- Email: [email protected]
Numerical simulation of operation of the target with converters on the side surface of the casing
Nuclear Instruments and Methods in Physics Research A 415 (1998) 110—115
Numerical simulation of operation of the target with converters on the side surface of the casing S. Skrypnik*, B. Voronin, V. Vatulin, V. Ermolovich, E. Shaporenko, A. Kazarin, S. Kibkalo Russian Federal Nuclear Center — VNIIEF, Arzamas-16, 607190 Sarov, Nizhni Novgorod Region, Russia
Abstract The presentation gives results of the numerical simulation of the operation of the heavy-ion fusion target rated for the driver energy of the order of 10 MJ with converters positioned on the side surface of the casing wall. The effect of casing design features and ion pulse shape on the target parameters is studied. X-ray transport is described in 2D geometry in the diffusion approximation. The results of preliminary computations of the target for the European Test Facility project (beam energy of the order of 2 MJ) are given. ( 1998 Elsevier Science B.V. All rights reserved.
1. Introduction Most efficient methods for numerical simulation of the processes occurring in inertial fusion targets are integrated computations including simulation of basic processes responsible for target operation and parameters. Inertial fusion targets are, in general, 3D systems and simulation of their operation requires 2D and 3D computer codes. This presentation gives the results of numerical simulation of the cylindrical target with converters on the side walls of the casing (Fig. 1). This target scheme is one of the many possible for use in the heavy-ion fusion project [1—8]. These studies are a continuation of the works begun in 1993, the results of which were reported at the 11th Sympo-
* Corresponding author. Fax: #7 83130 45761; e-mail: vvv—[email protected].
sium on Heavy Ion Fusion in Princeton [9]. The present studies are aimed at a more detailed specification of the target characteristics by a more accurate description of the target physics, a study of the target operation for varying ion beam parameters, and of varying target schemes and dimensions. Larger part of the numerical studies, the results of which are presented here, was conducted for ion beam energy of the order of 10 MJ. Some numerical investigations were conducted as a tentative study of a smaller target for driver energy 2—3 MJ (European project Test Facility) in order to try out the applicability of targets of this type for such experiments. The computations were conducted in 2D formulation using the code package capable to simulate the following processes: f Ion beam interaction with high-temperature plasma and ion beam energy conversion into X-ray energy;
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 0 3 - 8
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S. Skrypnik et al./Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 110–115 Table 1 CTF driver beam parameters
Fig. 1. Scheme of the target with converters positioned on the side surface of the chamber.
f X-ray transport in cavities of various shapes and dimensions; the presented results were obtained using one-group diffusion approximation; f hydrodynamic motion of high-temperature plasma; f thermonuclear burning kinetics. The basic technique [10] developed by the authors implies two mutually orthogonal Eulerian coordinates and one Lagrangian coordinate. This allows natural description of the geometry consisting of a set of layered regions with possible strong sliding shift of one region against another. The technique and code implementing it proved to be an effective tool for studying thermonuclear target implosion. One-temperature technique was used as a basis to develop the technique for solving the system of equations of 3D hydrodynamics and heat conduction with account of ion, electron and photon temperatures, electron—ion—photon relaxation and energy release from thermonuclear reactions.
2. The setup and results of 2D integrated calculations Major part of the numerical studies was carried out for ion beam energy of the order of 10 MJ and
Parameter
Classic driver
Charge symmetric driver
Ion energy (GeV) Ion current per chanel (kA) Pulse duration (ns) Focusing spot area (cm2) Brightness (TV/cm 2) Maximum number of channels Energy in one channel (MJ) Maximum energy (MJ)
10 +1.25 10 0.12 100 +20 0.12 2.4
10 +10 8 0.12 1000 +20 0.8 16
computed parameters of the charge-symmetric accelerator studied at ITEP (Moscow) [11] (Table 1). The computed model of the system is presented in Fig. 2. In contrast to the model presented in Ref. [9], vertical walls are placed at the converter edges to reduce energy release from the converter to the outside. Fig. 3 presents a cross-section of the HIGHSPEED capsule [12] used in this target: Table 2 gives the basic initial parameters of the above systems and integral computed data. Calculations 1—4 were carried out for energy release in the converters set corresponding to the ion beam energy release while being stopped by the converter materials. Calculation 5 was conducted with the outer ion beam set and ion energy conversion calculated by the code [13]. All the data are given for the time of ion pulse termination. Fig. 4 presents a typical pattern of energy distribution in the system from one of the calculations. The figure shows that in spite of extremely complicated energy distribution in the target cavity, quite a homogeneous X-ray field is formed on the capsule surface. More accurate kinetic computations are required to specify the process of X-ray field generation in the target cavity. The target dynamics is considerably affected by the filling target cavity with a light gas of a low atomic number up to densities at which the losses on gas internal energy are low. It considerably “quenches” hydrodynamic processes. A reduction in the ion pulse duration is also favourable for a more homogeneous energy distribution over the capsule.
