- Email: [email protected]
Charge compensated ion beam propagation in a reactor sized chamber
Nuclear Instruments and Methods in Physics Research A 415 (1998) 439—443
Charge compensated ion beam propagation in a reactor sized chamber J.L. Vay*, C. Deutsch LPGP1, BaL t. 212 Universite& Paris XI, 91405 Orsay, France
Abstract Final ion propagation in the space charge compensated scheme (ITEP) is contrasted to Hylife II scenario. A fully electromagnetic particle in cell—Monte Carlo code (PIC—MCC) is considered for the ballistic transport of intense ion beams in a reaction chamber field with Flibe gas surrounding a pellet with a thermonuclear fuel in it. For the latter, we identify a partial beam neutralization only through electron background. The former displays an acceptable focusing on the pellet. The background electron temperature has a significant influence on beam minimum radius. Transverse emittance is given specific attention. ( 1998 Elsevier Science B.V. All rights reserved. PACS: 28.50 Re; 41.75 Ak; 41.80 Gg; 29.27 Bd
Energetic and intense nonrelativistic (» &c ) " 3 heavy-ion beams focused on tiny and hollow fusion targets with a thermonuclear deuterium # tritium (DT) fuel are now routinely considered for producing an inertially driven compression [1—3]. Up to now, a lot of attention has been given to ion—target interaction [1—3] and beam dynamics as well [2—4]. However, in order to evaluate carefully the characteristics and merits of the whole concept elaborating on the scheme of heavy-ion driven inertial fusion one also needs a complete end to end and multi-dimensional simulation of the ion beams successive manipulation all along their way, from the * Correspondence address: Lawrence Berkeley National Laboratory, Bldg. 47/112, 1 Cyclotron Road, Berkeley, CA 94720, USA. Fax: #1 510 486 5392; e-mail: [email protected]. 1 Associe´ au CNRS.
ion sources to the pellet. In particular, we intend paying thorough attention to the ion beam propagation in the vicinity of the target within the reactor chamber, where the thermonuclear fusion energy is mostly converted into energetic neutrons and hard X-rays. Outstanding engineering and system studies have already been devoted to the reaction chamber part of the whole accelerator scenario [1,5]. However, the extreme technical performances imposed upon the materials involved as well as the very severe time constraints requested by an implosion duration in the several tens of nanosecond range demand that the relevant interaction physics be carefully cleared up, at a basic level. Specifically, one has to check that the inflight stability with no emittance growth can be secured for the propagation of kiloamperes of intense ion beams under the
0168-9002/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 8 ) 0 0 5 2 0 - 8
V. BEAMS
440
J.L. Vay, C. Deutsch/Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 439—443
influence of their own space charge while interacting with a residual pressure of Flibe (BeF #LiF) 2 gas around the pellet. Due attention has to be paid, particularly to the interaction between the ion beam and the ion debris resulting from the Flibe molecules fragmentation. Electrons due to Flibe ionization shall provide neutralization of the beam space charge while electron stripping of beam ions is expected to enhance their response to remaining space charge. In this context, complete beam neutralization demands a low thermal electron temperature. Toward this goal, we have implemented a fully electromagnetic particle in cell (PIC) code in three dimensions [6] based on specifically developed and novel numerical techniques. We consider intense and monoenergetic Pb` ion beams propagating typically at one-third the speed of light (» "c ), in a converging geometry, to se" 3 cure focalisation on a few millimeter spot size on the target. Fiducial beam parameters of current interest for heavy-ion fusion [1—4] are given in Table 1. Flibe gas consists of 90% BeF and 10% LiF. It 2 is produced by vaporization of the corresponding liquid shielding the chamber walls from the thermonuclear neutrons. The beam-Flibe gas interaction is essentially monitored by Pb` stripping and BeF ionization. 2 The total gas ionization cross-section is p'!4"0.9] *0/ pB%F2#0.1]pL*F out of the linear approximations *0/ *0/ pB%F2"pB% #2pF and pL*F"pL* #pF . *0/ *0/ *0/ *0/ *0/ *0/
