- Email: [email protected]
Simulations of the plasma dynamics in high-current ion diodes
Nuclear Instruments and Methods in Physics Research A 415 (1998) 473—477
Simulations of the plasma dynamics in high-current ion diodes O. Boine-Frankenheim!,*, T.D. Pointon", T.A. Mehlhorn" ! Gesellschaft fu( r Schwerionenforschung (GSI), Planckstrasse 1, 64291 Darmstadt, Germany " Sandia National Laboratories (SNL), Albuquerque, New Mexico 87185, USA
Abstract Our time-implicit fluid/Particle-In-Cell (PIC) code DYNAID [1] is applied to problems relevant for applied-B ion diode operation. We present simulations of the laser ion source, which will soon be employed on the SABRE accelerator at SNL, and of the dynamics of the anode source plasma in the applied electric and magnetic fields. DYNAID is still a test-bed for a higher-dimensional simulation code. Nevertheless, the code can already give new theoretical insight into the dynamics of plasmas in pulsed power devices. ( 1998 Elsevier Science B.V. All rights reserved. PACS: 52.65.-y; 52.75.Pv Keywords: Ion sources; Plasma simulation
1. Introduction Applied-B ion diodes efficiently produce an ion beam from electrical power supplied by an accelerator by inhibiting electron flow across the anode—cathode (A—K) gap with an externally applied magnetic field. Experiments on the PBFA II [2] (20—30 TW, 10—15 MV, 2 MA) and SABRE [3] (1 TW, 5 MV, 250 kA) accelerators at Sandia National Laboratories (SNL) have focused on producing Li`1 ion beams for inertial confinement fusion applications.
* Corresponding author. Fax: #49 6159 71 2985; E-mail: [email protected].
A simple scheme of applied-B ion diode operation is shown in Fig. 1. The ion beam is extracted from the anode source plasma by the applied electric field in x-direction. The electron flux from the cathode is inhibited by the applied B field. The z cathode electrons perform a E]B drift in y-direction and form a virtual cathode [4]. Efficient ion diode operation requires the generation of an ion source plasma at the anode before the power pulse is switched on. In future experiments on SABRE a laser will be used to produce a singly ionized Li plasma at the anode surface. Recent theoretical work at SNL focused on the coupled dynamics of dense, collisional plasmas arising at the anode, as for instance the ion source plasma or contaminant plasmas, and the low-density plasmas in the anode—cathode gap.
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 4 2 2 - 7
V. BEAMS
474
O. Boine-Frankenheim et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 473—477
Fig. 1. Schematic view of applied-B ion diode operation (B "2!10 ¹, E +10 MV/cm). The coordinate system is z x,.!9 chosen so that the applied electric field points in x-direction and the applied magnetic field in z-direction.
The simulation of plasmas in ion diodes with usual explicit fluid or PIC methods is greatly complicated by the wide range of time-scale parameters u *t and l*t (u plasma frequency, l collision 1 1 frequency between two species, *t simulation time step) across the anode—cathode gap. In order to run a simulation code with an acceptable large time step, but still account correctly for the electron dynamics at the time scale of the simulation the time-implicit evaluation of the electric field is required. Additionally, to account for the collisional coupling between species, the simultaneous time-implicit solution of the local collision forces between all species is necessary. Implicit time integration schemes for fluid or particle advance are accurate and stable over a wide range of timescale parameters [5,6]. For the simulation of the applied-B ion diode operation we are therefore developing the onedimensional (one space coordinate x, two velocities u , u ) time-implicit fluid/PIC hybrid code DYNx y AID, described previously in Ref. [1], designed to self-consistently simulate collisional plasma/neutral systems with an arbitrary number of interacting species, over greatly varying density regimes and together with applied electric and magnetic fields. Our multifluid code is based on the implicit algorithms of Rambo and Denavit [5], with changes to include applied and induced electric and magnetic fields in the transverse directions. The multifluid code also models inelastic collisions between fluids:
charge exchange between ions and neutrals, and impact ionization by both electrons and ions. The multifluid approach to plasma simulations fails under several circumstances (see for instance Ref. [7]). In these cases a kinetic description becomes necessary. Especially for applied-B ion diode applications it is important to treat the low-density electrons emitted from the cathode and the beam ions extracted from the anode plasma kinetically to account correctly for the instabilities leading to the divergence of the extracted ion beam. DYNAID includes an implicit particle handler. Within our code it is possible to convert a fluid into PIC particles and reverse using different criteria, based on the collision frequency or the density, for example. The PIC particles couple with the fluids due to the self-consistent electromagnetic fields and elastic collisions. In this paper we want to present results obtained with DYNAID concerning the generation of an anode source plasma with a laser and concerning the dynamics of an anode source plasma in the applied electromagnetic fields of an ion diode.