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S. Skrypnik et al./Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 110–115
Fig. 2. 2D computational model of the target.
Fig. 3. Scheme of HIGHSPEED capsule.
In most calculations ion beam brightness was about 1200 TW/cm2 for the selected converter size, which is somewhat higher than the current ITEF accelerator beam parameters. Conversion efficiency will be a little lower for lower beam brightness (Fig. 5). In this case absolute temperatures in the target cavity will decrease as compared to those presented in Table 2. Along with 10—15 ns monopulse, a time-profiled pulse can be formed for implementation of an energetically more beneficial mode of DT compression in the capsule. Fig. 6 presents one of the possible
ion pulse shapes proposed by Basko and Koshkarev [14]. According to their data, such a shape approximates the profiled pulse shape required for the capsules under consideration. For this system due to considerable increase of the pulse duration by the time when most ion beam energy is deposited, the external converter layer (gold) which must retain X-ray flux within the target cavity appears practically completely released, and a hole is formed in the target wall through which energy leaves the system intensively. As a result, while at the beginning of the main pulse (35 ns) the outgoing flux is less than 10% of the energy release in the converter (larger part of the energy remains in the converter), by 40 ns nearly 40% and by 45 ns nearly 70% of the energy is emitted outside. This leads to a sharp temperature drop in the target cavity (down to the order of 0.2 keV against
Table 2 Target computed data at beam energy 10 MJ N
Beam energy (Q, MJ)
Ion pulse duration (ns)
Gas density in the cavity (g/cm3)
Energy flux from the converter (%Q)
¹ cavity .!9 (keV)
Energy flux onto the capsule (%Q)
1 2 3 4 5
10 10 10 15 10
10 10 5 10 10
0.001 0.02 0.02 0.02 0.02
42 49 49 42 30
0.32 0.33 0.37 0.4 0.3
10 12 11 12 11
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S. Skrypnik et al./Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 110–115
Fig. 6. Profiled ion pulse shape [14].
Fig. 4. Temperature distribution in hohlraum with a cylinderical case and the converters on the lateral side (E "10 GeV, *0/4 E "10 MJ, ¼&1000 TVt/cm2, t"2.7 ns, ¹ &0.3 KeV). "%!. .!9
Fig. 5. Converters efficiency for Pt ions with E"10 MJ and t "10 ns. the converters having composition of Au#(Be, Al, *.1 Ti, Au).
0.3—0.4 keV given a short pulse) and reduction of the energy flux to the capsule. The energy flux to the capsule was only of the order of 5% of the ion beam energy. Due to the pulse duration increase, hydrodynamic effect of the products of the converter scattering into the capsule with inhomogeneity over the angle P /P higher than 10% begins to .!9 .*/ play its role. Maximum effect of the converter scattering on the capsule is at the time &30 ns, i.e., before the receipt of the basic fraction of ion pulse energy. This perturbation considerably affected the DT region compression symmetry (Fig. 7). Thus, in the target design without the filling the casing with light gas, computations demonstrated sharp deterioration of X-ray field parameters for a long pulse, and certain modifications of the target design are necessary to eliminate the detected effects. Some numerical studies were made for a smaller target as tentative investigations of applicability of targets of such type for experiments at the European Test Facility (driver energy 2—3 MJ). The following target dimensions were taken: casing diameter D"6 mm, casing length ¸"7 mm, capsule diameter D "2 mm. #!14 Currently we have no final data on parameters of such accelerators at our disposal and the computations were conducted for the Bi ion pulse (10 GeV) of 2 MJ energy, 4 ns duration, the number of beams were eight with diameters of each beam &2.5 mm.
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S. Skrypnik et al./Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 110–115
Fig. 7. State of DT-fuel (profiling impulse) near the moment of maximum compression. Density distribution.
