to overcome their mutual
electrostatic or
Coulomb repulsion. While it is now accepted that proton¨proton chain reactions
are the
dominant thermonuclear reactions fueling the sun and other stars, originally
the
temperature of the sun was thought to be too low to overcome the Coulomb
barrier.
However, through the discovery and development of quantum mechanics, it is now
postulated that tunneling of the reactant protons through the repulsive
electrostatic barrier
allows for the proton-proton chain reason to occur at lower temperatures than
the classical
prediction permitted.
[0019] The first of multiple steps in the proton-proton chain reaction
involves the
fusion of two protons into deuterium, in the process releasing a positron, a
neutrino and
energy, as one of the reactant protons beta decays into a neutron. This step
of the proton-
proton chain reaction may be expressed as:
D e
+ +0.42MeV (6)
where each H represents a proton, 21 D represents a product deuterium atom, e+
represents a positron, and ye represents a neutrino. This first step of the
proton-proton
chain is extremely slow, not just because the protons have to quantum tunnel
through their
Coulomb barrier, but also because the step depends on weak atomic
interactions. To
illustrate the speed of the reaction, deuterium-producing events are rare
enough in the sun
that a complete conversion of its hydrogen would take more than 1010 (ten
billion) years
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given the prevailing conditions of the sun core. The fact that the sun is
still shining is due to
the slow nature of this reaction; if the reaction went faster, it is theorized
that the Sun would
have exhausted its hydrogen long ago.
[0020] In the next step of the proton-proton chain reaction, the
positron is very
quickly annihilated by an electron and the combined mass energy of the
positron and
electron is converted into two gamma rays and energy according to:
e- +e- ¨>27+1.02MeV (7)
where each y represents a gammy ray. Subsequently, the deuterium atom produced
in the
first step of the proton-proton chain reaction fuses with another proton to
produce a light
isotope of helium, namely 3He, a further gamma ray and energy according to:
;D+:H-4He+ y+ 5.49Me V (8)
[0021] For temperatures in the range of about 10-14 MK (mega-kelvins),
in the final
step of the proton-proton chain reaction, two of the light isotopes of helium
fuse together to
form a 4He isotope, two protons and energy according to:
;He+;He--4He+,1H+1111+12.86MeV (9)
[0022] Combining the reaction steps expressed in equations (8) and (9) and
canceling intermediate products, yields the overall proton-proton reaction
given by:
21D+2,D241-/e + 2y+ 23.84Me V (10)
[0023] In the Sun, the fusion path expressed in Equation (10) occurs
with about 86%
frequency with the remaining 14% due to other fusion reactions that prevail at
temperatures
exceeding 14 MK.
[0024] Satisfactory conditions of plasma velocity, temperature and
density necessary
to initiate fusion have been achieved in various research facilities. However,
attempts to
achieve fusion with a net energy output have so far been unsuccessful. It is
thought that
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one reason for the lack of success is that confinement time has not been
sufficient due to
plasma instabilities.
[0025] Here, we show plasma instabilities may be suppressed by a four
plasma
beam configuration symmetrical in space according to the minimization
principle of
potential energy. It is thought that a similar principle also ensures the
stability of stars in
astrophysics where nuclear fusion reactions occur. Confirmation tests are
proposed using
wires containing or encapsulating deuterium. If successful, the results may
lead to a
feasible approach to achieve commercial fusion power from water without the
use of
expensive and radioactive tritium as fuel.
[0026] In one broad aspect, there is provided a thermonuclear reaction
system for
generating a thermonuclear reaction, the thermonuclear reaction system
comprising: a
reaction chamber; at least four particle beam emitters supported spatially
around and
oriented toward a common focal region of the reaction chamber for directing
energized
particles of at least one thermonuclear fuel type from the particle beam
emitters as a
plurality of particle beams converging symmetrically at the common focal
region to instigate
the thermonuclear reaction; at least four particle beam receivers supported
spatially around
and oriented toward the common focal region, each particle beam receiver being
located
opposite a corresponding one of the at least four particle beam emitters; and
at least one
voltage source operatively coupled to each particle beam emitter and its
corresponding
particle beam receiver for generating an electrical current through each
particle beam.
[0027] In some embodiments, the at least four particle beam emitters
are supported
and oriented such that an angle between each particle beam is about 109.5 .
[0028] In some embodiments, at least one of the at least four particle
beam emitters
comprises a particle beam tube at least partially composed of a high-melting
point material
having a melting point substantially above an equilibrium temperature of the
energized
particles in the high-energy plasma state.
[0029] In some embodiments, the particle beam tube is at least
partially composed
of two materials comprising the high-melting point material and another
material, and
wherein an inner cylindrical surface of the particle beam tube is coated with
a layer of the
high-melting point material.
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[0030] In some embodiments, the high-melting point material comprises
tungsten or
graphite.
[0031] In some embodiments, the at least one of the at least four
particle beam
emitters further comprises an electromagnetic system for generating an
electromagnetic
field to provide radial confinement and axial acceleration of the energized
particles in the
high-energy plasma state within the particle beam tube.
[0032] In some embodiments, the electromagnetic system comprises a
voltage
supply electrically coupled to the particle beam tube and configured to
generate a primary
electrical current in an electrically conductive outer cylindrical portion of
the particle beam
tube running between the first end portion and the second end portion for
generating a
secondary electrical current flowing generally axially in the energized
particles in the high-
energy plasma state, the secondary electrical current for generating an
inwardly directed
radial force field within the electrically conductive outer cylindrical
portion to urge the
energized particles in the high-energy plasma state toward a central axis of
the particle
beam tube and to accelerate the energized particles in the high-energy plasma
state
toward the second end portion.
[0033] In some embodiments, the electromagnetic system further
comprises a
plurality of electromagnetic coils aligned axially with and supported exterior
to and in close
proximity surrounding the particle beam tube along at least a portion of
particle beam tube,
the plurality of electromagnetic coils for generating an axial magnetic field
within the particle
beam tube to provide supplemental axial confinement of the energized particles
in the high-
energy plasma state within the particle beam tube.
[0034] In some embodiments, the thermonuclear reaction system further
comprises
at least one ignition laser supported spatially around and optically coupled
with the reaction
chamber, each of the at least one of ignition lasers oriented toward the
common focal
region to generate and emit a laser beam converging at the common focal region
with the
plurality of particle beams for assisting instigation of the thermonuclear
reaction.
[0035] In some embodiments, an inner wall of the reaction chamber is
coated with
an inner wall layer substantially encompassing the inner wall and formed of a
high-melting
point material for providing the reaction chamber with thermal and gamma-ray
insulation.
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[0036] In some embodiments, the high-melting point material is
selected from the
group consisting of tungsten, graphite or tantalum hafnium carbide (Ta4HfC5).
[0037] In some embodiments, the energized particles emitted from the
at least four
particle beam emitters are in a charged state.
[0038] In some embodiments, the thermonuclear reaction system further
comprises
at least one particle converging element for focusing the energized particles
in the charged
state at the common focal region of the reaction chamber.
[0039] In some embodiments, the at least four particle beam emitters
are supported
around the reaction chamber in a three-dimensional spatial orientation.
[0040] In some embodiments, the three-dimensional spatial orientation is
substantially spherical.
[0041] In some embodiments, the three-dimensional spatial orientation
is
substantially symmetric in at least three mutually orthogonal planes.
[0042] In some embodiments, the plurality of particle beam emitters
are
approximately equidistant from the common focal region.
[0043] In some embodiments, the at least one thermonuclear fuel type
comprises an
isotope of Hydrogen.
[0044] In some embodiments, the electromagnetic system and the at
least one
voltage source are configured to generate a plasma beam in a closed electric
loop, the
closed electrical loop running through the plasma beam and a plasma sphere
located at the
common focal region.
[0045] In some embodiments, the at least one voltage source is
configured to supply
a sufficiently high initial voltage to electrify particles of the at least one
thermonuclear fuel
type in the at least four particle beam emitters.
[0046] In some embodiments, the at least one voltage source is configured
to
subsequently reduce the initial voltage to a minimum maintenance voltage in
order to
supply a desired level of electrical current running through the plasma beam.
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[0047] In some embodiments, the particles of the at least one
thermonuclear fuel
type are initially at a relatively low temperature in the at least four
particle beam emitters, as
the fuel particles enter the at least four particle beam emitters, and wherein
the particles of
the at least one thermonuclear fuel type in each of the at least four particle
beam emitters
are turned into plasma in the form of a lightning beam due to Joule heating by
the
generated electrical current after entering the at least four particle beam
emitters.
[0048] In some embodiments, the at least one voltage source is
configured to
generate at least one sufficiently large DC, AC, or pulse current capable of
pinching each of
the plurality of particle beams into a continuous lightning beam, the
continuous lightening
beam having a level of electric current, a diameter, a velocity, and a
temperature similar to
these of a regular lightning beam in nature, whereby a hot and dense core
forms inside the
plasma sphere due to radial collapse under electro-magnetic fields, the core
being capable
of sustaining stable and continuous fusion reactions.
[0049] In some embodiments, the at least one voltage source is
configured to
generate a plurality of sufficiently large AC or pulse currents arranged to
generate shock
waves directed towards the common focal region to maximize an energy
concentration at
the plasma sphere.
[0050] In some embodiments, the thermonuclear reaction system further
comprises
a plurality of hollow starter inductors configured to establish initial
boundary conditions for
the plurality of particle beams so that the plurality of particle beams may
each converge into
a pinched configuration.
[0051] In some embodiments, the at least one voltage source is
configured to apply
a voltage to the plurality of hollow starter inductors, and wherein the
plurality of hollow
starter inductors are configured to melt and/or vaporize due to Joule heating,
starting from
the common focal region, whereby the plurality of particle beams rapidly
become
electrically conducting lightning beams that collide and penetrate each other
at the common
focal region.
[0052] In some embodiments, the generated electrical current through
each particle
beam is sufficient to accelerate electrons in each particle beam to sufficient
large velocities
in the applied electric field, and wherein the electrons in turn attract
oppositely charged
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nuclei to achieve large velocities that become temperature due to particle
collision and
penetration at the core to achieve a sufficient core temperature, and wherein
a sufficient
core density is achieved due to converging magnetic forces.
[0053] In another broad aspect, there is provided a method of
generating a
thermonuclear reaction, the method comprising: providing at least one
thermonuclear fuel
type; energizing a supply of the at least one thermonuclear fuel type to
provide energized
particles of the at least one thermonuclear fuel type; accelerating the
energized particles of
the at least one thermonuclear fuel type into a reaction chamber as at least
four particle
beams oriented symmetrically toward a common focal region of the reaction
chamber;
generating an electrical current through each of the at least four particle
beams; and
converging the at least four particle beams at the common focal region to
instigate the
thermonuclear reaction.
[0054] In some embodiments, the at least four particle beam are
generated using at
least four particle beam emitters supported and oriented such that an angle
between each
particle beam is about 109.5 .
[0055] In some embodiments, at least some of the energized particles
of the at least
one thermonuclear fuel type are in a high-energy plasma state.
[0056] In some embodiments, the method further comprises generating an
electromagnetic field to provide radial confinement and axial acceleration of
the energized
particles in the high-energy plasma state into the reaction chamber.
[0057] In some embodiments, generating the electromagnetic field
comprises
inducing a secondary electrical current flowing in a generally axial direction
through the
energized particles in the high-energy plasma state.
[0058] In some embodiments, generating the electromagnetic field
further comprises
forming an axial magnetic field within the energized particles in the high-
energy plasma
state to provide supplemental radial confinement.
[0059] In some embodiments, at least some of the energized particles
of the at least
one thermonuclear fuel type are in a charged state.
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[0060] In some embodiments, the method further comprises providing a
supply of a
low pressure gas to the reaction chamber, the low pressure gas being reactive
with the
energized particles in the charged state to neutralize the energized particles
in the charged
state prior to arrival at the common focal region.
[0061] In some embodiments, the method further comprises focusing the
energized
particles in the charged state at the common focal region of the reaction
chamber.
[0062] In some embodiments, the method further comprises generating
and
providing at least one laser beam to the reaction chamber, and converging the
laser beam
at the common focal region with the plurality of particle beams to assist
instigation of the
thermonuclear reaction.
[0063] In some embodiments, the at least one thermonuclear fuel type
comprises an
isotope of Hydrogen.
[0064] In some embodiments, the method further comprises generating a
closed
electric loop through each particle beam in the at least four particle beams,
the closed
electrical loop running through each plasma beam and a plasma sphere located
at the
common focal region.
[0065] In some embodiments, energizing the supply of the at least one
thermonuclear fuel type comprises applying a sufficiently high initial voltage
to electrify
particles of the at least one thermonuclear fuel type.
[0066] In some embodiments, the method further comprises subsequently
reducing
the initial voltage to a minimum maintenance voltage in order to supply a
desired level of
electrical current running through each of the at least four particle beams.
[0067] In some embodiments, the particles of the at least one
thermonuclear fuel
type are initially at a relatively low temperature as the fuel particles enter
at least four
particle beam emitters, and wherein the particles of the at least one
thermonuclear fuel type
in each of the at least four particle beam emitters are turned into plasma in
the form of a
lightning beam due to Joule heating by the generated electrical current after
entering the at
least four particle beam emitters.
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[0068] In some embodiments, generating the electrical current through
each of the at
least four particle beams comprises generating at least one sufficiently large
DC, AC, or
pulse current capable of pinching each of the plurality of particle beams into
a continuous
lightning beam, the continuous lightening beam having a level of electric
current, a
diameter, a velocity, and a temperature similar to these of a regular
lightning beam in
nature, whereby a hot and dense core forms inside the plasma sphere due to
radial
collapse under electro-magnetic fields, the core being capable of sustaining
stable and
continuous fusion reactions.
[0069] In some embodiments, generating the electrical current through
each of the at
least four particle beams further comprises generating a plurality of
sufficiently large AC or
pulse currents arranged to generate shock waves directed towards the common
focal
region to maximize an energy concentration at the plasma sphere.
