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A study of ion paths in curved parallel-plate electron multipliers with perpendicular magnetic field
NUCLEAR INSTRUMENTS AND METHODS 118 (1974) 509-513 ; C NORTH-HOLLAND PUBLISHING CO A STUDY OF ION PATHS IN CURVED PARALLEL-PLATE ELECTRON MULTIPLIERS WITH PERPENDICULAR MAGNETIC FIELD ROBERT B . :JANNEY and P, A. TOVE Electronics Department,Institute of Technology, Uppsala University, Uppmla, Sweden
Received 3 January 1974 A computer
study of ion paths in curved parallel-plate electron multipliers with a perpendicular magnetic field is `performed . The implications on the avoidance of ion feedback and on the possible construction ofa mass detector are discussed. Ions may be introduced in these multipliers either directly or by ionizationfrom the avalanching electrons. With given multi-
plier dimensions and magnetic field strength it is found that the structure is able to transport ions ofonly one mass. The influence of initial ion velocities which can be present is investigated . For low-energy ions it is found that a longitudinal velocity spread is unimportant while velocities perpendicular to the plates may influence the paths significantly.
1. Introduetioa Ion feedback plays a large role in the operation of electron multipliers with continuous dynodes . The basic mechanism of ion feedback in multipliers is the following : At the end of the path of the avalanching electrons, the probability of ionization increases because of the large number of electrons . Ionized atoms or molecules start with near-zero velocity and accelerate in the opposite direction to that of the electrons . Ifthey are able to pursue their paths without colliding with the wall; after the drift time (when they have reached the entrance of the multiplier) they will have acquired sufficient energy to start a new avalanche of electrons. This drift time is orders of magnitude longer than the transit time of the electrons but still sufficiently small to cause the several avalanches introduced by repeated ion feedback to appear as a single pulse when integrated by the stray capacitance at the output. In tubular multipliers this phenomenon is generally avoided by curving the tube with a sufficiently small radius') . In the ordinary place-parallel multiplier', ') ion feedback is present and is responsible both for the useful large amplitude of ,. he pulse and also for the worsening of the time resolution since the total pulse contains several electron avalanches separated by the time for ion drift between the entrance and output of the multiplier. A further disadvantage with ion feedback generally mentioned in connection with tubular multipliers is the resulting dependence of gain on pressure (which influences the ionization probability and hence the number ofcascades). This does not seem to be so pronounced ill parallel multipliers where ion feedback may be built more upon ionization of atoms adhering to the large area of the plates than upon gas residues').
It is of interest to look in more detail at the ion paths in the case of plane-parallel multipliers. One purpose of such a study is to see if ion feedback can be controlled, thereby improving the time resolution. For this purpose the influence of a magnetic field together with curving of the parallel plates was considered as a possible solution, and some representative ion paths for such a case were calculated. Another purpose is to study the feasibility of using a bent structure in a magnetic field for selection of ions of a certain mass .
509
2 . Analysis The channel electron multiplier is normally constructed of two parallel plates separated by a distance of a few tenths of a mm. The length of the plates is 50-100 times the spacing. A high voltage is applied, producing an electric field along the length of the plates (fig . 1) . A particle entering the grounded end of the multiplier knocks out one or more secondary electrons from the walls, which are accelerated toward the positive end . These electrons gain energy from the electric field and upon striking the walls again, knock out more electrons . By the time the cascade of electrons has traversed the
j i--
3 kV
Fig. 1. A channel electron
multiplier with an exciting parvcle or radiation at the input.
