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Low energy intense electron beams with extra-low energy spread
Nuclear Instruments and Methods in Physics Research A 340 (1994) 114-117 North-Holland
NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SectionA
Low energy intense electron beams with extra-low energy spread A.V. Aleksandrov a, R. Calabrese b G. Ciullo c, N.S. Dikansky a g. Guidi b,c,, N.C1. Kot a, V.I. Kudelainen a, G. Lamanna c, V.A. Lebedev ~, P.V. Logachov ", L. Tecchio c,a, B. Yang c " Institute of Nuclear Physics, Nouosibirsk, Russian Federation b Dipartimento di Fisica dell'Universith and INFN, 1-44100 Ferrara, Italy c Laboratori Nazionali di Legnaro, 1-35020 Legnaro, Italy a Dipartimento di Fisica Sperimentale dell'Unieersith and INFN, Torino, Italy
Maximum achievable intensity for low energy electron beams is a feature that is not very often compatible with low energy spread. We show that a proper choice of the source and the acceleration optics allows one to match them together. In this scheme, a GaAs photocathode excited by a single-mode infrared laser and adiabatic acceleration in fully magnetised optics enables the production of a low-energy-spread electron beam with relatively high intensity. The technological problems associated with the method are discussed together with its limitations.
1. I n t r o d u c t i o n
2.1. Negative electron affinity photoemission
Some specific applications (electron cooling, low noise rf tubes) for an electron beam at prefixed energy demand a low as possible energy spread. This can be achieved both by producing an electron beam with an intrinsically monoenergetic source and by accelerating the beam in such a way that the effect of repulsion between charges, producing additional spread, is minimized. So the problem of producing a low-energyspread electron beam at a given energy leads to the study of suitable source and acceleration optics. We shall discuss these two items separately in the following sections.
Some p-doped semiconductors (e.g. Ge, Si, GaAs) exhibit the interesting property that deposition of suitable compounds (activators) at their surface lowers the vacuum energy to a level below the bottom of the conduction band in the bulk of the semiconductor. This condition is referred to as negative electron affinity (NEA). The action of activators is to induce a charge dipole at the surface causing a local modification of the energy levels. Usually electro-positive elements such as cesium with the assistance of a stabilizer ( 0 2 and N F 3) are employed. In this state, all electrons that happens to be in the conduction band within a distance of the surface which is shorter than the recombination distance of minority carriers could potentially be emitted. Unfortunately, this is not completely true since trapping of electrons on surface states limits emission and only a certain proportion of the diffusing electrons leave the material. The requirement of high intensity for the source imposes a selection among semiconductors. Thus, a direct band-gap material (e.g. GaAs) should be preferred to one which is not (e.g. Si). Furthermore, GaAs is largely studied nowadays since it allows the production of electron beams with a high degree of polarisation [1]. Electrons excited in the conduction band rapidly relax to the bottom of the band through phonon exchange with the lattice. The tunneling of surface states does not affect the width of the energy distribution
2. S u b t h e r m a l s o u r c e
Photoemission from semiconductors yields an electron beam with a lower energy spread than thermoemission. Moreover, the energy spread at the source exhibits good constancy over a wide range of current. On the strength of these features, photoemission from semiconductors is the basis for a prototype high-intensity subthermal source. The following subsections give details on photoemission from semiconductors and the choice of the most appropriate light source.
* Corresponding author.