[0070] In some embodiments, the method further comprises providing a
plurality of
hollow starter inductors configured to establish initial boundary conditions
for the plurality of
particle beams so that the plurality of particle beams may each converge into
a pinched
configuration, and applying a voltage to the plurality of hollow starter
inductors, whereby the
plurality of hollow starter inductors melt and/or vaporize due to Joule
heating, starting from
the common focal region, and whereby the plurality of particle beams rapidly
become
electrically conducting lightning beams that collide and penetrate each other
at the common
focal region.
[0071] In some embodiments, the generated electrical current through
each particle
beam is sufficient to accelerate electrons in each particle beam to sufficient
large velocities
in the applied electric field, and wherein the electrons in turn attract
oppositely charged
nuclei to achieve large velocities that become temperature due to particle
collision and
penetration at the core to achieve a sufficient core temperature, and wherein
a sufficient
core density is achieved due to converging magnetic forces.
[0072] These and other aspects and features of various embodiments will
be
described in greater detail below.
BRIEF DESCRIPTION OF THE DRAWINGS
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[0073] A detailed description of various embodiments is provided
herein below with
reference to the following drawings, by way of example only, and in which:
[0074] Figure 1 is a schematic view of a thermonuclear reaction
system;
[0075] Figure 2 is a schematic view of an exemplary particle beam
emitter;
[0076] Figure 3 is a perspective schematic view of a configuration of
multiple particle
beam emitters in accordance with at least one embodiment;
[0077] Figure 4 is planar schematic view of the configuration of
multiple particle
beam emitters of Figure 3;
[0078] Figure 5A is a schematic profile view of a cross section of a
conducting
plasma beam in a radial direction;
[0079] Figure 5B is a schematic cross section view of a conducting
plasma beam
emitter;
[0080] Figure 6 is a schematic view of a dimensionless Lorentz force
distribution,
due to a uniform distribution of plasma density in a common focal region;
[0081] Figure 7 is a schematic view of a dimensionless Lorentz force
distribution,
due to an exponential distribution of plasma density in a common focal region;
[0082] Figure 8 is a schematic view of a thermonuclear reaction system
integrated
with an existing nuclear reactor design;
[0083] Figure 9 is a plot of simulation results showing temperature
and density
distributions in a radial direction for the common focal region of the
symmetrical four beam
configuration of Figure 3; and
[0084] Figure 10 is a plot of simulation results showing pressure
distribution in a
radial direction and fusion power output for the common focal region of the
symmetrical
four beam configuration of Figure 3.
[0085] It will be understood that reference to the drawings is made for
illustration
purposes only, and is not intended to limit the scope of the embodiments
described herein
below in any way. For simplicity and clarity of illustration, elements shown
in the figures
have not necessarily been drawn to scale. The dimensions of some of the
elements may be
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exaggerated relative to other elements for clarity. Further, where considered
appropriate,
reference numerals may be repeated among the figures to indicate corresponding
or
analogous elements.
DETAILED DESCRIPTION OF EMBODIMENTS
[0086] Various apparatuses, methods and compositions are described
below to
provide an example of an embodiment of each claimed invention. No embodiment
described below limits any claimed invention and any claimed invention may
cover
apparatuses and methods that differ from those described below. The claimed
inventions
are not limited to apparatuses, methods and compositions having all of the
features of any
one apparatus, method or composition described below or to features common to
multiple
or all of the apparatuses, methods or compositions described below. It is
possible that an
apparatus, method or composition described below is not an embodiment of any
claimed
invention. Any invention disclosed in an apparatus, method or composition
described below
that is not claimed in this document may be the subject matter of another
protective
instrument, for example, a continuing patent application, and the
applicant(s), inventor(s)
and/or owner(s) do not intend to abandon, disclaim, or dedicate to the public
any such
invention by its disclosure in this document.
[0087] It will be appreciated that numerous specific details are set
forth in order to
provide a thorough understanding of the exemplary embodiments described
herein.
However, it will be understood by those of ordinary skill in the art that the
embodiments
described herein may be practiced without these specific details. In other
instances, well-
known methods, procedures and components have not been described in detail so
as not
to obscure the embodiments described herein. Furthermore, this description is
not to be
considered as limiting the scope of the embodiments described herein in any
way, but
rather as merely describing implementation of the various embodiments
described herein.
[0088] The present application relates to fusion power based on the
concept of high
energy fuel carrying plasma beams passing through a common focal region.
Various
conditions including plasma velocity, temperature, and density are thought to
be necessary
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to initiate fusion reactions, and plasma stability is thought to be a
requirement to permit
sufficient confinement time.
[0089] Satisfactory conditions of plasma velocity, temperature, and
density
necessary to initiate fusion have been achieved in various research
facilities. However,
attempts to achieve fusion with a net energy output have so far been
unsuccessful. One
reason is that the repulsive forces among the particles having the same charge
near the
central region may make sufficient density concentrations difficult to
achieve. In general,
the lack of success is because confinement time has not been sufficient due to
plasma
instabilities.
[0090] Here, we show plasma instabilities may be suppressed by a four
plasma
beam configuration symmetrical in space according to the minimization
principle of
potential energy. Confirmation tests are proposed using wires containing or
encapsulating
deuterium. If successful, the results may lead to a feasible approach to
achieve commercial
fusion power from water without the use of expensive and radioactive tritium
as fuel.
Background
[0091] Stern Laboratories, of Hamilton, Ontario, Canada ["Stern"], is
equipped with a
16MW DC power supply with 13 individually controlled zones, which is one of
the highest
power and most versatile high current facilities in the world. Investigative
tests were carried
out at Stern where two plasma beams were successfully connected by an electric
current.
The connection centre of the plasma beams was observed to shift towards the
positively
charged electrode to an extent that the positive electrode was severely
damaged by the hot
plasma.
[0092] It is postulated here that this behaviour was caused by the
movement of the
electrons as a result of a physical attraction between the negatively charged
electrons and
the positively charged atomic nuclei in the plasma. The interaction between
electrons and
nuclei is consistent with a single plasma beam flowing in the same direction
of these
charged particles, in a way similar to the lightning strikes in nature, that
may provide an
alternative explanation on the source of neutrons detected during the Z-pinch
tests (Zeta
tests) performed at Harwell, UK in 1957 (Thonemann, P. C. et al., 1958).
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[0093] It is proposed that the electrons in these tests gained kinetic
energy
exceeding the bounding energy of the nuclei and was sufficient to split the
deuterons into
protons and neutrons. The energy of the deuterons, in equilibrium with that of
the electrons,
was adequate for fusion. Such equilibrium was reached for the Zeta tests with
a
confinement time in the order of 1 ms. However, fusion did not occur as all
the deuterons
travelled in the same direction without sufficient relative velocity to
overcome the energy
barrier for deuterium-deuterium (D-D) fusion. USSR Z-pinch tests carried out
in 1958
(Andrianov, A. M. et al., 1958) might have achieved some D-D fusion due to a
target /
beam mechanism, based on examination of the neutron energy spectra, although
the
amount of energy release was not adequate for the fusion reactions to be
confirmed by
measurements.
[0094] Early attempts to achieve controlled nuclear fusion were
typically based on
some variation of "pinch" machines where an axial electric current was applied
inside a
plasma in order to compress the plasma (see e.g. Thonemann, P. C. et al.,
1958;
.. Andrianov, A. M. et al., 1958; and McCracken, G. and Stott, P., 2005). In a
straight
cylindrical (linear) pinch, z is the axial coordinate and e is the azimuthal
coordinate; in a
toroidal pinch, the current is toroidal and the field poloidal. Early Z-pinch
tests were usually
characterized by kink and sausage instabilities (McCracken, G. and Stott, P.,
2005) which
prevented the achievement of a sufficient confinement time to ignite and
sustain fusion
reactions. After decades of efforts to resolve the instability issues
associated with the
earlier Z-pinch machines, the mainstream efforts to achieve fusion shifted to
tokamak
machines where hotter plasma temperatures were measured together with an
improvement
of plasma confinement. Tokamak machines however, are challenged by the
presence of an
edge-localized mode ["ELM"], micro-level turbulence, tritium retention and
material issues
.. as well as structural complexity.
[0095] Meanwhile, Z-pinch tests initially switched to implosion of
metal wires in an
attempt to achieve fusion and have so far generated powerful x-ray emissions
(Mosher, D.
et al., 1973; Pereira, N. R. and Davis, J., 1988). By arranging the metal
wires into an X-
shape [or "X-pinch"] (Zakharov, S., M. et al., 1982; Shelkovenko, T., A. et
al., 1999), using
two wires passing through a single point, a record near-solid density and a
temperature of
10 MK were observed at a micro pinch formed in the region of intersection
(Sinars, D. B. et
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al., 2003). Alternatively, metal wire arrays were arranged in parallel
(Burkhalter, P. et al.,
1979; Apruzese. J. P. et al., 2001) and a record temperature of 2 GK was
measured when
tungsten wires were replaced by steel wires at Sandia Labs (Haines, M. D. et
al., 2006).
Using 192 laser beams focusing into a small deuterium-tritium (D-T) target
through a
cylindrical gold hohlraum (indirect drive), a plasma density of 600 g/cc was
measured
recently (Glenzer, S. H. et at., 2012).
[0096] While recent experiments (e.g. Sinars, D. B. et al., 2003;
Haines, M. D. et at.,
2006; Glenzer, S. H. et al., 2012) demonstrated that the extreme temperature
and density
conditions existing naturally in the centres of the stars, such as the Sun,
have been
achieved in laboratory conditions, the confinement times were too short to
sustain fusion
reactions due to limitations imposed by plasma instability.
[0097] An alternative approach to fusion power was proposed based on
the concept
of high energy fuel carrying particle beams passing through a common focal
region,
optionally assisted by laser beams (Zheng, X. J., 2011), and, as an
enhancement, the
intersection of at least two plasma beams pinched by electric currents (Zheng,
X. J., 2012).
As further improvement to the X-pinch concept, this innovative approach
includes a multiple
beam configuration, symmetrical in three-dimensional space with respect to
each of the
beams, which may improve plasma stability in the common focal region.
[0098] Referring initially to Figure 1, there is illustrated a
schematic view of a
thermonuclear reaction system 100 in accordance with at least one embodiment
described
herein. Thermonuclear reaction system 100 includes a reaction chamber 110, a
fuel
injector 120, and a plurality of particle beam emitters 130 capable of
generating a plurality
of particle beams 135 composed of at least one type of thermonuclear fuel
particle. The
particle beam emitters 130 are supported spatially around and in fluid
communication with
reaction chamber 110, so that during operating of the thermonuclear reaction
system 100,
the particle beam emitters 130 emit the plurality of particle beams 135 into
the reaction
chamber 110. As discussed further below, the plurality of particle beams 135
are directed
into the reaction chamber 110 wherein they interact in such a way that a
thermonuclear
reaction may be instigated within the reaction chamber 110, which in at least
some cases
may be continuous (or pseudo-continuous) and self-sustaining.
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[0099] The particle beams 135 may be composed wholly or in some cases
only
partially of high energy particles existing in a plasma state. Where the
particle beams 135
are not composed wholly of plasma particles, the non-plasma particles within
the particle
beams 135 may retain a net charge, for example, a positive charge due to
electron loss
during ionization. In some embodiments, the non-plasma particles within the
particle beams
135 may be neutralized within the reaction chamber 110 subsequently to being
emitted
from the particle beam emitters 130. Alternatively, in some embodiments, the
non-plasma
particles within the particle beams 135 may retain their net charge within the
reaction
chamber 110. Either may be used for the design of thermonuclear reaction
system 100.
However, one disadvantage of utilizing particle beams 135 at least partially
containing
charged, non-plasma fuel particles may be the repulsive electrostatic forces
that exist
generally between any two charged particles. On account of the repulsive
electrostatic
force, it may be more difficult to realize a sufficiently high density of fuel
particles within the
reaction chamber 110 so as to initiate and sustain a thermonuclear reaction.
By neutralizing
any charged, non-plasma fuel particles within the reaction chamber 110 and
thereby
eliminating repulsive electrostatic forces between fuel particles in the
particle beams 135,
particle densities required for thermonuclear fusion may generally be easier
to attain within
the reaction chamber 110.
[00100] In some embodiments, the particle beams 135 may be generated by
ionizing
a supply of the at least one type of thermonuclear fuel particle provided by
the fuel injector
120. After ionization, the charged particles within the particle beam emitters
130 may then
be accelerated toward the reaction chamber 110. To neutralize any charged, non-
plasma
particles in the particle beams 135, for example, a supply of a low-pressure
reactive gas
may be pumped or otherwise provided into the reaction chamber 110 through a
suitable
gas inlet, so that individual charged particles in the particle beams 135
react with the
neutralizing gas within the reaction chamber 110 and lose any retained charge.
[00101] As shown in Figure 1, each of the particle beams 135 is
directed toward a
common focal region 140 of reaction chamber 110. The particle beams 135 may be
directed toward the common focal region 140 by arranging the particle beam
emitters 130
around the reaction chamber 110 in any suitable three-dimensional spatial
orientation. For
example, the particle beam emitters 130 may be arranged in a substantially
spherical
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CA 02887762 2015-04-10
arrangement around the reaction chamber 110 or otherwise so that the particle
beam
emitters 130 are essentially equidistant from the common focal region 140.
Alternatively,
the particle beam emitters 130 may be arranged to be substantially symmetric
in at least
three different planes (e.g., as defined in a Cartesian coordinate system),
which may in
some cases be mutually orthogonal. However, other three-dimensional spatial
orientations
for the particle beam emitters 130 are possible as well.
[00102] In some embodiments, converging elements 150 may be provided in
the path
of the particle beams 135 to assist in directing the particle beams 135
towards the common
focal region 140. While only one example of the converging elements 150 is
explicitly
illustrated in Figure 1, in some embodiments, additional converging elements
may be
included in thermonuclear reaction system 100. Each of the converging elements
150
included may be associated with a single one of the particle beams 135 or,
alternatively,
two or more of the particle beams 135.
