1. MHD Turbulence and Energetic Particles
Alex Lazarian (Astronomy, Physics and CMSO)
Thanks to: H. Yan, A. Beresnyak, J. Cho, G. Kowal, A. Chepurnov , G. Brunetti, V. Petrosian, E. Vishniac, G. Eyink, T. Jones, Pohl etc.

2. Example: Big Power Law reveals Kolmogorov spectrum of electron density fluctuations
ISM Turbulence Spectrum
Electron density spectrum
Slope ~ -5/3
WHAM emission: density fluctuations
Scincillations and scattering
from Armstrong, Rickett & Spanger 1994
E(k)~k-5/3 pc AU
Kolmorogov law for turbulence
Chepurnov & Lazarian 2010 2

3. Turbulent 2nd order Fermi Acceleration
This talk shows that turbulence is essential for understanding CR acceleration, makes 4 points:
Turbulent 2nd order Fermi Acceleration
Turbulence and shock acceleration
Turbulent reconnection induces acceleration “

4. Point I. Turbulence induces both scattering and the second order Fermi process
Magnetic
“clouds”

5. Resonance and Transit Time Damping (TTD) are examples of 2nd order Fermi processB rL
n=1
n=0

6. Diffusion in the fluctuating EM fields
Turbulence properties determine the diffusion and acceleration
Diffusion in the fluctuating EM fields
Collisionless Fokker-Planck equation
Boltzmann-Vlasov eq
dB, dv<<B0, V (at the scale of resonance)
Fokker-Planck coefficients: Dmm ≈ Dm2/Dt, Dpp ≈ Dp2/Dt are the
fundermental parameters we need. Those are determined by
properties of turbulence!
For TTD and gyroresonance,
tsc/ tac ≈ Dpp / p2Dmm ≈ (VA/v)2

7. l|| ~L1/3l^2/3 Alfven ~k-5/3 slow ~k-5/3 fast ~k-3/2
For acceleration and scattering it is important that MHD turbulence is anisotropic
Equal velocity correlation
contour (Cho & Lazarian 02, 03)
Alfven and slow modes (GS95)
l|| ~L1/3l^2/3
Alfven
~k-5/3
slow
~k-5/3 B
anisotropic eddies
fast
~k-3/2
fast modes

8. Alfvenic turbulence marginally scatter/accelerate cosmic rays
Beresnyak & Lazarian 08
(Kolmogorov)
Alfven modes
Big difference!!!
Streaming instability is suppressed by ambient turbulence: damping versus k
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
1. “random walk”
2rL B
Scattering frequency
lperp<< l|| ~ rL
l||
(Chandran 2000) B
eddies l⊥
scattering efficiency is reduced
Kinetic energy
Chandran 00, Yan & Lazarian 02, 04

9. Scattering depends on damping
Fast modes are identified as major agent of of Cosmic Rays scattering and 2nd order Fermi acceleration
Scattering depends on damping
fast modes
Damping depends on plasma magnetization. Observed secondary elements supports scattering by fast modes (Yan & Lazarian 02, 04). Application to galaxy clusters is in Brunetti & Lazarian (07, 11).

10. Fast modes explain observed flat dependence of mean free path of energy (Palmer consensus)
CR Transport in ISM
from Bieber et al 1994
Palmer consensus
Mean free path (pc)
Text
WIM
halo
Kinetic energy
Flat dependence of mean free path can occur due to collisionless damping (Yan & Lazarian 2004, 2009).

11. Whether and to what degree CRs diffusion is
Perpendicular diffusion is determined by magnetic wandering
Whether and to what degree CRs diffusion is
suppressed depends on || and MA.
|| > L, CR diffusion is controlled by field line wandering
MA< 1, CRs free stream over distance L, thus D⊥ =R2 /∆t= Lv|| MA4
MA >1, D⊥ = LA v||
At smaller scale superdiffusion y~ x3/2
Lazarian 2006, Yan & Lazarian 2010, Lazarian & Yan 2012

12. dB direction changes during cascade
To understand the perpendicular diffusion and fast mode damping one should take into account wandering of magnetic field lines induced by Alfvenic turbulence
Magnetic field wandering induced by Alfvenic turbulence was described in Lazarian & Vishniac 1999
dB direction changes during cascade
Field line wandering
Randomization of local B: field line
wandering by shearing via Alfven modes:
dB/B ≈ (V/L)1/2 tk1/2
Randomization of wave vector k:
dk/k ≈ (kL)-1/4 V/Vph k Q
Lazarian, Vishniac & Cho 2004 B
Yan & Lazarian 2004

13. Point II. Turbulence alters processes of Cosmic Ray acceleration in shocks
Acceleration in shocks requires scattering of particles back from the upstream region.
Downstream Upstream
Magnetic turbulence generated by shock
Magnetic fluctuations generated by streaming

14. Transient turbulent magnetic structures explain X-ray observations of young SNRs
Chandra
Alfvenic turbulence decays in one eddy turnover time (Cho & Lazarian 02), which results in magnetic structures behind the shock being traisient and generating filaments of a thickness of cm (Pohl, Yan & Lazarian 05).

