1. Plasmas in Laboratory and Astrophysics Alfven Wave Turbulence and Heating.
Center for Multi-scale Plasma Dynamics.
Bill Dorland, Maryland.
Alex Schekochihin, Cambridge.
Steve Cowley, UCLA/Imperial College.
Troy Carter, Brian Brugman,Warren Lyberger, Pat Pribyl, UCLA.
Greg Howes, Eliot Quataert, Berkeley.
Greg Hammett, Princeton.
Thanks to: Stewart Prager, U. Wisconsin and the members of the
Center for Magnetic Self Organization for data.

2. Accretion and MHD. Instability Tangled B Field.  Momentum transport.
Gravitational energy loss
Turbulent energy
Dissipation, Heat to ??
Electrons -- radiation.
Ions -- swallowed
by black hole.
Quataert and Gruzinov.

3. toroidal magnetic flux
Magnetic self-organization in the lab., MST Reversed Field Pinch at Wisconsin, Prager et. al.
magnetic fluctuations
toroidal magnetic flux
dynamo
heat flux
(MW/m2)
energy transport
rotation
(km/s)
momentum transport
ion temperature
(keV)
ion heating
time (ms)

4. Small Scales.
Kraichnan argued that the small scale motions will see a large quasi-uniform
field. The small scale motions will become Alfven/slow waves traveling along a
roughly uniform B.
Most of the dissipation happens at small scales -- these
arguments suggest that the dissipation is of small amplitude
Alfven/slow waves.

5. Introduction.
Need to understand the turbulent cascade of Alfven waves.
Many applications: astrophysics, fusion, space.
MHD regime -- Goldreich - Sridhar theory.
Collisionless regime -- gyrokinetics.
Heating in gyrokinetics
Simulations. Bill Dorland, Greg Howes.
Experiments. Troy Carter, Brian Brugman, Warren Lyberger, Pat Pribyl.

6. MHD Waves. (Review) k Slow Waves k, B0 and displacement coplanar.
Collision Mean
Free path
Damped by transit time damping when k||  mfp~1.
Displacement perpendicular to
B0 and k.
Alfven Waves k
Ion Larmor radius
No damping until k i ~1

7. Alfven Wave Interaction.
Incompressible MHD, Kraichnan, Goldreich and Sridhar.
B0=B0z
Positive and negative waves
traveling along B0.
Only oppositely going waves interact nonlinearly

8. Two Wave packets - passing through.
Three wave weak interaction for oppositely directed
waves gives.
Thus
and there is no cascade in

9. Strong Alfven Cascade.
Goldreich-Sridhar Komolgorov argument.
Alfven waves stirred at scale l0 with velocity v0
Energy flux from scale l to 2l
Constant from scale to scale.
Cascade time
Assuming
strong interaction
GS argue that the scale l is the perpendicular scale and
that the parallel scale is set by “critical balance.”
Nonlinear rate = Linear rate

10. Spectrum. Gyrokinetic regime Ek Slow Wave Alfven Wave Collisionless k
MHD simulations Maron & Goldreich confirm scaling.
Cyclotron frequency
Gyrokinetic regime Ek
Slow Wave
Alfven Wave
Collisionless k

11. . Gyro-kinetic Fluctuations. L|| Vion B p B Vflow L B0
Parallel scale >> Perpendicular scale, L|| >>L~i
Particle displacement, p ~ Of Order Field line displacement, B ~ O(L)

12. Gyro-kinetic Fluctuations.
Ion position
L||
Vion
“Ring”
Center=R B
Ring radius
=  = v/i B0
Parallel scale >> Perpendicular scale, L|| >>L~i
Particle displacement, p ~ Of Order Field line displacement, B ~ O(L)

13. Gyro-kinetic Equation.
Taylor and Hastie,Frieman and Chen ……
Ion kinetic energy
Maxwellian evolving
on slow heating
timescale
Shift in energy
Due to potential
Perturbed Distribution
Of “rings”
Collisions
Evolution of the Rings
5D!
+ Maxwell’s equations.

14. Box Gyro-kinetic Simulation MHD regime -- Bill Dorland.
Waves launched
by “numerical
antenna” driven
by stochastic
oscillator.

17. Gyro-kinetic heating. Collisional Time averaged qE.v energy exchange
Work done on particles
Numerically it is hard to compute the heating this way
because energy sloshes in and out of particles. We can
show that it is equivalent to an expression derived from
ENTROPY PRODUCTION.
This term is positive and much easier to average, heating always
comes from collisions even in collisionless regime!

18. Mixing in Phase Space.
f(r,v,t) is conserved along particle orbits in collisionless motion.
Stochasticity in orbits leads to fine scale mixing - jagged f. Less collisions  more jagged f. Entropy production becomes independent of collision rate. f v

19. New Simulations
Current simulations are doing the kinetic regime and caculating the ion and electron heating Qe=Qe(Te/Ti, ), Qi=Qi(Te/Ti, ) Bill Dorland, Greg Howes.
Need to understand the cascade in this regime and examine the dynamics.

20. Cavity Launched Wave Experiment Design LAPD.
Reflecting Cavity Design
Alfvén waves are launched into a plasma column terminated by a reflecting plate
Co- and Counter-propagating interactions occur
Single Pass Design.
Alfvén waves are launched into the open plasma column.
Only co-propagating geometry is possible.

21. The Spontaneous and Driven cavity waves in Concert are also Unstable
Using the Natural MASER as the pump wave and the Driven MASER as a sideband the  dependence of the instability may be investigated.

22. Possible Experiment Geometries
Single Pass, co-propagating and counter-propagating separately
Multiple pass, co-propagating and counter-propagating combined

23. CONCLUSIONS Well defined problem that needs a solution.
Excellent use of fusion codes - well adapted to the problem.
Experimental study on LAPD will yield further results this year.