[00103] In some embodiments, where the particle beams 135 contain at
least some
charged, non-plasma fuel particles, some of the convergent elements 150 may be
implemented using a magnetic lens. For example, the magnetic lens may consist
of several
electromagnetic coils arranged into a quadrupole, a sextupole, or some other
suitable
arrangement. When the electromagnetic coils are energized, the resulting
quadrupolar or
sextupolar magnetic field has a generally convex shape that deflects charged
particles
travelling through the magnetic field. The amount of deflection may be
controllable based
upon the strength of the magnetic field, which in turn may be controlled by
varying the
energizing current supplied to the electromagnetic coils. In this way, the
magnetic lens may
be effectively utilized to focus or otherwise converge the particle beams 135
at the common
focal region 140.
[00104] Alternatively, some of the converging elements 150 may be
implemented
using an electrostatic lens configured as a focusing element of charged
particle beams. For
example, in some embodiments, the electrostatic lens may be an Einzel lens, a
cylinder
lens, an aperture lens or a quadrupole lens. In some embodiments, the
converging
elements 150 may be a mixture of magnetic and electrostatic lenses.
- 20 -
CA 02887762 2015-04-10
[00105] Where the particle beams 135 are composed completely or nearly
completely
of plasma fuel particles, electrostatic or magnetic lenses will not generally
be suitable for
implementing the converging elements 150 because the plasma particles are
electrically
neutral overall and therefore not generally responsive to electromagnetic
fields. However, it
may still be possible to alter the path of a neutral particle beam existing in
complete or near
complete plasma state and thereby focus the particle beams 135 at the common
focal
region 140. One example configuration to achieving this result is described
below in more
detail with reference to Figure 2.
[00106] The inside surface of the reaction chamber 110 may be coated
with a suitable
insulating material to absorb any high energy gamma-rays produced during the
thermonuclear reactions taking place within the reaction chamber 110.
Different materials
having generally different thermal and electrical properties may be used to
coat the inside
surface of the reaction chamber 110. For example, melting point and heat
absorption
capability may be two of the relevant considerations for choosing an
appropriate coating
.. material. As a coolant liquid (not shown) may be applied also to the inside
surface of the
reaction chamber 110 in some embodiments, another relevant consideration for
the coating
material may be its chemical reactivity with the particular coolant fluid
used. A coating
material that is generally non-reactive with the coolant liquid may be
preferable. In some
embodiments, nuclear graphite or graphene, tungsten or other materials having
melting
points equal to or greater than those of graphite and tungsten may be used for
the material
used to coat the inside surface of the reaction chamber 110.
[00107] Converging the particle beams 135 at the common focal region
140 causes
the particle density existing at the common focal region 140 to increase. If
the particle
density rises to sufficiently high levels, a plasma sphere 145 having a
sufficiently high
temperature so as to instigate a thermonuclear fusion reaction within the
reaction chamber
110 may be created in the vicinity of the common focal region 140 and. For
example, the
density of the plasma sphere 145 may be comparable to the densities found in
the center of
the Sun (i.e., up to 160,000 kg/m3). By converging a sufficiently large number
of the particle
beams 135, each of which is composed of thermonuclear fuel particles
accelerated with
sufficient kinetic energy, the required particle densities for sustained
thermonuclear
reactions may be achieved in the reaction chamber 110. This result is also
achieved
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CA 02887762 2015-04-10
without the contribution of gravity effects present in stars that assist in
sustaining the
thermonuclear reactions that naturally occur in those and similar
environments. Rather,
particle and energy concentration may be realized in the reaction chamber 110
through the
acceleration and convergence of particle beams 135 at common focal region 140.
[00108] Optionally, an additional supply of input energy into the reaction
chamber 110
may be directed toward to the common focal region 140 in order to assisting in
igniting the
plasma sphere 145 and thereby instigate the thermonuclear reaction.
Accordingly, in some
embodiments, a plurality of lasers 160 may be arranged spatially around
reaction chamber
110 and, like the particle beam emitters 130, oriented toward common focal
region 140
near the center of the reaction chamber 110. The 160 may generate and emit a
plurality of
laser beams 165 that also are convergent at common focal region 140. In some
embodiments, laser guide tubes made of, for example, glass fibers (not shown)
may extend
some depth into reaction chamber 110 in order to guide the laser beams toward
the
common focal region 140.
[00109] In alternative embodiments, supplemental energy input devices (not
shown)
other than, or in addition to, the lasers 160 may also be used for igniting
the plasma sphere
145 to assist instigation of thermonuclear reactions. For convenience only,
and without
limitation, only a single one of the lasers 160 is shown explicitly in Figure
1, although more
than one laser or other supplemental energy input device may be used.
Moreover, any
number of lasers 160 may be included and may be arranged spatially around the
reaction
chamber 110 in any suitable arrangement in order to accommodate the desired
number of
lasers 160.
[00110] In some embodiments, the energy generated by the thermonuclear
fusion
reactions occurring at or near common focal region 140 may be sufficient to
maintain the
plasma sphere 145 at a sufficiently high temperature that continuous and
sustained
thermonuclear reactions may be instigated without the use of supplemental
energy input
devices (e.g., lasers 160). Accordingly, in some embodiments, the lasers 160
or other
supplemental energy input devices may be omitted from the thermonuclear
reaction system
100 and convergence of a sufficient number of the particle beams 135
accelerated to
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sufficient kinetic energies may suffice by themselves to both ignite and
sustain
thermonuclear fusion reactions.
[00111] However, convergence of the particle beams 135 by itself may
not be
sufficient to ignite the plasma sphere 145 and instigate a thermonuclear
fusion reaction.
Accordingly, in some embodiments, the lasers 160 or other supplemental energy
input
devices may be operated initially until a thermonuclear fusion reaction has
been instigated
within the reaction chamber 110, but thereafter then disabled. In that case,
the heat
generated from particle collisions due to convergence of the particle beams
135 may be
sufficient to sustain continuous thermonuclear reactions within the reaction
chamber 110
without benefiting from additional input energy supplied by the lasers 160 or
other
supplemental energy input devices.
[00112] In some embodiments, starter inductors (not shown) are used to
initiate the
fusion reaction. The starter inductors connect the particle beam emitters 130
through the
common focal region 140. These inductors may simply be hollow metal (e.g.,
copper) or
non-metal (e.g., graphite) pipes. Some of the inductors may contain particle
beams 135
directed towards the common focal region 140, while the others may contain
outgoing
particle beams along with fusion products. These starter inductors are used to
establish
initial boundary conditions for the colliding / penetrating fuel particle
beams to converge into
their final pinched configurations. Voltages and electric currents are then
applied to these
starter inductors and, when the starter inductors melt and/or vaporize due to
Joule heating,
starting from the common focal region 140, the particle beams 135 rapidly
become
electrically conducting lightning bolts that collide and penetrate each other
at the common
focal region 140.
[00113] It will be appreciated that different combinations and
configurations of the
elements described herein may be possible in different embodiments of the
thermonuclear
reaction system 100.
[00114] Reference is now made to Figure 2, which illustrates a
schematic view of an
exemplary particle beam emitter 200, which may be used to implement any or all
of the
particle beam emitters 130 shown in Figure 1 in accordance with at least one
embodiment.
Particle beam emitter 200 includes a hollow cylindrical particle beam tube 210
having a first
- 23 -
CA 02887762 2015-04-10
end portion 212, a second end portion 214 and an inner surface (not shown).
Particle beam
tube 210 may be composed of an electrically conductive material having a
melting
temperature substantially above an equilibrium temperature of the high energy
plasma or
ionized particles housed within the particle beam emitter 200. In certain
embodiments,
particle beam tube 210 may be formed of a material or composition having a
melting
temperature exceeding 1,800 C. Alternatively, the inner surface of the
particle beam tube
210 may be coated with a material or composition having a melting temperature
of 1,800 C
or higher. Examples of suitable materials for forming or coating the inner
surface of the
particle beam tube 210 include, but are not limited, to tungsten and graphite.
In some
embodiments, particle beam tube 210 may be composed of a hollow graphene
cylinder
coated on the inner surface with a layer of tantalum hafnium carbide
(Ta4HfC5), which has a
melting point of about 4200 C, or some other chemical compound having a
generally
higher melting point than carbon based materials such as graphene.
[00115] In the example arrangement illustrated in Figure 2, first end
portion 212 of
particle beam tube 210 is in fluid communication with a fuel injector (such as
fuel injector
120 shown in Figure 1) to receive a plasma 220 containing at least one type of
thermonuclear fuel particle. For example, the plasma 220 may contain particles
of :1-1 or
2,D or some other type of thermonuclear fuel particle. Plasma 220 may
typically be
provided by the fuel injector to the particle beam tube 210 at a relatively
high pressure and
temperature. In order to provide the supply of the plasma 220 to the particle
beam emitter
200, the fuel injector may convert an internal or separate external supply of
thermonuclear
fuel particles into their plasma state by heating and/or ionizing processes
prior to the
plasma 220 being received into the first end portion 212 of the particle beam
tube 210.
[00116] Second end portion 214 of particle beam tube 210 is located
opposite to the
first end portion 212 and may be in fluid communication with the reaction
chamber 110
(Figure 1). This allows particle beam emitter 200 to emit a corresponding one
of the particle
beams 135 (Figure 1) into reaction chamber 110. In some embodiments, at least
a portion
of second end portion 214 partially extends into reaction chamber 110 to a
desired depth.
The extension depth of the second end portion 214 may be varied depending on
the
application and to meet design and/or performance criteria for the
thermonuclear reaction
system 100 (Figure 1). However, a minimum distance between second end portion
214 of
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CA 02887762 2015-04-10
each particle beam tube 210 and common focal region 140 (Figure 1) should be
maintained
to ensure safe operation of the particle beam emitter 200 under the extreme
operating
conditions prevailing within reaction chamber 110. As discussed above, design
calculations, computer simulations and fine-tuning fusion firing tests are
required to
determine the design parameters of embodiments of thermonuclear reaction
system 100.
[00117] Particle beam emitter 200 may also include an electromagnetic
system 230
for generating an electromagnetic field (not shown) to provide radial
confinement and linear
acceleration of plasma 220 within particle beam tube 210 using a variation of
the "pinch"
concept (sometimes also referred to as the "Z-pinch" concept). According to
the pinch
concept, the interaction between an electrical current flowing through plasma
and an
induced (and/or externally applied) magnetic field causes inward compression
of the
plasma in a direction orthogonal to the direction of the current flow through
the plasma. In
effect, by inducing an axial current flowing in a direction parallel to a
central axis 216 of
particle beam tube 210, plasma 220 behaves somewhat like a plurality of
current-carrying
wires where each wire is carrying current in the same axial direction.
Consequently, the
plasma "wires" are each pulled toward each other by the mutually acting
Lorentz forces, the
overall result of which being that plasma 220 contracts itself inwardly toward
the central
axis 216 of particle beam tube 210 wherein the plasma 220 is concentrated. As
plasma 220
contracts inwardly and concentrates, the density of plasma 220 increases;
denser plasmas
may generate denser magnetic fields, increasing the inward force acting on
plasma 220,
and further compressing and concentrating the plasma 220 in the vicinity of
the central axis
216.
[00118] In order to achieve pinching of the plasma 220, the
electromagnetic system
230 may include a voltage supply 232 electrically coupled to particle beam
tube 210 and
configured to generate a primary electrical current 234 flowing in the hollow
cylindrical
section of particle beam tube 210. For example, the voltage supply 232 may
create a
potential difference between first end portion 212 and second end portion 214
so that the
primary electrical current 234 flows therebetween around the entire or
substantially the
entire periphery of the hollow cylindrical section. The magnetic field
associated with the
primary electrical current 234 induces a secondary electrical current 236
flowing generally
axially within plasma 220 that creates the z-pinch effect detailed above.
- 25 -
CA 02887762 2015-04-10
[00119] When the parameters of primary electrical current 234 are
suitably controlled
(e.g., frequency and amplitude), secondary electrical current 236 will
interact with the
magnetic field associated with the primary electrical current 234 to generate
a radial force
field 238 within particle beam tube 210. Radial force field 238 is directed
generally inwardly
towards central axis 216. Radial force field 238 will urge any plasma 220
present in particle
beam tube 210 toward central axis 216. As the density of plasma 220 increases,
the
resulting pressure gradient accelerates plasma linearly along central axis
216. A pressure
valve or the like (not shown) at first end portion 212 prevents the plasma 220
from flowing
back towards the fuel injector, and forces plasma 220 toward second end
portion 214 at a
relatively high velocity, where it is ejected from particle beam emitter 200
into the reaction
chamber 110 as one of the particle beams 135. The exit velocity of the
particle beams 135
may be controlled according to the pressure gradient experienced by plasma 220
during
the electromagnetic pinch: the higher the pressure gradient experienced by the
plasma
220, the higher the exit velocity of the particle beams 135.
[00120] In some embodiments, the voltage supply 232 may be coupled to the
particle
beam tube 210 included in each of an opposing pair of the particle beam
emitters 130. As
used herein, two of the particle beam emitters 130 may be understood to oppose
one
another when oriented approximately 180-degrees apart in a common plane so
that the
pair of particle beam emitters 130 are substantially in opposition to one
another along a
linear trajectory. Accordingly, when the particle beams 135 are emitted from
the particle
beam emitters 130 and the plasma sphere 145 is ignited, a closed electrical
loop may be
formed between each opposing pair of the particle beam emitters 130 and the
voltage
supply 232 via the particle beams 135 and the plasma sphere 145. The voltage
supply 232
(or alternatively another suitable voltage supply) may also be coupled to
multiple opposing
pairs of the particle beam emitters to form multiple corresponding closed
electrical loops.