In order to release the strong and always pervading space charge constraints on the final focusing of the intense ion beams on the target, one is tempted to reduce it drastically by considering a fully dynamical charge compensation. A significant step in this direction has recently been taken by Koshkarev et al. at ITEP (Moscow) [7] by proposing to accelerate simultaneously positive and negative ions of the same species and opposite charge state at the same energy. The corresponding hardware, outlined in Fig. 1, is built on two identical and parallel low-energy linac sections. Their highest energy (&1 MeV/u.m.a.) extremities are then bent towards each other. Then, successive funneling of positive and negative ions can occur within a third and central linear track parallel to linacs. Eight ion sources of eight of the platinum ions (PtB , PtB , PtB , PtB ) are divided into two 192 194 196 198 symmetrical arrays according to the sign of the ion charge and ion mass. Sources deliver identical parallel beams: 0.15 MeV energy, 0.2 cm radius and the same transverse emittance in each direction. The distance between arrays (measured from the middle axes) is 36 m. The sources of each array are positioned symmetrically with respect to the common axis of symmetry. The heaviest isotope source is located at largest distance from that axis.
Table 1 Ion beam parameters used for contrasting HYLIFE II (positive ions) and ITEP (charge compensated) heavy-ion beams in the reaction chamber M Ion mass @*0/ E Energy ion @*0/ N Flibe density '!4 I Beam average current !7%3!'% Longitudinal current profile R Initial radius */*5 .!9 » Initial thermal speed 5) e Initial transverse rms emittance 9 3.4 Total transverse emittance Focusing distance
200 amu 10 GeV 5]1013 cm~3 3.125 kA Parabolic 6 cm 1]10~4 c 5 mm mrad 20 mm mrad 3.14 m
Fig. 1. The total scheme of the linac for charge compensated acceleration: IS — ion sources; RFQ 1, 2, 3 — injector channels; TMD — transverse matching device; W — Wideroe channel; A1 and A2 — Alvarez channels; all lengths are measured in meters [Koshkarev et al., Fus. Eng. Des. 32—33 (1996) 355].
J.L. Vay, C. Deutsch/Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 439—443
The given negative ions are stable enough to sustain acceleration. Ion losses have to be kept below one percent during acceleration, accumulation and beam transport. In this context, it is a fortunate occurrence that heavy atoms with atomic mass '120 display an enhanced electron affinity. As far as the manipulation of intense ion beams is concerned, advantages appear substantial. The compensation of space charge forces through the simultaneous acceleration of negative ions permits the transport of very intense beams (P5100 TW) in a unique channel. Putting together ions with slightly different mass and same momentum enables a large velocity dispersion ($2%) in the final focusing system while the dispersion of the quantity of motion remains below 0.4%. f In contradistinction to standard accelerator scenarios [7], beam funneling may be operated for several charge to mass ratios q/A. This induces a much smaller dilution in longitudinal phase space. f Compression factor can get significantly enhanced (5200) together with a reduction of the radiofrequency (RF) electric field in view of the small phase space volume and compensation of the longitudinal space charge force. Transverse cross-section of the presently considered space charge compensated beam is given in Fig. 2. In order to focus the charge compensated beam with quadrupole lenses, we take it as a strong but not full overlap of two elliptical beams for each charge state. The systematic comparison detailed below rests on novel particles in cell codes PBIC3D and BPICRZ developed at Orsay [6]. The given simulation parameters are detailed in Table 2. Maximum ion temperature (200 keV) is three times smaller than the noncompensated one (cf. Fig. 3). Apparent dissymmetry between positive and negative is only an artefact due to selecting a given beam cut in Fig. 2. Perveance K parametrizes the beam space charge effects [2]. The electron temperature (Fig. 4) stays much lower than the ion temperature. Presently, the beam self-fields are much weaker than in similar situations with no charge compensation. The plateau is now about
441
Fig. 2. Transverse cross-section of the charge compensated ion beam built on positive (q"1) and negative (q"!1) ions with the same mass, flowing in crossed geometry.