2. Laser-generated anode plasma At SNL’s SABRE accelerator soon a 10 ns ND : YAG 0.1 J/cm2 laser will be employed to generate Li`1 ions at the anode surface. We deal here with the situation before the electrical power pulse is switched on, but the applied magnetic field of about 2 T is already present. The laser radiation generates a partly ionized Li vapor at the LiAg anode surface. The desired breakdown in the vapor expanding across the applied magnetic field can occur due to inverse Bremsstrahlung absorption of the laser light by the vapor. In the so-called, non-diamagnetic limit, where the magnetic field quickly penetrates into the plasma, the plasma particles (Li` ions and electrons) can expand across the applied magnetic field (+2T) due to an internal electric field E y E #u ]B "0. (1) y x z The internal electric field leads to a E]B drift across the magnetic field, with nearly the initial thermal velocity.
O. Boine-Frankenheim et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 473—477
The diamagnetic electron current induced by the space charge separation in the front of an expanding plasma causes an additional heating of the front layer. This front layer can reach high temperatures, because the heat flux back into the denser plasma is strongly reduced due to the applied magnetic field. For the simulation of the laser ion source operation we use the multifluid part of DYNAID with three fluids: neutrals, Li` ions and primary electrons evaporated from the anode surface and secondary electrons created by impact ionization. The fluid electrons can absorb the laser radiation by inverse Bremsstrahlung. The time-dependent evaporated flux of Li neutrals, Li` ions and electrons as a function of the laser light reaching the LiAg anode surface are calculated using an auxiliary code, which solves the one-dimensional heat flux equation in time and space for the 0.5 lm thick LiAg substrate on a Au layer. The values obtained by the auxiliary code are used as a time-dependent input for DYNAID.
475
In the experiment peak laser intensities of 2]108 W cm~2 are reached. Fig. 2 shows the simulation results 25 ns after the peak laser intensity. It can be seen that the expansion velocity of the neutral/plasma front is roughly 106 cm/s. The applied magnetic field inhibits the low density plasma ‘foot’ expanding with slightly higher velocity than the neutrals, which is seen in DYNAID simulations and experiments without the applied magnetic field. The magnetic field reverses the sign of the ambipolar field E at front of the plasma. This electric x field causes a diamagnetic drift current, which heats up the low-density electrons in the front layer of the expanding vapor to about 20 eV. The high temperatures are possible due to heat flux inhibition by the magnetic field. The heating of the front layer causes the generation of low-density secondary electrons in the front layer, but no breakdown. The magnetic field remains unchanged by the diamagnetic current.
Fig. 2. Expansion across an applied-B field (2 T). Results obtained with DYNAID at t"25 ns after the laser peak intensity of 2]108 W cm~2. Neutrals (n), primary electrons (e), secondary electrons (se) and ions (i). For the electrons the velocity in y-direction is given and the velocity in x-direction for the other fluids.
