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A static field mass spectrograph for laser induced plasma experiments
NUCLEAR INSTRUMENTS
AND METHODS
I39
(I976) 2 3 5 - 2 3 7 ;
©
NORTH-HOLLAND
PUBLISHING
CO.
A STATIC FIELD MASS S P E C T R O G R A P H FOR LASER INDUCED PLASMA EXPERIMENTS M. ORON Soreq Nuclear Research Centre, Yavne, Israel A method for multichannel analysis of ions blown off laser produced plasmas is described. The ions are separated in parallel magnetic and electrostatic fields, where they describe a circle. The masses are dispersed along the field lines and energy is determined by the time-of-flight method.
1. Introduction
Ions that are blown off laser produced plasmas have charge, mass and energy distributions that are related to the plasma parameters and composition. These distributions must be determined when plasma parameters are studied. Previous measurements, using a combination of two static analyzers in series, required many laser shots to generate a distribution. Recent works were aimed at the simultaneous determination of these distributions: (a) J. N. Olsen et al. 1) used a Thompson parabola spectrometer 2) to collect data on photographic films; (b) parallel magnetic and electrostatic fields, in a geometry where Thompson's parabolas degenerate into straight lines, were used by Hearrell and Van Hulsteyn 3) and (c) a dynamic spectrometer was used by Oron and Paiss < 5). All three approaches yield the desired information but the anticipated experimental problems are simpler to solve in the presently proposed spectrometer. The Thompson parabola spectrometer is inconvenient to use because of the non-linearity problems associated with photographic plates. These can be replaced by a multi-array capacitor-collector (as in b) but this calls for elaborate electronics. The dynamic spectrometer uses a complicated and expensive varying voltage generator. The use of parallel E and B static fields, where the
ions travel a full circle, yields a single spatial collection point for every charge-to-mass ratio (q/m) and permits the determination of the velocity distribution by the time-of-flight method. This can be done since all ions travel the same distance in the x-direction (see fig. 1) until they reach the spectrometer and remain in the spectrometer for a constant time (the cyclotron gyration time).
2. Analyzer theory The ion source (e.g. the laser produced plasma) is located at point A (fig. 1). An ion having an initial velocity V0 and a charge-to-mass ratio q/m leaves A at a time very close to the laser pulse and reaches the x = 0 point through a field-free region after the timeof-flight T = L~ Vo. It is exposed to the electric field (E) and the magnetic field (B). The action of the two fields can be separated since the Lorenz force is in the x-y plane and the electric force in the z direction. The Lorenz force causes the ions to circle in the cyclotron frequency where one period is To = (27r/B) (m/q),
(1)
which is independent of V0. The time spent in the spectrometer, until the ion reaches the collector is To. During this time the electric force
F = qE
(2)
displaces the ion in the z direction by Az
Az = 12 FIELD-FREE TUBULAR/ , f
-- ", !
ET~ = 27r2 ~
,
(3)
/'~/k/
Fig. 1. Schematic diagram of the spectrometer.
which is independent of V0 and is proportional to (re~q), i.e. mass dispersive. The ions having the same (re~q) describe helix-like trajectories and reach a single spatial collection point at x = 0 , y = 0 and z=Az(q/,~) but their time-ofVIII. MASS A N A L Y Z E R S
236
M. ORON
flight Tot will be velocity dependent:
Toe = T + To = L/Vo + Tc,
(4)
where T~ is constant for each q/m, thus enabling us to determine V0 easily. The different (q/m)'s are collected on a collector plate in the y - z plane. Mass dispersion is linear with the z axis according to eq. (3), as shown schematically in fig. 2.