[00121] A high voltage initially supplied by the voltage supply 232 may
be used to
electrify individual fuel particles contained in the opposing pair of the
particle beam emitters
130 forming part of the closed electrical loop. In some embodiments, the fuel
particles are
initially at a relatively low temperature (e.g. - 300 K) as they enter first
end portions 212 of
an opposing pair of the particle beam emitters 130. In response to application
of the high
voltage, the fuel particles may be turned into plasma 220 and thereafter
develop the
- 26 -
CA 02887762 2015-04-10
electrical current 236 that causes pinching of the plasma 220 toward the
central axis 216.
Due to the closed electrical looping, the pinching may occur both within the
particle beam
tube 210, but may also continue as the particle beams 135 travel toward and
converge at
the common focal region 140, thereby further raising the particle density
realized within the
plasma sphere 145. The initially applied high voltage may be maintained or
thereafter
reduced to a minimum maintenance voltage in order to supply a desired level of
constant
electrical current in order to achieve desired level of energy concentration
around the
central axis 216 in the opposing pair of the particle beams 135. However, a
sufficient
electric current needs to be maintained in order to pinch the particle beams
in the form of
lightning bolts into a desired size. The particle beams become plasma and
lightning bolts
due to Joule heating by the electric current soon after leaving their
emitters. The number of
pairs of the particle beams 135 included in closed electrical loops may also
vary in order to
create a desired level of energy concentration at common focal region 140 due
to focusing
of the particle beams 135.
[00122] In some embodiments, sufficiently large DC currents are used to
pinch the
particle beams 135 into continuous lightning bolts. In other embodiments,
sufficiently large
AC currents are used instead to form lightning bolts at reduced input power
costs. The AC
parameters such as intensity, frequency and phase angle may be optimized to
maximize
the fusion reaction rate based on computer simulation and test results. For
example, the
phase angles of the AC currents in multiple lightning bolts may be arranged to
generate
shock waves in the particle beams 135 directed towards the common focal region
140 to
maximize the energy concentration at the plasma sphere 145.
[00123] In some embodiments, sufficiently DC, AC, or pulse currents may
be used to
form plasma beams (which may be characterized as lightning bolts) having
levels of electric
current, beam diameter, beam velocity, and temperature similar to typically
occurring
lightning beams that may be observed in nature.
[00124] In some embodiments, electromagnetic system 230 also includes a
plurality
of electromagnetic coils 240 aligned axially about central axis 216 along at
least a portion
of particle beam tube 210. Electromagnetic coils 240 are used to generate an
axial
magnetic field (not shown) within particle beam tube 210 that provides
supplemental axial
- 27 -
CA 02887762 2015-04-10
confinement of plasma 220 within particle beam tube 210. Consequently, the
stability of the
plasma 220 is increased as the plasma 220 is compressed along central axis 216
(as will
be discussed further below). Electromagnetic coils 240 may typically surround
particle
beam tube 210 and may generally be located in close proximity to particle beam
tube 210.
In certain embodiments, the exterior of particle beam tube 210 supports the
electromagnetic coils 240, although electromagnetic coils 240 may be separated
from
particle beam tube 210 by suitable thermal and/or electrical insulation
members (not
shown). Inclusion of electromagnetic coils 240 within the particle beam
emitter 200 is
optional and, in some cases, may depend on the required velocity of particle
beams 135 for
a particular fusion reactor design.
[00125] Alternatively, or additionally, particle beam emitter 200 may
include external
magnets 250 to provide supplemental radial confinement of plasma 220 within
particle
beam tube 210. External magnets 250 may include permanent magnets or
electromagnets,
and may be arranged in any suitable configuration that provides the desired
magnetic field
and desired supplemental confinement. For example, the position of the
external magnets
250 relative to the particle beam tube 210 may be fixed or the external
magnets 250 may
be movably secured in relation to the particle beam tube 210 so as to be
movable about the
particle beam tube 210. The magnetic field generated by the external magnets
250 may
therefore be static or time-varying as the case may be.
[00126] In some embodiments, the particle beam emitter 200 may include one
pair of
permanent magnets or electromagnets that are rotatable about the central axis
216. The
time-varying magnetic field resulting from rotation of the external magnets
250 about the
central axis 216 is also used to induce the secondary electrical current 236
within plasma
220 flowing in a generally axial direction (i.e., parallel to the central axis
216). To be
rotatable about the central axis 216, the external magnets 250 may be attached
to or
otherwise supported by the particle beam tube 210. Alternatively, the external
magnets 250
may be supported by an external support system (not shown) proximate to the
particle
beam tube 210.
[00127] In some embodiments, the external magnets 250 may include more
than one
pair of permanent magnets or electromagnets. Each pair of permanent magnets or
- 26 -
CA 02887762 2015-04-10
electromagnets may be supported within the particle beam emitter 200 using a
similar
arrangement to what is described above. The configurations of each pair of
permanent
magnets or electromagnets may be identical or may vary with respect to one
another. For
example, the radial distance to the central axis 216 may be the same or
different from pair
to pair. Accordingly, at least one pair of permanent magnets or electromagnets
may be
spaced apart from the central axis 216 by a different radial distance from at
least one other
pair. Alternatively, each pair of permanent magnets or electromagnets may have
the same
radial spacing relative to the central axis 216.
[00128] The axial length and positioning of the external magnets 250
may also be
varied in different embodiments. For example, in some embodiments, the
external magnets
250 may span the entire axial length or nearly the entire axial length of the
particle beam
tube 210 (this arrangement is shown in Figure 2 for illustrative purposes
only). Alternatively,
in some embodiments, two or more of the external magnets 250 separated by air
gaps may
be arranged in axial alignment along the length of the particle beam tube 210.
In this case,
the width of the air gaps between the external magnets 250 in axial alignment
may be
approximately equal. For example, two or three or any other suitable number of
the
external magnets 250 may span the axial length of the particle beam tube 210.
[00129] In some embodiments, particle beam emitter 200 is operated with
a
thermonuclear fuel mixture comprised of hydrogen and deuterium gases. The
hydrogen
and deuterium gases are heated in a fuel injector (such as fuel injector 120)
in order to
dissociate electrons from the hydrogen and deuterium nuclei until the hydrogen
and
deuterium gases exist in their plasma states, thereby forming the plasma 220.
Typically,
this will involve heating the thermonuclear fuel mixture within the fuel
injector to a
temperature of at 1,800 C or higher. Once heated, the mixture of hydrogen and
deuterium
plasma is supplied to first end portion 212 of particle beam tube 210 from the
fuel injector.
Inside the particle beam tube 210, the primary electrical current 234
generated by
electromagnetic system 230 induces the secondary electrical current 236 within
the plasma
220. As discussed above, the resulting electromagnetic field provides radial
confinement
and axial acceleration of the plasma 220 toward the second end portion 214.
- 29 -
CA 02887762 2015-04-10
[00130] In order to heat up the hydrogen and deuterium gases, the fuel
injector in
some embodiments may include a plurality of fuel channels fed through at least
one high
temperature furnace. The hydrogen and deuterium gases are pumped through the
fuel
channels (each fuel channel may house only one of the two gases) wherein heat
radiated
from the high temperature furnace brings the hydrogen and deuterium gases to
the desired
temperatures. To withstand the heat generated by the high temperature furnace,
each of
the fuel channels may be composed of a material or material composition having
a very
high melting point, for example, well above 1,800 C. For example, as noted
above, graphite
and tungsten are some non-limiting examples of suitable materials for the fuel
channels.
[00131] Alternatively, in some embodiments, the hydrogen and deuterium
gases may
be mixed together within the fuel injector and converted into their plasma
states through
heating by other mechanisms or processes. For example, the mixture of hydrogen
and
deuterium gases may be subject to high-frequency electromagnetic waves during
transport
through the fuel injector to the particle beam emitter 200. The energy
imparted by the high-
frequency electromagnetic waves may be used to increase the kinetic energy of
the
pumped hydrogen and deuterium to high enough levels. Heating by high-frequency
electromagnetic waves is similar to what takes place in some current tokamak
machines,
such as ITER. The fuel injector again may be formed or coated from a material
or material
composition having a very high melting point, for example, well above 1,800 C.
Graphite,
tungsten and tantalum hafnium carbide (Ta4HfC5) provide some non-limiting
examples of
suitable materials for the fuel injector.
[00132] The schematic arrangement shown in Figure 2 is merely
illustrative, and other
arrangements could be used to effect particle beam emission. For example, each
particle
beam emitter 200 may comprise a plurality of particle beam tubes (similar to
the particle
beam tube 210), and each of the particle beam tubes may be capable of emitting
one of the
particle beams 135 into reaction chamber 110. That is, in some embodiments,
the particle
beam emitter 200 may be capable of emitting a plurality of particle beams 135
into reaction
chamber 110.
[00133] Referring now to FIGS. 1 and 2, in some embodiments, one or
more particle
beam tubes (such as the particle beam tube 210) may extend into reaction
chamber 110 by
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CA 02887762 2015-04-10
a certain distance to provide (additional) directional guidance to particle
beams 135 in order
to increase the convergence at common focal region 140 with other individual
particles
beams in the particle beams 135. However, a minimum distance between the
second end
portion 214 of each particle beam tube 210 and common focal region 140 should
be
maintained to ensure safe operation of particle beam emitters 130 under the
extreme
operating conditions in reaction chamber 110.
[00134] The second end portion 214 of the particle beam tube 210 may
also be
modified to have a gentle and smooth bend into a desired direction. The
curvature of the
second end portion 214 may be controlled to slightly alter or deviate the
direction of the
primary electrical current 234 near the second end portion 214. Consequently,
the
secondary electrical current 236 induced by the magnetic field associated with
the primary
electrical current 234 would also bend or deviate into the same desired
direction due to the
coupling between the primary electrical current 234 and the secondary
electrical current
236. The deviation of the secondary electrical current 236 then alters the
electromagnetic
field within the particle beam tube 210 in a way that the high-energy
particles emitted from
the particle beam tube 210 are focused at and converge upon the common focal
region
140. As noted above, this alternative confirmation of the particle beam
emitter 200 may be
used as an alternative or in addition to the converging elements 150.
Four Beam Configuration
[00135] A configuration with multiple sets of orthogonal pairs of particle
beam emitters
130 may be used in a spherical fusion chamber, in order to increase energy
concentration
by focusing, and also improve the stability of the plasma sphere 145.
[00136] The two beam connection tests at Stern were initially prepared
to achieve
collision of the two plasma beams at the geometric centre of the connection,
assuming that
.. the movement of the electrons driven by the applied voltage would not
affect the flows of
the two plasma beams. Contrary to expectations, the test results indicated a
clear shift in
connection centre towards the positively charged electrode. This indicates
that a spatial
symmetry may not be sustainable without counter balancing electro-magnetic
fields. While
it will be appreciated that symmetry in three-dimensional (3D) space cannot be
achieved by
two opposing plasma beams in one line (one-dimensional), nor may symmetry in
three-
- 31 -
CA 02887762 2015-04-10
dimensional (3D) space be achieved with two intersecting beams which are
planar (two-
dimensional). Furthermore, such symmetry cannot be arranged with three beams
in 3D
space, due to the existence of a nonzero vector sum of electric currents at
the connection
centre. Such a nonzero vector sum prevents the formation of counter balancing
electro-
.. magnetic fields in the plasma region at the connection centre.
[00137] At least four plasma beams are thought to be required to achieve
and sustain
spatial symmetry of a plasma sphere in three dimensions, as explained below.
The spatial
symmetry in the 3D space is defined here as having all beams identical to one
another
except for their orientations, with the relative angles between the beams
evenly distributed
in space. At the focal point of intersection, the vector sum of the counter-
balancing electro-
magnetic fields is preferably zero.
[00138] Figure 3 illustrates a system 100A comprising a four beam
configuration that
has spatial symmetry in 3-D space. Spatial symmetry in the 3-D space may be
characterized as having all beams identical to one another except for their
orientations, with
.. the relative angles between the beams evenly distributed in space. The
pyramid shape 125
is shown to assist visualization of the plasma beam orientations.
[00139] System 100A comprises four particle beam emitters 130A, 130B,
130C, and
130D that each emit a plasma beam 135A, 135B, 1350, and 135D, respectively,
towards a
common focal region 140, which is at the geometric center of system 100A. The
plasma
region 145 at the focal region 140 is expected to be spheroidal, with
identical (or
substantially identical) plasma dimensions in the axial directions of the four
beams, and is
approximated as a sphere in Figure 3. The plasma region 145 may be subjected
to
converging magnetic forces, as well as dynamic pressure due to converging
plasma flows,
as a consequence of applied electric currents. The plasma region may collapse
radially into
the geometric center under the applied currents.
[00140] Opposite each particle beam emitter 130A-D, on the other side of
focal region
140, is an associated particle beam receiver (not shown in Figure 3 for
clarity). A particle
beam receiver acts as an electrode for a plasma beam travelling from a
particle beam
emitter ¨ the particle beam emitter also functioning as an electrode ¨ so that
an electrical
current may be applied to the plasma beam. That is, a particle beam emitter
and its
- 32 -
CA 02887762 2015-04-10
associated particle beam receiver act as a pair of oppositely charged
electrodes in order to
connect a single plasma beam travelling between them. Preferably, the particle
beam
emitter acts as a negative electrode and the particle beam receiver acts as a
positive
electrode. The plasma beam flows from the negative to positive electrode in
the same
direction as the electrons.
[00141] In some embodiments, a particle beam receiver may comprise a
piece of
metal (and/or another electrically conductive material) that is positioned to
be in contact
with a plasma beam 135 being emitted by a particle beam emitter 130.
Preferably, such a
particle beam receiver has a similar structure to the particle beam emitter
200 shown in
Figure 2, except that the flow directions of electric current and plasma fluid
are reversed,
and the cylindrical wall of the emitter is connected to (and/or may function
as) the positive
electrode.
[00142] Also, where a particle beam receiver has a hollow structure
(e.g. where a
particle beam receiver has a similar structure to particle beam emitter 200),
the particle
beam emitter may allow passage and/or collection of the plasma fluid in a
plasma beam as
part of a closed loop fluid circulation system.