V. BEAMS
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O. Boine-Frankenheim et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 473—477
It is important to point out the parameters used in this simulation, which are: u *t[100, 1,% u *t+1.0 and l *t[3.4. u is the electron #,% %* 1,% plasma frequency, u is the electron—cyclotron #,% frequency and l is the electron—ion collision fre%* quency. Even for these high simulation parameters DYNAID runs stable. We checked the accuracy of the obtained results by varying the time step. At intensities of 4]108 W cm~2 and above with and without a magnetic field DYNAID simulations show that a plasma breakdown is induced, leading to a dense ('1019 cm~3), singly ionized Li plasma in front of the anode. The plasma front rapidly (v+107 cm/s) expands away from the anode surface. The induced diamagnetic current in the lowdensity plasma front leads to temperatures of about 100 eV, but is not sufficient to alter the magnetic field. It should be pointed out that the exact dynamics of a dense plasma expanding across a magnetic field is beyond the capabilities of our onedimensional multifluid code. The expanding plasma is unstable to several plasma instabilities (see, for instance, Ref. [8]). In our fluid model we can only approximate the effects of these instabilities by adding an anomalous collision frequency [9]. Our DYNAID simulation show, that with the laser employed at SABRE plasma breakdown in the expanding vapor may be incomplete. Below the breakdown threshold only a partly ionized vapor would be generated by the laser. Above threshold a dense plasma is created, expanding quickly into the A—K gap. DYNAID can be used to study the ion diode operation with an arbitrary anode vapor/plasma system generated by the laser. In the next section we will present results for the simple case of a fully ionized anode plasma.
3. Applied-B ion diode operation Within the limits of our one-dimensional approach we use DYNAID to gain some insight into the dynamics of an anode source plasma during the applied-B ion diode operation. The magnetic field generated by the cathode sheet electrons, which are not explicitly included in
our present model, is approximated by the assumption of pressure balance across the A—K gap [9] B2"B2#2k J(2m »/eZ)1@2. (2) ! # 0 i Here B is the magnetic field at the anode, B is ! # the magnetic field at the cathode side, J is the extracted ion current, » is the applied potential difference across the A—K gap. We start at t"0 with a magnetized (2 T), singly ionized, 3 mm thick, Li plasma layer of 1 eV temperature in front of the anode. The A—K gap is 1.1 cm wide and the peak applied potential across the gap is 3 MV. The power pulse has a sin2(pt/q) shape, with q"40 ns. The anode surface behind the plasma layer is treated as an ideal conductor. For the DYNAID simulation we use four fluids: primary electrons and Li` ions together with secondary electrons and Li2` ions created by impact ionization. Fig. 3 shows the results at peak power (t"20 ns). In the anode plasma the electric field is shielded out. The magnetic field produced by the sheet electrons quickly (+5 ns) penetrates into the anode plasma. The E]B drift current heats up the electrons in the front layer to about 1 keV, the heat flux back into the plasma is strongly inhibited by the generated magnetic field of about 5 T. These high electron temperatures cause the generation of undesired Li2` ions together with secondary electrons. The Li2` ions are extracted from the diode at a higher energy compared to the desired Li` ions. The density of Li2` ions in the front layer of the anode plasma stays below 1015 cm~3 in this example case. After the power pulse reached its peak value the anode plasma starts expanding towards the cathode. This expansion is pushed by the magnetic field gradient. The dropping potential difference across the gap leads to a dropping extracted ion flux and so to a lower magnetic field produced by the sheet electrons. The dropping magnetic field induced an electric field in y-direction, which in turn enhances the magnetic field at the anode compared to the cathode. The extracted total ion flux density as a function of time reaches a peak value of 0.6 kA/cm2. We found that the ion flux performs strong oscillations
O. Boine-Frankenheim et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 473—477
477
Fig. 3. Results for t"20 ns (peak power). Li` ions (i), Li2` ions (i2), primary electrons (e), secondary electrons (se). For the electrons the velocity in y-direction is shown and the velocity in x-direction for the other fluids. Simulation parameters: u *t[10, u *t[1.0, l *t[0.2. 1,% #,% %*
in time around the mean value due to space charge oscillations in the ion diode.
