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AN ANGULAR ALTGNEMENT OF THE TON DETECTOR SURFACE 1N TIME-OF-FLTGHT MASS
SPECTROMETERS
Field of the Invention
The invention relates to Time-of Flight Mass Spectrometers (TOF-MS) and more
particularly to the use of electrostatic deflectors in such mass spectrometers
with
homogeneous electric fields in the flight tube in order to steer the ions that
are analyzed in
a desired direction. According to the invention, the mass resolution of such a
TOF-MS can
be enhanced if the detector surface is aligned with a specific angle.
Background of the Invention
Time-of Flight Mass Spectrometers (TOF-MS) are devices used to analyze ions
with
respect to their ratio of mass and charge. Tn a typical linear TOF-MS, as it
is described e:g.
in US Patent 2,685,035 and Wiley et al., ions are accelerated in vacuum by
means of
electrical potentials which are applied to a set of parallel, substantially
planar electrodes,
which have openings that may be covered by fine meshes to assure homogeneous
electrical
fields, while allowing the transmission of the ions. The direction of the
instrument axis A
shall be defined as the direction normal to the flat surface of these
electrodes. Following the
acceleration by the electrical fields between said accelerator electrodes, the
ions drift
through a field free space or flight tube until they reach the essentially
flat surface of an ion
detector, further referred to as a detector surface, where their arrival is
converted in a way
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to generate electrical signals, which can be recorded by an electronic timing
device. An
example of such a detector is a mufti channel electron multiplier plate (MCP).
The
measured flight time of any given ion through the instrument is related to the
ion's mass to
charge ratio.
In another typical arrangement (See e.g., US Patent No. 4,072,862, Soviet
Union Patent
No. 198,034, and Karataev et al., Mamyrin et al.), the motion of the ions is
turned around
after a first field free drift space by means of an ion reflector. In such a
Reflector-TOF-MS
the ions reach the detector after passing through a second field free drift
space: The
properties of such ion reflectors allow one to increase the total flight time,
while
maintaining a narrow distribution of arrival times for ions of a given mass to
charge ratio.
Thus, mass resolution is greatly enhanced over that of a linear instrument.
It is common practice to use electrostatic deflectors with homogeneous fields
in TOF-MS
in order to steer the ions towards the detector. In one particular case, this
is done in order
to offset a common perpendicular component of motion of the ions prior to the
acceleration. In another case, deflectors are employed in order to establish a
V shaped
configuration of accelerator, reflector and detector in a Reflector-TOF-MS.
Traditionally,
the steering action required has been small and its impact on the mass
resolution of the
instrument has been neglected (Karataev et al., Mamyrin et al.).
Recently, however, new atmospheric pressure ionization techniques, which are
especially
well suited for the ionization of complex biomolecules, have renewed the
interest in the
orthogonal injection of externally generated ions into the accelerator of a
TOF-MS. This
method was originally described by O'Halloran et al.; recent implementations
are found in
Dawson et al., Dodonov et al., Verentchikov.
In this particular application of TOF-MS, the injected ions can have
substantial kinetic
energy and, hence, a substantial velocity component perpendicular to the
flight tube axis.
The result of this velocity component is an unwanted oblique drift of the ions
in the flight
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tube of the mass analyzer. It follows that a relatively strong steering action
is required to
redirect the ions towards the instrument axis and the detector. It was found
experimentally
that such steering causes distortions in the distribution of ion flight times
which can
considerably diminish the mass resolution of the instrument.
The present invention recognizes the physical reasons for distortions created
by the steering
of the ions, and corrects these distortions by mechanically adjusting the
detector surface at
a calculated angle that enhances the mass resolution of the instrument.
Objects and Brief Description of the Invention
It is an object of the invention to provide means that can compensate for the
reduction in
performance that occur in TOF-MS due to electrostatic steering of the ions in
the flight
path.
Ions accelerated inside a vacuum chamber from between two parallel lenses
ideally form a
thin sheet of ions of a given ratio of mass to charge moving in a common
direction at a
constant velocity down the flight tube. This constant velocity corresponds to
an initial
common accelerating electrical potential, whereafter the accelerated ions pass
through
apertures, shielding tubes or other electrodes held at a constant electrical
potential. At any
given point in time in the flight path, the positions of these ions form an
isochronous
surface in space. At first, this isochronous surface shall be perpendicular to
the direction of
motion of said ions.