510,
R. B. JANNEY AND P. A. TOPE
length of the multiplier, it is large enough to produce a vectors make, with the x axis. Then sizeable output pulse . Onc electron' at the input may yield as many as 108-109 electrons at the output. We will consider the multiplier plates to be bent into Since Fx =max and F,,= nw, eqs (1), (2) and (3) c:in a predetermined shape', and a magnetic field applied be combined and transformed into two differential perpendicularly to it (see fig . 2). An ionized, positively equations:' char atom or molecule formed at the positive end of the multiplier will be accelerated by the electric field and led by the magnetic field. If the plates are curved so as to exactly follow the ion path, it will not strike 8 , eE the walls. The shaperequired will tv determined by the ƒ = e x + -sin (tan-t Y/x), m - ; kil electric andmagnetic fields used as well as by thecharge and mass of the ion whose presence is assumed. Mathematically, the problem can be set up similarly where z and y are the first derivatives of the positions xand y, and z and y are the second derivatives. to the classical problem of perpendicular electric and A system of two` second-order linear differential magnetic fields, with the difference that in this case the position variables electric field is always directed along the instantaneous equations is obtained. However, theequations, so they, direction of motion of the particle, assuming perfect x and y do not appear in these two lengthwise alignment of the plates. This is due to the can be further simplified . Using 2i = x, requirement that theparticle follow thecurvature of the )z -1,, channel multiplier, and the electric field is directed ti = ü, tiz = v, along the channel. We define F = force, eB e8 , Sz -_ t -_ E = electric field, m ai e = electron charge magnitude (+, for ionized particle), the equations can be transformed to : B = magnetic field. (6) At = - St2z+ ;zcos(tan-',,/Ad , From fig . 2 the equations for the force in the x and y directions are readily written as: ~z = 41 ~t+Sz sin (tan -1 2z12t)Fx
= -eu,B+Ee Cos0,
Fy = eu,B+eE sin
0,
-
(1)
(2)
where 0 is the angle the electric-field and velocity "
This construction was successfully tried usingmultiplier plates fabricated from Kapton plastic sheets coveredwith potentialdivider and secondary-ernission layers in the usual way 4).
z Fig. 2. A bent channel electron multiplier, showing the electric and magnetic fields and thecoordinate system used .
Thevalues of xand -an then be found by integrating thevariables At and z with respectto time. A1 and h2 can be solved by numerically using a standard con= puter program for the solution of a system of linear differential equations. The ion paths were studied by solvingthe equations for realistic values of the parameters. The input parameters to thecomputer program are: 1) the magnetic field intensity B, 2) the voltage applied to the multiplier, 3) the mass of the particle (amu), 4) the length of the multiplier, 5) the initial x velocity. The electric field is calculated using theapplied voltage and the length of the multipliers. The initial velocities, of the ions in the x and y directions should be zero in the ideal case. The xvelocity was included as an input parameter in order to study the effect of a thermal x velocity upon the path of the ion. There are three possibilities for the path of an ionized atom: it may strike the wall before acquiring
ION PATHS IN ELFCTRON MTJLTBPLIERS
sufficient energy to produce additional electrons; it may strike the wall, after it has acquired sufficient energy to produce additional electrons, or it may traversethe multiplier without strikinf the walls at all, andbe ejectedfrom the'entrance. The firstcase is of no interest since the brief existence of the ion-in'no way affects the operation of the multiplier or the signal produced. The second case is that 'which occurs' in normal operation of these -multipliers (with' cascaded avalanches) ; and the third case would be a means of controlling the ionfeedback in such a multiplier. A typic.l designof the channel multiplier involves a path length of 50 mm, with a separation between the plates of approximately 1 mm, and an applied voltage of 3 kV . These parameters' were used in the calculations. In fig . 3 are shown the paths calculated by the computer program for an Oz molecule (singly ionized) for three different values of magnetic field. It is seen that practically obtainable values of magnetic field strength result in a small deflection of the path of the particle requiring a moderate degree of bending of the channel multiplier. This is for thespecific case of oxygen molecules. For comparison, the calculated path of a helium atom (singly ionized) is shown in fig. 4. It is seen, as expected, that the lighter helium atom is deflected more by the magnetic field than was the heavier'oxygen for' the same value of the magnetic field. In a practical situation, there may be several types of residual gas atoms or molecules present in the multi~
MOLECULE AT
plier. If the paths for two typesof particles of different masses. deviate from each otherat some point by more than the 0.5-1 mm separation of theplates of the multiplier, a collision with the wall must result for at least one of the species of particles. To investigate this, the paths of particles having . different masses were calculated assuming the same magnetic and electric' fields. The results are shown in fig. 5, which shows the fi r position of the particles for the -same arbitrary x position near the end of the multiplier. It is seen that for particles of moderate mass, the path difference is 4mm/atomic' mass' unit, which means that -ionic feedback by case (3) could be eliminated foronly one molecule in a given multiplier design and under given operating conditions. Particles having masses near the design mass would collide with one plate of the multiplier farther along, corresponding to case (2) mentioned earlier . Particles differing greatlyfrom thedesign mass would collide with a plate almost immediately, PATH FOR A SINGLY
IONIZED HELIUM ATOM
® s .10 WO-'
0
H rvL] T
3 DIFFERENT MAGNETIC . FIELD STRENGTHS
-~ 20 ~ X POSITION
30
t MM )
Fig . 4. Path for a singly ionized helium atom at a magnetic field strength of 0.10 W/m-. ylmnd 60
40
20 X
POSITION
(MM)
Fig. 3 . Paths for a singly ionized oxygen molecule at three different values of magnetic field strength : 0.10, 0.15, and 0.20 W/mQ.