0168-9002/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved SSDI 0 1 6 8 - 9 0 0 2 ( 9 3 ) E 0 9 9 6 - 6
A. V. Aleksandrov et al. / Nucl. Instr. and Meth. in Phys. Res. A 340 (1994) 114-117
very much and an electron beam with low energy spread is produced. Further details on the mechanism of photoemission can be found in the book of Bell [2]. The layer of activants which guarantees the maintainance of the N E A condition is very sensitive to contamination, resulting in a degradation of quantum yield with time [3]. Once the surface is polluted, photoemission is inhibited and the cathode must be regenerated [3]. Operation in the U H V is therefore needed; yet it turns out that even in the range of 10-11 mbar, degradation of the source still occurs and this presently constitutes the major drawback of photoemission by N E A materials. In particular, the most attractive N E A photoemitter, i.e. GaAs, seems to be most affected by degradation. Decay is mostly effective at high current [4] and, for 1 mA current over a few mm 2 beam size, the e-folding lifetime only seldomly exceeds 1 h. This snag severely limits the potentiality of the cathode. Some authors have succeeded in attenuating the decay of quantum efficiency by continuously feeding cesium [5]. This method can be used profitably in some applications, but extensive operation with continuous cesiation leads to the formation of a cesium layer on the electrodes and may cause sparking when high-voltage is needed. Very recently, the feasibility of using a GaAs source without decay was demonstrated with no cesium supply other than during initial cathode activation [6]. It was also demonstrated that the main requirement for achieving such a result was the maintainance of the system in a vacuum for a long time. A research program devoted to speeding up the "seasoning" of the system should therefore be initiated.
2.2. Light sources f o r N E A photoemission
Laser light can be used profitably for photoemission due to its extremely high brillance and excellent control over the space-time profile. The choice of the most appropriate frequency is dictated by the following considerations: it is clear that the higher the electrons are excited in the conduction band the less efficient is the relaxation to the bottom of the band. Therefore, a photon energy slightly greater than the energy of the band-gap would lead to the best results. Unfortunately, quantum efficiency increases with the photon frequency roughly according to Y = a ( h v - E g ) 1/2 [2] and, just beyond the threshold, this has a very low value. For GaAs a choice which is a compromise between these two antithetic requests is A = 800 rim. Another important factor to be taken into account is the number of longitudinal modes in the cavity of the laser. It has been demonstrated that multi-mode lasers produce beams whose energy distribution is several eV wide [7,8], which is much broader than those produced
115
by thermoemission. In this case, the subthermal property of a N E A source is lost. This effect was explained by considering the time profile of a multi-mode laser to be a sequence of power peaks. These produce an electron beam with many high-density charge clusters which rapidly relax giving rise to a broad distribution. With a single-mode laser this phenomenon is prevented and a beam with low energy spread ( < 100 meV) was observed up to 100 t~A [9].
3. Acceleration optics Once a source has emitted a beam with low energy spread the problem arises of handling and accelerating it up to kinetic energy W. Owing to charge repulsion, two kinds of relaxation occur. The first is due to the transfer of energy from the transverse degrees of freedom to the longitudinal one. This relaxation is referred to as transverse-longitudinal relaxation [9]. The remedy is to impose an axial magnetic field, the strength of which must be high enough to decouple the dynamics of electrons on the transverse degrees from that in the longitudinal axis. The magnetic field isolates the longitudinal axis, repulsion between charges causes the beam to relax longitudinally. This is called longitudinallongitudinal relaxation [9]. The remedy for this effect has been studied extensively in recent years. It was found that, if acceleration is imparted slowly, the energy distribution at the end of the acceleration section results in a lower energy spread relative to a conventional fast case [10]. This suggests the name adiabatic for the slow acceleration. We shall discuss the two relaxations in terms of the remedies one has to use to counteract their effects.
3.1. Magnetic field
The longitudinal energy spread in the frame comoving with the beam AEII0 is related to that in the laboratory system AEII through the formula [9]:
AEI~0 A Ell -
4W '
where W is the average kinetic energy of the beam. In the transverse plane the situation is different, the spread AE±0 being a constant of the motion. Thus, acceleration makes the beam unisotropic and a net amount of energy is transferred to the longitudinal axis through intrabeam collisions. A magnetic field substantially changes the dynamics of the electrons. The following formula is a purely experimental relationship II. CONTRIBUTIONS
A.V. Aleksandrot et al. / Nucl. Instr. and Meth. in Phys. Res. A 340 (1994) 114-117
116
for the rate of increase of AEII due to t r a n s v e r s e longitudinal relaxation [11]:
'~4.5 [.~
d(AE,,)
<35
dz
"e3j~ =
W
( C l exp
--
25
C2 e2 >.