[00143] Preferably, the particle beam receivers are designed to
minimize electric
current density at local regions and avoid possible melting of the component
under high
ternperature.
[00144] As shown in Figure 4, each plasma beam 135A-D has a negative end
136A-D
and a positive end 138A-D, respectively, with a particle beam emitter 130
located at the
negative end, and a particle beam receiver located at the positive end. Power
sources
230A-D are operatively coupled to the positive and negative end of each plasma
beam in
order to generate an electric current within each plasma beam. In this way,
power sources
230A-D may generate a closed electrical loop that runs through a plasma beam
135
between its emitter 130 and corresponding receiver, and through the plasma
region 145 in
the common focal region 140.
[00145] In some embodiments, at least four power sources 230A-D may be
able to
supply a sufficiently high voltage to electrify individual fuel particles
contained in the
opposing pair of particle beam emitters. Such a voltage may be maintained or
thereafter
- 33 -
CA 02887762 2015-04-10
reduced to a minimum maintenance voltage in order to supply a desired level of
electrical
current running through the entire plasma beam.
[00146] It will be appreciated that power sources 230A-2300 may be, for
example,
voltage or current sources, AC or DC sources, pulse width modulation sources,
or any
suitable combination thereof. It will also be appreciated that the positive
and negative ends
of each plasma beam may be switchable, although one would have to switch all
of the
positive and negative ends to maintain the symmetry for achieving stability at
the plasma
region 145. For example, in the case of an AC power source with a frequency of
60 Hz, the
emitter and receiver switch their roles 60 times in a second, but in the case
of a DC source,
their roles would not change over time.
[00147] As shown, each plasma beam flows through common focal region
140 and
plasma sphere 145 and exits from the other side. Any two beams moving into or
out of
common focal region 140 form an identical angle of 109.5 . For example, the
negative ends
136A and 136B of plasma beams 135A and 135B, respectively, have an angle of
109.5
between them, and the corresponding positive ends 138A and 138B of 135A and
135B,
respectively, on the other side of common focal region 140 also have an angle
of 109.5
between them.
[00148] In some embodiments, a plasma core temperature sufficient for
nuclear
fusion may be achieved due to a relatively high current running through each
plasma beam
that accelerates electrons into large velocities in the applied electric
field. These fast
moving electrons in turn attract the oppositely charged nuclei to achieve
large velocities
that become temperature due to particle collision and penetration at the dense
core.
[00149] The configuration illustrated in Figure 3 and Figure 4 is
preferred for its
simplicity associated with a minimum electro-magnetic interference among the
intersecting
beams, and may alternatively be referred to as a four beam "star-pinch" due to
its
symmetry in space. The characteristics of such a star-pinch include:
= Each plasma beam has materially similar, and preferably identical,
dimensions, and each beam is subject to a similar, and preferably identical,
applied current;
= Any two beams moving into or out of the connection centre form an angle
of
109.5';
- 34 -
CA 02887762 2015-04-10
= Each plasma beam preferably flows through the common focal region and
exits the common focal region on the opposite side;
= The common focal region is preferably a region of collision and
penetration
among electrons and ions;
= Collisions are expected as a result of plasma flow in each beam being
resisted by the three other opposing beams;
= The vector sum of the electric currents at the common focal region is
preferably as small as practicable, and more preferably zero;
= A hot and dense core may form within the plasma region, surrounded by a
cooler shell of plasma; and
= Such a hot and dense core may facilitate fusion reactions under the
condition
of plasma region stability.
[00150] Reference is next made to Figure 5A, which illustrates a
schematic profile 300
of a cross section of a conducting plasma beam (formed out of water in this
embodiment) in
a radial direction. Plasma beam profile 300 comprises a plasma beam 335,
plasma fluid
345 (e.g. deuterium), and a cylindrical oxygen shell 355 that encircles plasma
beam 335.
The arrows show the flow direction of the plasma fluid that is the same as the
flow direction
of the electrons (opposite to the current direction). The cylindrical oxygen
shell can act as a
resistive wall to confine and stabilize the hydrogen isotopes (e.g.,
deuterium) for fusion
reactions at the common focal region.
[00151] Reference is next made to Figure 5B, which illustrates a
schematic cross-
section of a conducting plasma beam emitter 400. Plasma beam emitter 400
comprises an
electrode 460A and 460B, and the Figure illustrates a plurality of electrons
450A-D
travelling in the direction of the corresponding electron flow 470A-D to form
a plasma beam
435 travelling in the direction indicated, and also illustrates the reduction
of beam diameter
as the beam is 'pinched'. it will be appreciated that the view shown in Figure
5B may be
characterized as a high-level schematic view of an emitter 200 (e.g. as shown
in Figure 2).
- 35 -
CA 02887762 2015-04-10
Lorentz force distribution in radial direction
[00152] Consider a point along the axis for an arbitrary first one of
the four plasma
beams, at a distance of r away from the geometric centre. The magnetic field
within this
first beam along its central axis (due to the applied electric current) is
expected to be zero.
Assuming uniform distributions of density and electric charges in the four
plasma beams,
and neglecting the term due to the electric field, the magnetic field B
generated by an
electric current Ic for each of the remaining three plasma beams may be
calculated by:
if, I,
B = (r cos fi) (11)
2R
fowl
where R1081 (> r) is the cross-sectional radius of each plasma beam, also
considered here
to be the radius of the region of intersection, and r cos ,8is the distance
from the central
axis of the first beam to the central axes of the remaining three beams (i3 is
defined here as
109.5 -90 , i.e., 13=19.5 , to avoid a negative sign in Equation (11)).
[00153] As a positively charged nucleus enters into the common focal
region along
the axis of the first beam, it immediately experiences the coupling "glue"
effect due to the
fast moving electrons from the three opposing beams. The combined electric
force is in
balance with the total Lorentz force experienced by the electrons. The Lorentz
force per
unit volume for a plasma region, fm, may be calculated as:
___________________________________ ofõ =3B c s /3 = 3/10/:r(cos fi)2
(12)
71-R` 2,2 p4
fot al Jowl
[00154] Alternatively, the total Lorentz force per unit mass, in the
unit of acceleration,
may be calculated as
________________________________ õ cos g,(r)¨ ¨3B 2
3p0/,2x(cos /6)2
p (13)
I) heal P peafR 1,), = 271-2P R;oc,/
- 36 -
CA 02887762 2015-04-10
[00155] The above Lorentz force per unit volume is due to the remaining
three plasma
beams converging in the radially inward direction. Equation (12) may be
rewritten in a
dimensionless form, e.g.:
2A-2R 310,w
gm= __ fõ= 3 (cos18)2( __ ) (14)
,1101( R focal
[00156] Equation (14) reflects a self-focusing effect of the four beams
passing through
the common region of intersection. The relationship between the above
dimensionless
Lorentz force and r is linear. A similar linear relationship is observed on
gravity for a
massive sphere with a uniform density of ps , i.e.:
g(r)=41r Gpsr (15)
3
where G is the gravitational constant. This reveals a mathematical similarity
between
Lorentz force and gravity, both converging towards the geometric center and
may confine
fusion reactions.
[00157] Integration of Equation (12) over a plasma sphere of radius
Rfocal gives its
total Lorentz force, Frotail
r(cosfi)2 3,ttoP(cosfl)2
______________________________________ 411-r2 dr= ______________ (16)
221-2R4
mcd
[00158] Similarly, integration of Equation (15) over a massive sphere of
radius Rs
gives its total gravity, Fmassive
47z-
Gpsr- 4n-r2psdr= 47z-2 Gps2,Rs4.=3G11/1'2' (17)
Finassive
0 3 3 4R2
- 37 -
CA 02887762 2015-04-10
[00159] Further dimensional analysis gives the following ratio of two
pressures, pfocal
for the small plasma sphere of radius Rfocai and ps for the massive sphere of
radius Rs,
Plowt _ Flom I R .12 mu! _31-101 (WS )6)2 4R4, _ 2/.212.(cosii)2R,s4.
(18)
Rs2' 271-R2 3GM2 R:R2cai GM2
s fo ,s
[00160] Consider the 2D surface of the 3D common focal region 140 in
Figure 1.
Similar in a way to earth's surface, there are at least four points of
mathematical symmetry
where the four plasma beams enter/cross the 2D surface. At each of the four
points of
symmetry, the net electro-magnetic force in a plane tangential to the 2D
surface is equal to
zero. Connecting any two points of symmetry along the 20 surface with a
shortest path, it
may be visualized that the mid-point along the path is also a point of
symmetry. This
process may be repeated to generate an infinite number of symmetry points. It
can be
shown in this iterative process that there are no magnetic forces other than
those in the
radial direction.
[00161] It is possible to modify the mathematical equations describing
a stellar
structure (Prialnik, 2000) using a corrected gravitational constant. Put
another way, based
on mathematical equivalence between the common focal region 140 and a star,
such as
the Sun, equations have been developed for computer simulation of a spherical
common
focal region. For a stellar structure, such as the Sun, the momentum equation
may be
calculated as:
dP Gin
(19)
dr r`
[00162] A simple dimensional analysis with consideration of Equation 19
leads to:
Gioeõ, p fõ,/ ps Ms _ 2,1101:.(cos R!, M , I 1?"'s
(20)
Ps Rs Plocal M100, 71. R focal" SI I cal M0 I R .13
owl
[00163] Equation (20) may be further simplified as:
- 38 -
CA 02887762 2015-04-10
214j2(COS Ri2rõ,,
_ (
õ
21)
Li peal
jowl
[00164] Substitution of the corrected constant described in Equation
(21) into
Equation (19) gives a momentum equation, which may also be referred to as a
hydrostatic
equilibrium equation, for the common focal region:
dp 401,2(cos Rf2ocal pm
d ¨ ______________________________________________________________ (22)
r
ur2 r2
" /ow/
[00165] Additional equations for the common focal region may be based
on equations
describing a stellar structure (see e.g. Prialnik, 2000) under a similar dense
plasma
environment. For example, a continuity equation for the common focal region
may be:
dm = 4irr2p (23)
dr
[00166] A radiative transfer equation ¨ provided radiative diffusion
constitutes the only
means of energy transfer ¨ for the common focal region may be:
dT 3 lip F
(24)
dr 4ac T3 4n-r2
[00167] A thermal equilibrium equation for the common focal region may
be:
¨dF 417rr2 pq (25)
dr
[00168] Equations (23) to (25) may be supplemented by the following
relations:
- 39 -
CA 02887762 2015-04-10
R 1 A
P=¨pT+p+¨ar (26)
3
icop"Th (27)
q=qoPmT" (28)
where Equations (26) to (28) are explained as follows.
[00169] For a plasma medium formed out of heavy water vapour, the total
number of
ions in a unit volume is given by summation over all the ion species, i.e.,
deuterons and
oxygen nuclei, and may be calculated as:
p X X
( " + ") (29)
mff 2 16
where n, is the number of ions for the i-th species, mt_, is the mass of each
nucleon, e.g.,
proton, and XD and X0 are the mass volume fraction of deuterons and oxygen
nuclei
respectively. The mean atomic mass of the plasma medium Ai/ is defined by
1 Xi) X
_= + L)
(30)
,u/ 2 16
[00170] Following Equation (30), the value of Al] is determined to be
6.6667.
[00171] Assuming that the deuterium and oxygen atoms are fully ionized
in the
plasma region, the number of electrons per nucleon is /le = 2. Such a complete
ionization
condition usually exists in hydrogen-depleted stars in astrophysics.
Neglecting the electron
degeneracy pressure (Prialnik, 2000) that exists in an extreme density
environment due to
the Heisenberg uncertainty principle in quantum mechanics, the electrons can
be described
by the ideal gas law and the corresponding electron pressure is given by:
- 40 -
CA 02887762 2015-04-10
= R pT (31)
lie
kJ
where R is the ideal gas constant with a value of 8.31451
kg. K
[00172] Substitution of Equation (31) into Equation (26) gives:
P=¨RpT+¨RpT+-1ar (32)
/11 jt 3
________________________________________________________ where the third term
reflects radiation pressure with a= 7.5646x10-16
mi = K4
[00173] Equations (24) and (27) describe the radiative heat transfer
due to interaction
between photons and matter within the plasma region. The most important
interactions
within a high temperature plasma region are those involving free electrons,
rather than the
much heavier nuclei (Prialnik, 2000), i.e.,
= Electron scattering ¨ the scattering of a photon by a free electron. This is
known as
Compton scattering, or in the non relativistic case, Thompson scattering; and
= Free-free absorption ¨ the absorption of a photon by a free electron,
which makes a
transition to a higher energy state that can interact with a nucleus or ion.
The inverse
process, leading to the emission of a photon, is known as bremsstrahlung.
[00174] The opacity coefficient 'in Equation (27) can be written for each
of the above
two mechanisms. The opacity resulting from electron scattering is temperature
and density
independent, i.e., a = b = 0, can be calculated as:
1
"es = 'es (33)
pe 2
where iç0 =0.04 m2 I kg.
-41-
CA 02887762 2015-04-10
[00175] The opacity resulting from free-free absorption is known as
Kramers opacity
law, with a = 1 and b = -7/2, can be calculated as:
1
' = -x 7.5x ¨
2Z pT -7,2, (m2 kg)
(34)
2 A
where the units for density and temperature are g/cm3and K respectively, and:
K¨Z2)=IX,--L-Z2 =XD-12+X0-82 =0.1+3.2=3.3 (35)
A 2 16
for heavy water composition. Combining Equations (33) and (34) gives:
lc= 0.02 +1.2375 x 1022p7-72, (rn2 I kg) (36)
[00176] Calculation of fusion power output requires a relationship for
fusion reaction
rate. As discussed further below, such a relationship has been developed for D-
D reactions
in a dense plasma environment, based on a quantum wave theory associated with
an
enhancement factor and in combination with solar information:
( \ 3 \ 35
pq= Rõ= 4.518 x1025 Pdeureron (W I m3) (37)
15.42 glem' 15.7 M"K
where the deuteron density is taken to be 20% of the overall density for the
plasma mixture
and a slightly conservative exponent of 3.5 is used as the exponent for
temperature, as
compared with e.g. Equation (51) and its associated derivation discussed
below. Without
the enhancement factor, the current theory of reaction cross section (Clayton,
D. D., 1968;
Burbidge, E. M. et al., 1957) may be overly conservative.