2—3 keV instead of 15 keV with the positive ion beam only. This huge discrepancy highlights that a large fraction of the initial and potential electric energy is transformed into electron kinetic energy in the noncompensated situation. The corresponding rise of electron temperature leads to a less efficient beam neutralization and to an increased emittance due to the residual and nonlinear electrostatic field. Fig. 5 shows e emittance for ion beams of 9 3.4 either charge and the former three propagation scenarios. As far as practical applications to the beam—target interactions are considered, it appears highly gratifying that the time dependence remains rather weak. Finally, it now appears appropriate to extend the diagram beam radius-propagation penetration in the reaction chamber in the laboratory system to the configurations of present concern. In Fig. 6, we thus contrast the usual heavy-ion chamber scenario (Hylife II) [5] to the space charge neutralized [7] for the same beam and chamber parameters (see Table 1). The space charge compensated beam converges to a much smaller radius &2.5 mm whereas that of the noncompensated Hylife II one is &5.7 mm.
V. BEAMS
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J.L. Vay, C. Deutsch/Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 439—443
Table 2 Simulation parameters The grid transverse size follows successively the beam convergence and divergence, which optimizes transverse resolution. The beam center is taken at longitudinal coordinate Z"0. A. ºncompensated beam (HYLIFE-II) f Cylindrical symmetry RZ f Z "!1 m, Z "50 cm .*/ .!9 f R "0, R "52 cm N 10.2 cm N 10.2 cm N 52 cm .*/ .!9 at t"0 ns 34.5 ns 39.5 ns 69.45 ns f NR meshes"320 f NZ meshes"60 f Nb beam macroparticles"5000 f Nb macroelectrons " 0 at t"0 and up to &50 000 B. Compensated beam f 3DXYZ with symmetry planes XZ and YZ f Z "!1 m, Z "60 cm .*/ .!9 f X "½ "0, X "½ "52 cm N 6 cm N 6 cm N 52 cm .*/ .*/ .!9 .!9 at t"0 ns 34.5 ns 39.5 ns 69.45 ns f Nx meshes " NY meshes " 150 f NZ meshes " 60 f Nb beam macroparticles #"40 000 f Nb beam macroparticles !"40 000 f Nb macroelectrons " 0 at t"0 and up to &8 000 000
Fig. 3. Time evolution of ion temperatures (over entire beam) for positive and negative ion beams in several distinct propagation schemes.
Fig. 4. Same caption as in Fig. 3 for electron temperature.
Obviously, charge compensation appears to be of great help in securing adequate beam focusing on the target. Electromagnetic simulation codes have been developed for investigating the final propagation of intense ion beams in a reaction chamber envisioned for driving inertially a thermonuclear pellet.
They provide access to the dependence of minimum focusing radius with respect to ion beam and Flibe gas stripping cross-sections. These codes have unambiguously highlighted the significance of the background electron temperature for the focusing radius at the pellet. We have also been able to proceed for the very first time to a detailed chamber
J.L. Vay, C. Deutsch/Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 439—443
443
port essentially arises from beam space charge at the chamber entrance. The given initial and potential electro-static energy is then converted to transverse emittance and enhanced temperature of the background electrons. Both effects result in increased beam spot size on the target. The present approach to space charge reduction should be contrasted to other scenarios highlighting the splitting of the initial beam into beam arrays, or the use of co-moving electrons [8—10].
Acknowledgements Fig. 5. Time dependence of e emittance (averaged over the 9 3.4 entire beam) for the propagation of a space charge compensated ion beam in Flibe, void with KO0 and K"0, respectively.