4. Conclusion Our code DYNAID is already a powerful new tool to study the dynamics of plasmas in applied-B ion diodes. Within DYNAID we can study the performance of the anode source plasma creation and we can follow the time evolution of the anode plasma in the applied electromagnetic fields. An important example is the simulation of the heating of the electron component of the anode plasma due to the applied fields. Further development will concentrate on a two-dimensional version of the code, with possible applications also in other fields where laboratory plasmas with density and/or temperature variations of several orders of magnitude are of importance. Examples are, for instance, ion sources for particle accelerators, ion beam transport in gases or fast igniter studies.
Acknowledgements O.B.F. was supported by the Deutsche Forschungsgemeinschaft (DFG). Part of this work was supported by the U.S. Department of Energy under Contract DE-AC04-94-AL85000. References [1] T.D. Pointon, O. Boine-Frankenheim, T.A. Mehlhorn, Proc. 13th Conf. on Laser Interaction and related Plasma Phenomena, Monterey, 13—18 April 1997, AIP Conference Proceedings 406 (1997) 67. [2] A.B. Filuk, T.A. Mehlhorn et. al., in: J. Coutant (Ed.), Proc. IAEA Technical Committee on Drivers for Inertial Confinement Fusion, IAEA, Paris, 1995, p. 233. [3] M.E. Cuneo et al., IEEE Trans. Plasma Sci. 25 (1997) 229. [4] M.P. Desjarlais, Phys. Fluids B 1 (1989) 1709. [5] P.W. Rambo, J. Denavit, J. Comput. Phys. 98 (1992) 317. [6] M.R. Gibbons, D.W. Hewett, J. Comput. Phys. 120 (1995) 231. [7] M.S. Benilov, Phys. Plasmas 4 (1997) 521. [8] T.A. Peyser et al., Phys. Fluids 4 (1992) 2448. [9] S.A. Slutz, J. Appl. Phys. 61 (1986) 1288.
V. BEAMS
Simulations of the plasma dynamics in high-current ion diodes O. Boine-Frankenheim!,*, T.D. Pointon", T.A. Mehlhorn" ! Gesellschaft fu( r Schwerionenforschung (GSI), Planckstrasse 1, 64291 Darmstadt, Germany " Sandia National Laboratories (SNL), Albuquerque, New Mexico 87185, USA
Abstract Our time-implicit fluid/Particle-In-Cell (PIC) code DYNAID [1] is applied to problems relevant for applied-B ion diode operation. We present simulations of the laser ion source, which will soon be employed on the SABRE accelerator at SNL, and of the dynamics of the anode source plasma in the applied electric and magnetic fields. DYNAID is still a test-bed for a higher-dimensional simulation code. Nevertheless, the code can already give new theoretical insight into the dynamics of plasmas in pulsed power devices. ( 1998 Elsevier Science B.V. All rights reserved. PACS: 52.65.-y; 52.75.Pv Keywords: Ion sources; Plasma simulation
1. Introduction Applied-B ion diodes efficiently produce an ion beam from electrical power supplied by an accelerator by inhibiting electron flow across the anode—cathode (A—K) gap with an externally applied magnetic field. Experiments on the PBFA II [2] (20—30 TW, 10—15 MV, 2 MA) and SABRE [3] (1 TW, 5 MV, 250 kA) accelerators at Sandia National Laboratories (SNL) have focused on producing Li`1 ion beams for inertial confinement fusion applications.
* Corresponding author. Fax: #49 6159 71 2985; E-mail: [email protected].
