Weibel instability and filamentary structures of a relativistic electron beam in plasma

Transcription

1 Mitglied der Helmholtz-Gemeinschaft 7 th Direct Drive and Fast Ignition Workshop Prague, 3-6 May, 009 Weibel instability and filamentary structures of a relativistic electron beam in plasma Anupam Karmakar Institute for Advanced Simulation Jülich Supercomputing Centre Forschungszentrum Jülich, Germany Collaborations: N. Kumar, A. Pukhov ITP1, University of Düsseldorf, Germany G. Shvets IFS, University of Texas at Austin, USA 19. Mai 009

2 Overview Weibel instability : introductory remarks Role of temperature and collisions. D and 3D-PIC Simulation results. Theoretical model for collisional Weibel instability. Conclusions. 19. Mai 009 A. Karmakar et al., Phys. Rev. Lett. 101, (008), Phys. Plasmas, 15, 1070 (008) Phys. Rev. E (in press) (009), EPJD (DOI: /epjd/e ) (009)

3 Beam filamentation in fast ignition I I A 19. Mai 009 Such currents can only propagate as charge neutralized currents

4 Beam filamentation: Weibel and two-stream instabilities in FI The Weibel instability dominates in relativistic conditions. E. S. Weibel, Phys. Rev. Lett., 83, (1959) In 3D geometry, coupling of both instabilities causes filamentation. R. Lee et al. Phys. Rev. Lett. (1973), A. Pukhov et al. Phys. Rev. Lett. (1997), L. O. Silva et al. Phys. Plasmas, 9, 458 (00), Bret et al. Phys. Rev. E. 70, (004), J. Honrubia et al. Nucl. Fusion 46, L5 (006) 19. Mai 009

5 Relevance of temperature and collisions on filamentation Role of beam temperature: Threshold temperature T nb Weibel Instability mc n0 disappears! L. O. Silva et al. Phys. Plasmas (00) Role of collisions in return plasma current Quite complicated and unclear C. Deutsch et al. PRE (005) 19. Mai 009

6 Simulation Geometry (D): The D Transverse Geometry Simulation dimensions 19. Mai 009

7 Simulation Geometry (3D): Y v pz e z v bz e z plasma Y beam V beam >V plasma n beam < n plasma Z X X 19. Mai 009

8 VLPL PIC Simulation parameters [D (3D) Simulations] VLPL Beam and plasma density and simulation parameters Simulation parameters Mesh of 64 numerical particles per cell. Resolution: ions are fixed Electron beam temperature, T b = 70 kev Collisions frequency 19. Mai 009

9 Different simulation case (a) Cold electron beam in a collisionless background plasma (b) Cold electron beam in a collisional background plasma (c) Warm electron beam in a collisionless background plasma (d) Warm electron beam in a collisional background plasma 19. Mai 009

10 D PIC results (a) Cold beam in a cold collisionless plasma 19. Mai 009

11 19. Mai 009 D PIC results (b) Cold e-beam in a cold collisional plasma

12 D PIC results (c) Warm e-beam in a cold plasma 19. Mai 009 L. O. Silva et al., Phys. Plasmas (00)

13 19. Mai 009 D PIC results (d) Warm e-beam in a cold collisional plasma

14 Filaments stopping and collective merging Honda, Pukhov, Meyer-ter-vehn, PRL, Mai 009

15 3D filamentary structures Can temp. suppress filamentation in 3D geometry? Karmakar et al. PoP 15, 1070, (008) Instability is not suppressed! (d) (b) (c) (a) Warm Cold Cold beam beam and and collisionless collisional collisionless plasma plasma 19. Mai 009

16 Mag. field structures: 3D simulation [case (a)] 19. Mai 009

17 Field energies development: 3D simulations 19. Mai 009

18 Theoretical model: Karmakar et al. PRL 101, 55001, (008) The model assumes an infinite beam propagating in z-direction. The dominant electric and magnetic fields of the beam-plasma system 19. Mai 009

19 Theoretical model (contd.): Eq. of motions for beam and plasma electrons are v t d pz j v dt j v pz e mc e( v jz Az t v mc ; pz ) A z ν collision frequency Conservation of energy equation : j j mc mv m B 0 pz vpz x j d xlz d xlz j 8 n Mai 009

20 19. Mai 009 Dispersion relations Dispersion relation for finite plasma resistivity : i k k k k c pe b s 1 0 For collisionless plasma and long wavelength perturbation c k p 0 0 n n c c c k c b s s s For cold beam Unstable and leads to the Weibel instability 0 0 n n c c b s 3 th c s v

21 Dispersion relations For smaller collision frequency : i c s k 0 s i c n c n 0 b c n c n 0 s 0 b negative energy mode Negative energy waves can be destabilized by the resistivity of the plasma 19. Mai 009 H. Pecseli, Plasma Physics. 17,497 (1975)

22 Conclusions D and 3D PIC simulations show that Weibel instability might be a matter of concern in fast ignition scenario. Collisions seem to play a deleterious role in the energy transportation to the core. The role is attributed to the generation of negative energy waves in the beam-plasma system In 3D geometry, the two-stream instability generated turbulence might provide effective collisionality to the beamplasma system, which can drive the Weibel instability. 19. Mai 009