We have derived a lot of benefit from the fruitful discussions with J.C. Adam, R. Bangerter, N. Barboza, D.A. Callahan, A. Friedman, W. Herrmannsfeldt, D.G. Koshkarev, B. Langdon, R. Moir and M. Reiser.
References
Fig. 6. Beam radius in terms of penetration distance.
analysis of a novel accelerator scheme advocating space charge compensation. For this case, it has been shown that a 2.5 mm beam spot size on the pellet is achievable for ballistic transport with parameters of significance for heavy-ion driven inertial fusion. It should be appreciated that the main difference between uncompensated and compensated trans-
[1] Proc. Int. Symp. on Heavy Ion Inertial Fusion, 6—9 September 1995, Princeton, USA, Fus. Eng. Des. 32—33, 1996, p. 1. [2] M. Reiser, Theory and Design of Charged Particle Beams, Wiley, New York, 1994. [3] C. Deutsch, Ann. Phys. Fr. 11 (1986) and also Fusion Technol. 29 (1996) 306. [4] A. Friedman, D.P. Grote, I. Haber, Phys. Fluids B 4 (1992) 2203. [5] R.W. Moir, Part. Accel. 37—38 (1992) 459 and also Fusion Technol. 19 (1991) 617. [6] J.-Vay, C. Deutsch, Fus. Eng. Des. 32—33 (1996) 467 and J.-Vay, Ph.D. Thesis, Universite´ Paris XI, September 1996. [7] D.G. Koshkarev, Nuovo Cimento 106A (1993) 1567 also A.V. Barkhudaryan, D.G. Koshkarev, P.P. Zenkevich, Nuovo Cimento 106A (1993) 1751. [8] D.A. Callahan, A.B. Langdon, Fus. Eng. Des. 32/33 (1996) 441. [9] K. Hahn, E. Lee, Fus. Eng. Des. 32/33 (1996) 417. [10] A. Tauschwitz et al., Fus. Eng. Des. 32/33 (1996) 493.
V. BEAMS
Charge compensated ion beam propagation in a reactor sized chamber J.L. Vay*, C. Deutsch LPGP1, BaL t. 212 Universite& Paris XI, 91405 Orsay, France
Abstract Final ion propagation in the space charge compensated scheme (ITEP) is contrasted to Hylife II scenario. A fully electromagnetic particle in cell—Monte Carlo code (PIC—MCC) is considered for the ballistic transport of intense ion beams in a reaction chamber field with Flibe gas surrounding a pellet with a thermonuclear fuel in it. For the latter, we identify a partial beam neutralization only through electron background. The former displays an acceptable focusing on the pellet. The background electron temperature has a significant influence on beam minimum radius. Transverse emittance is given specific attention. ( 1998 Elsevier Science B.V. All rights reserved. PACS: 28.50 Re; 41.75 Ak; 41.80 Gg; 29.27 Bd
Energetic and intense nonrelativistic (» &c ) " 3 heavy-ion beams focused on tiny and hollow fusion targets with a thermonuclear deuterium # tritium (DT) fuel are now routinely considered for producing an inertially driven compression [1—3]. Up to now, a lot of attention has been given to ion—target interaction [1—3] and beam dynamics as well [2—4]. However, in order to evaluate carefully the characteristics and merits of the whole concept elaborating on the scheme of heavy-ion driven inertial fusion one also needs a complete end to end and multi-dimensional simulation of the ion beams successive manipulation all along their way, from the * Correspondence address: Lawrence Berkeley National Laboratory, Bldg. 47/112, 1 Cyclotron Road, Berkeley, CA 94720, USA. Fax: #1 510 486 5392; e-mail: [email protected]. 1 Associe´ au CNRS.