In the computations the beam brightness is kept on the level of that accepted in the computations for the target of E"10 MJ. For such a target and ion pulse parameters a homogeneous X-ray field of
maximum temperature 0.3—0.4 keV is formed on the capsule surface. For lower beam brightness the absolute temperature values will naturally become lower (Fig. 5). The integral parameters of the small
Table 3 Computed data for beam energy 2 MJ and ion pulse duration 4 ns No 1
Pulse brightness (TW/cm)
Gas density in the cavity (g/cm)
Energy flux from the converter (%Q)
¹ in the .!9 cavity (keV)
Energy flux onto the capsule (%Q)
7 8 9 10
1200 1000 800 1200
0.02 0.02 0.02 0.02
28 22 19 16.5
0.4 0.36 0.32 0.33
10 8 6.5 6.2
S. Skrypnik et al./Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 110–115
target at time 4 ns from integrated computations are presented in Table 3. Computations 7—9 were conducted for model energy release in the converters, computation 10 for a preset external ion flux. The boundary conditions from integrated 2D computations 2 and 8 were used to calculate implosion of the HIGHSPEED capsule of appropriate dimensions in the three-temperature formulation. According to these calculations, the shape of the internal thermonuclear regions proved compact, density and temperature of the DT region in the large capsule (for driver energy 10 MJ) were close to those sufficient for thermonuclear burning.
3. Conclusion The 2D integrated computations of the target with converters on the side surface of the casing, the results of which are presented in this report, confirmed the earlier [9] conclusion regarding the possibility of production of quite a homogeneous X-ray field on the capsule surface in such a design. The kinetic and spectral effects can somewhat distort the obtained results and this calls for a thorough consideration. However, the target design allows some refinement in this case. More essential is the issue of provision of the required cavity energy (temperature of the order of 0.3—0.4 keV). The results presented are obtained for the beam brightness of the order of 1000 TW/cm2. According to the computed converter efficiency for brightness of the ion beam E "10 GeV less than *0/ 300 TW/cm2 the conversion efficiency appears less than 10% which is insufficient to obtain the required conditions on the target surface.
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Acknowledgements This work was carried out within the frame work of the ISTC Project d154. References [1] S. Atzeni, A.R. Piriz et al., Target design activities for the European Study Group: Heavy Ion Ignition Facility. Proc. 11th Int. Symp. on Heavy Ion Inertial Fusion, Princeton, 1995, 61. [2] M. Tabak, A distributed radiator heavy ion target, Physics of High density in Matter Workshop Hirschegg, Austria, February 2—7, 1997. [3] J. Mejer-ter-Vehn, Nucl. Instr. and Meth. A 278 (1989) 25. [4] K.J. Lutz, J.A. Maruhn, R.G. Arnold, Nucl. Fusion 32 (1992) 1609. [5] M. Murakami, J. Mejer-ter-Vehn, Nucl. Fusion 31 (1991) 1315. [6] M. Temporal, S. Atzeni, Nuovo Cimento 106 A (1993) 1925. [7] J.D. Lindl, Nuovo Cimento 106 A (1993) 1467. [8] J. Meyer-ter Vehn, M. Basko, R. Ramis, A. Rickert, Nuovo Cimento 106 A (1993) 1883. [9] V. Vatulin, B. Voronin, V. Zagrafov, G. Remizov, G. Skidan, S. Skrypnik, Numerical investigation of performance of some designs of heavy ion thermonuclear fusion target. Proc. 11th Int. Symp. on Heavy Ion Inertial Fusion, Princeton, 1995, 609. [10] B. Voronin, S. Skrypnik, I. Sofronov, VANT. Ser. Met. i Progr, Chisl. Resh. Zad. Mat. Fiziki. 3 (1988) 3. [11] D. Koshkarev, Nuovo Cimento 106 A (1993) 1567. [12] V. Vatulin, V. Ermolovich, S. Skrypnik, Nuovo Cimento, 106 A (1993) 1931. [13] V. Vatulin, V. Yermolovich, A. Kazarin, S. Skrypnik, B. Sharkov, A technique for numerical studies of ion pulse effect on cylindric targets. Presented at the 12th Symp. on Heavy Ion Fusion, Heidelberg, Germany, September 22—27, 1997. [14] M. Basko, M. Churasov, D. Koshkarev, ITEP conception of a heavy ion fusion facility. Proc. 11th Int. Symp. on Heavy Ion Inertial Fusion, Princeton, 1995, 73.