p(eanl/2 + C3AEII )
w h e r e p is the L a r m o r radius, A E ± the transverse energy spread, e and m the electron's charge and mass, j the c u r r e n t density and p the average radius of the helixes described by electrons. T h e values C l = 23.5, C 2 = 1.30 and C 3 = 0.17 arc results of the fit. The transverse energy spread at the source A E • o is not yet known, t h o u g h its m e a s u r e m e n t is u n d e r consideration. W h e n the magnetic field is strong e n o u g h so that the average radius p is m u c h s h o r t e r t h a n the m e a n interparticle distance ( ~ hi/3), a d a m p i n g of t r a n s v e r s e longitudinal relaxation is reached. It was found that a 3 kG magnetic field allowed control of the relaxation over an intense b e a m (1 m A c u r r e n t and 2 m m diameter) within a length of the acceleration optics of 2 m
[91.
3.2. Adiabatic acceleration T h e effect of the axial m a g n e t i c field is to decouple the transverse degrees of f r e e d o m from the longitudinal direction. In this o n e - d i m e n s i o n a l system, repulsion b e t w e e n charges causes a f u r t h e r increase in the longitudinal spread according to [9]:
AEI~ + CeZn l/~, AEI4- 4W where C is a c o n s t a n t d e p e n d i n g on the way in which acceleration is imparted. It was d e m o n s t r a t e d that the constant C attains smaller values w h e n electrons are accelerated slowly. In o r d e r to illustrate the concept of adiabatic acceleration we resort to the following simple example. T h e energy spread AW m e a s u r e d by a movable energy analyser at different longitudinal positions is plotted in Fig. 1 for two situations. Curve 1 records the values for fast acceleration up to W = 800 eV, taking place at position A. T h e same final energy W was o b t a i n e d in a two-stage aeceleratkm (curve 2) at A and B; the interm e d i a t e energy at A was W = 250 eV. It is clear from the figure that the two-stage acceleration produces a lower energy spread. This is certainly an i m p r o p e r way of accelerating an electron beam, but it suggests that gradually i m p a r t e d acceleration would lead to a b e t t e r result. A n estimate for the adiabaticity of acceleration must c o m p a r e the cooling time provided by kinematic contraction to the plasma period, this b e i n g the charac-
~15 '13
~, 0.5" A E Z
!
!
|
50
70
90
Axial coordinate z (cm) Fig. 1. Relationship between the normalized longitudinal energy spread AEll/e2n 1/3 versus the z-coordinate for fast acceleration (1) and two-stage acceleration with intermediate drift space (2); I = 100 ~A, W = 800 eV, B - 3 kG for the oxide thermocathode. A - position of the first acceleration Gap, B - position of the second.
teristic time t a k e n by the b e a m to attain complete relaxation [9]. Thus, A=
1 d(AEII) . - ~o0AEII dt
w h e n A < 1 the acceleration adiabatic structure is defined as adiabatic. T h e r e are mainly two limitations associated with the use of adiabatic acceleration. Firstly, the low electric field at the c a t h o d e caused by an adiabatic structure does not allow the effect of space-charge to be overcome and the c u r r e n t would as a result be limited. O n e can cope with this using a fast initial acceleration to extract electrons followed by an adiabatic stage. At first sight, it might seem that the slower the acceleration the lower the spread, but this is not completely true. We have in fact assumed the system to be one-dimensional, i.e. totally decoupled from the transverse coordinates, a n d this c a n n o t work for an arbitrarily long structure. T h e effect of a strong m a g n e t i c field is damping, not suppression, so that for too long an adiabatic structure t r a n s v e r s e - l o n g i t u d i n a l relaxation b e c o m e s dominant. With a p r o p e r choice of the length an adiabatic section accelerates a b e a m to a given energy with minimal energy spread.