:0
30
40
NO _ maw
Fig. i . y-position at x=45 mm vs mass number, B=0.30 W/m2.
512
R. E. IANNEY AND P. A. TOYE
ore acxluiring the energy - needed to knock out tr corresponding ,to caw(1). It has been assumed throughout the previous disttheionizedmolecules areat rest when they s up my theelectric field. of the multiplier. This applyifthe m were adheredto theplates . If y are free they will always have a certain the m a of om thermal velocity obeying a fioliznn distribution. The- average thermal energy (% jkT) foran oxygen molecule at 300 K corresponds toSince a velocity " ;t 5 x 10a,m/S: this is as average velocity, asignificant number will be present having this initial velocity of mice and velocities several times, larger. The effect of this initial velocity in the x dire;.:tion has been considered by using different values of initial velocity in the x tion . The resulis of such calculations areshown in . á. The three velocities chosen are zero (for referv), thermal velocity (300 in/s), and 10 timesthermal velocity ( m/s).It iS seen that thex velocity does not hnve a great effect on thw path . This is not at all surprising since according to the description of the problem, the initial acceleration of the particles by the electric field is in the x direction, and they almost immediately attain a vriocity so large that the thermal velocity is negligible. The problem is more difficult to analyze with respectto the effects of an initial yvelocity. This is due to the fact that according to the definition of the problem, the elmtric field is coincident with the initial velocity of the particle, which is in thexdirection. In the case of an initial x velocity, this can simply be inserted as an initial condition in the differential 5Z INITIAL X VELOC171ES OF 0 . 500 . S000 11
M/SEC
equations . This cannot be done foran initial yvelocity; since : such a velocity causes the initial' direction of tale electric field to change:' Oneway to approach theproblem is to consider th . :t within the first mm of theion path down themultiplier, the direction of the electric field :does not deviaïe significantly from the x direction and the problem reduces to the classical one of perpendicular electric andmagnetic heids. Such pathsfortheoxygen ions using the same parameters as used previously are shown in figs 7 and 8, for different values of initial y velocity. INITIAL Y VELOCITIES OF 50 . . SOO . MISEC
X POSITION
(MM)
Fig. 7. Paths for initial y-velocities of 50 and 500mis in the classical cross-field problem. INITIAL Y VELOCITIES OF 5000 . AND SOOOO. MISEC S.,
m000 MISEC
SM MISEC ' -~r-r-r- -, .
X POSITION
IMMI
0
50
Fig. é. Paths for initial x-velocities of 0, 500 and 5000 mis. Singly i oxygert moleculesat 8= 0.30 w/me.
19
10
X POSITION
3ü
IMM)
a0
50
Fig. 8. Paths forinitial y-velocities of 5000 and 50 000mis in the classical cross-field problem.