[00177] Equations (22) through (25) can be solved numerically together
with
Equations (32), (36), and (37). The following boundary conditions are applied:
- 42 -
CA 02887762 2015-04-10
1// = 0 at r=0 (38)
F=0 at r=0 (39)
T=Lo at r=0 (40)
P=0 at r = Rfr,cõ, (41)
where it is assumed that the plasma velocity To is consistent with the
velocity of plasma
observed in naturally occurring lightning (e.g. 137 km/s). For example, a
typical lightning
beam velocity of 137 km/s can turn into a peak temperature of 12 MK at the
common focal
region of the four-beam configuration due to thermal collision of the four
beams.
[00178] Numerical simulations were conducted to calculate expected
fusion power
output for the region of intersection (i.e. the common focal region) using the
following input
data, which was based on data for regular lightning beams observed in nature:
= Fuel is heavy water in its plasma state, in the form of regular lightning
beams;
= The radius of each beam and common focal region Rfocal = 5 mm;
= Velocity of each beam VI_ = 137 km/s (equivalent to a peak temperature of
12 M K);
and,
= The applied electric current for each beam / = 100,000 A.
[00179] Results of these numerical simulations are shown in Figures 9
and 10. As
shown in Figure 9, the peak density was calculated to be 799 g/cm3 for the
common focal
region, as compared to e.g. the peak density of 158 g/cm3 thought to exist at
the solar core.
As shown in Figure 10, the peak fusion power output was calculated to be 168
GW, or 840
times the estimated input power of 0.2 GW (see e.g. Equation (66)). This
suggests that net
energy output can be achieved with the four-beam configuration of Figure 3.
This
simulation result is also consistent with the results of other methods of
calculating an
estimated energy output (see e.g. Equation (64) and its associated derivation
discussed
below, which includes some additional simplifying assumptions, e.g. uniform
temperature
and density distributions assumed for the core of the common focal region).
- 43 -
CA 02887762 2015-04-10
Possible diverging effects
[00180] In addition to the self-focusing or converging effect, in the
star-pinch
configuration of Figures 3 and 4 there may be a diverging effect due to the
electro-magnetic
coupling of adjacent plasma beams. For each incoming plasma beam flowing
towards the
geometric center, for example, there are expected to be two diverging
components: i) a
primary component in the direction opposite to the incoming plasma flow; and
ii) a
secondary component perpendicular to the flow in radially outward directions.
[00181] The primary diverging component of the Lorentz forces is
expected to be
overcome by the electric fields that drive the electrons and the ions, i.e.,
plasma fluids, to
move towards and through the geometric centre. This component does not
contribute to the
shape and stability of the region of intersection. The secondary diverging
component is
expected to be zero along the four axes, due to complete cancellation of
coupling effects
among the four opposing plasma beams, and may be ignored in other locations.
[00182] A three-dimensional distribution of gm was calculated, by
summation of the
Lorentz forces due to the four beams at each location of the sphere ¨ assuming
a uniform
density distribution ¨ and the results are represented in Figure 6, where
Lorentz force
regions 610, 620, 630, 640, 650, 660, 670, 680, and 690 are shown for a plasma
sphere
600 formed at the intersection of plasma beams 635A, 635B, 6350, and 635D (not
shown;
flowing directly into the page towards the intersection of beams 635A-C). The
observed
uniformity indicates that Equation (14) applies generically to all radial
directions.
[00183] However, the distribution of converging Lorentz force shown in
Figure 6 may
not be sustainable. The larger forces near the outer surface (not shown) will
drive the
plasma to concentrate towards in the central region of the plasma spheroid
through a
process known as 'radiative collapse' in the literature. This process may be
initiated by the
dynamic effects of the four plasma flows driven by electric fields through the
geometric
centre and stopped by one or more of these physical mechanisms: (1) Joule
heating, (2)
heat generated by fusion reactions, (3) quantum pressures similar to those
existed in white
dwarfs or neutron stars.
[00184] Quantitative studies of density distributions after
stabilization of the radiative
collapse are on-going research activities. In order to provide a qualitative
view of the
- 44 -
CA 02887762 2015-04-10
n ?õ)
plasma spheroid, a density factor of lu(4 I -rII
(i.e. an exponential density factor) was
applied to the Lorentz force distribution shown in Figure 6 following
information obtained
from modelling of the solar core (J. Christensen-Dalsgaard, et al., 1996),
with a value of 1
at the outer surface and 10,000 at the centre. An increase in density,
associated with a
larger pressure, must be balanced by an increasing Lorentz force. The results
are
represented in Figure 7, where Lorentz force regions 710, 720, 730, 740, 750,
760, 770,
780, and 790 are shown for a plasma sphere 700 formed at the intersection of
plasma
beams 735A, 735B, 735C, and 735D (not shown; flowing directly into the page
towards the
intersection of beams 735A-C). Redistribution of plasma density as well as
Lorentz force
along the radial direction produces a closed wall of magnetic resistance
surrounding the
centre (shown in Figure 7 at about regions 780 and 790), within which it may
be possible to
sustain fusion reactions in a stable furnace environment. Regions 780 and 790
represent
the largest converging Lorentz force values. For example, a calculated
numerical value of
the dimensionless Lorentz force is relatively small (i.e. almost zero) at the
outer surface
(i.e. at about region 710) of the plasma sphere, and reaches a peak value
(e.g. ¨1064) near
regions 780 and 790, and reduces to zero at the very centre of the plasma
sphere.
[00185]
Possible radiative collapse at the region of four plasma beam intersection
may reduce the channel cross section for each plasma beam flow, such a
reduction in
channel cross-section being necessarily associated with increases in plasma
density,
velocity, and temperature. This may, in theory, introduce a point of
singularity with zero
sectional areas when Joule heating, fusion reactions, and quantum pressures
fail to resist
the process. Applying a current density factor of (R0 ir)2 due to conservation
of electric
charges, for example, Equation (14) becomes:
g,õ =_ 27T2R02 [(Ro)2]2
3(cosj3)2 (¨Ro (42)
r
[00186]
Practically, under laboratory conditions, radiative collapse at instability
locations may introduce an energy (Thonemann, P. C. et al., 1958) or density
(Sinars, D. B.
-45-
CA 02887762 2015-04-10
et al., 2003) concentration exceeding three orders of magnitude compared to
the lightning
strikes in nature.
Stability and Confinement Time
[00187] Steady-state plasma flows in the four beams may be necessary
for controlled
release of nuclear reactions. Stability of the plasma region under the counter
balancing
electro-magnetic fields may be encouraged by the minimization principle of
potential
energy. If the plasma region is higher in one plasma beam direction, the
radial magnetic
force brings it down while doing work to minimize its potential energy during
the process.
The spheroidal shape of the plasma region may therefore be maintained and its
stability
enhanced (if not ensured) during the radial collapse of the plasma region to
eventually
ignite and sustain fusion reactions. The minimization principle manifests
itself during the
stable gravitational collapse of hydrogen gas clouds into stars and eventually
into black
holes for more massive stars.
[00188] The results of X-pinch experiments (Sinars, D. B. et al., 2003)
demonstrated
that a collapse of plasma in the region of intersection occurred prior to kink
and/or sausage
instabilities of the two beams, likely due to the dynamic effects of plasma
flows with
electrons (driven by voltage supply) through the point of intersection. The X-
pinches were
not symmetrical in space, and as a result, a micro pinch formed in the region
of
intersection, which eventually lost its stability at a later stage (Sinars, D.
B. et al., 2003).
The four beam configuration illustrated in Figures 3 and 4 is anticipated to
avoid this type of
micro-pinch instability as a consequence of the zero vector sum of the four
electric currents
at the connection centre (i.e. the common focal region). The minimization
principle of
potential energy, which keeps a star shape spherical during its gravitation
collapse, applies
to the region of intersection in the four beam configuration to ensure
identical plasma
region dimensions in the axial directions of the four beams.
[00189] Instability issues addressed by the four beam configuration are
thought to
include:
= Kink / sausage instabilities ¨ such instabilities should be incompatible
with the
spheroidal shape of the plasma region;
- 46 -
CA 02887762 2015-04-10
= Micro-pinch instability in X-pinches ¨ such instabilities are expected to
be
avoided by zero vector sum of the four electric currents; and
= Rayleigh ¨ Taylor instability ¨ such instability may be mitigated by
increasing
the period of the electric pulses, for example using AC currents, to minimize
the particle
acceleration into the plasma region.
[00190] A stable collapse of the plasma region permits a controllable
and sufficiently
long confinement time, which in combination with necessary temperature and
density
conditions may ignite / sustain fusion reactions and achieve a net energy
output (Lawson,
J.D., 1957). For continued operation of a fusion power plant, the confinement
time should
preferably exceed the pulse time, which for an AC current with a frequency of
50 Hz is 10
ms. A target confinement time of 10 ms would therefore be sufficient for
continuous power
generation. Such a confinement time was exceeded by tokamak machines where the
confinement time was measured in the order of seconds. The stability of the
four beam
configuration illustrated in Figures 3 and 4 is expected to be comparable or
better than that
of tokamak machines considering the spheroidal shape of the plasma region
where the
minimization principle of magnetic potential energy is applicable to encourage
stability. The
target confinement time of 10 ms is therefore expected to be achievable.
Nuclear Fusion Within Dense Plasma Enhanced by Quantum Particle Waves
[00191] The proton-proton (p-p) chain reaction is the fusion reactions
by which stars
the size of the Sun or smaller convert hydrogen into helium. According to
classical laws of
physics, such reactions require sufficient kinetic energy, e.g., temperature,
available to
overcome the Coulomb repulsion between positively charged nuclei. The
temperature of
the Sun was considered too low for this to occur in the 1920s (McCracken, G.
and Stott, P.,
2005). After the development of quantum mechanics, it was discovered that
tunnelling of
the wave functions of the protons through the repulsive barrier allows for
fusion at a lower
temperature than the classical prediction (M. Kikuchi, 2010). These quantum
waves of fuel
particles, (e.g. protons, deuterons), could also become interconnected under
the condition
of sufficient plasma density to form a continuum of waves.
[00192] The following is a theory of ¨ and also an attempt to quantify
¨ the possible
effect of such interconnected quantum waves within dense plasma on fusion
reactions.
- 47 -
CA 02887762 2015-04-10
Theory
Assumptions
[00193] The assumptions listed below are adopted in order to quantify
the rate of
fusion reactions for the participating fuel particles within a dense plasma
environment:
= The quantum waves of fuel particles are interconnected to form a
continuum
of waves.
= The fusion reaction rate is proportional to a penetration factor for the
waves.
= The wave penetration factor is proportional to the density of the
participating
fuel particles.
= The temperature dependency relationship is as described by the current
theory.
Mathematical Relationship
[00194] In order to develop a mathematical relationship for the fusion
reaction rate for
dense plasma with quantum wave effects, let's first examine the density
condition at the
solar core. The radius of the core is about 25% of the total radius for the
Sun. The density
at the core is in the range of 20 g/cm3 at the edge to 150 g/cm3 at the centre
(J.
Christensen-Dalsgaard, et al., 1996). At these densities, the wave
characteristics inherent
in microscopic particles in quantum mechanics start to influence the fusion
reactions in a
fundamental way. For example, the quantum tunnelling of wave functions of the
protons
through the Coulomb barrier directly facilitates the p-p fusion reactions.
Without the
enhancement role of the quantum particle waves, p-p reactions are not possible
at the
temperatures within the solar core (M. Kikuchi, 2010), i.e., 700 to 1500 MK
(Clayton, D. D.,
1968).
[00195] It is postulated that the quantum particle waves of the protons
have become
interconnected to form an ocean of the waves under the density condition
within the solar
core. When a fuel particle, such as a deuteron, travels within the solar core,
it constantly
encounters the quantum probability waves of the protons, experiencing a
quantum
pressure and a nonzero probability for fusion no matter where it goes.
Consequently, it is a
-48-
CA 02887762 2015-04-10
certainty for the travelling deuteron to eventually fuse with a proton, as
soon as its
accumulated probability of encountering the quantum waves of the protons
becomes unity,
i.e., when an entire proton has been experienced by the travelling deuteron.
[00196] The fusion reaction rate between fuel particles 1 and 2 is
anticipated to be
proportional to a penetration factor characterizing the quantum waves of the
two fuel
particles. Denoting the quantum probability waves of fuel particle 1 as fi(x,
y,z, t), those of
fuel particle 2 as f2(x,y,z, t), and including a sufficient time-space to
contain a large
number of individual fuel particles 1 and 2 within it, the penetration factor
for the quantum
waves, F12, may be defined as:
Ax AY Az At
1
F12 = AxyAzAt f (x,3 t) " f2 (x, y, z, t) dxdydzdt
(43)
0000
where the dimension of F12 is 1nn3. To maintain its physical meaning, F12 has
to be a real
number. This requires probability wave functions fl(x, y, z, t) and f2(x, y,
z, t) to be complex
conjugate to each other. The time t in the complex probability wave functions
certainly
describes the random thermal movement of the fuel particles. In addition, the
inherent
frequencies due to the internal energies of the nuclei of the fuel particles
should be
considered as required.
[00197] The fusion reaction rate F12 between fuel particles 1 and 2 may
be calculated
as follows:
Ax Ay Az At
C132 (T)n1n2 f iff
r12 ¨ xAyAzAt (x, y, z, t) f2 (x, y, z, t) dxdydzdt
(44)
A
0000
.. where the dimension of r12 is //m3/s, n1 and n2 are number densities for
particles 1 and 2,
respectively, T is temperature, and the term C102(T)n1n2 reflects the average
frequency of
encounters, with a dimension of -1/s, between an arbitrary pair of fuel
particles 1 and 2.
