Nonresonant pitch angle scattering of electrons and breakdown of

adiabatic invariance: Modeling

Surja Sharma, Alexey Karavaev, Erin Lynch, Nail Gumerov, Xi Shao, Dennis PapadopoulosUniversity of Maryland, College Park

Yuhou Wang, Walter Gekelman, Patrick PribylUniversity of California Los Angeles

LAPD Expt: Mirror trapped electrons3 m mirror (~1.5), high power microwave produces energetic electrons

Alfven waves produced by rotating magnetic field antenna scatters energetic electrons

Numerical Simulations

Simulation parameters

Alfven wave generation by RMF

Mirror configuration

Magnetic field

Electric field

Energization of electrons Test particles 22,500 electrons uniformly distributed in the

mirror regionInitial pitch angles : 80 – 90 degInitial energies: 1 keVIntegrate:

€

d

dt

m0v

γ

⎛

⎝ ⎜

⎞

⎠ ⎟=− e E+v× B( ),

Evolution of Pitch Angles

Electron scatteringResonance condition:

€

k||v|| −ω =Ωce

γ,

For the low freq. and keV energy:

€

k||v|| ≈ω

VAv|| <

ω

VAv << Ωce.

Non-resonant scattering

Spatial distribution of electronsAt 25 wave periods

Single loop antenna

RMF - Left hand polarization

RMF - Right hand polarization

Evolution of Pitch Angles

Surface of Section PlotsA surface of section (SoS) plots Vperp vs. Vpar as an electron crosses the plane x = 0 from right to left.

Escaped electron

SoS: Trapped electron

• Here is a similar plot for another particle that did not escape.

SoS: Escaping electron

• This surface of section depicts a particle that did escape from the simulation.

SoS : 5 wave cycles

SoS: 10 wave cycles

SoS: 25 wave cycles

Surfaces of Section

5 wave cycles

10 wave cycles 25 wave cycles

Pitch angle distribution functions

Single loop antenna Rotating Field: Left and Right handed

Summary

Interaction of energetic electrons with RMF generated Alfven waves

Electron scattering by Alfven waves computed from numerical model

Nonresonant scattering leads to pitch angle scattering

Surface of section plots to analyze electron velocity evolution

Trapped electrons escape at ~ 10 wave periods

Combined effects of the pitch angle scattering and breakdown of adiabatic invariance