CA 0220~989 1997-0~-16
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ELECTROM GUN
FIELD OF THE INVENTION
The present invention is related to elec_ron guns.
More specifically, the present invention is related to an elec-
5 tron gun that uses an RF cavity subjected to an oscillatingelectric field.
BACKGROUND OF THE INVENTION
The development of high-current, short-duration pulses
of electrons has been a challenging problem for many years.
10 High-current pulses are widely used in injector systems for
electron accelerators, both for industrial linacs as well as
high-energy accelerators for linear colliders. Sho:t-duration
pulses are also used for microwave generation, in kl~7strons and
related devices, for injectors to perform research on advanced
15 methods of particle arceleration, and for injectors used as
free-electron-laser (FEL) drivers.
The difficulty in generating very high-current pulses
of short duration can be illustrated by e~mln~tion of a modern
linac injector system. A good example is the system designed and
20 built for the Boeing 120 MeV, 1300 MHz linac, which in turn is
used as an FEL driver [J.L. Adamski et al., IEEE Trans. Nucl.
Sci. NS-32, 3397 (1985) ; T.F. Godlove and P. Sprangle, Particle
Accelerators 34, 169 (1990)]. The Boeing system uses: (a) a
gridded, 100 kV electron gun; (b) two low-power prebw~chers, the
25 first operating at 108 MHz and the second at 433 MHz; and (c) a
high-power, tapered-velocity buncher which accelerat~s the beam
bunches up to 2 MeV. The design relies on extensive calculations
with codes such as EGUN, SUPERFISH and PARMELA. A carefully ta-
pered, axial magnetic field is applied which starts f:rom zero at
CA 0220~989 1997-0~-16
the cathode and rises to about 500 Gauss. With this relatively
complex system Boeing obtains a peak current of up to about 400 A
in pulses of 15 to 20 ps duration, with good emitt~nce. The
bunching process yields a peak current which is two orders of
5 magnitude larger than the electron gun current. Space charge
~orces, which cause the beam to expand both radially and axially,
are balanced by using a strong electric field in the high-power
buncher, and finally are balanced by forces due to the axial
magnetic field. The performance achieved by Boeing appears to be
10 at or near the limit of this type of injector.
During the last few years considerable effort has also
been applied to the development of laser-initiated photocathode
lnjectors [M.E. Jones and W. Peter, IEEE Trans. Nucl. Sci. 32
(5), 1794 (1985); P. Schoessow, E. Chojnacki, W. Gai, C. Ho, R.
15 Konecny, S. Mtingwa, J. Norem, M. Rosing, and J. Sim~)son, Proc.
of the 2nd European Particle Accel.Con~. 606 (1990); K. Batche-
lor et al, Nucl. Instr. and Meth. in Phy. Res. A318, 372 (1992);
S.C. Hartman et al, Part. Accel. Conf., IEEE Cat. 93CH:3279-1, 561
(1993); I. Ben-Zvi, Part. Accel. Con~., IEEE Cat 33CH3279-1,
20 2962 (1993); I. S. Lehrman et al, Part. Accel. Conf., IEEE Cat.
93CH3279-1 3012 (1993); C. Travier, Nucl. Instr. and Meth. in
Phy. Res. A340, 26 (1994)]. The best of these have somewhat
higher brightness than the Boeing injector, but the :reliability
depends on the choice of photocathode material, with the more
25 reliable materials requiring a larger laser illumination.
SUMMARY OF THE INVENTION
Micro-pulses are produced by resonantly amplifying a
current of secondary electrons in an RF cavity operating in, for
example, a TMo20 mode (F'ig. 1) or a TMolo mode (Fig. 2) [F. Mako
30 and W. Peter, Part. Accel. Con~., IEEE Cat. 93CH3279-1 2702
(1993)]. Figure 1 shows a perspective view of the micropulse gun
emitting electron-bunches in an annular geometry. Figure 2 shows
~ =
CA 0220~989 1997-0~-16
a side view of the micropulse gun emitting electron-bunches in a
solid bunch geometry. Bunching occurs rapidly and is followed by
saturation of the current density in typically ten to fifteen RF
periods. "Bunching" occurs by phase selection of resonant parti-
5 cles. The bunch that :s formed is much shorter than the RF pe-
riod which is due to the resonant nature of this process. Also,
the micropulse gun produces a narrow bunch every RF period in the
output direction. Bunch transmission is accomplished by use of a
transparent grid. ~ocalized secondary emission in the micropulse
10 gun is dictated by material selection. Radial space charge ex-
pansion in the micropulse gun cavity can be reduced by using ei-
ther electric or magnetic focusing, or both. Radial electric
focusing in the cavity is accomplished by a concave shaping of
the cavity, as shown in Fig. 2. The grid not only allows trans-
15 mission of bunches but can also provide an emitting surface forelectron multiplication. A path for the RF current can be main-
tained by using a grid of wires. The double grid isolates an
external accelerating field from "pulling out" n~n-resonant
electrons which would form a dc baseline. Also, the two grids
20 are electrically isolated to allow for dc biasing to create a
barrier for low energy electrons. Axial and radial expansion of
the bunch is minimized outside the micropulse gun cavity by using
various combinations of rapid acceleration, electric and magnetic
focusing.