The kinetic energy of the particle is determined by measuring the time of flight, or the V0 and calculating ½mV 2. The Vo distribution is determined by placing an ion collector in the proper position in the y - z plane (see fig. 2) and taking its output into a scope or transient recorder which is triggered by the laser pulse. Since the total time of flight is given by eq. (4) one has to delay triggering the scope by To in order to get the display inversely proportional to Vo. The accuracy of the measurement of Vo is determined by three factors: (a) the lifetime of the ion source, (b) the finite diameter of the source and, (c) the deviation of the beam angle from the x-axis (A~) due to the diameter of the entrance slit of the spectrometer. These three factors can be summarized as follows:
A Vo
Vo
=--
Ax
AT
+ - - +
L
A~,
(5)
T
where Ax - the diameter of the ion source, L - the distance from the source to the analyzer, A T - the lifetime of the ion source, Ae - the deviation of the beam from the x-axis. Typical values for laser produced plasma are: A T " 10 -1° s, T ~ 2.5 x 10 -6 s, L = 50 cm, Ax = 1 0 - 2
~~~,~,l r\
jx
B,E, FIELDS
A "/ION/~S ~-J
AE~
2 (AVo'~,
E~
\ Vo/
(6)
where E k is the kinetic energy of the ion and A E k the resolvable energy increment. Using the above values we obtain:
AEk -- 2 ( 10-2 10-1° ) Ek ~ - ~ + 2 . 5 x 1 0 -6 + 5 x 1 0 - 3 -~10-2"
3. Energy resolution
- -
cm and Aa = 5 x 10- a rad. The A~. corresponds to a 0.5 cm slit. The energy resolution would be
FIELD SHIELD
(q/m)2
It can be seen that the major limitation to the resolution is due to Ac~. Thus, this parameter is chosen as a compromise between energy resolution and total current collected (solid angle). 4. q / m
resolution
Since the cyclotron frequency is constant the (q/m) resolution is dependent only on the dimension of the entrance slit, or the A~. An ion entering Aw has a velocity component along the E field of VoA~. Its displacement along the z-axis would be
Az = ½(q/m) E T 2 - VoAc~To.
I would be displaced by dz' from the ideal point of impingement where
Az' = VoAc~Tc =- (Vo27c/B) (m/q) Acz,
COLLECTOR z
Fig. 2. Set-up of proposed analyzer.
(S)
and thus the collector dimension along the z-axis should be 2Az' or A z + A z ' . Since mass dispersion is linear, it is interesting to examine in detail (here Az is taken for A~ = 0):
Az'
--=
Az
B VoA~--. roe
(9)
The linear dependence of Az'/Az on VoAo~ results in a resolution loss for high velocity ions and large acceptance angles. Therefore, a small d a in the z direction is required when analyzing energetic ions. As a numerical example, taking 2 k e V deuterons, Vo = 4 . 3 7 x 1 0 s m/s, A~ for a 5 r a m slit at 5 0 0 m m distance is 5 x 10- 3 rad, B = 910 G (corresponding to a 1 0 0 m m radius for 2 k e V deuterons) and E = 4.05 x 103 V/m (corresponding to z = 200 m m for D + ions) we get
Az'/Az = 4.8x 10 .2
\
(7)
~ 5~o.
(10)
It is een that with moderate E and B fields, small dimensions and an appreciable solid angle, plasmas of low Z materials can be analyzed,
237
S T A T I C F I E L D MASS S P E C T R O G R A P H
free tube and locate the collectors at the edge of the field, which is an advantage.
6. Discussion
COLLECTOR
Fig. 3. A 540 ° deflection analyzer.
5. Proposed design parameters For plasmas containing D, T, C, Li, O, having velocities up to 4.5 x 105 m/s, the proposed fields are B = 9 1 0 G and E = 4 x 103V/re. These fields yield a maximal gyration radius of 100 mm and a 200 mm z displacement for D + ions. Energy resolution is 1% and mass resolution about 5%, for an entrance aperture of 5 mm diameter located at a distance of 500 mm from the source. Some perturbation of the field will be caused by the field-free entrance tube, but it is assumed that it will be small or negligible. Using the geometry shown in fig. 3, a 540 ° deflection permits one to omit the field-
The proposed static spectrograph has the following advantages over previously used analyzers: a) The fields involved are static and simple. b) The integral of the ion current in each collector represents the total yield of the collected q/rn. c) Since ions here gain energy along the E field, it may be possible to use an ion multiplier or a solid state detector as the collector. This would facilitate low current counting (ion counting), permitting a decrease in the collection solid angle and improved resolution. This research is supported by the United StatesIsrael Binational Science Foundation, Jerusalem, Israel.
References ~) 2) a) 4) s)
J. N. Olsen et al., J. Appl. Phys. 44, no. 5 (1973) 2275. j. j. Thompson, Phil. Mag. 21 (1911) 225. D. B. Van Hulsteyn et al., Rev. Sci. Instr. 45 (1974) 819. M. Oron et al., Rev. Sci. Instr. 44 (1973) 1293. M. Oron, Thesis (Univ. o f Rochester, N.Y., 1975).