ion sources to the pellet. In particular, we intend paying thorough attention to the ion beam propagation in the vicinity of the target within the reactor chamber, where the thermonuclear fusion energy is mostly converted into energetic neutrons and hard X-rays. Outstanding engineering and system studies have already been devoted to the reaction chamber part of the whole accelerator scenario [1,5]. However, the extreme technical performances imposed upon the materials involved as well as the very severe time constraints requested by an implosion duration in the several tens of nanosecond range demand that the relevant interaction physics be carefully cleared up, at a basic level. Specifically, one has to check that the inflight stability with no emittance growth can be secured for the propagation of kiloamperes of intense ion beams under the
0168-9002/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 8 ) 0 0 5 2 0 - 8
V. BEAMS
440
J.L. Vay, C. Deutsch/Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 439—443
influence of their own space charge while interacting with a residual pressure of Flibe (BeF #LiF) 2 gas around the pellet. Due attention has to be paid, particularly to the interaction between the ion beam and the ion debris resulting from the Flibe molecules fragmentation. Electrons due to Flibe ionization shall provide neutralization of the beam space charge while electron stripping of beam ions is expected to enhance their response to remaining space charge. In this context, complete beam neutralization demands a low thermal electron temperature. Toward this goal, we have implemented a fully electromagnetic particle in cell (PIC) code in three dimensions [6] based on specifically developed and novel numerical techniques. We consider intense and monoenergetic Pb` ion beams propagating typically at one-third the speed of light (» "c ), in a converging geometry, to se" 3 cure focalisation on a few millimeter spot size on the target. Fiducial beam parameters of current interest for heavy-ion fusion [1—4] are given in Table 1. Flibe gas consists of 90% BeF and 10% LiF. It 2 is produced by vaporization of the corresponding liquid shielding the chamber walls from the thermonuclear neutrons. The beam-Flibe gas interaction is essentially monitored by Pb` stripping and BeF ionization. 2 The total gas ionization cross-section is p'!4"0.9] *0/ pB%F2#0.1]pL*F out of the linear approximations *0/ *0/ pB%F2"pB% #2pF and pL*F"pL* #pF . *0/ *0/ *0/ *0/ *0/ *0/
In order to release the strong and always pervading space charge constraints on the final focusing of the intense ion beams on the target, one is tempted to reduce it drastically by considering a fully dynamical charge compensation. A significant step in this direction has recently been taken by Koshkarev et al. at ITEP (Moscow) [7] by proposing to accelerate simultaneously positive and negative ions of the same species and opposite charge state at the same energy. The corresponding hardware, outlined in Fig. 1, is built on two identical and parallel low-energy linac sections. Their highest energy (&1 MeV/u.m.a.) extremities are then bent towards each other. Then, successive funneling of positive and negative ions can occur within a third and central linear track parallel to linacs. Eight ion sources of eight of the platinum ions (PtB , PtB , PtB , PtB ) are divided into two 192 194 196 198 symmetrical arrays according to the sign of the ion charge and ion mass. Sources deliver identical parallel beams: 0.15 MeV energy, 0.2 cm radius and the same transverse emittance in each direction. The distance between arrays (measured from the middle axes) is 36 m. The sources of each array are positioned symmetrically with respect to the common axis of symmetry. The heaviest isotope source is located at largest distance from that axis.
Table 1 Ion beam parameters used for contrasting HYLIFE II (positive ions) and ITEP (charge compensated) heavy-ion beams in the reaction chamber M Ion mass @*0/ E Energy ion @*0/ N Flibe density '!4 I Beam average current !7%3!'% Longitudinal current profile R Initial radius */*5 .!9 » Initial thermal speed 5) e Initial transverse rms emittance 9 3.4 Total transverse emittance Focusing distance
200 amu 10 GeV 5]1013 cm~3 3.125 kA Parabolic 6 cm 1]10~4 c 5 mm mrad 20 mm mrad 3.14 m
Fig. 1. The total scheme of the linac for charge compensated acceleration: IS — ion sources; RFQ 1, 2, 3 — injector channels; TMD — transverse matching device; W — Wideroe channel; A1 and A2 — Alvarez channels; all lengths are measured in meters [Koshkarev et al., Fus. Eng. Des. 32—33 (1996) 355].