In one embodiment of the invention, two parallel flat plate electrodes of a
given dimension
are arranged such that these ions enter the space between these plates in a
direction which
is essentially parallel to the surface of the plates. If an electrical
potential difference is
applied to the plate electrodes, preferentially in such a way that one plate
is held at a
potential +V12, and the other at a potential -V/2 with respect to the other
electrodes or
shielding tubes preceding the plates, then the direction of motion of said
ions is deflected by
a certain angle. It is taught by the invention that a further result of the
deflecting electric
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field between the plate electrodes is a tilt in the space of the isochronous
surface formed by
the ions.
If, as in, for example, a linear TOF-MS, the ions of a single mass ion package
shall be
detected essentially simultaneously by an ion detector, then, according to the
invention, it is
required that the detector surface be tilted with respect to a plane which is
thought parallel
to the original isochronous surface of said ions.
In order to achieve the optimum performance it is furthermore required,
according to the
invention, that the tilting of the detector surface must be accomplished in
such a way that
the tilt angle lies in the plane of deflection and is equal to the angle of
deflection but in the
opposite sense of rotation.
Further aspects and implications of the invention as well as its advantages in
several
preferred embodiments will become clear from the following detailed
description.
Brief Description of the Drawings
FIG. lA and FIG. 1B shows a pair of typical electrostatic deflector plates
with ideal
instantaneous onset of the homogeneous field; the coordinate system follows
the central
trajectory; the central trajectory (x=0) and two (positive) ion trajectories
passing the
isochronous plane t=t p at distances x = +dand x = d from the centerline are
shown.
FIG. 2 shows the isochronous plane of the ions tilted by angle ~i=ao
FIG. 3A and 3B show the first order tilting of the isochronous surface by an
electrostatic
deflector.
a) ions entering parallel to the axis and leaving under an angle oc.
b) ions entering under an angle a and leaving parallel to the axis.
FIG. 4 is the schematic representation of the linear time of flight mass
spectrometer with
orthogonal injection of externally generated ions, electrostatic deflector and
tilted
detector conversion surface.
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FIG. 5 is the schematic representation of a Reflector TOF with parallel
reflector and
accelerator electrodes and fields.
FIG. 6 is the schematic representation of a Reflector-TOF MS with inclined
reflector
FIG. 7 shows the broadening w4 of an ion package focused in time at the plane
z--zf due to
a distribution of axial kinetic energies.
FIG. 8 shows the valuation of the distribution of arrival times induced by a
spread in the
orthogonal injection energy.
Detailed Description of the Preferred Embodiments
The electrostatic deflector
Electrostatic deflectors with a homogeneous electrical field which is oriented
perpendicular
to the axis of a charged particle beam are used to steer or deflect this beam
of ions or
electrons into a desired direction. The ion deflecting trajectories are
independent of the
particles' mass to charge ratio and depend only on electric potentials. This
feature makes it
especially suitable for TOF-MS in that all ions can be accelerated by the same
electric
potential difference. In the embodiment that is shown in FIG. lA,
electrostatic deflectors
consist of two parallel plate electrodes 11 and 12 spaced an equal distance
apart with the
beam of charged particles 13 entering at the symmetry plane between the
deflector plates.
One plate is held at a positive electrical potential while the other is held
at a negative
electrical potential with respect to the last electrode, aperture or shielding
tube 14 that was
passed by the ion beam prior to entering the deflector. This reference
potential wilt be
referred to as beam potential. The electric field between the plates
accelerates the charged
particles perpendicular to the direction of the incoming beam and therefore
changes the
direction of the beam.
Properties of the electrostatic deflector
In order to evaluate the electrostatic deflector, let 1 be the length of the
plates and d the
distance between them as it is defined in Fig. 1 a; the applied deflection
voltage Y is split
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symmetrically with respect to the beam potential for the sake of simplicity.
Then, in the
symmetry plane between the plates 11 and 12 of a deflector, the potential
inside the
deflector is equal to the beam potential; the trajectory of ions 13 that enter
the deflector in
said symmetry plane is the reference trajectory. Ions enter the deflecting
field with kinetic
energy qUo ,where q is the ion's electrical charge, and Uo the total ion
acceleration
electrical potential difference.
If the dimensions of the plates are such that both length and width are
sufficiently larger
than the separation of the plates and if the beam dimensions are small
compared to both,
then the effects of the fringing fields at the ends of the plates are of minor
concern as the
ions spend much more time in the homogeneous field between the plates than in
the
inhomogeneous fields near the entry and exit of the deflector. It is known
from Herzog that
with special apertures close to the ends of the deflector plates the electric
field in a close
approximation acts as an ideal deflection field with instantaneous onset of a
homogeneous
perpendicular field at an effective field boundary which is determined only by
the geometry
of apertures and deflector plates.