This micro-pulse electron gun should provide a high
peak power, multi-kiloampere, picosecond-long electron source
which is suitable for many applications. Of particular interest
are: high energy picosecond electron injectors :Eor linear
colliders, free electron lasers and high harmonic RF generators
30 for linear colliders, or super-power nanosecond radar.
The present invention pertains to an electron gun. The
electron gun comprises an RF cavity having a first side with an
emitting surface and a second side with a transmitting and emit-
35 ting section. The gun is also comprised of a mechanism for pro-
ducing an oscillating force which encompasses the emitting
CA 0220~989 1997-0~-16
.,
surface and the section so electrons are directed between the
emitting surface and the section to contact the emitt:ing surface
and generate additional electrons and to contact the section to
generate additional electrons or escape the cavity t:hrough the
5 section.
The section preferably isolates the cavity :~rom exter-
nal forces outside and adjacent the cavity. T.-Le section
preferably includes a transmitting and emitting screen. The
screen can be of an annular shape, or of a circular shape, or of
1o a rhombohedron shape.
The mechanism preferably includes a mechanism for pro-
ducing an oscillating electric field that provides the force and
which has a radial component that prevents the electrons from
15 straying out of the region between the screen and the emitting
sur~ace. Additionally, the gun includes a mechanism :-or produc-
ing a magnetic field to force the electrons between the screen
and the emitting surface.
The present invention pertains to a method :-or produc-
20 ing electrons. The method comprises the steps of movi:-Lg at least
a first electron in a first direction. Next there is the step of
striking a first area with the first electron. Then there is the
step of producing additional electrons at the first area due to
the first electron. Next there is the step of moving electrons
25 from the first area to a second area and transmitting electrons
through the second area and creating more electrons due to elec-
trons from the first area striking the second area. These newly
created electrons from the second area then strike the first
area, creating even more electrons in a recursive, repeating
30 manner between the first and second areas.
BRIEF DESCRIPTION OF THE DRAWINGS
CA 0220~989 1997-0~-16
J
In the accom~anying drawings, the preferred embodiment
of the invention and p:referred methods of practicing the inven-
tion are illustrated in which:
Figure 1 is a perspective view of the mic:~opulse gun
for a hollow beam using the TMozo mode. The inner conductor is
not shown.
Figure 2 is a schematic of micropulse gun for solid
beam using the TMolo mode. This side view of solid beam micro-
10 pulse gun cavity showing double grid and emitting and transmit-
ting surfaces. Beam pulses and concave shaping of the micropulse
gun cavity are shown. Figure is not to scale. A coaxial feed or
side coupling or coupling loops can be used for RF input (not
shown).
Figure 3 Plot of current density vs. time for simula-
tion with RF frequency 2.85 GHz and aO= eVO/(m~2d2) = 0.373. d =
1.5 cm with peak RF voltage amplitude 153 kV.
Figure 4 Comparison of saturated current density in
kA/cm2 versus frequency for simulation and analytic theory for a
20,gap length of d = 1.0 cm and drive parameter aO = eVO/(m~2d2)
= 0.373.
Figure 5 Saturated Current Density vs Drive Voltage,
f = 2.85 GHz. The curves are for different gap spacings.
Figure 6 Micro-Pulse Width vs Drive Voltage, f =
25 2.85 GHz.
Figure 7 Emlttance growth due to double-g:rid extrac-
tion with an in~ection beam energy of 114 kV. The wire thickness
is set 0.1 mm.
CA 0220~989 1997-0~-16
Figure 8 Experimental Data: Current trace of the mi-
cropulse gun Micro Bunches.