4. Conclusions W h e n all the specifications discussed in the preceding sections are c o m b i n e d together, the p r o d u c t i o n of relatively high-intensity electron b e a m s with low energy spread is possible. A useful estimate for the b e a m
A.V. Aleksandrov et al. /Nucl. Instr. and Meth. in Phys. Res. A 340 (1994) 114-117 t e m p e r a t u r e which allows for t h e intensity of the b e a m is the p l a s m a p a r a m e t e r F defined as [12]:
(4_~_~)1/3e2nl/3 F=
kT
W h e n a G a A s p h o t o c a t h o d e is excited by a single-mode laser (A = 800 n m ) a n d the electron b e a m p r o d u c e d is a c c e l e r a t e d by an adiabatic section i m m e r s e d in a strong axial m a g n e t i c field, a plasma p a r a m e t e r g r e a t e r t h a n unity can b e achieved [10]. This m e a n s t h a t the p o t e n t i a l energy of the b e a m exceeds the t h e r m a l energy. A b e a m with t h e s e f e a t u r e s would b e of great interest in several r e s e a r c h areas.
References [1] T. Maruyama et al., Appl. Phys. Lett. 55 (1989) 1686. [2] R.L. Bell, Negative Electron Devices (Clarendon, Oxford, 1973). [3] D.T. Pierce, R.J. Celotta, G.-C. Wang, W.N. Unertl, A. Galejs, C.E. Kuyatt and S.R. Mielczarek, Rev. Sci. Instr. 51 (1980) 478.
117
[4] R. Calabrese, V. Guidi, G. Lamanna and L. Tecchio, J. Phys. III France 2 (1992) 473. [5] F.C. Tang, M.S. Lubelle, K. Rubin and A. Vasilakis, Rev. Sci. Instr. 57 (1986) 3004. [6] R. Calabrese, G. Ciullo, V. Guidi, G. Lamanna, P. Lenisa, B. Maciga, L. Tecchio and B. Yang, to be published in Rev. Sci. Instr. [7] U. Kolak, M. Donath, K. Ertl, H. Liebl and V. Dose, Rev. Sci. Instr. 59 (1988) 1933. [8] A.V. Aleksandrov, R. Calabrese, N.S. Dikansky, V. Guidi, N.Ch. Kot, V.I. Kudelainen, V.A. Lebedev, P.V. Logachov and L. Tecchio, Phys. Lett. A 163 (1992) 77. [9] A.V. Aleksandrov, R. Calabrese, G. Ciullo, V. Guidi, N.Ch. Kot, V.I. Kudelainen, G. Lamanna, V.A. Lebedev, P.V. Logachov and L. Teechio, Phys. Rev. A 46 (1992) 6628. [10] A.V. Aleksandrov, R. Calabrese, N.S. Dikansky, V. Guidi, N.Ch. Kot, V.I. Kudelainen, V.A. Lebedev, P.V. Logachov and L. Tecchio, Europhys. Lett. 18 (1992) 1133. [11] A.V. Aleksandrov, R. Calabrese, G. Ciullo, V. Guidi, N.Ch. Kot, V.I. Kudelainen, V.A. Lebedev, P.V. Logachov, L. Tecchio and B. Yang, Meas. Sci. and Technol. 4 (1993) 764. [12] S. Ishimaru, Rev. Mod. Phys. 54 (1982) 1017.
II. CONTRIBUTIONS
NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SectionA
Low energy intense electron beams with extra-low energy spread A.V. Aleksandrov a, R. Calabrese b G. Ciullo c, N.S. Dikansky a g. Guidi b,c,, N.C1. Kot a, V.I. Kudelainen a, G. Lamanna c, V.A. Lebedev ~, P.V. Logachov ", L. Tecchio c,a, B. Yang c " Institute of Nuclear Physics, Nouosibirsk, Russian Federation b Dipartimento di Fisica dell'Universith and INFN, 1-44100 Ferrara, Italy c Laboratori Nazionali di Legnaro, 1-35020 Legnaro, Italy a Dipartimento di Fisica Sperimentale dell'Unieersith and INFN, Torino, Italy
Maximum achievable intensity for low energy electron beams is a feature that is not very often compatible with low energy spread. We show that a proper choice of the source and the acceleration optics allows one to match them together. In this scheme, a GaAs photocathode excited by a single-mode infrared laser and adiabatic acceleration in fully magnetised optics enables the production of a low-energy-spread electron beam with relatively high intensity. The technological problems associated with the method are discussed together with its limitations.