Now let the length of the equivalent deflection field between the effective
field boundaries
be equal to the length l as it is indicated in Fig. lb. For such an ideal
deflector it can be
readily shown that the angle of deflection of an ion entering at x is given by
Equation (1 ).
Only small angles are to be considered and the approximation ~~tan~~sin~ is
valid and will
be used for all the angles (angles are in units of radians);
(la a,(x) - ao ~ 1- vx -ao2
) ~ Uod
or equivalently;
(lb) a(x)=ao~~l+2.U d+2aoz+...~ .
0
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ao is the first order angle of deflection of the reference trajectory (x=D):
__! _v
(2) a° 2d ~ U°
From Equations (1) and (2) it is evident that the angle of deflection is
independent of
charge q and mass m of the particles. Here, only small angles of deflection
are to be
considered and quantities of higher order in ao are very small. Under the
presuppositions
made above the quantity VxlUod «1 is also a small quantity and the
approximation
a(x) ~ ao is justified in many applications.
Residence time inside the deflector
Ions moving above or below the reference trajectory are decelerated or
accelerated by
entering the deflecting field; accordingly they spent more (or less time) in
the deflecting
field than the central reference trajectory of the beam. This difference in
residence times is
of primary interest for TOF-MS.
To quantify this difference, two coordinate system (x,y,z) and (x',y',z') are
introduced in
Fig. lb; the z-axis of the unprimed coordinate system lies in the symmetry
plane between
the plates, the x-axis is perpendicular to the deflector plates 11 and 12. The
axis of the
primed system are parallel to the unprimed ones, but the origin of the primed
coordinate
system moves with the reference trajectory. The in-going and out-going beams
define the
x-z plane as.the plane of deflection. Ion trajectories start at a time t=to in
the x-y plane and
move in direction of the z-axis towards the deflector. At any given time t>to
the package of
ions forms an isochronous surface, given by the location of all the particles
on their
respective trajectories at that time.
Positive ions entering the ideal deflecting field are accelerated (x<0) or
decelerated (x>D)
instantaneously in z-direction (for negative ions signs have to be inverted
but the contents
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of the equations is left unchanged). The kinetic energy in the z-direction
inside the
deflecting field is a function of the entry coordinate x and given by the
relation:
v
(3 ) 9UZ ~x)~:L.m~ - q ' ( Uo - d ' x)
The reference trajectory with x=0 is not shifted in energy or time compared to
the
undeflected beam inside the deflector. The difference i in residence time with
respect to the
reference trajectory is given by:
T i~x~ TR~x~ Tir~~~ vz~x) vZ~~) !. 29 .C Ul~x) Uo J
(4 continued) _ ! ~ ~ 1 -1
29Uo . 1_ V.x
Uo~d
Here, qUZ, and v2 are the ion kinetic energy and velocity in the z-direction
inside the
deflector, TR(x) is the residence time as a function of the entry coordinate
x. VxlUod is small
compared to 1 and to first order, i,, the residence time difference, is given
as a function of
entry coordinate x by the relation:
m lV
(5) i ~ i, = 2gUo ~ 2dUo ~ x
This difference in residence time inside the deflector results in a difference
in arrival time
with respect to the reference trajectory at any x-y plane at z=zf after the
deflector. To
evaluate the effect in the deflected beam the transition is made to the primed
coordinate
system. With the approximations a(x) = ao i.e. x'(x)=x, and vZ (x)=vo=vZ(Uo)
the
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difference in the time of arrival is transformed into a spatial shift y of
isochronous points in
negative z'-direction.
W '
m
The first order the time shift i, is a linear function of x or x'. In space
the isochronous
surface ~,(x) is a plane tilted by an angle (3 with respect to the x'-y'
(parallel to the x-y)
plane (Fig. 2):
p=~i(x'>
x'
Inserting (5) and (6) into Equation (7) and comparing with the equation for
the deflection
angle ao (Equ. 2) reveals that:
(8) , p _ IV = a
2dUo °
Equation (8) contains the primary discovery underlying the invention: A
package of ions 21
that is isochronous in the x-y plane entering an electrostatic deflector along
the z-axis and
that is deflected by a certain small angle in the x-z plane is tilted in space
with respect to the
x-y plane by that same angle but in the opposite sense of rotation (Fig. 3a).
