Particle Acceleration by MHD turbulence in Solar flares Huirong Yan (CITA) Collaborator: Alex Lazarian (UW-Madison)

Re ~VL/ >> 1 ~ r L v th, v th < V, r L << L Cosmic ray acceleration is a general problem (ISM,  ray burst, solar flares). Energy transport - MHD turbulence Large scale particle energy release acceleration MHD turbulence From Krucker (2004)

Particle Interaction w ith turbulence Post-shockPre-shockregion 1st order Fermi 2nd order Fermi Acceleration Shock front Magnetic “clouds” Efficiency of interactions depend on scattering!

Diffusion in the fluctuating EM fields CollisionlessFokker-Planck equation Boltzmann-Vlasov eq   B,  v<<B 0, V (at the scale of resonance) Fokker-Planck coefficients: D  ≈  2 /  t, D pp ≈  p 2 /  t are the fundermental parameters we need. And they are determined by properties of turbulence! How do we study stochastic acceleration and scattering?, For TTD and gyroresonance,  sc /  ac   sc /  ac  ≈ D pp / p 2 D  ≈ (V A /v) 2

Examples of MHD modes (P mag > P gas ) Alfven mode (v=V A cos  ) incompressible; restoring force=mag. tension k B slow mode (v=c s cos  ) fast mode (v=V A ) restoring force = P mag + P gas B k B restoring force = |P mag -P gas |

Models 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 fast modes Equal velocity correlation contour contourB

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/r L Resonance mechanism B

Acceleration by Alfvenic turbulence Alfven modes contribute marginally to particle acceleration if energy is injected from large scale! 2r L scattering efficiency is reduced l  << l || ~ r L 2. “steep spectrum” E(k  )~ k  -5/3, k  ~ L 1/3 k || 3/2 E(k || ) ~ k || -2 steeper than Kolmogorov! Less energy on resonant scaleeddies B l || llll 1. “ random walk” B

Alfven modes are inefficient. Fast modes dominate CR scattering and acceleration in spite of damping. Scattering by MHD turbulence: Examples of ISM D pp /p 2 = D  (V A /v) 2  D   1  2 (Kolmogorov) Alfven modes Big difference!!! Fast modes Depends on damping (Yan & Lazarian 2002)

Damping of fast modes Viscous damping Collisionless damping Ion-neutral damping increase with both plasma  and the angle  between k and B. Cutoff wave number k c : defined as the scales on which damping rate is equal to cascading rate  k -1 =   (k c v k ) 2 = (k c L) 1/2 V 2 /V ph.

Transit Time Damping (TTD) Transit time damping (TTD) Compressibility required! Landau resonance condition:  k || v || V ph =  k v || cos  k no resonant scale From Suzuki, Yan, Lazarian, Cassenelli (2005)

  complication: randomization of  during cascade Randomization of wave vector k: dk/k ≈ (kL) -1/4 V/V A Randomization of local B: field line wandering by shearing via Alfven modes: dB/B ≈ [(V/V A ) 2 cos  (kL) -1/2 + (V/V A sin    kL) -1/3 ] 1/2 Anisotropic Damping of fast modes k B  Damping depends on the angle 

Thermal damping of fast modes in solar flares  Yan & Lazarian 2006)  10 8 cm Without randomization With randomization  The angle between k and B Truncation wavenumber of fast modes k c L

Damping of fast modes by nonthermal particles Damping cutoff scale of fast modes 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 by fast modes is an important mechanism to generate high energy particles in Solar flares (Yan, Lazarian 2006);

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.