15. Precursor forms in front of the shock and it gets turbulent as precursor interacts with gas density fluctuation
Beresnyak, Jones & Lazarian 2009

16. Turbulence efficiently generates magnetic fields as shown by Cho et al
hydrodynamic
cascade
MHD scale

17. Magnetic field generated by precursor -- density fluctuations interaction may be larger than the arising from Bell’s instability
current instability
jCR B

18. Point III. Fast reconnection of 3D weakly turbulent magnetic fields can efficiently accelerate Cosmic Rays
LV99 reconnection:
1. Outflow is determined by field wandering.
2. Reconnection is fast with Ohmic resistivity only.
B dissipates on a small scale || determined by turbulence statistics.
Lazarian & Vishniac (1999)
henceforth referred to as LV99

19. Simulations with *different* types of driving confirm LV99 predictions
Reconnection rate
Lazarian & Vishniac (1999) prediction is Vrec~ Pinj1/2
New simulations
Turbulent power
Kowal et al. 2012

20. In LV99 reconnection model energetic particles get accelerated by First Order Fermi mechanism
(Similar to Drake 2006).
Cosmic rays get spectrum steeper than from shocks
From Lazarian 05
Published in De Gouveia Dal Pino & Lazarian 2003
Effects of compressibility see Drury 2012

21. Convergence between the plasma-based reconnection and LV99 model is evident!
Paradigm 1999
LV99 model
Hall effect is required
Hall effect is not required
Paradigm 2012
(Fully 3D, turbulence)
3D simulations without turbulence show transfer to turbulent state (e.g. Karimabadi 2012)
Drake et al. 2006
Tearing reconnection (Hall effect is not required )

22. MHD calculations reproduce parallel acceleration in 2D PIC calculations by Drake et al and go beyond
Zoom in into itrajectories
Regular energy increase
Multiple reconnection layers are used to produce volume reconnection.
Kowal et al. 2010

23. First order Fermi acceleration happens also for perpendicular components
Converging flow

24. Perpendicular First order Fermi acceleration may dominate in 3D reconnection in the presence of turbulence
Kowal et al. 2012

25. Acceleration in sites of turbulent reconnection may be important for many astrophysical settings. *Selected* ones:
Acceleration of anomalous cosmic rays (Lazarian & Opher 2009, Drake et al. 2010)
Acceleration of cosmic rays in heliotail (Lazarian & Desiati 2010)
Acceleration of particles during gamma ray bursts (Lazarian et al. 2003, Zhang & Yan 2011)

26. Turbulence and its effects are essential for understanding cosmic ray spectrum
Recent example: turbulent reconnection allows a new First order Fermi acceleration mechanism

27. Non-linear extension of QLT are necessary to describe diffusion and acceleration, especially by TTD mechanism
Numerical testing
Momentum diffusion
from adiabatic invariant
TTD scattering by slow modes
broadened resonance function
Basis of Nonlinear QLT (Yan & Lazarian 2008)
Applied for Solar acceleration in
Yan, Lazarian & Petrosian 2008
Beresnayk, Yan & Lazarian 2011

28. Streaming instability is inefficient for producing large field in the preshock region
Beresnyak & Lazarian 08
Decay rate of waves in turbulence k
shock
Streaming instability is suppressed in the presence of external turbulence (Yan & Lazarian 02, Farmer & Goldreich 04, Beresnyak & Lazarian 08).
Non-linear stage of streaming instability is inefficient (Diamond & Malkov 07).

29. What does happen: parallel or perpendicular First order Fermi acceleration?
Lazarian 2005
Parallel acceleration (similar to that
In Drake et al. 2006)
Perpendicular acceleration

30. VCA and VCS are our new techniques to study supresonic turbulence
VCA and VCS are our new techniques to study supresonic turbulence. Sparsely sampled data can be delt with VCS.
VCS
Developed in Lazarian & Pogosyan 00, 06, 08

31. VCA and VCS techniques (Lazarian & Pogosyan 00, 04, 06, 08) reveal turbulence velocity spectra in agreement with expectations for supersonic turbulence
Kowal & Lazarian 2010
Kowal, Lazarian & Beresnyak 2007
Velocity spectrum gets steep
Density spectrum gets shallow
Expectations for supersonic turbulence
Selected results for the techniques
VCS gets
for high latitude galactic HI Ev~k (Chepurnov et al.08,10)
for 13CO for the NGC 1333 Ev~k1.85 (Padoan et al. 09) indicating supersonic turbulence. Density is shallow ~k-0.8

32. Big Implication: LV99 means that magnetic field in turbulent fluids is not frozen in
Hannes Alfven
Violation of magnetic field frozen in condition in turbulent fluids discussed in Eyink (2010, 2011). The equivalence of this to LV99 approach was demonstrated in Eyink, Lazarian & Vishniac Recent numerical evidence is in Eyink et al. (2012, Nature, submitted).

33. Bell (2004) proposed a solution based on the current instability
jCR B
shock

34. The model allows to calculate the parameters of magnetic field
Beresnyak, Jones & Lazarian 2010

35. Streaming instability in the preshock region is a textbook solution for returning the particles to shock region vA B
shock