Symmetry considerations show that a beam entering the deflector under an angle
and
leaving it along the axis undergoes the same tilting of the isochronous
surface (Fig. 3b). In
general any deflection of monoenergetic ion packages is accompanied by a
tilting of the
isochronous surface in the plane of deflection by the deflection angle and in
the direction
opposite to the direction of deflection. The result can in principle be
applied to
monoenergetic ion packages independent of the initial shape of the isochronous
surface
prior to deflection, as any additional distortion is preserved. Hence,
multiple deflections can
be superimposed, leading to a compound angle inclination of the isochronous
surface.
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Alignment of the detector surface
The mass resolution of a time-of flight spectrometer is defined as
R=MI~M=T120T=Leql2w ,where M is the ion mass to charge ratio, OII~I the full
width at
half maximum (FWF~VI) of the corresponding monoisotopic mass peak, T the mean
total
flight time ofthese ions, OT the arnval time distribution (FWI~VI), Leq=T/vo
the equivalent
length of the flight path, and w the apparent width of the ion package upon
arrival at the
detector surface.
In a conventional TOF-MS the detector surface is mounted perpendicular to the
axis of the
instrument, i.e. lies in the x'-y' plane. Let wo be the width of the
undeflected package in
z'-direction and b is its width in x-direction determined either by beam
limiting apertures
or by the open width of the detector itself. Then, the apparent width of the
package as it is
seen by the detector surface is;
(9) w=wo+w, ; w, =b~ap
Depending on the magnitudes of both b and ao the mass resolution can be
considerably
diminished. As an example, for a deflection angle of 3 degrees, ao=0.0524 rad,
and for
typical instrument parameters wo=O.Smm, b=20 mm, the mass resolution R=Leql2w
achieved would be only one third of the optimum value Ro=Le~2wo.
More generally, with the isochronous ion surface inclined by an angle a and
the detector
surface inclined by an angle 'y with respect to the x'-y' plane the apparent
broadening of the
ion package w1 is given by the relation;
(10) w~ =b~(a-y)
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Its contribution to the apparent width w (Equ. 9) vanishes if the two surfaces
become
aligned, i.e. a - y = 0. Only then, the package width w that is seen by the
detector surface is
minimized and equal to wo.
The invention therefore states, that, in order to achieve the optimum mass
resolution in a
linear TOF-MS instrument that uses electrostatic deflectors, the detector
surface has to be
tilted with respect to the instrument axis in the plane of deflection by an
angle equal to the
angle of deflection but in the opposite sense of rotation.
Misalignment between the isochronous ion package surface and the detector
surface may
also be caused by mechanical tolerances of the vacuum chambers or mounting
fixtures, by
the bending of chambers or flanges when under the force of outside atmospheric
pressure
or by other mechanical distortions. It is known in the field of TOF-MS that in
order to
correct the alignment of the two planes and optimize the performance of a TOF-
MS
instrument, adjustable detector mounts may be used. It is the new feature of
this invention
to relate the bias angle of the detector surface directly to the angle of
deflection in an
instrument that employs electrostatic deflectors.
Linear TOF-MS with orthogonal injection of externally generated ions
A linear TOF-MS is shown schematically in FIG. 4, comprising an ion
accelerator with two
stages 26 and 27, a drift space 28, and an ion detector 40 with detector
surface 34 . The
first stage accelerator 26 is formed by repeller electrodes 21 and 22 and the
second stage
accelerator 27 is formed by the electrodes 22 and 23. These electrodes are
essentially flat
and mounted parallel to each other and perpendicular to the instrument axis
24. Central
openings in electrodes 22 and 23 are covered with meshes 29 and 30 to assure
homogenous electric fields in spaces 26 and 27 when electrical potentials are
applied to
electrodes 21, 22 and 23. It is taught in U.S. Patent No. 2,685,035 (Whey) and
in Wiley et
al., that if suitable electric potentials are applied to electrodes 21, 22,
23, a spatial
distribution of ions 32 in space 26 with axial width w is expelled from that
space and
accelerated towards the detector 40 in such a way that the longitudinal
distribution in flight
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direction is compressed to a thin sheet of ions 33 with width w' at the
location of the
detector 40. Tlus effect is called space focusing or longitudinal focusing.
Other variants of a linear TOF-MS may comprise additional electrodes, shields,
apertures,
etc. to suffice for specific needs.