II. TARGETS
Numerical simulation of operation of the target with converters on the side surface of the casing S. Skrypnik*, B. Voronin, V. Vatulin, V. Ermolovich, E. Shaporenko, A. Kazarin, S. Kibkalo Russian Federal Nuclear Center — VNIIEF, Arzamas-16, 607190 Sarov, Nizhni Novgorod Region, Russia
Abstract The presentation gives results of the numerical simulation of the operation of the heavy-ion fusion target rated for the driver energy of the order of 10 MJ with converters positioned on the side surface of the casing wall. The effect of casing design features and ion pulse shape on the target parameters is studied. X-ray transport is described in 2D geometry in the diffusion approximation. The results of preliminary computations of the target for the European Test Facility project (beam energy of the order of 2 MJ) are given. ( 1998 Elsevier Science B.V. All rights reserved.
1. Introduction Most efficient methods for numerical simulation of the processes occurring in inertial fusion targets are integrated computations including simulation of basic processes responsible for target operation and parameters. Inertial fusion targets are, in general, 3D systems and simulation of their operation requires 2D and 3D computer codes. This presentation gives the results of numerical simulation of the cylindrical target with converters on the side walls of the casing (Fig. 1). This target scheme is one of the many possible for use in the heavy-ion fusion project [1—8]. These studies are a continuation of the works begun in 1993, the results of which were reported at the 11th Sympo-
* Corresponding author. Fax: #7 83130 45761; e-mail: vvv—[email protected].
sium on Heavy Ion Fusion in Princeton [9]. The present studies are aimed at a more detailed specification of the target characteristics by a more accurate description of the target physics, a study of the target operation for varying ion beam parameters, and of varying target schemes and dimensions. Larger part of the numerical studies, the results of which are presented here, was conducted for ion beam energy of the order of 10 MJ. Some numerical investigations were conducted as a tentative study of a smaller target for driver energy 2—3 MJ (European project Test Facility) in order to try out the applicability of targets of this type for such experiments. The computations were conducted in 2D formulation using the code package capable to simulate the following processes: f Ion beam interaction with high-temperature plasma and ion beam energy conversion into X-ray energy;
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 0 3 - 8
111
S. Skrypnik et al./Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 110–115 Table 1 CTF driver beam parameters
Fig. 1. Scheme of the target with converters positioned on the side surface of the chamber.
f X-ray transport in cavities of various shapes and dimensions; the presented results were obtained using one-group diffusion approximation; f hydrodynamic motion of high-temperature plasma; f thermonuclear burning kinetics. The basic technique [10] developed by the authors implies two mutually orthogonal Eulerian coordinates and one Lagrangian coordinate. This allows natural description of the geometry consisting of a set of layered regions with possible strong sliding shift of one region against another. The technique and code implementing it proved to be an effective tool for studying thermonuclear target implosion. One-temperature technique was used as a basis to develop the technique for solving the system of equations of 3D hydrodynamics and heat conduction with account of ion, electron and photon temperatures, electron—ion—photon relaxation and energy release from thermonuclear reactions.
2. The setup and results of 2D integrated calculations Major part of the numerical studies was carried out for ion beam energy of the order of 10 MJ and
Parameter
Classic driver
Charge symmetric driver
Ion energy (GeV) Ion current per chanel (kA) Pulse duration (ns) Focusing spot area (cm2) Brightness (TV/cm 2) Maximum number of channels Energy in one channel (MJ) Maximum energy (MJ)
10 +1.25 10 0.12 100 +20 0.12 2.4
10 +10 8 0.12 1000 +20 0.8 16
computed parameters of the charge-symmetric accelerator studied at ITEP (Moscow) [11] (Table 1). The computed model of the system is presented in Fig. 2. In contrast to the model presented in Ref. [9], vertical walls are placed at the converter edges to reduce energy release from the converter to the outside. Fig. 3 presents a cross-section of the HIGHSPEED capsule [12] used in this target: Table 2 gives the basic initial parameters of the above systems and integral computed data. Calculations 1—4 were carried out for energy release in the converters set corresponding to the ion beam energy release while being stopped by the converter materials. Calculation 5 was conducted with the outer ion beam set and ion energy conversion calculated by the code [13]. All the data are given for the time of ion pulse termination. Fig. 4 presents a typical pattern of energy distribution in the system from one of the calculations. The figure shows that in spite of extremely complicated energy distribution in the target cavity, quite a homogeneous X-ray field is formed on the capsule surface. More accurate kinetic computations are required to specify the process of X-ray field generation in the target cavity. The target dynamics is considerably affected by the filling target cavity with a light gas of a low atomic number up to densities at which the losses on gas internal energy are low. It considerably “quenches” hydrodynamic processes. A reduction in the ion pulse duration is also favourable for a more homogeneous energy distribution over the capsule.
