1. Alfvén-cyclotron wave mode structure: linear and nonlinear behavior J. A. Araneda 1, H. Astudillo 1, and E. Marsch 2 1 Departamento de Física, Universidad de Concepción, Chile 2 Max Planck Institute for Solar System Research, Katlenburg-Lindau, Germany Vlasov-Maxwell kinetics: theory, simulations and observations Wolfgang Pauli Institute, Vienna, March 2011

2. Introduction  The purpose of this talk is to show some “new” aspects of the plasma kinetic theory which may be important in space plasma physics.  We emphasize the roles of higher-order modes and of spontaneous electromagnetic fluctuations.  We also consider the role of self-consistent electromagnetic fluctuations, which scatter plasma particles and which may couple to other modes via wave-wave interactions.

3. Linear kinetic theory: normal and higher-order modes  To begin with, le us to consider the solutions of the linear kinetic dispersion relation for (for simplicity) parallel propagating waves.  We compute all roots of the equation where  is the anisotropy, V the drift speed, v the thermal speed, and Z the plasma dispersion function.

4. Linear Mode Structure Isotropic single proton distribution  || << 1 Higher-order modes Normal modes Increasing damping

5. Linear Mode Structure Isotropic single proton distribution  || = 0.1 No mode region

6. Linear Mode Structure Isotropic single proton distribution  || = 0.3 No mode enhanced region

7. Linear Mode Structure Electron -  particles (only) Plasma  -particles higher-order modes 

8. Linear Mode Structure e – p -  particles plasma (n  /n e =0.0001)

9. Linear Mode Structure e – p -  particles plasma (n  /n e =0.01)

10. Linear Mode Structure e – p -  particles plasma (n  /n e =0.04)

11. Linear Mode Structure e – p -  particles plasma (n  /n e =0.047)

12. Linear Mode Structure e – p -  particles plasma (n  /n e =0.05)

13. Spontaneous Fluctuations Theory and Observations  Even in the absence of plasma instabilities, a finite-temperature plasma has small but detectable electromagnetic fluctuations (see Electromagnetic Fluctuations in a Plasma, A. G. Sitenko, 1967; Statistical Plasma Physics, S. Ichimaru).  Quasi-thermal electrostatic emissions in the outer magnetosphere (Shaw and Gurnett, 1975), in the solar wind (Meyer-Vernet et al., 1986)  The spontaneous emission of magnetic field fluctuation is supposed to provide the seed perturbation for the Weibel instability (Yoon, Phys. Plasmas, 2007; Tautz and Schlickeiser Phys. Plasmas, 2007)  Possible role of spontaneous magnetic field fluctuations in the description of the turbulence cascade (Yoon, Phys. Plasmas, 2008)

14. Spontaneous Fluctuations Theory  We use the fluctuation-dissipation theorem (balance between emission and damping) to calculate the spontaneous spectrum of magnetic (or electric) fluctuations

15. Spontaneous Fluctuations  B 2   k Isotropic single proton distribution  || = 0.01

16. Spontaneous Fluctuations Isotropic single proton distribution  || = 0.1

17. Spontaneous Fluctuations Isotropic single proton distribution  || = 0.3

18. PIC Simulations Hybrid Method (Particle ions and Fluid electrons) 1D, 2048 cells, 800 particles/cell, L ~ 512 V A /  p

19. Spontaneous Fluctuations (Simulations) Isotropic single proton distribution  || << 1

20. Spontaneous Fluctuations (Simulations) Isotropic single proton distribution  || = 0.1

21. Spontaneous Fluctuations (Simulations) Isotropic single proton distribution  || = 0.3

22. Spontaneous Fluctuations: Heavy Ions Case (He +2, n  /n e = 0.05) with  i << 1 Araneda et al., Phys. Plasmas (2011)

23. Spontaneous Fluctuations (Simulations) (He +2, n  /n e = 0.05) with  i << 1

24. Transverse Mode Structure, Heavy Ions Case (He +2, n  /n e = 0.05, U = 0.1V A ) with  i << 1

25. Spontaneous Fluctuations (Simulations) (He +2, n  /n e = 0.05, U = 0.1V A ) with  i << 1

26. Harmonic Generation Analytical Theory Computer Simulations Particle simulations for MHD conditions (β p ~ 0)

27. Power spectra for β p << 1 The kinetic plasma response differs from fluids even for a small but finite value of proton plasma β Original position of the MHD instability Two new types of kinetic instabilities instead

28. IAW driven by the Decay or Beat instabilities have low phase speeds IAW driven by the Modulational instability have larger phase speeds (slope ~ 0.7 V A ) Driven Ion Acoustic Waves

29. IAW driven by the M instability trap ions localized on the tail of the distribution

30. Trapping and Induced Pitch-angle Scattering Pitch-angle scattering induced by the growing parallel electric fluctuations Initial distribution too cold,  cyclotron resonance may be effective only after heating, and... Proton core gets anisotropically heated Araneda, Marsch, Vinas, PRL 2008

31. Heavy Ions Case (He +2, n  /n e = 0.05) with  i << 1 Selective trapping! Alphas are too heavy  Ion trapping again, but…

32.   Alphas are not trapped, but the induced pitch-angle scattering produce preferentially heated heavy ion distributions Preferential heating of alpha particles As a result, we observe the anisotropically heated proton core, the beam, and the heated alphas Araneda, Maneva, Marsch, PRL 2009

33. Preferential acceleration of heavy ions Such processes are effective for low betas plasmas  differential motion take place close to the Sun

34. Preferential acceleration of heavy ions For lower alpha densities, the relative drift speed is even larger n  /n e =0.01 n  /n e =0.04