In one aspect of the invention, which is shown as preferred embodiment in Fig.
4, a
continuous beam of ions 41 is at first generated externally to the actual TOF-
MS by means
of an ion source 10 and accelerating, focusing, and steering electrodes, which
comprise an
ion transfer system 20. This transfer system may guide the ions through one or
more stages
of differential pumping and may include means to effectively assimilate the
motion of all
ions in said beam, preferentially in a high pressure radio-frequency-ion-
guide.
When exiting from the transfer system 20 said ions 41 shall have a mean
kinetic energy qU;;
where g is the ion charge and U; is a total accelerating electrical potential
difference. This
initial beam of ions is directed into the gap 26 between the first two
electrodes 2i and 22 of
the ion accelerator of the linear TOF-MS. It was found to be advantageous
(O'Halloran et
al.), if the injection is done in such a way that the direction of motion of
the initial ion beam
41 is parallel to the accelerator electrodes 21 and 22, hence orthogonal to
the instrument
axis 24.
Ions are admitted into the space between electrodes 21 and 22, while those are
held at a
common electrical potential equal to the electrical potential of the last
electrode used to
form the initial ion beam, which in turn is preferentially held at ground
potential.
Then, electrical potentials are applied to one or both of said accelerator
electrodes 21 and
22 by means of external power supplies and suitable switches. This generates
an electric
field between these electrodes, which accelerates the ions in space 26. The
direction of this
accelerating field is orthogonal to the direction of the initial ion beam 41
and is established
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in such a way that the ions in that space begin to move towards the ion
detector 40. At the
same time, this field effectively blocks ions of the initial beam from
entering into said space.
In one variant of the preferred embodiment, first stage accelerator 26 may be
effectively
divided by an additional electrode, the purpose of that electrode being to
shield the space
where the ions from the initial beam enter the accelerator from the electrical
field which
penetrates into space 26 from space 27 through the mesh 29. In another
variant, additional
electrodes held at electrical potentials intermediate to the potentials
applied to either
electrodes 21 and 22 or 22 and 23, and proportional to their distance from
those
electrodes, may be used to extend the length of each accelerator stage.
After the ions have left the accelerator region 26, the electrical potentials
applied to the
accelerator electrodes 21 and 22 can be reset to their original values, so
that new ions from
the initial beam 41 can enter into the space between them and a new cycle may
begin.
After passing through the accelerating stages 26 and 27 of the TOF-MS, the
ions reach the
field free drift space 28. Due to the initial perpendicular motion, the drift
direction is
oblique to the axis of the accelerator fields and the instrument axis 24. The
magnitude of
the obliqueness depends only the various energies of the ions when they enter
the region 26
and the field free drift region 28.
Let gU; be the kinetic energy of the ions orthogonal to the axis 24 of the TOF-
MS
instrument and Uo be the a total electrical potential difference that
accelerates the ions
towards the detector 40. Without steering, the angle of the ion trajectories
with respect to
the axis of the instrument in the field free drift region 28 is given by the
ratio of the
velocities:
v; _ U;
(11)
~o Uo
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With typical parameters the drift angle ~ is of the order of several degrees.
In order to steer the ions in a direction which is parallel to the instrument
axis, an
electrostatic deflector with plate electrodes 11 and 12 and entrance and exit
apertures 14 is
employed in the preferred embodiment. The gap between the plates 11 and 12 is
chosen but
not restricted to be at least twice as wide as the width of the ion beam, and
the length of
the plates is chosen to be at least twice as long as the gap. The width of the
plates is chosen
accordingly to the width of the ion beam in that direction, but at least 1.5
times the width
ofthe gap.
In the preferred embodiment of Fig. 4, the angle of deflection is made equal
but opposite to
the drift angle, ao = -~ by adjusting the electrical potential difference
between the deflector
plates 11 and 12. As a result, the ions will drift parallel to the instrument
axis 24 when
leaving the deflector and reach the ion detector 40 at the end of the drift
space 28.
As a further result of the deflection, as it is taught by the invention, the
isochronous surface
of an ion packet is tilted. This is shown in FIG. 3B and is indicated in FIG.
4 by
isochronous surfaces s, and s2. Hence, according to the invention, it is
required that the ion
detector surface 34 is tilted with respect to a plane perpendicular to the
instrument axis 24,
the tilt angle lying in the plane of deflection and being equal to the angle
of deflection but in
the opposite sense of rotation. From Equation (11) the initial drift angle can
be calculated. .