A simple scheme of applied-B ion diode operation is shown in Fig. 1. The ion beam is extracted from the anode source plasma by the applied electric field in x-direction. The electron flux from the cathode is inhibited by the applied B field. The z cathode electrons perform a E]B drift in y-direction and form a virtual cathode [4]. Efficient ion diode operation requires the generation of an ion source plasma at the anode before the power pulse is switched on. In future experiments on SABRE a laser will be used to produce a singly ionized Li plasma at the anode surface. Recent theoretical work at SNL focused on the coupled dynamics of dense, collisional plasmas arising at the anode, as for instance the ion source plasma or contaminant plasmas, and the low-density plasmas in the anode—cathode gap.
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 4 2 2 - 7
V. BEAMS
474
O. Boine-Frankenheim et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 473—477
Fig. 1. Schematic view of applied-B ion diode operation (B "2!10 ¹, E +10 MV/cm). The coordinate system is z x,.!9 chosen so that the applied electric field points in x-direction and the applied magnetic field in z-direction.
The simulation of plasmas in ion diodes with usual explicit fluid or PIC methods is greatly complicated by the wide range of time-scale parameters u *t and l*t (u plasma frequency, l collision 1 1 frequency between two species, *t simulation time step) across the anode—cathode gap. In order to run a simulation code with an acceptable large time step, but still account correctly for the electron dynamics at the time scale of the simulation the time-implicit evaluation of the electric field is required. Additionally, to account for the collisional coupling between species, the simultaneous time-implicit solution of the local collision forces between all species is necessary. Implicit time integration schemes for fluid or particle advance are accurate and stable over a wide range of timescale parameters [5,6]. For the simulation of the applied-B ion diode operation we are therefore developing the onedimensional (one space coordinate x, two velocities u , u ) time-implicit fluid/PIC hybrid code DYNx y AID, described previously in Ref. [1], designed to self-consistently simulate collisional plasma/neutral systems with an arbitrary number of interacting species, over greatly varying density regimes and together with applied electric and magnetic fields. Our multifluid code is based on the implicit algorithms of Rambo and Denavit [5], with changes to include applied and induced electric and magnetic fields in the transverse directions. The multifluid code also models inelastic collisions between fluids:
charge exchange between ions and neutrals, and impact ionization by both electrons and ions. The multifluid approach to plasma simulations fails under several circumstances (see for instance Ref. [7]). In these cases a kinetic description becomes necessary. Especially for applied-B ion diode applications it is important to treat the low-density electrons emitted from the cathode and the beam ions extracted from the anode plasma kinetically to account correctly for the instabilities leading to the divergence of the extracted ion beam. DYNAID includes an implicit particle handler. Within our code it is possible to convert a fluid into PIC particles and reverse using different criteria, based on the collision frequency or the density, for example. The PIC particles couple with the fluids due to the self-consistent electromagnetic fields and elastic collisions. In this paper we want to present results obtained with DYNAID concerning the generation of an anode source plasma with a laser and concerning the dynamics of an anode source plasma in the applied electromagnetic fields of an ion diode.
2. Laser-generated anode plasma At SNL’s SABRE accelerator soon a 10 ns ND : YAG 0.1 J/cm2 laser will be employed to generate Li`1 ions at the anode surface. We deal here with the situation before the electrical power pulse is switched on, but the applied magnetic field of about 2 T is already present. The laser radiation generates a partly ionized Li vapor at the LiAg anode surface. The desired breakdown in the vapor expanding across the applied magnetic field can occur due to inverse Bremsstrahlung absorption of the laser light by the vapor. In the so-called, non-diamagnetic limit, where the magnetic field quickly penetrates into the plasma, the plasma particles (Li` ions and electrons) can expand across the applied magnetic field (+2T) due to an internal electric field E y E #u ]B "0. (1) y x z The internal electric field leads to a E]B drift across the magnetic field, with nearly the initial thermal velocity.