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S. Skrypnik et al./Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 110–115
Fig. 2. 2D computational model of the target.
Fig. 3. Scheme of HIGHSPEED capsule.
In most calculations ion beam brightness was about 1200 TW/cm2 for the selected converter size, which is somewhat higher than the current ITEF accelerator beam parameters. Conversion efficiency will be a little lower for lower beam brightness (Fig. 5). In this case absolute temperatures in the target cavity will decrease as compared to those presented in Table 2. Along with 10—15 ns monopulse, a time-profiled pulse can be formed for implementation of an energetically more beneficial mode of DT compression in the capsule. Fig. 6 presents one of the possible
ion pulse shapes proposed by Basko and Koshkarev [14]. According to their data, such a shape approximates the profiled pulse shape required for the capsules under consideration. For this system due to considerable increase of the pulse duration by the time when most ion beam energy is deposited, the external converter layer (gold) which must retain X-ray flux within the target cavity appears practically completely released, and a hole is formed in the target wall through which energy leaves the system intensively. As a result, while at the beginning of the main pulse (35 ns) the outgoing flux is less than 10% of the energy release in the converter (larger part of the energy remains in the converter), by 40 ns nearly 40% and by 45 ns nearly 70% of the energy is emitted outside. This leads to a sharp temperature drop in the target cavity (down to the order of 0.2 keV against
Table 2 Target computed data at beam energy 10 MJ N
Beam energy (Q, MJ)
Ion pulse duration (ns)
Gas density in the cavity (g/cm3)
Energy flux from the converter (%Q)
¹ cavity .!9 (keV)
Energy flux onto the capsule (%Q)
1 2 3 4 5
10 10 10 15 10
10 10 5 10 10
0.001 0.02 0.02 0.02 0.02
42 49 49 42 30
0.32 0.33 0.37 0.4 0.3
10 12 11 12 11
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S. Skrypnik et al./Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 110–115
Fig. 6. Profiled ion pulse shape [14].
Fig. 4. Temperature distribution in hohlraum with a cylinderical case and the converters on the lateral side (E "10 GeV, *0/4 E "10 MJ, ¼&1000 TVt/cm2, t"2.7 ns, ¹ &0.3 KeV). "%!. .!9
Fig. 5. Converters efficiency for Pt ions with E"10 MJ and t "10 ns. the converters having composition of Au#(Be, Al, *.1 Ti, Au).
0.3—0.4 keV given a short pulse) and reduction of the energy flux to the capsule. The energy flux to the capsule was only of the order of 5% of the ion beam energy. Due to the pulse duration increase, hydrodynamic effect of the products of the converter scattering into the capsule with inhomogeneity over the angle P /P higher than 10% begins to .!9 .*/ play its role. Maximum effect of the converter scattering on the capsule is at the time &30 ns, i.e., before the receipt of the basic fraction of ion pulse energy. This perturbation considerably affected the DT region compression symmetry (Fig. 7). Thus, in the target design without the filling the casing with light gas, computations demonstrated sharp deterioration of X-ray field parameters for a long pulse, and certain modifications of the target design are necessary to eliminate the detected effects. Some numerical studies were made for a smaller target as tentative investigations of applicability of targets of such type for experiments at the European Test Facility (driver energy 2—3 MJ). The following target dimensions were taken: casing diameter D"6 mm, casing length ¸"7 mm, capsule diameter D "2 mm. #!14 Currently we have no final data on parameters of such accelerators at our disposal and the computations were conducted for the Bi ion pulse (10 GeV) of 2 MJ energy, 4 ns duration, the number of beams were eight with diameters of each beam &2.5 mm.
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S. Skrypnik et al./Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 110–115
Fig. 7. State of DT-fuel (profiling impulse) near the moment of maximum compression. Density distribution.