Hence the required deflection angle is known, as well as the mounting angle of
the detector
surface and the voltage required to achieve such a deflection for a given
deflector
geometry.
In order to accomplish the tilt of the detector surface 34, in the preferred
embodiment, the
alignment of said detector surface is preset by means of an angular spacer or
fixture 3 5. In
addition, the mounting of the detector is made adjustable by means of one or
two adjustors
36, adjusting the tilting in the plane of deflection, and the inclination in
the perpendicular
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plane. Preferentially, the adjustors 36 are made in such a way as to allow one
to align the
surface of the detector while operating the TOF-MS.
In another variant of the preferred embodiment, the predetermined tilt angle
is preset by
means of the adjustor or adjustors 36 according to the relations which specify
the tilt angle
of the isochronous surface of the ion packages.
Reflector TOF-MS with parallel reflector and accelerator electrodes
The V-shaped geometry of a Reflector-TOF-MS is schematically shown in Fig. 5,
the
embodiment comprising a single stage accelerator formed by electrodes 51 and
52, a
deflector 53, an ion reflector 54 with homogeneous fields, the reflector
having one or more
stages, and a detector with detector surface 55.
According to the invention, it is now known that the isochronous surface is
tilted by the
angle of deflection which is indicated in the FIG. 5 by isochronous surfaces
sl, and s2. By
following the trajectories 56 and 57 from surfaces s2 to s3 through the
reflection of the ion
package it becomes evident that the angle of inclination with respect to the
plane normal to
the reflector axis S8 changes its sign.
Hence, it follows as essential part of the invention in this preferred
embodiment, that the
detector surface 55 must be inclined with respect to the instrument axis 24 in
the plane of
deflection, by the angle of deflection and in the direction of rotation of the
deflection.
As before, this angle may be preset by angular spacers, or preset by
adjusters, and may be
adjustable around that preset value. Furthermore, by means of multiple,
preferentially
mutually orthogonal deflectors, a multiple deflection may be facilitated,
which, according to
the invention, will require a compound angle of the detector surface.
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Reflector TOF-MS with inclined reflector axis
It was proven that it is unfavorable for the resolution of a Reflector -TOF-
MS, if the
surface of the in-going and out-going ion package is not aligned parallel with
the
equipotential or electrode surface of the ion reflector (Karataev et al.).
Therefore, it is advantageous to employ a setup according to the embodiment of
the
invention which shown schematically in FIG. 6. It includes the same
accelerator, deflector,
and reflector as FIG. 5, the deflection angle being aa. In this variant, the
reflector axis 59
is inclined with respect to the instrument axis 24, the inclination being in
the plane of
deflection, and by the angle of deflection.
In this way, the reflector surface 61 becomes parallel with the isochronous
surface s2 of the
ion packages, which themselves are tilted due to the deflection by the
electrostatic deflector
53. After reflection, the isochronous surface s3 remains parallel to the
reflector surface 61,
indicated by parallel planes pl, pz, p3, and p4.
To minimize the width of the ion package which is seen by the detector surface
65, it is
furthermore part of this embodiment of the invention, that the detector
surface 65 is
mounted parallel to the reflector surface 61, by the means as they were
already described
above.
Second order approximation of the residence time inside the deflector
Taylor expansion of Equation (1) to second order in the small quantity VxIUod
leads to the
equarion:
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2 ~ ~~ +T2
(12) ~ - ! _3 V 1z,xz 1 3 .a z,xz
z 2 U . 8.Cd.UoJ =vo.2.l o
q o
m
where T, is the first order shift in time as calculated above (Equ. 4) and i2
is the second
order shift; i2 gives only positive contributions; ions with x D arrive later
than it is expected
from the first order approximation. In space, the isochronous surface is
curved:
(13) ~~x~~ ~~i +~z =°~o'x'+23l'a.°z .x~z
With the beam density being constant in the x-y plane, the second order
contribution w2 to
the apparent width is found to be at the most:
(I4) wz 23l ~a°z ~~2~z
For small detectors (i.e. small b) w2 is small. With big area detectors,
however, w2 limits the
mass resolution of a TOF instrument. In this case, the inverse dependency of
w2 from the
plate length l indicates that it is advantageous to utilize rather long
deflectors.
Axial Energy changes induced by de8ectio~
Due to action of the perpendicular field inside the deflectors, ions do not
leave at the same
x-position as they enter but at a position slightly shifted in the direction
of the deflection by
the small quantity s=s(x) as can be seen in Fig. 1 A. Upon leaving the
deflectors they are
therefore not regaining the initial energy Uo but the energy Uo," that is
slightly smaller than
Uo.
