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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
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