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.