In the computations the beam brightness is kept on the level of that accepted in the computations for the target of E"10 MJ. For such a target and ion pulse parameters a homogeneous X-ray field of
maximum temperature 0.3—0.4 keV is formed on the capsule surface. For lower beam brightness the absolute temperature values will naturally become lower (Fig. 5). The integral parameters of the small
Table 3 Computed data for beam energy 2 MJ and ion pulse duration 4 ns No 1
Pulse brightness (TW/cm)
Gas density in the cavity (g/cm)
Energy flux from the converter (%Q)
¹ in the .!9 cavity (keV)
Energy flux onto the capsule (%Q)
7 8 9 10
1200 1000 800 1200
0.02 0.02 0.02 0.02
28 22 19 16.5
0.4 0.36 0.32 0.33
10 8 6.5 6.2
S. Skrypnik et al./Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 110–115
target at time 4 ns from integrated computations are presented in Table 3. Computations 7—9 were conducted for model energy release in the converters, computation 10 for a preset external ion flux. The boundary conditions from integrated 2D computations 2 and 8 were used to calculate implosion of the HIGHSPEED capsule of appropriate dimensions in the three-temperature formulation. According to these calculations, the shape of the internal thermonuclear regions proved compact, density and temperature of the DT region in the large capsule (for driver energy 10 MJ) were close to those sufficient for thermonuclear burning.
3. Conclusion The 2D integrated computations of the target with converters on the side surface of the casing, the results of which are presented in this report, confirmed the earlier [9] conclusion regarding the possibility of production of quite a homogeneous X-ray field on the capsule surface in such a design. The kinetic and spectral effects can somewhat distort the obtained results and this calls for a thorough consideration. However, the target design allows some refinement in this case. More essential is the issue of provision of the required cavity energy (temperature of the order of 0.3—0.4 keV). The results presented are obtained for the beam brightness of the order of 1000 TW/cm2. According to the computed converter efficiency for brightness of the ion beam E "10 GeV less than *0/ 300 TW/cm2 the conversion efficiency appears less than 10% which is insufficient to obtain the required conditions on the target surface.
115
Acknowledgements This work was carried out within the frame work of the ISTC Project d154. References [1] S. Atzeni, A.R. Piriz et al., Target design activities for the European Study Group: Heavy Ion Ignition Facility. Proc. 11th Int. Symp. on Heavy Ion Inertial Fusion, Princeton, 1995, 61. [2] M. Tabak, A distributed radiator heavy ion target, Physics of High density in Matter Workshop Hirschegg, Austria, February 2—7, 1997. [3] J. Mejer-ter-Vehn, Nucl. Instr. and Meth. A 278 (1989) 25. [4] K.J. Lutz, J.A. Maruhn, R.G. Arnold, Nucl. Fusion 32 (1992) 1609. [5] M. Murakami, J. Mejer-ter-Vehn, Nucl. Fusion 31 (1991) 1315. [6] M. Temporal, S. Atzeni, Nuovo Cimento 106 A (1993) 1925. [7] J.D. Lindl, Nuovo Cimento 106 A (1993) 1467. [8] J. Meyer-ter Vehn, M. Basko, R. Ramis, A. Rickert, Nuovo Cimento 106 A (1993) 1883. [9] V. Vatulin, B. Voronin, V. Zagrafov, G. Remizov, G. Skidan, S. Skrypnik, Numerical investigation of performance of some designs of heavy ion thermonuclear fusion target. Proc. 11th Int. Symp. on Heavy Ion Inertial Fusion, Princeton, 1995, 609. [10] B. Voronin, S. Skrypnik, I. Sofronov, VANT. Ser. Met. i Progr, Chisl. Resh. Zad. Mat. Fiziki. 3 (1988) 3. [11] D. Koshkarev, Nuovo Cimento 106 A (1993) 1567. [12] V. Vatulin, V. Ermolovich, S. Skrypnik, Nuovo Cimento, 106 A (1993) 1931. [13] V. Vatulin, V. Yermolovich, A. Kazarin, S. Skrypnik, B. Sharkov, A technique for numerical studies of ion pulse effect on cylindric targets. Presented at the 12th Symp. on Heavy Ion Fusion, Heidelberg, Germany, September 22—27, 1997. [14] M. Basko, M. Churasov, D. Koshkarev, ITEP conception of a heavy ion fusion facility. Proc. 11th Int. Symp. on Heavy Ion Inertial Fusion, Princeton, 1995, 73.
II. TARGETS