J.L. Vay, C. Deutsch/Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 439—443
The given negative ions are stable enough to sustain acceleration. Ion losses have to be kept below one percent during acceleration, accumulation and beam transport. In this context, it is a fortunate occurrence that heavy atoms with atomic mass '120 display an enhanced electron affinity. As far as the manipulation of intense ion beams is concerned, advantages appear substantial. The compensation of space charge forces through the simultaneous acceleration of negative ions permits the transport of very intense beams (P5100 TW) in a unique channel. Putting together ions with slightly different mass and same momentum enables a large velocity dispersion ($2%) in the final focusing system while the dispersion of the quantity of motion remains below 0.4%. f In contradistinction to standard accelerator scenarios [7], beam funneling may be operated for several charge to mass ratios q/A. This induces a much smaller dilution in longitudinal phase space. f Compression factor can get significantly enhanced (5200) together with a reduction of the radiofrequency (RF) electric field in view of the small phase space volume and compensation of the longitudinal space charge force. Transverse cross-section of the presently considered space charge compensated beam is given in Fig. 2. In order to focus the charge compensated beam with quadrupole lenses, we take it as a strong but not full overlap of two elliptical beams for each charge state. The systematic comparison detailed below rests on novel particles in cell codes PBIC3D and BPICRZ developed at Orsay [6]. The given simulation parameters are detailed in Table 2. Maximum ion temperature (200 keV) is three times smaller than the noncompensated one (cf. Fig. 3). Apparent dissymmetry between positive and negative is only an artefact due to selecting a given beam cut in Fig. 2. Perveance K parametrizes the beam space charge effects [2]. The electron temperature (Fig. 4) stays much lower than the ion temperature. Presently, the beam self-fields are much weaker than in similar situations with no charge compensation. The plateau is now about
441
Fig. 2. Transverse cross-section of the charge compensated ion beam built on positive (q"1) and negative (q"!1) ions with the same mass, flowing in crossed geometry.
2—3 keV instead of 15 keV with the positive ion beam only. This huge discrepancy highlights that a large fraction of the initial and potential electric energy is transformed into electron kinetic energy in the noncompensated situation. The corresponding rise of electron temperature leads to a less efficient beam neutralization and to an increased emittance due to the residual and nonlinear electrostatic field. Fig. 5 shows e emittance for ion beams of 9 3.4 either charge and the former three propagation scenarios. As far as practical applications to the beam—target interactions are considered, it appears highly gratifying that the time dependence remains rather weak. Finally, it now appears appropriate to extend the diagram beam radius-propagation penetration in the reaction chamber in the laboratory system to the configurations of present concern. In Fig. 6, we thus contrast the usual heavy-ion chamber scenario (Hylife II) [5] to the space charge neutralized [7] for the same beam and chamber parameters (see Table 1). The space charge compensated beam converges to a much smaller radius &2.5 mm whereas that of the noncompensated Hylife II one is &5.7 mm.
V. BEAMS
442
J.L. Vay, C. Deutsch/Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 439—443
Table 2 Simulation parameters The grid transverse size follows successively the beam convergence and divergence, which optimizes transverse resolution. The beam center is taken at longitudinal coordinate Z"0. A. ºncompensated beam (HYLIFE-II) f Cylindrical symmetry RZ f Z "!1 m, Z "50 cm .*/ .!9 f R "0, R "52 cm N 10.2 cm N 10.2 cm N 52 cm .*/ .!9 at t"0 ns 34.5 ns 39.5 ns 69.45 ns f NR meshes"320 f NZ meshes"60 f Nb beam macroparticles"5000 f Nb macroelectrons " 0 at t"0 and up to &50 000 B. Compensated beam f 3DXYZ with symmetry planes XZ and YZ f Z "!1 m, Z "60 cm .*/ .!9 f X "½ "0, X "½ "52 cm N 6 cm N 6 cm N 52 cm .*/ .*/ .!9 .!9 at t"0 ns 34.5 ns 39.5 ns 69.45 ns f Nx meshes " NY meshes " 150 f NZ meshes " 60 f Nb beam macroparticles #"40 000 f Nb beam macroparticles !"40 000 f Nb macroelectrons " 0 at t"0 and up to &8 000 000
Fig. 3. Time evolution of ion temperatures (over entire beam) for positive and negative ion beams in several distinct propagation schemes.