O. Boine-Frankenheim et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 473—477
The diamagnetic electron current induced by the space charge separation in the front of an expanding plasma causes an additional heating of the front layer. This front layer can reach high temperatures, because the heat flux back into the denser plasma is strongly reduced due to the applied magnetic field. For the simulation of the laser ion source operation we use the multifluid part of DYNAID with three fluids: neutrals, Li` ions and primary electrons evaporated from the anode surface and secondary electrons created by impact ionization. The fluid electrons can absorb the laser radiation by inverse Bremsstrahlung. The time-dependent evaporated flux of Li neutrals, Li` ions and electrons as a function of the laser light reaching the LiAg anode surface are calculated using an auxiliary code, which solves the one-dimensional heat flux equation in time and space for the 0.5 lm thick LiAg substrate on a Au layer. The values obtained by the auxiliary code are used as a time-dependent input for DYNAID.
475
In the experiment peak laser intensities of 2]108 W cm~2 are reached. Fig. 2 shows the simulation results 25 ns after the peak laser intensity. It can be seen that the expansion velocity of the neutral/plasma front is roughly 106 cm/s. The applied magnetic field inhibits the low density plasma ‘foot’ expanding with slightly higher velocity than the neutrals, which is seen in DYNAID simulations and experiments without the applied magnetic field. The magnetic field reverses the sign of the ambipolar field E at front of the plasma. This electric x field causes a diamagnetic drift current, which heats up the low-density electrons in the front layer of the expanding vapor to about 20 eV. The high temperatures are possible due to heat flux inhibition by the magnetic field. The heating of the front layer causes the generation of low-density secondary electrons in the front layer, but no breakdown. The magnetic field remains unchanged by the diamagnetic current.
Fig. 2. Expansion across an applied-B field (2 T). Results obtained with DYNAID at t"25 ns after the laser peak intensity of 2]108 W cm~2. Neutrals (n), primary electrons (e), secondary electrons (se) and ions (i). For the electrons the velocity in y-direction is given and the velocity in x-direction for the other fluids.
V. BEAMS
476
O. Boine-Frankenheim et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 473—477
It is important to point out the parameters used in this simulation, which are: u *t[100, 1,% u *t+1.0 and l *t[3.4. u is the electron #,% %* 1,% plasma frequency, u is the electron—cyclotron #,% frequency and l is the electron—ion collision fre%* quency. Even for these high simulation parameters DYNAID runs stable. We checked the accuracy of the obtained results by varying the time step. At intensities of 4]108 W cm~2 and above with and without a magnetic field DYNAID simulations show that a plasma breakdown is induced, leading to a dense ('1019 cm~3), singly ionized Li plasma in front of the anode. The plasma front rapidly (v+107 cm/s) expands away from the anode surface. The induced diamagnetic current in the lowdensity plasma front leads to temperatures of about 100 eV, but is not sufficient to alter the magnetic field. It should be pointed out that the exact dynamics of a dense plasma expanding across a magnetic field is beyond the capabilities of our onedimensional multifluid code. The expanding plasma is unstable to several plasma instabilities (see, for instance, Ref. [8]). In our fluid model we can only approximate the effects of these instabilities by adding an anomalous collision frequency [9]. Our DYNAID simulation show, that with the laser employed at SABRE plasma breakdown in the expanding vapor may be incomplete. Below the breakdown threshold only a partly ionized vapor would be generated by the laser. Above threshold a dense plasma is created, expanding quickly into the A—K gap. DYNAID can be used to study the ion diode operation with an arbitrary anode vapor/plasma system generated by the laser. In the next section we will present results for the simple case of a fully ionized anode plasma.