1. I n t r o d u c t i o n
2.1. Negative electron affinity photoemission
Some specific applications (electron cooling, low noise rf tubes) for an electron beam at prefixed energy demand a low as possible energy spread. This can be achieved both by producing an electron beam with an intrinsically monoenergetic source and by accelerating the beam in such a way that the effect of repulsion between charges, producing additional spread, is minimized. So the problem of producing a low-energyspread electron beam at a given energy leads to the study of suitable source and acceleration optics. We shall discuss these two items separately in the following sections.
Some p-doped semiconductors (e.g. Ge, Si, GaAs) exhibit the interesting property that deposition of suitable compounds (activators) at their surface lowers the vacuum energy to a level below the bottom of the conduction band in the bulk of the semiconductor. This condition is referred to as negative electron affinity (NEA). The action of activators is to induce a charge dipole at the surface causing a local modification of the energy levels. Usually electro-positive elements such as cesium with the assistance of a stabilizer ( 0 2 and N F 3) are employed. In this state, all electrons that happens to be in the conduction band within a distance of the surface which is shorter than the recombination distance of minority carriers could potentially be emitted. Unfortunately, this is not completely true since trapping of electrons on surface states limits emission and only a certain proportion of the diffusing electrons leave the material. The requirement of high intensity for the source imposes a selection among semiconductors. Thus, a direct band-gap material (e.g. GaAs) should be preferred to one which is not (e.g. Si). Furthermore, GaAs is largely studied nowadays since it allows the production of electron beams with a high degree of polarisation [1]. Electrons excited in the conduction band rapidly relax to the bottom of the band through phonon exchange with the lattice. The tunneling of surface states does not affect the width of the energy distribution
2. S u b t h e r m a l s o u r c e
Photoemission from semiconductors yields an electron beam with a lower energy spread than thermoemission. Moreover, the energy spread at the source exhibits good constancy over a wide range of current. On the strength of these features, photoemission from semiconductors is the basis for a prototype high-intensity subthermal source. The following subsections give details on photoemission from semiconductors and the choice of the most appropriate light source.
* Corresponding author.
0168-9002/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved SSDI 0 1 6 8 - 9 0 0 2 ( 9 3 ) E 0 9 9 6 - 6
A. V. Aleksandrov et al. / Nucl. Instr. and Meth. in Phys. Res. A 340 (1994) 114-117
very much and an electron beam with low energy spread is produced. Further details on the mechanism of photoemission can be found in the book of Bell [2]. The layer of activants which guarantees the maintainance of the N E A condition is very sensitive to contamination, resulting in a degradation of quantum yield with time [3]. Once the surface is polluted, photoemission is inhibited and the cathode must be regenerated [3]. Operation in the U H V is therefore needed; yet it turns out that even in the range of 10-11 mbar, degradation of the source still occurs and this presently constitutes the major drawback of photoemission by N E A materials. In particular, the most attractive N E A photoemitter, i.e. GaAs, seems to be most affected by degradation. Decay is mostly effective at high current [4] and, for 1 mA current over a few mm 2 beam size, the e-folding lifetime only seldomly exceeds 1 h. This snag severely limits the potentiality of the cathode. Some authors have succeeded in attenuating the decay of quantum efficiency by continuously feeding cesium [5]. This method can be used profitably in some applications, but extensive operation with continuous cesiation leads to the formation of a cesium layer on the electrodes and may cause sparking when high-voltage is needed. Very recently, the feasibility of using a GaAs source without decay was demonstrated with no cesium supply other than during initial cathode activation [6]. It was also demonstrated that the main requirement for achieving such a result was the maintainance of the system in a vacuum for a long time. A research program devoted to speeding up the "seasoning" of the system should therefore be initiated.
