1. Cosmic Ray Scattering in MHD Turbulence
Andrey Beresnyak, Huirong Yan, Alex Lazarian
Univ. of Wisconsin-Madison

2. What is the interaction dominant in space?
Textbooks say: electric charges cancel, gravity is the
only relevant interaction.
But in a conductive (ionized) matter currents (and magnetic fields) exist on all scales! Local dynamics is often dominated by kinetic motions, magnetic fields and Cosmic Rays.
Evolution of Knowledge
of baryon matter dynamics:
gravity(acting on pressureless “dust” matter) ->
gravity+fluid (with pressure) ->
gravity+magnetized fluid (MHD) ->
gravity+magnetized fluid +CRs

3. (near Earth wCR~1 eV/cm3)
In fact CR pressure is important in most environments,
being of the order of magnetic and kinetic pressures.
(near Earth wCR~1 eV/cm3)
Galaxies
B~5G
(1eV/cm3)
Clusters
B~1G
Sources of energy for B and CRs:
1. Directly from gravity (e.g., MRI)
2. AGN jets
3. Stellar winds
4. SN explosions
CR scattering is fundamental for understanding interaction of fluid and CRs. Simplistic, ad-hoc models of scattering lead to poorly based acceleration models.

4. Concepts in scattering
Scattering by existing fields
Self-scattering(instabilities) - not in this talk…
see, e.g. Lazarian&Beresnyak, MNRAS (2006),
Beresnyak&Lazarian, ApJ (2008)
Regular field
Magnetic mirrors
D~const
D/~r
Random field
Resonant scattering B
D/ ~r2.5

5. 3D direct numerical simulations
up to points B w- w+
Elsasser variables - vector amplitudes of waves
(include both Alfven and pseudo-Alfven mode)

6. Structure of perturbations in MHD turbulence
<(B(r)-B(r+l))2>
driving
Perpendicular distance
dissipation
parallel distance (along B)
Turbulence fields are neither regular, nor fully random (-correlated).

7. quality-controlled particle tracer)
Particle scattering
measured
D/~r
— gyration frequency,
L — outer scale of turbulence.
D/~r2.5
(obtained from a realistic B and E fields from direct numerical simulations+
quality-controlled particle tracer)

8. Space diffusion along B0 A measure of the scattering
transAlfvenic B~B0
along B0
A measure of the scattering
A measure of the field line diffusion
subAlfvenic B~B0/10
perpendicular to B0

9. Conclusion
Magnetic fields and Cosmic rays are important for dynamics in most environments.
Scattering transfers momentum and energy between fluid and CRs.
Resonance theory predicts scattering which is way too low.
Most of the scattering comes from large scale magnetic bottles.
Perpendicular diffusion is due to field wandering.