3. Applied-B ion diode operation Within the limits of our one-dimensional approach we use DYNAID to gain some insight into the dynamics of an anode source plasma during the applied-B ion diode operation. The magnetic field generated by the cathode sheet electrons, which are not explicitly included in
our present model, is approximated by the assumption of pressure balance across the A—K gap [9] B2"B2#2k J(2m »/eZ)1@2. (2) ! # 0 i Here B is the magnetic field at the anode, B is ! # the magnetic field at the cathode side, J is the extracted ion current, » is the applied potential difference across the A—K gap. We start at t"0 with a magnetized (2 T), singly ionized, 3 mm thick, Li plasma layer of 1 eV temperature in front of the anode. The A—K gap is 1.1 cm wide and the peak applied potential across the gap is 3 MV. The power pulse has a sin2(pt/q) shape, with q"40 ns. The anode surface behind the plasma layer is treated as an ideal conductor. For the DYNAID simulation we use four fluids: primary electrons and Li` ions together with secondary electrons and Li2` ions created by impact ionization. Fig. 3 shows the results at peak power (t"20 ns). In the anode plasma the electric field is shielded out. The magnetic field produced by the sheet electrons quickly (+5 ns) penetrates into the anode plasma. The E]B drift current heats up the electrons in the front layer to about 1 keV, the heat flux back into the plasma is strongly inhibited by the generated magnetic field of about 5 T. These high electron temperatures cause the generation of undesired Li2` ions together with secondary electrons. The Li2` ions are extracted from the diode at a higher energy compared to the desired Li` ions. The density of Li2` ions in the front layer of the anode plasma stays below 1015 cm~3 in this example case. After the power pulse reached its peak value the anode plasma starts expanding towards the cathode. This expansion is pushed by the magnetic field gradient. The dropping potential difference across the gap leads to a dropping extracted ion flux and so to a lower magnetic field produced by the sheet electrons. The dropping magnetic field induced an electric field in y-direction, which in turn enhances the magnetic field at the anode compared to the cathode. The extracted total ion flux density as a function of time reaches a peak value of 0.6 kA/cm2. We found that the ion flux performs strong oscillations
O. Boine-Frankenheim et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 473—477
477
Fig. 3. Results for t"20 ns (peak power). Li` ions (i), Li2` ions (i2), primary electrons (e), secondary electrons (se). For the electrons the velocity in y-direction is shown and the velocity in x-direction for the other fluids. Simulation parameters: u *t[10, u *t[1.0, l *t[0.2. 1,% #,% %*
in time around the mean value due to space charge oscillations in the ion diode.
4. Conclusion Our code DYNAID is already a powerful new tool to study the dynamics of plasmas in applied-B ion diodes. Within DYNAID we can study the performance of the anode source plasma creation and we can follow the time evolution of the anode plasma in the applied electromagnetic fields. An important example is the simulation of the heating of the electron component of the anode plasma due to the applied fields. Further development will concentrate on a two-dimensional version of the code, with possible applications also in other fields where laboratory plasmas with density and/or temperature variations of several orders of magnitude are of importance. Examples are, for instance, ion sources for particle accelerators, ion beam transport in gases or fast igniter studies.
Acknowledgements O.B.F. was supported by the Deutsche Forschungsgemeinschaft (DFG). Part of this work was supported by the U.S. Department of Energy under Contract DE-AC04-94-AL85000. References [1] T.D. Pointon, O. Boine-Frankenheim, T.A. Mehlhorn, Proc. 13th Conf. on Laser Interaction and related Plasma Phenomena, Monterey, 13—18 April 1997, AIP Conference Proceedings 406 (1997) 67. [2] A.B. Filuk, T.A. Mehlhorn et. al., in: J. Coutant (Ed.), Proc. IAEA Technical Committee on Drivers for Inertial Confinement Fusion, IAEA, Paris, 1995, p. 233. [3] M.E. Cuneo et al., IEEE Trans. Plasma Sci. 25 (1997) 229. [4] M.P. Desjarlais, Phys. Fluids B 1 (1989) 1709. [5] P.W. Rambo, J. Denavit, J. Comput. Phys. 98 (1992) 317. [6] M.R. Gibbons, D.W. Hewett, J. Comput. Phys. 120 (1995) 231. [7] M.S. Benilov, Phys. Plasmas 4 (1997) 521. [8] T.A. Peyser et al., Phys. Fluids 4 (1992) 2448. [9] S.A. Slutz, J. Appl. Phys. 61 (1986) 1288.
V. BEAMS