2.2. Light sources f o r N E A photoemission
Laser light can be used profitably for photoemission due to its extremely high brillance and excellent control over the space-time profile. The choice of the most appropriate frequency is dictated by the following considerations: it is clear that the higher the electrons are excited in the conduction band the less efficient is the relaxation to the bottom of the band. Therefore, a photon energy slightly greater than the energy of the band-gap would lead to the best results. Unfortunately, quantum efficiency increases with the photon frequency roughly according to Y = a ( h v - E g ) 1/2 [2] and, just beyond the threshold, this has a very low value. For GaAs a choice which is a compromise between these two antithetic requests is A = 800 rim. Another important factor to be taken into account is the number of longitudinal modes in the cavity of the laser. It has been demonstrated that multi-mode lasers produce beams whose energy distribution is several eV wide [7,8], which is much broader than those produced
115
by thermoemission. In this case, the subthermal property of a N E A source is lost. This effect was explained by considering the time profile of a multi-mode laser to be a sequence of power peaks. These produce an electron beam with many high-density charge clusters which rapidly relax giving rise to a broad distribution. With a single-mode laser this phenomenon is prevented and a beam with low energy spread ( < 100 meV) was observed up to 100 t~A [9].
3. Acceleration optics Once a source has emitted a beam with low energy spread the problem arises of handling and accelerating it up to kinetic energy W. Owing to charge repulsion, two kinds of relaxation occur. The first is due to the transfer of energy from the transverse degrees of freedom to the longitudinal one. This relaxation is referred to as transverse-longitudinal relaxation [9]. The remedy is to impose an axial magnetic field, the strength of which must be high enough to decouple the dynamics of electrons on the transverse degrees from that in the longitudinal axis. The magnetic field isolates the longitudinal axis, repulsion between charges causes the beam to relax longitudinally. This is called longitudinallongitudinal relaxation [9]. The remedy for this effect has been studied extensively in recent years. It was found that, if acceleration is imparted slowly, the energy distribution at the end of the acceleration section results in a lower energy spread relative to a conventional fast case [10]. This suggests the name adiabatic for the slow acceleration. We shall discuss the two relaxations in terms of the remedies one has to use to counteract their effects.
3.1. Magnetic field
The longitudinal energy spread in the frame comoving with the beam AEII0 is related to that in the laboratory system AEII through the formula [9]:
AEI~0 A Ell -
4W '
where W is the average kinetic energy of the beam. In the transverse plane the situation is different, the spread AE±0 being a constant of the motion. Thus, acceleration makes the beam unisotropic and a net amount of energy is transferred to the longitudinal axis through intrabeam collisions. A magnetic field substantially changes the dynamics of the electrons. The following formula is a purely experimental relationship II. CONTRIBUTIONS
A.V. Aleksandrot et al. / Nucl. Instr. and Meth. in Phys. Res. A 340 (1994) 114-117
116
for the rate of increase of AEII due to t r a n s v e r s e longitudinal relaxation [11]:
'~4.5 [.~
d(AE,,)
<35
dz
"e3j~ =
W
( C l exp
--
25
C2 e2 >.
p(eanl/2 + C3AEII )
w h e r e p is the L a r m o r radius, A E ± the transverse energy spread, e and m the electron's charge and mass, j the c u r r e n t density and p the average radius of the helixes described by electrons. T h e values C l = 23.5, C 2 = 1.30 and C 3 = 0.17 arc results of the fit. The transverse energy spread at the source A E • o is not yet known, t h o u g h its m e a s u r e m e n t is u n d e r consideration. W h e n the magnetic field is strong e n o u g h so that the average radius p is m u c h s h o r t e r t h a n the m e a n interparticle distance ( ~ hi/3), a d a m p i n g of t r a n s v e r s e longitudinal relaxation is reached. It was found that a 3 kG magnetic field allowed control of the relaxation over an intense b e a m (1 m A c u r r e n t and 2 m m diameter) within a length of the acceleration optics of 2 m
[91.