ION PATHS IN ELECTRON MULTIPLIERS
These arevalid approximations to the present problem only for the first mm or leiof the path, but indicate that an initiai y velocity may affect' the ion path significantly . 3. Discussion
The calculations have indicated that ions of a given mass will follow the path of a suitably bent ,channel electron multiplier if this is placed in rite correct magnetic field. Only ions which satisfy the two conditions that they have a mass quite close to (but not equal to) the given design mass and a small thermal velocity perpendicular to the plates, will be able to contribute to ionic feedback. Ionic feedback due to ions which do not satisfy these two conditions will be eliminated by either the ion colliding with the plates before acquiring sufficient energy to produce electrons or in rare cases, by the ion travelling the length of the multiplier and being ejected from the input opening. 4. Conclusion 4.1 . ION FEEDBACK AND ITS AVOIDANCE
It has been shown that it should be possible in a practically realizable experimental set-up to substantially reduce theamount ofionic feedback in the output pulse from aparallel-plate electron multiplierandthereby improve the time resolution attainable with these devices. Since the large amplitude of the output pulse from these devices is partially dependent on the presence of ionic feedback, the improvement in time resolution would be obtained at the cost of a smaller output pulse amplitude. However, it is expected that this would be acceptable in those cases where time resolution is of sufficient interest to justify the bending of the multiplier and the provision for the application of a magnetic field .
4.2. UTILIZATION OF uENT DETECTION
51 3
srRVcrvRm -mAss
It wasnoted in connection with fig. 5 that only those ions having masses quite close to thegivendesign mass wouldproduce ionic feedback. This ability to distinguish a particular rnase from the form of the output pulse produced indicates that it might be possible to use these devices as quite simple and inexpensive detectors for a given type of ion, i .e., it could function as a mass detector. 'The structure would function both as a selector for the, chosen masses and as a detector (because of the large output pulse obtainable from these multipliers). 4.3. IMPLICATION of IONIC FEEDBACK
It was shown (in fig. 8) that the presence of a y velocity component could affect the ion path. The implication of this on the ionicfeedback is that it would rarely happen that a released ion would have both a small y velocity and the exactxvelocity component for following thebent path. Thus ionic feedback should be practically eliminated. If we want to utilize bent structures (in a magnetic field) for detection of definite masses, y verity components should be eliminated, e.g ., by using a collimator at theentrance. The influence of a spread in xverity is negligible even for relatively high values of this velocity, as seen from fig. 6. Such a device could find applications for study of the atom masses present in a vacuum chamber or in the upper atmosphere. References, 1) D . S . Evans, Rev . Sci. Instr. 36 (1965) 375.
$) O. Nil--, L. Hasselgren, K . Siegbahn, S . Sers, L. P . Anderson and P. A. Tove, Nucl. Instr . and Meth . 84 (1970) 301 . s) A . van der Ziel, Solid-srare physical eleerraraies (2nd led . . Prentice-Hall, New vork) . a) B. Erieson, unpublished Hork.
Received 3 January 1974 A computer
study of ion paths in curved parallel-plate electron multipliers with a perpendicular magnetic field is `performed . The implications on the avoidance of ion feedback and on the possible construction ofa mass detector are discussed. Ions may be introduced in these multipliers either directly or by ionizationfrom the avalanching electrons. With given multi-
plier dimensions and magnetic field strength it is found that the structure is able to transport ions ofonly one mass. The influence of initial ion velocities which can be present is investigated . For low-energy ions it is found that a longitudinal velocity spread is unimportant while velocities perpendicular to the plates may influence the paths significantly.
1. Introduetioa Ion feedback plays a large role in the operation of electron multipliers with continuous dynodes . The basic mechanism of ion feedback in multipliers is the following : At the end of the path of the avalanching electrons, the probability of ionization increases because of the large number of electrons . Ionized atoms or molecules start with near-zero velocity and accelerate in the opposite direction to that of the electrons . Ifthey are able to pursue their paths without colliding with the wall; after the drift time (when they have reached the entrance of the multiplier) they will have acquired sufficient energy to start a new avalanche of electrons. This drift time is orders of magnitude longer than the transit time of the electrons but still sufficiently small to cause the several avalanches introduced by repeated ion feedback to appear as a single pulse when integrated by the stray capacitance at the output. In tubular multipliers this phenomenon is generally avoided by curving the tube with a sufficiently small radius') . In the ordinary place-parallel multiplier', ') ion feedback is present and is responsible both for the useful large amplitude of ,. he pulse and also for the worsening of the time resolution since the total pulse contains several electron avalanches separated by the time for ion drift between the entrance and output of the multiplier. A further disadvantage with ion feedback generally mentioned in connection with tubular multipliers is the resulting dependence of gain on pressure (which influences the ionization probability and hence the number ofcascades). This does not seem to be so pronounced ill parallel multipliers where ion feedback may be built more upon ionization of atoms adhering to the large area of the plates than upon gas residues').