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(15) Uo"r - Uo _ d .s
s=s(x) is easily found from the equation of motion inside the deflectors:
(16) s(x)=ao ~2- lyx =ao-~-i l+Utlxd+..~
1_ o
Uo-d
As s=s(x) depends on the entry position, this shift introduces a distribution
of axial
energies. As a result, the ions travel with different velocities and the
arrival time
distribution at the detector (i.e. the longitudinal focus plane) at a distance
L from the
deflector exit will be affected. It can be shown that the additional shifts of
isochronous
points are given by the relation:
(I7) ~3(X') ~ ~ -ao' .xr
This is only of third order in ao but depends in first order on Lll suggesting
again that
rather long deflectors should be used whenever a long flight tube is required.
The effect as
approximated is also linear in the coordinate x' and therefore leads to a
small additional tilt
of the isochronous surface. Its impact upon mass resolution can in principle
be made to
vanish in the same way as the first order effect discussed above as long as
the total tilt
angle is small.
Axial energy distribution
So far, only monoenergetic ion beams or ion packages with initial kinetic
energy qU=qUo
in z-direction were considered. A distribution of energies qU= q(1+s)Uo around
qUo with ~
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g~«1 , b=(U Uo)lUo will result in a distribution of deflection angles around
the angle ao.
For small angles, one finds for the angular dispersion from Equation (2):
(1$) 8a.=a-ao =_b.ao
In TOF-MS, by means of accelerator configurations Iike the Wiley/McLaren two
stage
TOF-accelerator, ions have different energies due to different starting points
in the
accelerator, but are brought to a longitudinal focus at a plane z=zf. At this
plane of interest,
at a distance L from the deflector an ion with energy U=Uo arnves at point X
(FIG. 7),
whereas an ion with energy U=(I +8) Uo will arrive at a different point X' in
the same plane
z=zf. Ions with energy Uo are deflected by an angle ao and form the
isochronous plane P
inclined by the angle ao according to the first order result. Ions with energy
U=(1+8)Uo
are deflected by ao+~. and form a plane P' separated from plane P; note that
r'3a, is
negative when b is positive; also, P' would be inclined by the angle ao+~a.
Sao as is
obvious from Equations (1), (2) and (8). The angular dispersion causes a
broadening of the
ion package in z'-direction to the width w4 . With the total relative energy
given by:
(~max U~I Uo)= s it is found that
(19) w4 ~ L.c'~x,.ov,o =8.L.aoZ
This broadening is of second order in the angle ao and of first order in the
relative energy
spread 8, which is also a small quantity. However, as L increases, the effect
will limit the
achievable mass resolution.
Distribution of injection energies orthogonal to the flight aais
The effect of an energy spread of the orthogonally injected beam 41 upon the
arnval time at
the location of the time focus z=zf can be evaluated as follows. First, assume
all ions
experience the same deflection ao and they all travel with energy qUo in z
direction (see
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FIG. 8). The higher orders in residence time and final energy were already
considered
separately above. The central ion trajectory with qU;=qU;o will start at the
point Xo (xo, 0, 0)
and arnve at the point F=(O,O,z~. Any ion with qU;i<qU;o will initially travel
under the
angle a,<ao and will leave the deflector at an angle a~ - ao<0. In order to
arrive at F, this
ion would have to start at a different location X~ (xl, 0, 0) with xl>xa.
Inside the deflector
this ion follows a trajectory that is more in the "slower" section. Similarly,
an ion with
initial orthogonal energy qU;2>qU;o will travel through the deflector in the
"faster" section.
Given the distance L and the difference in exit angle a; - ao the coordinate x
of the
trajectory inside is found; then, by using the first order result for the
residence time, the
arrival time difference is readily evaluated. Consider the inverted problem:
Trajectories
leave point F with UZ=Uo towards the deflector under an angle y with respect
to the
symmetry plane (z-y plane). One finds for y:
(20) Y =ao -a; = Uso _ U to
The orthogonal injection energy can be written as:
(21) qU; =q~(I+s)~U,,o
Then, inserting (21 ) into (20)
{22) y =ao ~(1- 1+e)
Under the assumption of small angles the deflector entry position in the
inverted problem is
now found easily:
(23) x= L~~y = L~ao(I- 1+e)
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For the difference of residence times inside the deflector between an ion that
enters at x 0
compared to the reference ion with x=0 one has from the first order relation:
(24) ~ = T(x) - Tea) ~ _r _i v
1~x
vo .C2 . Uod,
va=vZ(Uo) is the velocity of an ion of energy qUo in the z-direction.