Figure 9 Expansion of micro-pulse from space charge
during acceleration, neglecting energy spread. The a,-celeration
5 field is 50 MV/m and the axial space charge electric field is
1.33 MV/m (or about 35 ~lC/cm3).
DESCRIPTION OF THE PREFERRED EMBODIMENT
Referring now to the drawings wherein like reference
numerals refer to similar or identical parts throughout the sev-
10 eral views, and more speci~ically to Figure 2 thereof, there isshown an electron gun 10. The electron gun 10 comprises an RF
cavity 12 having a first side 14 with an emitting suri-ace 16 and
a second side 18 with a transmitting and emitting sect:ion 20. The
gun lû i~ also comp-I-ised of a mecnanism 22 for produclng an os-
15 cillating force which encompasses the emitting surface 16 and thesection 20 so electrons 11 are directed between the emitting
surface 16 and the section 2û to contact the emitting surface 16
and generate additional electrons 11 and to contact t:he section
20 to generate additional electrons 11 or escape the cavity 12
20 through the section 20.
The section 20 preferably isolates the cavity 12 ~rom
external forces outside and adjacent the cavity 12. l'he section
20 preferably includes a transmitting and emitting screen 24. The
screen 24 can be of an annular shape, or of a circular shape, or
25 Of a rhombohedron shape.
The mechanism 22 preferably includes a mechanism 26 for
producing an oscillating electric fielcl that provides the force
and which has a radial component that prevents the e].ectrons 11
from straying out of the region between the screen 24 and the
30 emitting surface 16. Additionally, the gun 10 -ncludes a
CA 0220~989 1997-0~-16
mechanism 28 for producing a magnetic field to force the elec-
trons 11 between the sc:reen 24 and the emitting surface 16.
The present invention pertains to a method :Eor produc-
ing electrons 11. The method comprises the steps of moving at
5 least a first electron 11 in a first direction. Next there is the
step of striking a first area with the first electron 11. Then
there is the step of producing additional electrons 11 at the
first area due to the first electron 11. Next there is the step
of moving electrons from the first area to a secon~ area and
10 transmitting electrons through the second area and creating more
electrons 11 due to electrons from the first area striking the
second area. This process is repeated until the device is shut
off by removing the RF power source.
A schematic of one embodlment of the propose~1 device is
15 given in Figures 1 and 2. Although the design shown is not
necessarily optimum it provides a basis for describing the
invention. Shown in figures 1 and 2 is a side view of a
cylindrically symmetric device. RF power may be fed into the
cavity through several means including: a low impedance coaxial
20 transmission line conne~ted to the back perimeter of l_he cavity,
side coupling using a tapered waveguide or coupling loops. The
appropriate mode is then set up in this case a TMo1o for a circu-
lar cavity (as in Fig. .2) or a TMo20 for the circular cavity as in
Figure 1. An annular bunch is generated by secondary emission at
25 the second peak of the electric field in the cavity operating in
a TMo20 mode (Fig. 1). The first peak may be eliminated by plac-
ing an inner conducting cylinder at the first zero of the TMo20
mode. In Figure 2 a solid bunch is created on the axis by
secondary emission. The right wall of the cavity in Fi~ure 2(also
30 see detail) is constructed with a transmitting double screen or
grid which allows for the transmission of electron bunches. The
crossed wires of the grid maintain a path for the RF current. The
double grid isolates an external electric field from pulling out
non-resonant electrons. Also, the grids are electrically
CA 0220~989 1997-05-16
insulated to allow for biasing to create a barrier for unwanted
electrons
To conceptualize how rapidly the current cLensity can
build up in the micropulse gun cavity a simplified model is pre-
5 sented which excludes space charge, transit time, amplitude andphasing effects but shows the principle behind utilizing multi-
pacting for the micropu~se gun. In Fig. 2 is shown an RF cavity
operating in for example a TMo1o mode. Assume that at the grid-
ded wall of the cavity there is a single electron at rest on
10 axis, which transits the cavity in about one-hal~ the RF period
and is in proper phase with the ~ield. This e:'ectron is
accelerated across the cavity and strikes the sur~ace S. A num-
ber ~1 of secondary electrons are emitted off this electrode,
where ~1 is the secondary electron yield of surface ',. Assume
lS the electrons transit the cavity in one-half the RF period and
they are in proper phase with the field, these electrons will be
accelerated back to the grid. After reaching the grid, ~lT elec-
trons will be transmitted, where T is the ratio of transmitted to
incident electrons for t:he grid. The number of electrons which
20 are absorbed by the grid is then ~1(1-T). After one cycle the
number of electrons that are produced by the grid is ~2 [~1 (l-T)],
where ~2 iS the grid secondary yield. To have electron gain, the
number of secondaries must be greater then one, i.e. ~2~1 (1-T)
1. Current amplification occurs by repeating this proc~ss. This
25 is analogous to a laser cavity with the grid acting as a
partially-silvered mirror. The gain of electrons after N RF pe-
riods is G = [~z~l (l-T) ] N, If there is a "seed" current density
Jseed in the cavity initially, then after N RF periods the current
density will be given by ~ = GJseed= ~seed ~2Sl (1 -T)] N~ unt.il space-
30 charge limits the current density. For a very low seed currentdensity a high current density can be achieved in a ~ery short
time. For example, if ~2 = ~1 = 8, T = 0 50, and ~seed= 1.3 x 1o~12
A/cm2, in ten RF periods ~ =1500 A/cm2!