It is of interest to look in more detail at the ion paths in the case of plane-parallel multipliers. One purpose of such a study is to see if ion feedback can be controlled, thereby improving the time resolution. For this purpose the influence of a magnetic field together with curving of the parallel plates was considered as a possible solution, and some representative ion paths for such a case were calculated. Another purpose is to study the feasibility of using a bent structure in a magnetic field for selection of ions of a certain mass .
509
2 . Analysis The channel electron multiplier is normally constructed of two parallel plates separated by a distance of a few tenths of a mm. The length of the plates is 50-100 times the spacing. A high voltage is applied, producing an electric field along the length of the plates (fig . 1) . A particle entering the grounded end of the multiplier knocks out one or more secondary electrons from the walls, which are accelerated toward the positive end . These electrons gain energy from the electric field and upon striking the walls again, knock out more electrons . By the time the cascade of electrons has traversed the
j i--
3 kV
Fig. 1. A channel electron
multiplier with an exciting parvcle or radiation at the input.
510,
R. B. JANNEY AND P. A. TOPE
length of the multiplier, it is large enough to produce a vectors make, with the x axis. Then sizeable output pulse . Onc electron' at the input may yield as many as 108-109 electrons at the output. We will consider the multiplier plates to be bent into Since Fx =max and F,,= nw, eqs (1), (2) and (3) c:in a predetermined shape', and a magnetic field applied be combined and transformed into two differential perpendicularly to it (see fig . 2). An ionized, positively equations:' char atom or molecule formed at the positive end of the multiplier will be accelerated by the electric field and led by the magnetic field. If the plates are curved so as to exactly follow the ion path, it will not strike 8 , eE the walls. The shaperequired will tv determined by the ƒ = e x + -sin (tan-t Y/x), m - ; kil electric andmagnetic fields used as well as by thecharge and mass of the ion whose presence is assumed. Mathematically, the problem can be set up similarly where z and y are the first derivatives of the positions xand y, and z and y are the second derivatives. to the classical problem of perpendicular electric and A system of two` second-order linear differential magnetic fields, with the difference that in this case the position variables electric field is always directed along the instantaneous equations is obtained. However, theequations, so they, direction of motion of the particle, assuming perfect x and y do not appear in these two lengthwise alignment of the plates. This is due to the can be further simplified . Using 2i = x, requirement that theparticle follow thecurvature of the )z -1,, channel multiplier, and the electric field is directed ti = ü, tiz = v, along the channel. We define F = force, eB e8 , Sz -_ t -_ E = electric field, m ai e = electron charge magnitude (+, for ionized particle), the equations can be transformed to : B = magnetic field. (6) At = - St2z+ ;zcos(tan-',,/Ad , From fig . 2 the equations for the force in the x and y directions are readily written as: ~z = 41 ~t+Sz sin (tan -1 2z12t)Fx
= -eu,B+Ee Cos0,
Fy = eu,B+eE sin
0,
-
(1)
(2)
where 0 is the angle the electric-field and velocity "
This construction was successfully tried usingmultiplier plates fabricated from Kapton plastic sheets coveredwith potentialdivider and secondary-ernission layers in the usual way 4).
z Fig. 2. A bent channel electron multiplier, showing the electric and magnetic fields and thecoordinate system used .