C102(T), in m6/s, is a temperature dependent constant of fuel particles 1 and
2 addressing
the combined effect of all the physical considerations listed below, and is
anticipated to
- 49 -
CA 02887762 2015-04-10
increase exponentially with T based on existing laboratory observations on
fusion reaction
rate:
= Coulomb barrier between atomic nuclei, shielded by electrons in the
plasma
= Pressure due to quantum waves, a direct consequence of the uncertainty
principle
= Penetration depth related to Coulomb barrier, quantum pressure and T
= A probability of encounter as a function of the penetration depth
= Characteristic volumes for fuel particles 1 and 2
= Characteristic length of penetration defining fusion between fuel
particles 1
and 2
= Relative velocity between fuel particles 1 and 2, and its statistical
distribution
[00198] In a dense plasma environment, with the individual quantum
waves
interconnected to form a continuum of fuel particle waves, the average level
of penetration
for the quantum waves is anticipated to be proportional to an average density,
¨01/77.2, of the
participating fuel particles 1 and 2. As a result, Equation (44) may be
simplified using the
mathematical relationship:
r12 Ci 2(nnin2Fr2 = C12 (T)(nin2)3l2 (45)
where C12 (T) is proportional to C102 (T). For identical particles, Equation
(45) becomes:
r11 = = (7') (ni)3 (46)
[00199] Equations (45) and (46) differ from the current theory (Clayton, D.
D., 1968;
Burbidge, E. M. et al., 1957) based on the concept of reaction cross section,
in that the
reaction rate is now proportional to density cubed, and not density squared.
The additional
density factor is derived from the penetration level for the interconnected
quantum waves,
characteristic of a dense plasma environment, as an enhancement factor.
- 50 -
CA 02887762 2015-04-10
[00200]
The relationship between the reaction rate and temperature T remains the
same as the current understanding, as the quantum waves introduced here
reflect a
physical concept independent of temperature T.
Reaction-rate Relationship
[00201] The mathematical similarity between Lorentz forces and gravity
discussed
above under the heading "Lorentz force distribution in radial direction",
suggests that a
reaction-rate relationship derived from solar information (Clayton, D. D.,
1968) may be
appropriate. Limited data from the original work by Stromgrew in 1965 are
listed in Table 1,
1 R radius ,õ,,
where the ratio of
provides a relative location within the Sun for the fusion rate.
The information on density is based on the current state of the solar modeling
(J.
Christensen-Dalsgaard, et al., 1996). The proton concentration by mass at the
center of the
Sun, currently at its mid-life, is assumed to be 37.5%, or 50% of the value of
75% (the
balance as He) at the edge region of the solar core. Examination of the data
on fusion rate
indicates that the extent of fusion burning at the edge region of the solar
core is negligible
compared to the center. Consequently, the proton concentration at the edge
region has
been assumed to be the same as the rest of the universe, i.e., 75%.
Proton
radius! 3 Concentration, Proton Fusion Rate,
T, M K Density, g/cm
Rs. Assumed at Mid- Density, g/cm3 Watt/m3
Life of the Sun
0 15.7 153.89 37.5% 57.71 276.5
24% 8.1 23.20 75.0% 17.40 0.67
29% 7.1 13.47 75.0% 10.11 0.09
Table 1 - Fusion Reaction Rates at Center and Edge Region of the Solar Core
(Clayton, D. D., 1968)
[00202]
The current understanding of the fusion reactions related to hydrogen
isotopes, such as D-T and D-D fusion reactions, suggests that an exponential
form of T
dependency is appropriate, with the exponent p in the range of 3 - 4 for the
temperature
range listed in Table 1. Considering the current theory (Clayton, D. D., 1968;
Burbidge, E.
M. et al., 1957), as well as the quantum wave theory proposed above under the
heading
"Nuclear Fusion Within Dense Plasma Enhanced by Quantum Particle Waves", a
general
form of fusion reaction rate for the p-p reactions inside the Sun may be
written as:
- 51 -
CA 02887762 2015-04-10
= Co nc0-13 , 3 < < 4 (47)
where Co is a fuel particle constant independent of T and n1 . The exponent a
would be 2 if
the current theory is applicable, or 3 if the quantum wave theory is
appropriate. The value
of a may be derived based on relationship (47), using the data of fusion rate
listed in Table
1 for a given 13. Taking two data sets 1st and 2nd, out of the three sets/rows
in Table 1, a
may be related to as:
1st (nlst (Tist )/3 (P4toton Tist
(48)
2nd 2nd T2nd
rn Tzna pp2rnaton
where n
r proton is the proton mass density in the solar core and the superscripts
distinguish
one data set from the other. The value of a as a function of p was calculated
using
Equation (48) and the results are listed in Table 2 for the central and edge
regions of the
solar core.
a
Central Region Edge Region
0 5 radius / Rsun 24% 24% 5 radius / Rsun 5 29%
Individual Average Individual Average
3.0 3.37 2.97
3.2 3.26 2.92
3.4 3.15 2.87
3.09 2.85
3.6 3.04 2.82
3.8 2.93 2.77
4.0 2.81 2.73
Table 2 - Derived Values of u for Central and Edge Regions of the Solar Core
[00203] The derived
values of a in the central and edge regions are within 5%, on
average, of the theoretical value of 3 postulated above under the heading
"Nuclear Fusion
Within Dense Plasma Enhanced by Quantum Particle Waves". This is remarkable
considering that the fusion rate data were derived from independent modeling
of the solar
- 52 -
CA 02887762 2015-04-10
core. The new theory based on the concept of quantum waves has thus survived
its first
reality check from the Sun.
[00204] The above fusion rate results may be fitted into the following
relationship
within 6% accuracy:
\ 3 7 \ 3 6
Pproton
(W I in') (49)
R11¨ 276'557.71 glcm3, 15.7 M". K "
where R11 is the fusion rate for proton-proton reactions occurring within the
Sun. The above
relationship differs from the current theory (Clayton, D. D., 1968; Burbidge,
E. M. et al.,
1957), with a density squared relationship, which assumes reaction cross
section is a
function of temperature independent of density. Such an assumption may not be
applicable
for a dense plasma environment where fuel particles may block one another's
movement
due to their own physical existence in the form of interconnecting quantum
waves.
[00205] Equation (49) may be used to derive for practical deuteron-
deuteron reaction-
rate, R22, considering that deuteron mass density is twice as much as proton
mass density
for a given number density:
\ 3 7 \ 3 6
R22 = 276.5 fleulercm Pdenleron
_________________________________________________________________ (W 110
(50)
115.42 gl cm' 15.7M".K1
where flew¨, is an additional correction factor to account for the following:
2.141018
= A conversion factor of 4.01 to p-D
reactions (Adelberger, et al., 2011);
= A second factor of 10 to reflect D-D reactions, which is faster than p-D
reactions (Adelberger, et al., 2011; R. Feldbacher, 1987);
= A third factor of 2 to correct for the energy content, from p-p to D-
D; and
3.65
= A fourth factor of 23.84 to account for incomplete burning of deuterons.
- 53 -
CA 02887762 2015-04-10
[00206] The energy released by each D-D reaction is 3.65 MeV, based on
average of
the two known branches of D-D fusion reactions (each with 50% probability of
occurrence)
in human laboratories associated with intermediate products such as helium-3,
tritium and
neutrons. As a comparison, deuterons are fully reacted within the Sun to
eventually form
helium-4 (Clayton, D. D., 1968; Burbidge, E. M. et al., 1957), with a total
energy release of
23.84 MeV.
[00207] Consideration of the above correction factors leads to the
following
relationship for deuteron-deuteron reactions under relatively low temperatures
(e.g., 6 -
15.7 M K) in a dense plasma environment:
( \ 3 6
R22 = 4.518x 1025 Aleufrroti
(W /m') (51)
115.42 glcm3) 15.7M"K1
Fusion Power Output
[00208] As an example calculation to demonstrate the value of the
proposed four
beam configuration, fusion power output may be calculated following a
simplified analytical
approach for the region of intersection using the input data listed below.
= Fuel is heavy water in its plasma state, in the form of regular lightning
beams.
= Temperature of each beam: To = 25,000 K.
= Radius of each beam: Ro = 5 mm.
= Velocity of each beam: VL = 137 km/s.
= Applied electric current for each beam: / = 100,000 A.
= Length of each beam: L = 1 m.
= Applied voltage for each beam: Vapply = 500 V.
[00209] The above input data are consistent with regular lightning beams
observed in
nature. Assuming uniform distributions of density and electric charges in each
plasma
- 54 -
CA 02887762 2015-04-10
beam, and neglecting the term due to elastic field, the magnetic field B1
generated by an
electric current / may be calculated by:
B, = ______________________________________ r, (52)
27t-A;
where ''is the distance to the centre of axis. Lorentz force per unit length,
FA, may be
calculated as follows:
,2
FA= B, __ 27z-r, dr, ¨0/ (53)
rt-RO2 3n-R0
0
[00210] On the other hand, the force due to pressure per unit length
may be
calculated by:
= 2R-Ropo (54)
[00211] The Lorentz and pressure forces have to be in global
equilibrium, i.e.:
/1012 ¨211-R0p0 (55)
3 iz-Ro
[00212]
Solving Equation (55) for the pressure of the lightning beam,P0, we have
,u0/2 4n-x10-7 x100,0002 6
, = õ ¨8.488x10 (56)
6rric- 671--x(5x10¨)- (Pa)
[00213] The density of the lightning beam may be calculated following
the ideal gas
law, i.e.:
M po _ 0.006667x8.488x106
Po¨ . =0.2724 (57)
R To 8.31x25,000 (kg/m3)
- 55 -
CA 02887762 2015-04-10
where FR'' is the ideal gas constant and M is the average molar mass for the
plasma formed
out of heavy water vapour. The deuteron mass density, Piu), is subsequently
calculated to be
0.0545 kg/m3.
[00214] Consider a hot and dense core of radius Rf, , temperature Tf and
deuteron
mass density PfD, within the common focal region, where the lightning velocity
of 137 km/s
is completely converted into temperature. Since the oxygen atom contributes to
majority of
the mass in a heavy water molecule, the lightning velocity of 137 km/s is a
good
approximation of the average velocity of the oxygen nuclei in the plasma
mixture formed
out of the heavy water vapour. With thermal equilibrium reached in the core
among
deuterons and oxygen nuclei, the average velocity of deuterons may be
calculated by:
Vdeuteron = Vg' n ¨ XY 2
16 x137 -- 387.5 (58)
deiveron () ' ¨ ¨ (km/s)
[00215] Equating thermal and kinetic energies gives
IkT =-1 m v2 (59)
2 / 1 deuteron deuteron
where k is the Boltzman constant. Solving Equation (59) for Tf, we have:
0.002 46.02 x1023)x (387.5x103)2
7' ¨ ___________________________________________ =12x106 (60)
1 - 3x1.38x10-23 ( K)
[00216] Meanwhile, deuterons flow from each lightning beam and
eventually squeeze
into the core (assumed here to have uniform temperature and density
distributions) at the
velocity of 387.5 km/s. Mass conservation at a constant velocity for the four
beams gives:
( \ 2
4x 71-R(2, R 0
PI)¨ Pi")¨ R P-
D (61)
A1 r2
-00-
CA 02887762 2015-04-10
[00217] Applying Equation (51) to the core, with consideration of
Equation (61), we
have:
"N3 ( \6 \ 6
R22 =4.518x1025 pi())
Ro
=1.81x106 ________________________________________________ (W/m3) (62)
115.42 g 1 cm' 15.7 APK,
[00218] Fusion energy output P is balanced by energy loss to the
environment due to
radiation, i.e.:
005m 4
P -=1.81x106 0. x¨rtle =5.67 x10-8 x 4 n-R2 x(12x106)4 (W)
(63)
3 R1
[00219] Solving Equation (63) for Rf and P, we have
P=34x109 W=34 GW, at RI =.1.52x10-6 M=1.52/M1 (64)
[00220] Assuming a typical energy conversion rate of 30%, the net
energy output may
be calculated by
Põ, = 34 x 30%=10 (GW) (65)
[00221] The calculated net energy output is equivalent to more than ten
nuclear
fission reactors, each with a capacity of 1 GW or less. As a comparison, the
total input
power for the four beams is
P = 4x100, 000>< 500 = 0.2x109 (W)= 0.2 (GW) (66)
nP1,1
[00222] The net energy output is thus calculated to exceed the total
input power by a
comfortable margin.
- 57 -
CA 02887762 2015-04-10
[00223] Recent test results (Sinars, D. B. et al., 2003; Glenzer, S. H.
et al., 2012)
demonstrated that the solar density condition is achievable for a plasma
region. The
confinement times were, however, shorter than 1 nanosecond (ns). With the
improvement
in stability as described above under the heading "Stability and Confinement
Time", it is
anticipated that the four beam configuration may reach the solar density
condition for a
sufficiently long duration, e.g., 10 miliseconds (ms), suitable for commercial
power
generation. A significant increase in plasma density may permit utilization of
diluted
deuterium to satisfy the demands for fusion energy output, and a decreasing
deuterium
concentration within hydrogen or water may in turn promote clean hydrogen-
deuterium
fusion reactions occurring naturally inside the Sun.
Proof-of-Concept Experiments
[00224] The stability of the four beam configuration, referred to as a
"star-pinch", may
be demonstrated by experiments similar to those for two beam X-pinches
(Sinars, D. B. et
al., 2003), except that the two metal wires in a plane must be replaced with
the four metal
wires symmetrical in 3D space, as illustrated in Figures 3 and 4. The X-pinch
results
demonstrated satisfactory connection of two or more beams at the point of
intersection,
prior to formation of a micro-pinch instability (Sinars, D. B. et al., 2003).