CA 0220~989 1997-0~-16
.
The seed current density ~seed can be created by several
sources including: thermionic emission, radioactivity, field
emission, cosmic rays, a spark or ultraviolet radiation.
The secondary emission yield ~ is defined to be the
5 average number o~ secondary electrons emitted for each incident
primary electron and is a function o~ the primary elec ron energy
~. ~ for all materials increases at low electron energies,
reaches a maximum ~max at energy ~maxl and monotonicall~ decreases
at high energies. Table I gives some commonly usecL materials
10 with high and low values o~ ~ [3.E.Gray(coord. Ed.), Amer. Inst.
o~ Physics Handbook, 3rd Edition, McGraw-Hill; E. L. Garwin, F.
K. King, R. E. Kirby and 0. Aita, J. Appl. Phys. 61, 1145 (1987);
A. R. Nyaiesh, et al., J. Vac. Sci. Tech. A, 4, 2356 (1986); G.
T. Mearini, etal., Appl Phys. Lett. 66 (2), 242 (19951].
Table I Secondary emission coe~icient of ~ome
common materials.
Materi.~l ~max ~maX (keV)
GaP+Cs (crystal)147 5
Diamond +Cs 55 5
MgO (crystal) 20-25 1.5
TiN coating 1-1.6 0.3
A universal yield curve good for all materials (and
experimentally veri~ied) ~or normal primary incidence is given by
~ = ~max (2~/~maX )/[l+(~/~maX ) 8 (2~ ) ] where Z and A are the arithmetic mean
20 atomic number and atornic weight, respectively [B.K. Agarwal,
Proc. Roy. Soc. 71, 851 (1958)]. At 2.85 GHz and for a 1.5 cm
cavity gap the particle energy turns out to be about 114 keV.
The yield ~or diamond at 114 keV is ~ 7.7. I~ T = 0.5, there
would be gain since ~2~1 ( l-T) ~ 1, (assuming ~2 = ~
CA 0220~989 1997-0~-16
Several photomultipliers (RCA C31024, RCA C31050 and
RCA 8850) are built with GaP dynodes. GaP is not sensitive to
oxygen but is sensitive to water. With very thin coatings on the
5 surface of GaP, it can be made to allow secondaries to leave and
at the same time prevent contamination. Also, GaP can be doped to
eliminate charge builcL-up. Thus GaP could be an excellent
candidate at high energy (up to 100's of keV). MgO is a good
candidate for lower particle energy (<60 keV) and would have to
10 be applied in a thin layer in order to minimize charge build-up.
Another very robust emitter material that is currently under
intensive study is diamond ~ilm [M.W. Geiss, et al., IEEE Elec-
tron Device, Letters, 12, 8 (1991)]. Single cryst:al alumina
(sapphire) or polycrystalline alumina are also excel ent robust
15 emitterS~
The entire MP~ cavity (except ~or the specified secon-
dary emission sites) needs to be built with a lo~ secondary
emission coefficient. Cavity surface coatings can reduce secon-
20 dary emission and also isolate electrical whiskers from the cav-
ity and serve as a trap for slow electrons [W. Peter, Journal of
Applied Physics 56, 1546 (1984)]. CaF2 and TiN [E. L. Garwin, F.
K. King, R. E. Kirby and O. Aita, J. Appl. Phys. 61, 1145
(1987); A. R. Nyaiesh, et al., J. Vac. Sci. Tech. A, 4, 2356
25 (1986)] are excellent candidates for cavity coatinc~s. Also,
cavities built from 304 stainless steel or titanium wo:-k well for
the low secondary emission areas.
Secondary emission involves electron diffu~;ion, which
implies finite emission time. A simple diffusion ana ysis shows
30 that the emission time for several emitters is several picosec-
onds or longer [P.T. Farnsworth, J. Franklin Institute, 218, 411
(1934)]. This emission time will limit the maximum cavity
frequency.
CA 0220~989 1997-0~-16
.
11
Secondary electrons are not emitted norr~al to the
surface, but follow an angular distribution which is nearly
independent of the angle of lncidence of the primary electrons.
This angular distribution comes from secondary electron scatter-
5 ing in the material which ends up as emittance in the beam.