Thevalues of xand -an then be found by integrating thevariables At and z with respectto time. A1 and h2 can be solved by numerically using a standard con= puter program for the solution of a system of linear differential equations. The ion paths were studied by solvingthe equations for realistic values of the parameters. The input parameters to thecomputer program are: 1) the magnetic field intensity B, 2) the voltage applied to the multiplier, 3) the mass of the particle (amu), 4) the length of the multiplier, 5) the initial x velocity. The electric field is calculated using theapplied voltage and the length of the multipliers. The initial velocities, of the ions in the x and y directions should be zero in the ideal case. The xvelocity was included as an input parameter in order to study the effect of a thermal x velocity upon the path of the ion. There are three possibilities for the path of an ionized atom: it may strike the wall before acquiring
ION PATHS IN ELFCTRON MTJLTBPLIERS
sufficient energy to produce additional electrons; it may strike the wall, after it has acquired sufficient energy to produce additional electrons, or it may traversethe multiplier without strikinf the walls at all, andbe ejectedfrom the'entrance. The firstcase is of no interest since the brief existence of the ion-in'no way affects the operation of the multiplier or the signal produced. The second case is that 'which occurs' in normal operation of these -multipliers (with' cascaded avalanches) ; and the third case would be a means of controlling the ionfeedback in such a multiplier. A typic.l designof the channel multiplier involves a path length of 50 mm, with a separation between the plates of approximately 1 mm, and an applied voltage of 3 kV . These parameters' were used in the calculations. In fig . 3 are shown the paths calculated by the computer program for an Oz molecule (singly ionized) for three different values of magnetic field. It is seen that practically obtainable values of magnetic field strength result in a small deflection of the path of the particle requiring a moderate degree of bending of the channel multiplier. This is for thespecific case of oxygen molecules. For comparison, the calculated path of a helium atom (singly ionized) is shown in fig. 4. It is seen, as expected, that the lighter helium atom is deflected more by the magnetic field than was the heavier'oxygen for' the same value of the magnetic field. In a practical situation, there may be several types of residual gas atoms or molecules present in the multi~
MOLECULE AT
plier. If the paths for two typesof particles of different masses. deviate from each otherat some point by more than the 0.5-1 mm separation of theplates of the multiplier, a collision with the wall must result for at least one of the species of particles. To investigate this, the paths of particles having . different masses were calculated assuming the same magnetic and electric' fields. The results are shown in fig. 5, which shows the fi r position of the particles for the -same arbitrary x position near the end of the multiplier. It is seen that for particles of moderate mass, the path difference is 4mm/atomic' mass' unit, which means that -ionic feedback by case (3) could be eliminated foronly one molecule in a given multiplier design and under given operating conditions. Particles having masses near the design mass would collide with one plate of the multiplier farther along, corresponding to case (2) mentioned earlier . Particles differing greatlyfrom thedesign mass would collide with a plate almost immediately, PATH FOR A SINGLY
IONIZED HELIUM ATOM
® s .10 WO-'
0
H rvL] T
3 DIFFERENT MAGNETIC . FIELD STRENGTHS
-~ 20 ~ X POSITION
30
t MM )
Fig . 4. Path for a singly ionized helium atom at a magnetic field strength of 0.10 W/m-. ylmnd 60
40
20 X
POSITION
(MM)
Fig. 3 . Paths for a singly ionized oxygen molecule at three different values of magnetic field strength : 0.10, 0.15, and 0.20 W/mQ.
:0
30
40
NO _ maw
Fig. i . y-position at x=45 mm vs mass number, B=0.30 W/m2.
512
R. E. IANNEY AND P. A. TOYE
ore acxluiring the energy - needed to knock out tr corresponding ,to caw(1). It has been assumed throughout the previous disttheionizedmolecules areat rest when they s up my theelectric field. of the multiplier. This applyifthe m were adheredto theplates . If y are free they will always have a certain the m a of om thermal velocity obeying a fioliznn distribution. The- average thermal energy (% jkT) foran oxygen molecule at 300 K corresponds toSince a velocity " ;t 5 x 10a,m/S: this is as average velocity, asignificant number will be present having this initial velocity of mice and velocities several times, larger. The effect of this initial velocity in the x dire;.:tion has been considered by using different values of initial velocity in the x tion . The resulis of such calculations areshown in . á. The three velocities chosen are zero (for referv), thermal velocity (300 in/s), and 10 timesthermal velocity ( m/s).It iS seen that thex velocity does not hnve a great effect on thw path . This is not at all surprising since according to the description of the problem, the initial acceleration of the particles by the electric field is in the x direction, and they almost immediately attain a vriocity so large that the thermal velocity is negligible. The problem is more difficult to analyze with respectto the effects of an initial yvelocity. This is due to the fact that according to the definition of the problem, the elmtric field is coincident with the initial velocity of the particle, which is in thexdirection. In the case of an initial x velocity, this can simply be inserted as an initial condition in the differential 5Z INITIAL X VELOC171ES OF 0 . 500 . S000 11
M/SEC
equations . This cannot be done foran initial yvelocity; since : such a velocity causes the initial' direction of tale electric field to change:' Oneway to approach theproblem is to consider th . :t within the first mm of theion path down themultiplier, the direction of the electric field :does not deviaïe significantly from the x direction and the problem reduces to the classical one of perpendicular electric andmagnetic heids. Such pathsfortheoxygen ions using the same parameters as used previously are shown in figs 7 and 8, for different values of initial y velocity. INITIAL Y VELOCITIES OF 50 . . SOO . MISEC
X POSITION
(MM)
Fig. 7. Paths for initial y-velocities of 50 and 500mis in the classical cross-field problem. INITIAL Y VELOCITIES OF 5000 . AND SOOOO. MISEC S.,
m000 MISEC
SM MISEC ' -~r-r-r- -, .
