particle acceleration by mhd turbulence in solar flares huirong yan (cita) collaborator: alex...
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Particle Acceleration by Particle Acceleration by MHD turbulence in Solar MHD turbulence in Solar
flaresflares
Huirong YanHuirong Yan (CITA) (CITA)
Collaborator: Collaborator:
Alex Lazarian (UW-Madison)Alex Lazarian (UW-Madison)
• Re ~VL/ >> 1
~ rLvth, vth < V, rL<< L
Cosmic ray acceleration is a general problem (ISM, ray burst, solar flares).
Energy transport - MHD turbulence
Energy transport - MHD turbulence
Large scale particleenergy release acceleration
MHD turbulence
From Krucker (2004)
Particle Interaction with turbulence
Particle Interaction with turbulence
Post-shock Pre-shockregion region
1st order Fermi 2nd order Fermi
•Acceleration
Shock frontMagnetic “clouds”
Efficiency of interactions depend on scattering!Efficiency of interactions depend on scattering!
Diffusion in the fluctuating EM fields
Collisionless Fokker-Planck equationBoltzmann-Vlasov eq
B, v<<B0, V (at the scale of resonance)
Fokker-Planck coefficients: D≈ 2/t, Dpp ≈ p2/t are the fundermental parameters we need. And they are determined by properties of turbulence!
How do we study stochastic acceleration and scattering?How do we study stochastic acceleration and scattering?
For TTD and gyroresonance, , scsc//acac≈ Dpp / p2D ≈ (VA/v)2
Examples of MHD modes (Pmag > Pgas)
Alfven mode (v=VA cos)
incompressible;restoring force=mag. tension
k
B
slow mode (v=cs cos)
fast mode (v=VA)restoring force = Pmag + Pgas
Bk
B
restoring force = |Pmag-Pgas|
Models of MHD turbulenceModels of MHD turbulence
• Earlier models 1. Slab model: Only MHD modes propagating along the magnetic field are counted (most calculation were done within this model).
2. Kolmogorov turbulence: isotropic, with 1D spectrum E(k)~k-5/3
• Realistic MHD turbulence (Cho & Lazarian 2002, 2003)
1. Alfven and slow modes: Goldreich-Sridhar 95 scaling
2. Fast modes: isotropic, similar to accoustic turbulence
Anisotropy of MHD modes
Alfven and slow modes Alfven and slow modes fast modes fast modes E
qual
vel
ocity
cor
rela
tion
Equ
al v
eloc
ity c
orre
latio
n c
onto
urco
ntou
r
BB
Gyroresonance
- k||v|| = n(n = ± 1, ± 2 …),
Which states that the MHD wave frequency (Doppler shifted)
is a multiple of gyrofrequency of particles (v is particle speed).
So, k||,res~ /v = 1/rL
Resonance mechanismResonance mechanism
BB
Acceleration by Alfvenic turbulence
Acceleration by Alfvenic turbulence
Alfven modes contribute marginally to particle acceleration if energy is injected from large scale!
2rL
scattering efficiency is reduced
l << l|| ~ rL
2. “steep spectrum”
E(k)~ k-5/3, k~ L1/3k||
3/2
E(k||) ~ k||-2
steeper than Kolmogorov!Less energy on resonant scale
eddieseddiesBB
ll||||
ll
1. “random walk”
B
Alfven modes are inefficient. Fast modes dominate CRscattering and acceleration in spite of damping.
Scattering by MHD turbulence: Examples of ISM
Scattering by MHD turbulence: Examples of ISM
Dpp/p2= D (VA/v)2 D12
(Kolmogorov)
Alfven modesAlfven modes
Big difference!!!Big difference!!!
Fast modesFast modes
Depends on dampingDepends on damping
(Yan & Lazarian 2002)
Damping of fast modesDamping of fast modes
Viscous damping
Collisionless damping
Ion-neutral damping
increase with both plasma and the
angle between k and B.
Cutoff wave number kc :
defined as the scales on which damping rate is equal to
cascading rate
k-1
= (kc vk)2 = (kc L)1/2 V2/Vph .
Transit Time Damping (TTD)
Transit Time Damping (TTD)
Transit time damping (TTD)
Compressibility required!
Landau resonance condition: k||v|| Vph = k v|| cos
kk
no resonant scaleno resonant scaleFrom Suzuki, Yan, Lazarian, From Suzuki, Yan, Lazarian, Cassenelli (2005)Cassenelli (2005)
complication: randomization of during cascade
Randomization of wave vector k:
dk/k ≈ (kL)-1/4 V/VA
Randomization of local B: field line wandering by shearing via Alfven modes:
dB/B ≈ [(V/VA)2cos (kL)-1/2 + (V/VAsin kL)-1/3]1/2
Anisotropic Damping of fast modes
Anisotropic Damping of fast modes
kkBB
Damping depends on the angle
Thermal damping of fast modes in solar flares
Thermal damping of fast modes in solar flares
Yan & Lazarian 2006)
108cm
Without randomizationWith randomization
The angle between k and B
Tru
nca
t ion
wavenu
mber
of
f ast
mod
es
k cL
Damping of fast modes by nonthermal particles
Damping of fast modes by nonthermal particlesD
am
pi n
g c
ut o
ff s
cal e
of
f as t
mod
es
kcL
The angle between k and B
Transit time damping with nonthermal particle is subdominate comparing with thermal damping taking into account field line wandering.
(Yan & Lazarian 2006)
Acceleration via TTD by fast modes
Acceleration via TTD by fast modes
Acceleration by fast modes is an important mechanism to generate high energy particles in Solar flares (Yan, Lazarian 2006);
Summary Summary
• Energy released from large scale burst naturally excites turbulence due to the large Reynolds number of the plasma.
•MHD turbulence is essential for energy transport.
• Fast MHD modes are identified as a major agent for particle acceleration.
• Acceleration is dependent due to damping of fast modes.
• Back reaction from nonthermal particles in many cases is neglegible, which entails decoupling of turbulence damping from particle acceleration and simplifies the problem.