Secondary electrons follow an angular distribution according to a
cos2~ law [J.L. H. ~onker, Philips Research Repts. 12, 249
(1957)].
An estimate o~ the normalized transverse emittance can
10 be obtained from the expression, ~D=2rb(~T~/mc2)"2 where, kTt repre-
sents the average transverse thermal kinetic energy, :rb the beam
radius and mc2 the electron rest mass energy. The secondary
electron energy distribution typically has a spread of much less
then an eV. We will take rb= 1 mm, and since most of the parti-
15 cles have been shown to come out at ~30~ then kTt is about 0.25
eV. From the above equation the normalized emittance is 1.4 mm-
mrad. This emittance is comparable to that ach:eved from
thermionic emitters or photo-cathodes. Since the angular
distribution or emittance of the secondary electrons does not
20 depend on the angle of incidence of the primary electrons, the
emittance does not increase on successive RF periods inside the
cavity.
The preceding discussion has focused on the secondary
emission yield at a constant temperature, essentially room tem-
25 perature. In high power RF cavities the electrodes become hot.
However, temperature has little effect on the seconda~y emitters
for the micropulse gun [~. Blankenfeld, Ann. Physik 9, 48 (1950);
J.B. Johnson and K.G. McKay, Phys. Rev. 91, 582 (1953); A.J.
Dekker, Phys. Rev. 94, 1179 (1954); A.R Shuylman and B.P. De-
30 mentyev, Sov. J.Tech. Phys. 25, 2256 (1955)].
In this section we will describe the solut on to the
self-consistent steady state or saturation current density for a
CA 0220~989 1997-0~-16
12
beam that is already presumed to be-"bunched". Reference [F. Mako
and W. Peter, Part. Accel. Conf., IEEE Cat. 93CH~279-1 2702
(1993)] gives a detailed evaluation of the saturated current
density. The axial bunch length (z-axis) is sO, the axial gap
5 spacing between two parallel metal grounded plates or cavity
walls is d, and the bunch density is Il. We evaluate the equa-
tions of motion for electrons "attached" to the ~ront; ("f") and
back ("b") of the bunch. The quantities Eo and Eqc are the magni-
tudes of the RF and space charge electric fields, respectively.
10 Resonance is imposed on the particles, i.e., the particles are
forced to cross the gap d in half an RF period. We now define
some quantities, aO = eEOlm~2d, as = eEsclm~2d ~ Esc = neso/2~o wh~re e,m are
the electron charge and mass respectively, ~ is the -adian fre-
quency and ~O is the p~rmittivity of free space, for use in the
15 analysis that follows.
The saturated bunch current density inside the cavity
can be determined from the above evaluation and val:dated with
simulation , and in practical units is expressed as,
J(AIcm2)=145.5f3(GHz)dl7s(cm)[aO-0.2126] (1)
20 for 0.2126 <aO< 0.38. It can be seen in Eq. (1) that the current
density scales with frequency like ~3 . This result is also de-
rivable from the time-dependent current-voltage relation in a
diode [A. Kadish, W. Peter, and M.E. Jones, Appl. Phys. Letters
47, 115 (1985)]. The ~3 scaling law is an important characteri-
25 zation of the micropulse gun. In going from 1 to 12 GHz thecurrent density increases from Amp's/cm2 to tens of kA/cm2 (with
variable aOand d). aO= 0.373 gives the maximum satura~ed current
density and at values greater than this there is no resonance.
The ~3 scaling law resu]ts from above will be compared to simula-
30 tion results where we find excellent agreement between theory andsimulation. The corresponding electric field to mai~ltain reso-
nance requires only modest gradients.
CA 0220~989 1997-0~-16
. , 1 1
13
It is important to estimate the likelihood of electri-
cal breakdown in the micropulse gun. ~ilpatrick's criterion
[W.D. Kilpatrick, Rev. Sci. Inst. 28, ~24 (1957)] is based phe-
nomenologically on elect:rical breakdown due to secondary electron
5 emission from ion bomba:rdment. However, with advances in clean-
ing, conditioning and better vacuum techniques (that do not in-
troduce cont~mln~nts), Kilpatrick's criterion overestimates the
likelihood of breakdown by a factor of two or three for cw [R.A.
~ameson, High-Brightness Accelerators, Plenum Press, ~L97 (1988)]
10 ancl five to six for short pulses [S.O. Schriber, Proc ]986 Linear
Accelerator Conference, ~une 2-6 (19~6)]. A more recently
established breakdown result comes from J. W. Wang at ',LAC [J. W.
