Alfvén-cyclotron wave mode structure: linear and nonlinear behavior

J. A. Araneda1, H. Astudillo1, and E. Marsch2

1Departamento de Física, Universidad de Concepción, Chile2Max Planck Institute for Solar System Research, Katlenburg-Lindau,

GermanyVlasov-Maxwell kinetics: theory, simulations and observations

Wolfgang Pauli Institute, Vienna, March 2011

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.

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.

0112222

ss

s

ss

s

ssssps kv

kVZkv

kVck

Linear Mode StructureIsotropic single proton distribution || << 1

Higher-order modesNormal

modes

Increasing

damping

Linear Mode StructureIsotropic single proton distribution || = 0.1

No mode region

Linear Mode StructureIsotropic single proton distribution || = 0.3

No mode enhanced region

Linear Mode StructureElectron - particles (only) Plasma

-particles higher-order modes

Linear Mode Structuree – p - particles plasma (n/ne=0.0001)

Linear Mode Structuree – p - particles plasma (n/ne=0.01)

Linear Mode Structuree – p - particles plasma (n/ne=0.04)

Linear Mode Structuree – p - particles plasma (n/ne=0.047)

Linear Mode Structuree – p - particles plasma (n/ne=0.05)

Spontaneous FluctuationsTheory 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)

Spontaneous FluctuationsTheory

We use the fluctuation-dissipation theorem (balance between emission and damping) to calculate the spontaneous spectrum of magnetic (or electric) fluctuations

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2

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jlkimnkji DDkkkkcTiBB

ijijkji

kmljmilkji

DDTiJJ

JJDDEE

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Spontaneous Fluctuations B2k

Isotropic single proton distribution || = 0.01

Spontaneous FluctuationsIsotropic single proton distribution || = 0.1

Spontaneous FluctuationsIsotropic single proton distribution || = 0.3

PIC SimulationsHybrid Method (Particle ions and Fluid electrons)

1D, 2048 cells, 800 particles/cell, L ~ 512 VA/p

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

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

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

Spontaneous Fluctuations: Heavy Ions Case (He+2, n/ne = 0.05) with i << 1

Araneda et al., Phys. Plasmas (2011)

Spontaneous Fluctuations (Simulations)(He+2, n/ne = 0.05) with i << 1

Transverse Mode Structure, Heavy Ions Case (He+2, n/ne = 0.05, U = 0.1VA) with i << 1

Spontaneous Fluctuations (Simulations)(He+2, n/ne = 0.05, U = 0.1VA) with i << 1

Harmonic Generation

Analytical Theory

Computer Simulations

• Particle simulationsfor MHD conditions (βp ~ 0)

Power spectra for βp << 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

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 VA)

Driven Ion Acoustic Waves

Driven Ion Acoustic Waves

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

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

Heavy Ions Case (He+2, n/ne = 0.05) with i

<< 1

Selective trapping!

Alphas are too heavy

Ion trapping again, but…

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

Preferential acceleration of heavy ions

Such processes are effective for low betas plasmas

differential motion take place close to the Sun

Preferential acceleration of heavy ions

For lower alpha densities, the relative drift speed is even larger

n/ne=0.01n/ne=0.04