alfvén-cyclotron wave mode structure: linear and nonlinear behavior j. a. araneda 1, h. astudillo...
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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,
Germany
Vlasov-Maxwell kinetics: theory, simulations and observations
Wolfgang Pauli Institute, Vienna, March 2011
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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.
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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.
01
12222
ss
s
ss
s
ssssps kv
kVZ
kv
kVck
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Linear Mode StructureIsotropic single proton distribution || << 1
Higher-order modesNormal
modes
Increasing
damping
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Linear Mode StructureIsotropic single proton distribution || = 0.1
No mode region
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Linear Mode StructureIsotropic single proton distribution || = 0.3
No mode enhanced region
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Linear Mode StructureElectron - particles (only) Plasma
-particles higher-order modes
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Linear Mode Structuree – p - particles plasma (n/ne=0.0001)
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Linear Mode Structuree – p - particles plasma (n/ne=0.01)
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Linear Mode Structuree – p - particles plasma (n/ne=0.04)
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Linear Mode Structuree – p - particles plasma (n/ne=0.047)
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Linear Mode Structuree – p - particles plasma (n/ne=0.05)
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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)
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Spontaneous FluctuationsTheory
We use the fluctuation-dissipation theorem (balance between emission and damping) to calculate the spontaneous spectrum of magnetic (or electric) fluctuations
1123
2
4 nknklm
jlkimnkji DDk
kkkcTiBB
ijijkji
kmljmilkji
DDTi
JJ
JJDDEE
4
/)4( 1122
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Spontaneous Fluctuations B2k
Isotropic single proton distribution || = 0.01
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Spontaneous FluctuationsIsotropic single proton distribution || = 0.1
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Spontaneous FluctuationsIsotropic single proton distribution || = 0.3
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PIC SimulationsHybrid Method (Particle ions and Fluid electrons)
1D, 2048 cells, 800 particles/cell, L ~ 512 VA/p
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Spontaneous Fluctuations (Simulations)Isotropic single proton distribution || << 1
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Spontaneous Fluctuations (Simulations)Isotropic single proton distribution || = 0.1
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Spontaneous Fluctuations (Simulations)Isotropic single proton distribution || = 0.3
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Spontaneous Fluctuations: Heavy Ions Case (He+2, n/ne = 0.05) with i << 1
Araneda et al., Phys. Plasmas (2011)
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Spontaneous Fluctuations (Simulations)(He+2, n/ne = 0.05) with i << 1
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Transverse Mode Structure, Heavy Ions Case (He+2, n/ne = 0.05, U = 0.1VA) with i << 1
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Spontaneous Fluctuations (Simulations)(He+2, n/ne = 0.05, U = 0.1VA) with i << 1
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Harmonic Generation
Analytical Theory
Computer Simulations
• Particle simulations
for MHD conditions (βp ~ 0)
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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
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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
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Driven Ion Acoustic Waves
IAW driven by the M instability trap ions localized on the tail of the distribution
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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
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Heavy Ions Case (He+2, n/ne = 0.05) with i
<< 1
Selective trapping!
Alphas are too heavy
Ion trapping again, but…
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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
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Preferential acceleration of heavy ions
Such processes are effective for low betas plasmas
differential motion take place close to the Sun
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Preferential acceleration of heavy ions
For lower alpha densities, the relative drift speed is even larger
n/ne=0.01n/ne=0.04