Wang, SLAC-Report-339 July (1989)]. Wang expressed this formula
in the form, EO(MV/m) = 195 [f (GHz)] 1/2 where Eo is th~ peak sur-
15 face electric field. For a cavity operating at 2.85 GHz, thecritical surface electric field is 329 MV/m. The req~.ired reso-
nant electric field in lhe micropulse gun is substantially lower
than the critical surface field. With gap lengths between 0.5 and
2 cm and ~0= 0.373 the resonant field varies from 3.4 to 13.6
20 MV/m. Thus, breakdown is not a problem in the micropulse gun
cavity.
The sections below show high current density, short
pulse operation is possible with the micropulse gun.
The micropulse gun has been fully characterized using
an FMT developed proprietary 2 1/2-D relativistic electromagnetic
PIC code FMTSEC (that includes secondary emission~. Input
parameters for the micropulse gun are: RF voltage, frequency,
cavity gap spacing, and magnetic focusing field. Output parame-
30 ters are: current densit:y, particle energy, transverse emittance
and pulse width. Figure 3 shows the current density ~s a func-
tion of time for: f = 2.85 GHz, d = 1.5 cm, and VO= 153 kV. Cur-
rent density is evaluated near the exit grid (right side, Fig.
2). A positive current density is the current that travels from
CA 0220~989 1997-0~-16
J
14
right to left. A negative current density describes the exiting
beam. Current asymmetry occurs because the positive/negative
beam pulses have substantially different charge densities and
velocities at the exit grid. In Fig. 3 at a gap length of 1.5
5 cm, the saturated current density Js after about 10 RF periods is
1150 A/cm2 at VO= 153 kV with aO = 0-373-
To strengthen the understanding of the micropulse gun,theory and simulation are compared in this section. The satu-
rated current density is de~ined to be the peak current density
- 10 after 10 to 15 RF cycles, i.e. where the amplitude becomes con-
stant. A number of computer runs at various frequencies were
per~ormed to determine the current density inside (with T = 0)
the micropulse gun. Fig. 4 shows the results from several simu-
lations for the saturated current density J5 vs. RF fr~quency for
15 a cavity with a 1.0 cm gap length and for aO = 0.373. The curve
obeys a power law ~5 o; ~3 . For f =2.85 GHz the saturated cur-
rent density is about 500 A/cm2. Excellent agreement is shown
between theory and simulation for the ~3 scaling law. Note that
Vo o~ ~2 must be maintained for resonance at fixed aO.
The saturated current density rises approximately
linearly with the drive voltage, aO (= eV0/m~2d2), within the
resonance window (Fig. 5). Each curve is a spline fit to the
FMTSEC simulation data. The saturated current density is the
peak current density, after 10 to 15 cycles, from t:he current
25 density vs time traces. The current density plots also show the
"tuning range" for the micropulse gun. A very tolerant tuning
range is a key result. Even if the electric field cha~ged by 30%
from, say, beam loading, resonance would still occu-~ but at a
lower current density.
Figure 6 shows that the micro-pulse width can be ad-
justed using the drive voltage. Depending on gap spacing and aO
the pulse width can be adjusted from 1.5% to 10% of the rf
CA 0220~989 1997-0~-16
.
period. For the case: o~0 ~ O.373, the bunch length is 7 ps at
frequency of 2.85 GHz.
The bunch energy per rf period that is transmitted out
of the cavity is given by, Eot = ~pZVpT where ~p iS t~.Le particle
5 energy at the peak of the energy distribution, Np is the number
of~ particles in a bunch inside the micropulse gun cavi.ty. There
is one bunch transmitted per RF period from the micropulse gun.
The RF power provides all the energy for the left- and right-
traveling bunches inside the cavity. Therefore, the RF energy
10 that feeds one bunch in an RF period is given by, Erf = 2~pNp.
Next the particle energy ~p will be determined. Con-
sider a particle at the center of a bunch. This particle is also
at the peak of~ the distribution. A sinusoidal electric :Eield is
applied to this particle at a phase angle of (p. For the particle
15 to be resonant, it must cross the gap spacing in (p+ ~. PIC simu-
lation shows that the initial phase angle ~ is near zero. The
resulting particl:e energy can be shown to be, ~p=2evOaO where e is
the electron charge. The transmitted power in a bunch, Pbt/ and
the RF power required to drive a bunch, Prf,in, is then
Pbt - 2eVOo~ONpTf (2)
Prf,in = 4eVOo~ONpf . ( 3)
For example,if f = 2.85 GHz, d = 1.5 cm, VO= 153 kV aO=0-373
and T = 0.5,then Np= 2 X 109, Prf,in= 208.2 kW and Pbt = 52 kW.