Collecting terms, the
total difference in flight time between an ion with orthogonal energy qU; and
the reference
trajectory with U;=U;o is found as a function of the parameter s:
(25) i= I ~ao~ ~L~(1- 1+s~
vo
With ~ s ~ « 1 this can be approximated by expansion of the square root:
(26) i v ~a°2 ~L~~( 2~'e+....~
0
The total relative energy spread is given as ((U;,max - U;,m;~~Ua,o) °
Emax ' Emu = E.
Consequently, one has for the total flight time distribution from the
orthogonal injection
input line to the point F:
(27) o~=~T~E~)-i(Em~)~= 2v ~aoz ~L~s
0
This is evidently equivalent with the arrival time distribution at point F for
ions starting at
the same time along the input line. This spread of arrival times at the point
F corresponds
to a broadening of the ion package:
(28) ws =Di.vo = 2.s.L.aoz
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The effect is found to be of second order in ao and small only if the product
L~ a is much
smaller than 1/ao. It follows that in order to achieve best mass resolution
results it is
necessary to control the relative distribution of orthogonal injection
energies. Hence, it is
advantageous, according to the invention, to include means into the ion
transfer system
between the ion source 10 and the TOF-MS (FIG. 4), that effectively normalizes
or
homogenizes the relative motions of the ions.
Deflectors and focusing elements
Electrostatic lenses are used to focus the ions on the detector of the TOF-MS
in order to
improve the sensitivity of the instrument. In a focused beam, a trajectory
that starts with
the coordinate x will be at a distance x'=~,~x with ~,<1 from the reference
trajectory at the
plane z=zf. If the focusing lens does not introduce any additional time shifts
then ~, will be
unchanged. Hence, the angle of inclination of the isochronous plane will be
increased:
a'=z; _~'P
Focusing of the beam to half the original size in x-direction will double the
tangent of the
inclination angle of the isochronous surface. For stronger focusing , i. e.
~,«l, (3' becomes
impractically large. Obviously this strong effect limits the use of deflectors
in combination
with focusing elements. For moderate ~,, however, the correction by tilting
the detector
surface at the appropriate angle can be applied.
Although the invention has been described in terms of specific preferred
embodiments, it
will be obvious and understood to one of ordinary skill in the art that
various modifications
and substitutions are contemplated by the invention disclosed herein and that
all such
modifications and substitutions are included within the scope of the invention
as defined in
the appended claims.
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References Cited
The following references are referred to above
U.S. Patent Documents:
2,68S,03S July 27, 1954 Wiley
4,072,862 Feb. 7, 1978 Mamyrin et al.
Foreign Patent Documents:
198,034 Soviet Union (Mamyrin Russian Patent, filed 1966)
Other Publications:
W. C. Wiley, I. H. McLaren, Rev. Sci. Inst. 26, 11 SO (1955)
G. J: O'Halloran, R. A. Fluegge, J. F. Betts, W. L. Everett, Report No. ASD-
TDR 62-
644, Prepared under Contract AF 33(616)-8374 by The Bendix Corporation
Research
Laboratories Division, Southfield, Michigan (1964)
J. H. J. Dawson, M. Guilhaus, Rapid Commun. Mass Spectrom. 3, 15S (1989)
A. F. Dodonov, I. V. Chernushevich, V. V. Laiko, 12th Int. Mass Spectr.
Conference,
Amsterdam ( 1991 );
O. A. Mgorodskaya, A. A. Shevchenko, I. V. Chernushevich, A. F. Dodonov, A. I.
Miroshnikov, Anal. Chem. 66, 99 (1994)
A. N. Verentchikov, W. Ens, K. G. Standing, Anal. Chem. 66, 126 (1994)
R. F. Herzog, Z. Phys. 89 (1934), 97 (1935); Z. Naturforsch 8a, 191 (1953),
10a, 887
(19SS)
V. I. Karataev, B. A. Mamyri~, D. V. Shmikk; Sov. Phys. Tech. Phys. 16, 1177
(1972);
B. A. Mamyrin, V. I. Karataev, D. V. Shmikk, V. A. Zagulin, Sov. Phys. JETP
37, 4S
(1973)