V I I I , MASS A N A L Y Z E R
AND METHODS
I39
(I976) 2 3 5 - 2 3 7 ;
©
NORTH-HOLLAND
PUBLISHING
CO.
A STATIC FIELD MASS S P E C T R O G R A P H FOR LASER INDUCED PLASMA EXPERIMENTS M. ORON Soreq Nuclear Research Centre, Yavne, Israel A method for multichannel analysis of ions blown off laser produced plasmas is described. The ions are separated in parallel magnetic and electrostatic fields, where they describe a circle. The masses are dispersed along the field lines and energy is determined by the time-of-flight method.
1. Introduction
Ions that are blown off laser produced plasmas have charge, mass and energy distributions that are related to the plasma parameters and composition. These distributions must be determined when plasma parameters are studied. Previous measurements, using a combination of two static analyzers in series, required many laser shots to generate a distribution. Recent works were aimed at the simultaneous determination of these distributions: (a) J. N. Olsen et al. 1) used a Thompson parabola spectrometer 2) to collect data on photographic films; (b) parallel magnetic and electrostatic fields, in a geometry where Thompson's parabolas degenerate into straight lines, were used by Hearrell and Van Hulsteyn 3) and (c) a dynamic spectrometer was used by Oron and Paiss < 5). All three approaches yield the desired information but the anticipated experimental problems are simpler to solve in the presently proposed spectrometer. The Thompson parabola spectrometer is inconvenient to use because of the non-linearity problems associated with photographic plates. These can be replaced by a multi-array capacitor-collector (as in b) but this calls for elaborate electronics. The dynamic spectrometer uses a complicated and expensive varying voltage generator. The use of parallel E and B static fields, where the
ions travel a full circle, yields a single spatial collection point for every charge-to-mass ratio (q/m) and permits the determination of the velocity distribution by the time-of-flight method. This can be done since all ions travel the same distance in the x-direction (see fig. 1) until they reach the spectrometer and remain in the spectrometer for a constant time (the cyclotron gyration time).
2. Analyzer theory The ion source (e.g. the laser produced plasma) is located at point A (fig. 1). An ion having an initial velocity V0 and a charge-to-mass ratio q/m leaves A at a time very close to the laser pulse and reaches the x = 0 point through a field-free region after the timeof-flight T = L~ Vo. It is exposed to the electric field (E) and the magnetic field (B). The action of the two fields can be separated since the Lorenz force is in the x-y plane and the electric force in the z direction. The Lorenz force causes the ions to circle in the cyclotron frequency where one period is To = (27r/B) (m/q),
(1)
which is independent of V0. The time spent in the spectrometer, until the ion reaches the collector is To. During this time the electric force
F = qE
(2)
displaces the ion in the z direction by Az
Az = 12 FIELD-FREE TUBULAR/ , f
-- ", !
ET~ = 27r2 ~
,
(3)
/'~/k/
Fig. 1. Schematic diagram of the spectrometer.
which is independent of V0 and is proportional to (re~q), i.e. mass dispersive. The ions having the same (re~q) describe helix-like trajectories and reach a single spatial collection point at x = 0 , y = 0 and z=Az(q/,~) but their time-ofVIII. MASS A N A L Y Z E R S
236
M. ORON
flight Tot will be velocity dependent:
Toe = T + To = L/Vo + Tc,
(4)
where T~ is constant for each q/m, thus enabling us to determine V0 easily. The different (q/m)'s are collected on a collector plate in the y - z plane. Mass dispersion is linear with the z axis according to eq. (3), as shown schematically in fig. 2.