25 The stored energy in the cavity is given by U = ~o [~rc (Rm) 2
d] [Vo/d] 2[Jl2(Xom )/2] where, xom are the zeros of the J0 Bessel
:Eunction and Rm is the resonant cavity radius. For f=2.85 GHz,
m=l, d=l . 5 cm, Rl =4.0, cm, VO= 153 kV and for o~0=0 373. The
stored energy is U=9.49 mJ. Next the loaded QL Of~ the cavity can
30 be estimated from QL = C)U/prf~in~ For the example at 2.85 GHz the
QL loaded by the beam is 816. To minimize power losses to the
wall, it is desirable to have an unloaded QU ~> QL A coated
CA 0220~989 1997-0~-16
.
16
copper cavity could be used to keep the cavity secondary emission
low and the unloaded Qu high. The fill time for the cavity is
given by ~f = 2QL/~ . Again for the 2.~5 GHz case the fill time
is, roughly 260 RF periods. Since the fill time is long compared
5 to the current density saturation time, the transmitted beam
current rise time is determined by the fill time which in this
case is 91 ns.
FMT has performed 3-D PIC code (SOS) simulations to
determine bunch emittance growth from the micropulse gun grid.
10 Emittance was evaluated before and a~ter the grids. Emittance
can be substantially reduced by using a dense grid of wires, but
at the expense of reducing transmission. Results have shown a
lower emittance than anticipated. This occurs because the
transverse electric fie:Ld at the grid wires is small during bunch
15 extraction. The inherent mechanism for bunch formation captures
the bunch at a phase angle near zero. Bunch arrival at the grid
~/~ later occurs when the electric field is again near zero.
This is a big advantage for the micropulse gun as coTnpared to a
Pierce gun with a grid which exposes electrons to t-he maximum
20 field. Input parameters are supplied from the results of FMTSEC.
They are: ~p = 114 keV, ~5 = 1150 A/cm2, ~ = 7 ps, bunch area 4
mm2, 2 x 109 electrons in a bunch, initial normalized emittance
before the grid = 1.6 mm-mrad (the contribution from the secon-
dary emission process is 1.4 mm-mrad and the micropul~3e gun 0.84
25 mm-mrad) for a frequency of 2.85 GHz and gap d = 1.5 cm.
Figure 7 shows the beam emittance and transmission
versus the grid wire density for a wire thickness of 0.1 mm and
density of 28 wires/cm the results give a transmission of ~53%
and a total (all sources) normalized transverse beam emittance of
30 about 2.3 mm-mrad. This final emittance is nearly the same as the
emittance before the double grid.
CA 0220~989 1997-0~-16
17
The grids will heat up primarily due to electron beam
impact. Consider a molybdenum grid with a thin coating of
secondary emitting material. A thin layer of secondary emitter
is used in order to reduce charge build-up, thus most of the
5 charge is deposited in the molybdenum. Pre~erably the material
will be made electrically conducting by doping, thus ~liminating
charge build-up.
The average power/unit area delivered to the molybdenum
10 grid structure is
Pavg = 2~o(1- ~VoJsf~fr~d (4)
where, Id and fr are the macro-pulse duration and repetition rate,
respectively, and ~ is the FWHM of the micro-pulse cur:rent and f
is the cavity drive frequency. If T = 0.50, f = 2.~,5 GHz, d =
15 1.5 cm, V0 = 153 kV, Js = 1150 A/cm2, aO ~ 0-373, ~=7 ps/ fr = 0.2
kHz and Td = 1.0 ~s then Pavg = 262 W/cm2.
To estimate the temperature rise, we assume that the
power (Pavg) flows only conductively through the molybdenum grid
wires from the center to edge of the circular grid area (Fig. 2).
20 If the grid material has a thermal conductivity of k and axial
thickness ~t (i.e, thickness in the direction of beam motion),
then the temperature difference (~Tg ) between the center and edge
(radius = 1) radius is given by: ~Tg =PaVg ~ /(2k~t). For a molybdenum
grid, k = 1.39 W/cm-~C, ~t = 0.038 cm, l = 0.1 cm, we get ~Tg =
25 24.8 oc. The grid will not get hot and this temperature rise is
not destructive to the secondary emitter.