A more stable
connection is expected for the four beam star-pinch. The current confinement
times of
plasma regions with densities approaching (Sinars, D. B. et al., 2003) or
exceeding
(Glenzer, S. H. et al., 2012) solid density are in the order of picoseconds
(ps). A significant
increase in confinement time to the order of nanoseconds (ns), for example,
may be
considered as initial success in the proof-of-concept by experiments. The
power source
used for the two beam X-pinches is an XP pulser (Kalantar, D. H., 1993) at
Cornell
University capable of generating a 470 kA, 100 ns current pulse. The lengths
of the wires
were less than an inch. The experimental setup (Sinars, D. B. et al., 2003)
was relatively
simple compared to those at Sandia with metal wire arrays (Haines, M. D. et
al., 2006) or
Livermore using laser beams (Glenzer, S. H. et al., 2012).
[00225] Hydrogen isotopes may precipitate as metal hydrides in a
particular group of
metals, including titanium (Williams, D. N., 1962), zirconium (Coleman, C. E.
and Hardie,
D., 1966), niobium (Grossbeck, M. L. and Birnbaum, H. K., 1977) and vanadium
(Takano,
- 58 -
CA 02887762 2015-04-10
S. and Suzuki, T., 1974). In CANDU reactors, for example, deuterium atoms from
the
heavy water coolant were found to diffuse into the zirconium pressure tubes to
form metal
hydrides (Perryman, E. C., 1978; Cann, C. D. and Sexton, E. E., 1980).
Zirconium is
routinely hydride or deuterided in laboratories for experiments (Simpson, L.
A. and Cann,
C. D., 1979). Following achievements in this area, metal hydride wires
containing
deuterium as fuel may be prepared as a further step to demonstrate fusion, and
possibly
net energy output as well, using the four beam star-pinch.
[00226] Alternatively, deuterated-polystyrene (DPS) wires were
fabricated recently for
use in Z-pinch experiments. Using 1 gram of DPS as the raw material, uniform
DPS wires
with diameters from 30pm to 100pm were prepared (Fu, Z. B., Qiu, L. H., Liu D.
B., Li, B.
and Yu, B., 2005). Recent Z-pinch experiments utilizing DPS wires produced a
peak
neutron yield of about 2 x 109 /cm. It is not yet clear if the neutrons were a
result of D-D
fusion or a phenomenon similar to the dissociation observed in the 1957 UK
Zeta tests. The
DPS wires may be arranged in connection with electrically conducting metal
wires in the
star-pinch configuration.
[00227] It is theorized that the star-pinch configuration will produce
sufficient
confinement time for D-D fusion. The basic elements of a test plan include:
= Metal/carbon wire/filament experiments to demonstrate stability of the
intersection region of the star pinch plasma beam configuration, and;
= Experiments using wires/filaments containing deuterium to
demonstrate
fusion.
[00228] Successful tests may lead to further tests using fluids (argon,
air, deuterium
and/or water) as plasma media, eventually moving towards an experimental
pilot.
Power Generation
[00229] A thermonuclear reaction system 100 may operate using one or more
types
of suitable thermonuclear fuel particles as part of one or more known fusion
reaction paths.
For example, thermonuclear reaction system 100 may use deuterium, tritium, and
lithium to
effect a deuterium-tritium reaction cycle, as discussed above. In some
embodiments,
thermonuclear reaction system 100 uses a combination of ,11-1 and 21 D in
order to effect a
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CA 02887762 2015-04-10
proton-proton fusion cycle, also discussed above. While 21 D is the primary
source of energy
in a proton-proton fusion cycle, ,Ihr particles are employed to produce a
sufficient quantity
of the intermediate product ;He with the participation of 21 D, although as
discussed above
:H may also be converted to 21 D in a slow process due to the effects of
quantum tunneling
and weak interactions.
[00230] The
supply of ,'H and 27D thermonuclear fuel particles for such a proton-
proton reaction is virtually inexhaustible, as approximately one in every
6,500 hydrogen
atoms on Earth is a deuterium atom, and both ,'H and 21 D may be readily
extracted from
seawater. One gallon of seawater would, in some embodiments, provide the
equivalent
energy output of approximately 300 gallons of gasoline.
[00231]
Referring now to Figure 8, a schematic view of a thermonuclear reaction
system integrated with an existing nuclear fission reactor design (such as the
CANDU
design) is illustrated in accordance with at least one embodiment. In this
example
embodiment, a continuous proton-proton fusion reaction is generated in a
thermonuclear
reaction system (such as the thermonuclear reaction system 100 shown in Figure
1), and
hydrogen and deuterium thermonuclear fuel particles are extracted from
seawater in a
separation facility 810.
[00232]
After the removal of impurities, seawater containing deuterated water
(sometimes referred to as HDO) and H20 enters a separation facility 810, where
,1H and
D are separated from 02. The ,'H and 21 D gases produced by separation
facility 810
subsequently enter a fuel injector 820 (which may be similar or equivalent to
fuel injector
120 as described herein above with reference to Figure 1) where the ,'H and
2,D gases are
heated to form a plasma of thermonuclear fuel particles to be provided to one
or more
particle beam emitters 830 (which may be similar or equivalent to particle
beam emitter 200
as described herein above with reference to Figure 2).
[00233] As
described above, particle beam emitters 830 may emit particle beams
consisting of thermonuclear fuel particles towards a common focal region 835
of a reaction
chamber 840, creating density and temperature conditions sufficient to
instigate and, in at
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CA 02887762 2015-04-10
least some cases, sustain a continuous (or pseudo continuums) thermonuclear
fusion
reaction.
[00234] A primary cooling system 850 uses water (or any other suitable
coolant liquid)
to absorb at least some of the heat generated by the thermonuclear fusion
reaction taking
place within reaction chamber 840. Primary cooling system 850 is also
connected to one or
more steam generators 860; steam output from steam generator 860 may be used
to drive
turbines and generators (not shown) to produce electricity.
[00235] Integration with an existing nuclear reactor design may minimize
the duration
for design and manufacturing of an overall fusion reactor. For example, the
existing
CANDU reactor may be modified in accordance with embodiments of the present
thermonuclear reaction system by substituting the Calandria fission reactor
core with a
fusion reaction chamber, removing the fuel bundles and fuelling machines,
replacing the
fuel channel assemblies with simple pressure tubes, installing particle beam
emitters
surrounding the fusion chamber, replacing the heavy water used in the CANDU
design with
regular water (as no neutrons need to be moderated), replacing the heavy water
pressure
reservoir with a gas collection tank 870, and adding the separation facility
810.
[00236] Gas collection tank 870 is used to collect un-reacted
thermonuclear fuel
particles and fusion reaction products, as not all of the ,IH and 21 D
particles injected into the
reaction chamber may undergo a fusion reaction with another reactant particle.
In some
embodiments, the gas collection tank 870 may operate based on the relative
buoyancies of
different fuel particles. For example, there is a relatively large difference
in density between
the reactant fuel particles in a thermonuclear reaction (e.g., the ,11-1 and
2,D particles) and
the product particles of the fusion reaction (e.g., He particles), on the one
hand, and the
coolant fluid, on the other hand. Accordingly, the lighter gas particles will
generally flow up
through the coolant fluid due to buoyancy effects, resulting in a
concentration of the lighter
gas particles at an upper portion of the gas collection tank 870. The
relatively heavy coolant
fluid will correspondingly concentrate toward the lower portion of the gas
collection tank
870.
[00237] In order to separate the lighter gas particles from the heavier
liquid coolant,
the gas collection tank 870 may include an outlet valve or other external feed
in the upper
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CA 02887762 2015-04-10
portion through which the gas may be continually pumped. As the lighter gases
exist as a
mixture with the coolant fluid flowing through the primary cooling system,
some of the
gases may remain un-collected after one cycle of the coolant fluid through the
primary
cooling system. However, un-collected gases may eventually be collected by the
gas
collection tank 870 as the coolant liquid is continually pumped through the
primary cooling
system during additional cycles.
[00238] The un-reacted gases and fusion product collected in gas
collection tank 870
may then be delivered to separation facility 810 for reuse. In addition to the
un-reacted
gasses and the fusion product, a small amount of coolant water close to the
central region
may dissociate into 112, D2 and 02 due to the heat generated by a
thermonuclear fusion
reaction taking place within reaction chamber 840. If coolant water
dissociates into H2, D2
and 02, the H2, D2 and 02 will be collected in gas collection tank 870 and
moved to
separation facility 810, following the similar path as H2, 02 and He gases
shown in Figure 8.
[00239] In some embodiments, the gas collection tank 870 may be
modified by
installation of at least one pressure valve in order to achieve an added
functionality, i.e.,
coolant water pressure reservoir. This modification to the gas collection tank
870 would
permit the gas collection tank 870 to control and achieve a desired level of
pressure for the
coolant liquid being pumped through the primary cooling system.
[00240] In order to maintain a desired level of 21 D concentration in
the fuel particle
circulation, for optimal performance of the thermonuclear reaction system,
certain amount
of ;I/ gas may be moved out of separation facility 810, along with the 02 and
He gases.
The desired level of 21 D concentration may be determined by detailed design
calculations;
the higher the 21D concentration, the larger the fusion energy output of the
thermonuclear
reaction system.
[00241] In some embodiments, un-reacted fuel particles collected from the
gas
collection tank 870 may be mixed together with newly supplied fuel particles
of the same or
a different type in a closed loop circulation. For example, particles of
Hydrogen-1 or a
mixture of Hydrogen-1 and Hydrogen-2 collected from the gas collection tank
870 may be
mixed together with a new supply of Hydrogen-1 or a mixture of Hydrogen-1 and
Hydrogen-
2. However, this example is not limiting. The resulting closed loop
circulation of collected
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CA 02887762 2015-04-10
and new fuel particles may include one or more separation facilities (e.g.,
separation facility
810 in Figure 8), one or more fuel injectors (e.g., fuel injector 120 in
Figure 1) and a
plurality of particle beam emitters (e.g., particle beam emitter 200 in Figure
2). The
minimum operating temperature in the closed loop circulation may be maintained
at 1800 C
or greater by the heat generated from thermonuclear fusion reactions occurring
within the
reaction chamber 110 as described herein. As a result, the fuel particles used
to drive the
thermonuclear fusion reactions are maintained essentially continuously in a
plasma state
without having to re-heat the fuel particles into plasma in the fuel injector
prior to supplying
the fuel particles to the particle beam emitter for re-emission in the
reaction chamber 110.
[00242] As discussed above, thermonuclear reaction system 100 preferably
uses a
combination of ,'H and 2,D in order to effect a proton-proton fusion cycle.
However, future
generations of nuclear fusion reactors, may also be able to employ other
elements ¨ such
as isotopes of He, B, Li, C, Ne, 0, etc. ¨ as thermonuclear fuel. In theory, a
series of fusion
reactions may be designed in order to maximize the energy output from a fusion
reaction
path (For example, a fusion reaction could be designed with the fusion path H
4 He 4 C
4 Ne 4 0 4 Si).
[00243] In some embodiments, seawater may be purified to remove sand,
salt or
other impurities and provided, through at least one fuel injector, to some or
all of the
particle beam emitters 200 shown in reference to Figure 2 as a source of
thermonuclear
fuel. The purified seawater may be heated up in the at least one fuel injector
or
subsequently in the particle beam emitters. Heating of the purified seawater
causes the
water molecules to dissociate into 02, H2 and D2 gases and, with a
sufficiently hot source of
heat, at least some part of the H2 and D2 gases further turn into plasma due
to increasing
temperature. Accordingly, in some embodiments, the purified seawater is
automatically
separated into different thermonuclear fuel types by heating inside the at
least one fuel
injector or subsequently inside at least some of the particle beam emitters
200.
Consequently no additional separation facilities will be needed in at least
some cases to
provide the thermonuclear fuel used in the thermonuclear reaction system 100.
[00244] In some embodiments, regular water, containing 0.01% of
deuterium particles
.. and becoming plasma mixture of oxygen and hydrogen isotopes inside the
fusion chamber,
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CA 02887762 2015-04-10
are used as fuel for the fusion reaction. In other embodiments, regular water
enriched by
heavy water is used in order to increase fusion power. The level of heavy
water
concentration determines the level of fusion power generation, the higher the
heavy water
concentration, the higher the deuterium particle concentration, and therefore
the larger the
energy output. The oxygen particles are used in these embodiments in order to
(1) contain
hydrogen isotopes in liquid form under low temperatures for easy handling and
(2) enforce
effective collisions and therefore fusion of the hydrogen isotopes in the
focal region of the
fusion chamber as resistive walls consisting of heavy nuclei.
[00245] In some embodiments, heavy elements (such as oxygen in water,
nitrogen in
air, Na/CI in oceanwater or metal elements) are added in order to accelerate
the fusion
reaction as catalysts, by acting as resistive walls to enforce effective
thermal collisions in
the common focal region.
[00246] Through the symmetrical four beam 'star-pinch' configuration,
plasma
instabilities may be addressed, and nuclear fusion may be demonstrated using
wires
containing deuterium. This is supported by the following:
= The counter-balancing electro-magnetic fields in the star pinch
configuration
will stabilize the intersection region, providing longer confinement times;
= The converging magnetic forces will provide stability and density, in a
manner
similar to the stability achieved during star formation under gravitational
forces;
= Necessary density and temperature conditions, e.g., solar conditions,
have
already been achieved by other researchers following Z-pinch and laser beam
approaches;
and
= A confinement time of 10 ms to achieve continuous fusion has been
exceeded by tokamak;
[00247] With the potential improvement in plasma stability ¨ and therefore
its
confinement time, density and temperature ¨ the four beam star-pinch
configuration may
potentially lead to continuous fusion power from water without the need for
tritium in the
fuel.
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CA 02887762 2015-04-10
[00248] While the above description provides examples of the embodiments,
it will be
appreciated that some features and/or functions of the described embodiments
are
susceptible to modification without departing from the spirit and principles
of operation of
the described embodiments. Accordingly, what has been described above has been
intended to be illustrative only and non-limiting.
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CA 02887762 2015-04-10
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