Fig. 4. Same caption as in Fig. 3 for electron temperature.
Obviously, charge compensation appears to be of great help in securing adequate beam focusing on the target. Electromagnetic simulation codes have been developed for investigating the final propagation of intense ion beams in a reaction chamber envisioned for driving inertially a thermonuclear pellet.
They provide access to the dependence of minimum focusing radius with respect to ion beam and Flibe gas stripping cross-sections. These codes have unambiguously highlighted the significance of the background electron temperature for the focusing radius at the pellet. We have also been able to proceed for the very first time to a detailed chamber
J.L. Vay, C. Deutsch/Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 439—443
443
port essentially arises from beam space charge at the chamber entrance. The given initial and potential electro-static energy is then converted to transverse emittance and enhanced temperature of the background electrons. Both effects result in increased beam spot size on the target. The present approach to space charge reduction should be contrasted to other scenarios highlighting the splitting of the initial beam into beam arrays, or the use of co-moving electrons [8—10].
Acknowledgements Fig. 5. Time dependence of e emittance (averaged over the 9 3.4 entire beam) for the propagation of a space charge compensated ion beam in Flibe, void with KO0 and K"0, respectively.
We have derived a lot of benefit from the fruitful discussions with J.C. Adam, R. Bangerter, N. Barboza, D.A. Callahan, A. Friedman, W. Herrmannsfeldt, D.G. Koshkarev, B. Langdon, R. Moir and M. Reiser.
References
Fig. 6. Beam radius in terms of penetration distance.
analysis of a novel accelerator scheme advocating space charge compensation. For this case, it has been shown that a 2.5 mm beam spot size on the pellet is achievable for ballistic transport with parameters of significance for heavy-ion driven inertial fusion. It should be appreciated that the main difference between uncompensated and compensated trans-
[1] Proc. Int. Symp. on Heavy Ion Inertial Fusion, 6—9 September 1995, Princeton, USA, Fus. Eng. Des. 32—33, 1996, p. 1. [2] M. Reiser, Theory and Design of Charged Particle Beams, Wiley, New York, 1994. [3] C. Deutsch, Ann. Phys. Fr. 11 (1986) and also Fusion Technol. 29 (1996) 306. [4] A. Friedman, D.P. Grote, I. Haber, Phys. Fluids B 4 (1992) 2203. [5] R.W. Moir, Part. Accel. 37—38 (1992) 459 and also Fusion Technol. 19 (1991) 617. [6] J.-Vay, C. Deutsch, Fus. Eng. Des. 32—33 (1996) 467 and J.-Vay, Ph.D. Thesis, Universite´ Paris XI, September 1996. [7] D.G. Koshkarev, Nuovo Cimento 106A (1993) 1567 also A.V. Barkhudaryan, D.G. Koshkarev, P.P. Zenkevich, Nuovo Cimento 106A (1993) 1751. [8] D.A. Callahan, A.B. Langdon, Fus. Eng. Des. 32/33 (1996) 441. [9] K. Hahn, E. Lee, Fus. Eng. Des. 32/33 (1996) 417. [10] A. Tauschwitz et al., Fus. Eng. Des. 32/33 (1996) 493.
V. BEAMS