A proof-of-principle micropulse gun experiment has been
conducted. [J. Shiloh, F. Mako and W. Peter, Proceed ngs of the
11th Int. Conf. on High Power Particle Beams, Karel Jungwirth,
30 Jiri Ullschmied, Eds. Institute of Plasma Physics, Czech Academy
of Sciences, Prague, 437 (1996).] The micropulse gun cavity is
CA 0220~989 1997-0~-16
' b ~ :
18
designed for a TMo1o mode and is fed from an L-band (1.2-1.3 GHz)
magnetron which delivers about 50 kW to the beam load. We
developed a direct charge measurement system for the bunches us-
ing a 50 GHz bandwidth sampling scope (HP-54720A). The magnetron
5 is operated at 300 ~z repetition rate. Each microwave pulse
lasts for 5 ~s and contains about 6500 electron bunches (1 for
each RF period). A very accurate timing system is used to trig-
ger the scope so that, if the micropulse gun pulses are repro-
ducible, it is possible to measure the current as a iunction of
10 time. The collected charge generates a signal that propagates
through a custom made 50 ohm, 50 GHz coaxial feedthrough. We
were successful in performing a direct measurement of l,he bunches
and were able to prove the ~easibility of the micropulse gun
concept.
When we use the ~ast 50 GHz sampling oscilloscope and
look at a 5 ns slice of the macropulse we can see the
micropulses.
Figure 8 shows a measurement of the bunches on a
500 ps/div time scale. The bunches appear with the periodicity
20 of the RF field (~300 ps), in excellent agreement with simula-
tion. More detailed measurements show that the actual bunch
length is about 50 ps (FWHM) which is about 6.5 % of the RF pe-
riod at a current density of about 22 A/cm2. This is about 1.1
nC or 7 x lO9electrons per RF period.
In this section the axial spatial expansion and tempo-
ral bunching are examined by including either the axial space
charge electric field or an initial energy spread combined with
rapid acceleration. Phase focusing is not included. The expan-
sion is examined starting from just outside the micropulse gun
30 cavity and through the high energy acceleration region. We will
derive an approximate expression for the space charge expansion
first. The axial Lorent:z equation can be written in the follow-
ing form
CA 0220~989 1997-0~-16
~ , ,
19
~t ~3 ~s (5)
where aa= eE~ /mc and aSC = eE6c /mc. Ea and EsC are the accelerat-
ing and space charge electric fields, respectively. Note that
5 EsC is the space charge field in the moving frame of the micro-
pulse. The inductive electric ~Cield reduction of the space
charge electric field is taken into account in Eq. (5) by the
additional ~2, The equation for the time evolution of the
length, s, of the micro--pulse is given by
~t=(~c-~f)C (6)
where the subscript c refers to the center of the micro-pulse and
the subscript ~ refers to the front face of the m:icro-pulse.
Define the change in ~ from the front to the center of the micro-
15 pul~e by ~ f-Yc~ Assume that ~/~<<1, ~>>1, ~f>>1. From Eqs
(5), (6), the definition of ~, dropping the subscripts on ~ and
assuming that ~=~0+ aat where ~0 is the initial value of ~ we ob-
tain the following pair of equations
(~s) I Esc ~mc2 ~ ( 7 )
5~ sc 6so~o Ea ~eEa)
~= ~ E (8)
where ~s, sO are the change and initial length of the micro-
pulse. Consider the micropulse gun operating at 2.85 GHz, d= 1.5
cm, VO = 153 kV, a bunch radius = 1.13 mm and T = 0.5. Then the
25 pulse duration is ~ = 7 ps, the particle energy is 114 keV, and
the transmitted number of electrons is 1 x 109. These results
are equivalent to sO = 0.115 cm, ~O = 1.2, and Esc = 1. 33 MV/m.
Also consider the following parameters~=11and Ea= 50 MV/m. The
resulting length change is 2.3% and tlle energy spread due to
CA 0220~989 1997-0~-16
space charge 0.2~. Equations (7,8) don't estimate spread cor-
rectly since ~0 is not large. Figure 9 shows numeric~l integra-
tion for the spatial bunch length and temporal pulse w.idth versus
energy. The bunch length expands by 10.7%. The pulse is com-
5 pressed to 4.3 ps. Additional bunching can be acconlplished ifphase focusing is considered.
The expansion of the micro-pulse due only to an initial
energy spread can be calculated by a similar method clS outlined
above for space charge expansion. We present the resu:Lt:
0 (5~ ) E 25o y2 ( eEa )
For the above sample parameters and an initial ~ O= 2% then a
7.4% expansion occurs along with a temporal pulse reduction to
4.1 ps. Numerical integration gives a 3.9% expans:Lon of the
15 spatial bunch length ancl a temporal compression to 4 p'3.
Although the invention has been described in detail in
the foregoing embodiments for the purpose of illustrat.ion, it is
to be understood that such detail is solely for that purpose and
that variations can be made therein by those skilled in the art
20 without departing from the spirit and scope of the in~rention ex-
cept as it may be described by the ~ollowing claims.