X POSITION
IMMI
0
50
Fig. é. Paths for initial x-velocities of 0, 500 and 5000 mis. Singly i oxygert moleculesat 8= 0.30 w/me.
19
10
X POSITION
3ü
IMM)
a0
50
Fig. 8. Paths forinitial y-velocities of 5000 and 50 000mis in the classical cross-field problem.
ION PATHS IN ELECTRON MULTIPLIERS
These arevalid approximations to the present problem only for the first mm or leiof the path, but indicate that an initiai y velocity may affect' the ion path significantly . 3. Discussion
The calculations have indicated that ions of a given mass will follow the path of a suitably bent ,channel electron multiplier if this is placed in rite correct magnetic field. Only ions which satisfy the two conditions that they have a mass quite close to (but not equal to) the given design mass and a small thermal velocity perpendicular to the plates, will be able to contribute to ionic feedback. Ionic feedback due to ions which do not satisfy these two conditions will be eliminated by either the ion colliding with the plates before acquiring sufficient energy to produce electrons or in rare cases, by the ion travelling the length of the multiplier and being ejected from the input opening. 4. Conclusion 4.1 . ION FEEDBACK AND ITS AVOIDANCE
It has been shown that it should be possible in a practically realizable experimental set-up to substantially reduce theamount ofionic feedback in the output pulse from aparallel-plate electron multiplierandthereby improve the time resolution attainable with these devices. Since the large amplitude of the output pulse from these devices is partially dependent on the presence of ionic feedback, the improvement in time resolution would be obtained at the cost of a smaller output pulse amplitude. However, it is expected that this would be acceptable in those cases where time resolution is of sufficient interest to justify the bending of the multiplier and the provision for the application of a magnetic field .
4.2. UTILIZATION OF uENT DETECTION
51 3
srRVcrvRm -mAss
It wasnoted in connection with fig. 5 that only those ions having masses quite close to thegivendesign mass wouldproduce ionic feedback. This ability to distinguish a particular rnase from the form of the output pulse produced indicates that it might be possible to use these devices as quite simple and inexpensive detectors for a given type of ion, i .e., it could function as a mass detector. 'The structure would function both as a selector for the, chosen masses and as a detector (because of the large output pulse obtainable from these multipliers). 4.3. IMPLICATION of IONIC FEEDBACK
It was shown (in fig. 8) that the presence of a y velocity component could affect the ion path. The implication of this on the ionicfeedback is that it would rarely happen that a released ion would have both a small y velocity and the exactxvelocity component for following thebent path. Thus ionic feedback should be practically eliminated. If we want to utilize bent structures (in a magnetic field) for detection of definite masses, y verity components should be eliminated, e.g ., by using a collimator at theentrance. The influence of a spread in xverity is negligible even for relatively high values of this velocity, as seen from fig. 6. Such a device could find applications for study of the atom masses present in a vacuum chamber or in the upper atmosphere. References, 1) D . S . Evans, Rev . Sci. Instr. 36 (1965) 375.
$) O. Nil--, L. Hasselgren, K . Siegbahn, S . Sers, L. P . Anderson and P. A. Tove, Nucl. Instr . and Meth . 84 (1970) 301 . s) A . van der Ziel, Solid-srare physical eleerraraies (2nd led . . Prentice-Hall, New vork) . a) B. Erieson, unpublished Hork.