The kinetic energy of the particle is determined by measuring the time of flight, or the V0 and calculating ½mV 2. The Vo distribution is determined by placing an ion collector in the proper position in the y - z plane (see fig. 2) and taking its output into a scope or transient recorder which is triggered by the laser pulse. Since the total time of flight is given by eq. (4) one has to delay triggering the scope by To in order to get the display inversely proportional to Vo. The accuracy of the measurement of Vo is determined by three factors: (a) the lifetime of the ion source, (b) the finite diameter of the source and, (c) the deviation of the beam angle from the x-axis (A~) due to the diameter of the entrance slit of the spectrometer. These three factors can be summarized as follows:
A Vo
Vo
=--
Ax
AT
+ - - +
L
A~,
(5)
T
where Ax - the diameter of the ion source, L - the distance from the source to the analyzer, A T - the lifetime of the ion source, Ae - the deviation of the beam from the x-axis. Typical values for laser produced plasma are: A T " 10 -1° s, T ~ 2.5 x 10 -6 s, L = 50 cm, Ax = 1 0 - 2
~~~,~,l r\
jx
B,E, FIELDS
A "/ION/~S ~-J
AE~
2 (AVo'~,
E~
\ Vo/
(6)
where E k is the kinetic energy of the ion and A E k the resolvable energy increment. Using the above values we obtain:
AEk -- 2 ( 10-2 10-1° ) Ek ~ - ~ + 2 . 5 x 1 0 -6 + 5 x 1 0 - 3 -~10-2"
3. Energy resolution
- -
cm and Aa = 5 x 10- a rad. The A~. corresponds to a 0.5 cm slit. The energy resolution would be
FIELD SHIELD
(q/m)2
It can be seen that the major limitation to the resolution is due to Ac~. Thus, this parameter is chosen as a compromise between energy resolution and total current collected (solid angle). 4. q / m
resolution
Since the cyclotron frequency is constant the (q/m) resolution is dependent only on the dimension of the entrance slit, or the A~. An ion entering Aw has a velocity component along the E field of VoA~. Its displacement along the z-axis would be
Az = ½(q/m) E T 2 - VoAc~To.
I would be displaced by dz' from the ideal point of impingement where
Az' = VoAc~Tc =- (Vo27c/B) (m/q) Acz,
COLLECTOR z
Fig. 2. Set-up of proposed analyzer.
(S)
and thus the collector dimension along the z-axis should be 2Az' or A z + A z ' . Since mass dispersion is linear, it is interesting to examine in detail (here Az is taken for A~ = 0):
Az'
--=
Az
B VoA~--. roe
(9)
The linear dependence of Az'/Az on VoAo~ results in a resolution loss for high velocity ions and large acceptance angles. Therefore, a small d a in the z direction is required when analyzing energetic ions. As a numerical example, taking 2 k e V deuterons, Vo = 4 . 3 7 x 1 0 s m/s, A~ for a 5 r a m slit at 5 0 0 m m distance is 5 x 10- 3 rad, B = 910 G (corresponding to a 1 0 0 m m radius for 2 k e V deuterons) and E = 4.05 x 103 V/m (corresponding to z = 200 m m for D + ions) we get
Az'/Az = 4.8x 10 .2
\
(7)
~ 5~o.
(10)
It is een that with moderate E and B fields, small dimensions and an appreciable solid angle, plasmas of low Z materials can be analyzed,
237
S T A T I C F I E L D MASS S P E C T R O G R A P H
free tube and locate the collectors at the edge of the field, which is an advantage.
6. Discussion
COLLECTOR
Fig. 3. A 540 ° deflection analyzer.
5. Proposed design parameters For plasmas containing D, T, C, Li, O, having velocities up to 4.5 x 105 m/s, the proposed fields are B = 9 1 0 G and E = 4 x 103V/re. These fields yield a maximal gyration radius of 100 mm and a 200 mm z displacement for D + ions. Energy resolution is 1% and mass resolution about 5%, for an entrance aperture of 5 mm diameter located at a distance of 500 mm from the source. Some perturbation of the field will be caused by the field-free entrance tube, but it is assumed that it will be small or negligible. Using the geometry shown in fig. 3, a 540 ° deflection permits one to omit the field-
The proposed static spectrograph has the following advantages over previously used analyzers: a) The fields involved are static and simple. b) The integral of the ion current in each collector represents the total yield of the collected q/rn. c) Since ions here gain energy along the E field, it may be possible to use an ion multiplier or a solid state detector as the collector. This would facilitate low current counting (ion counting), permitting a decrease in the collection solid angle and improved resolution. This research is supported by the United StatesIsrael Binational Science Foundation, Jerusalem, Israel.
References ~) 2) a) 4) s)
J. N. Olsen et al., J. Appl. Phys. 44, no. 5 (1973) 2275. j. j. Thompson, Phil. Mag. 21 (1911) 225. D. B. Van Hulsteyn et al., Rev. Sci. Instr. 45 (1974) 819. M. Oron et al., Rev. Sci. Instr. 44 (1973) 1293. M. Oron, Thesis (Univ. o f Rochester, N.Y., 1975).
V I I I , MASS A N A L Y Z E R