3.2. Adiabatic acceleration T h e effect of the axial m a g n e t i c field is to decouple the transverse degrees of f r e e d o m from the longitudinal direction. In this o n e - d i m e n s i o n a l system, repulsion b e t w e e n charges causes a f u r t h e r increase in the longitudinal spread according to [9]:
AEI~ + CeZn l/~, AEI4- 4W where C is a c o n s t a n t d e p e n d i n g on the way in which acceleration is imparted. It was d e m o n s t r a t e d that the constant C attains smaller values w h e n electrons are accelerated slowly. In o r d e r to illustrate the concept of adiabatic acceleration we resort to the following simple example. T h e energy spread AW m e a s u r e d by a movable energy analyser at different longitudinal positions is plotted in Fig. 1 for two situations. Curve 1 records the values for fast acceleration up to W = 800 eV, taking place at position A. T h e same final energy W was o b t a i n e d in a two-stage aeceleratkm (curve 2) at A and B; the interm e d i a t e energy at A was W = 250 eV. It is clear from the figure that the two-stage acceleration produces a lower energy spread. This is certainly an i m p r o p e r way of accelerating an electron beam, but it suggests that gradually i m p a r t e d acceleration would lead to a b e t t e r result. A n estimate for the adiabaticity of acceleration must c o m p a r e the cooling time provided by kinematic contraction to the plasma period, this b e i n g the charac-
~15 '13
~, 0.5" A E Z
!
!
|
50
70
90
Axial coordinate z (cm) Fig. 1. Relationship between the normalized longitudinal energy spread AEll/e2n 1/3 versus the z-coordinate for fast acceleration (1) and two-stage acceleration with intermediate drift space (2); I = 100 ~A, W = 800 eV, B - 3 kG for the oxide thermocathode. A - position of the first acceleration Gap, B - position of the second.
teristic time t a k e n by the b e a m to attain complete relaxation [9]. Thus, A=
1 d(AEII) . - ~o0AEII dt
w h e n A < 1 the acceleration adiabatic structure is defined as adiabatic. T h e r e are mainly two limitations associated with the use of adiabatic acceleration. Firstly, the low electric field at the c a t h o d e caused by an adiabatic structure does not allow the effect of space-charge to be overcome and the c u r r e n t would as a result be limited. O n e can cope with this using a fast initial acceleration to extract electrons followed by an adiabatic stage. At first sight, it might seem that the slower the acceleration the lower the spread, but this is not completely true. We have in fact assumed the system to be one-dimensional, i.e. totally decoupled from the transverse coordinates, a n d this c a n n o t work for an arbitrarily long structure. T h e effect of a strong m a g n e t i c field is damping, not suppression, so that for too long an adiabatic structure t r a n s v e r s e - l o n g i t u d i n a l relaxation b e c o m e s dominant. With a p r o p e r choice of the length an adiabatic section accelerates a b e a m to a given energy with minimal energy spread.
4. Conclusions W h e n all the specifications discussed in the preceding sections are c o m b i n e d together, the p r o d u c t i o n of relatively high-intensity electron b e a m s with low energy spread is possible. A useful estimate for the b e a m
A.V. Aleksandrov et al. /Nucl. Instr. and Meth. in Phys. Res. A 340 (1994) 114-117 t e m p e r a t u r e which allows for t h e intensity of the b e a m is the p l a s m a p a r a m e t e r F defined as [12]:
(4_~_~)1/3e2nl/3 F=
kT
W h e n a G a A s p h o t o c a t h o d e is excited by a single-mode laser (A = 800 n m ) a n d the electron b e a m p r o d u c e d is a c c e l e r a t e d by an adiabatic section i m m e r s e d in a strong axial m a g n e t i c field, a plasma p a r a m e t e r g r e a t e r t h a n unity can b e achieved [10]. This m e a n s t h a t the p o t e n t i a l energy of the b e a m exceeds the t h e r m a l energy. A b e a m with t h e s e f e a t u r e s would b e of great interest in several r e s e a r c h areas.
References [1] T. Maruyama et al., Appl. Phys. Lett. 55 (1989) 1686. [2] R.L. Bell, Negative Electron Devices (Clarendon, Oxford, 1973). [3] D.T. Pierce, R.J. Celotta, G.-C. Wang, W.N. Unertl, A. Galejs, C.E. Kuyatt and S.R. Mielczarek, Rev. Sci. Instr. 51 (1980) 478.
117
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II. CONTRIBUTIONS