Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Plasma Physics
Volume 67, Number 15
Monday–Friday, October 17–21, 2022; Spokane, Washington
Session PO07: Fundamental Plasmas: Waves, Oscillations, Instabilities
2:00 PM–5:00 PM,
Wednesday, October 19, 2022
Room: 401 ABC
Chair: Stephen Vincena, UCLA
Abstract: PO07.00008 : Multimode theory of electron hole instability
3:24 PM–3:36 PM
Presenter:
Ian Hutchinson
(Massachusetts Institute of Technology MI)
Authors:
Ian Hutchinson
(Massachusetts Institute of Technology MI)
Xiang Chen
(Massachusetts Institute of Technology MI)
and lifetime, of an initially planar electron hole (BGK) structure.
The $f_1(v)$ is found by integration along unperturbed orbits in
a non-sinusoidal potential perturbation shape (parallel to $B$)
expanded in eigenfunctions of the adiabatic Poisson operator. This
generalizes the prior assumption of a rigid shift of the equilibrium.
The shiftmode is then modified by a second discrete mode plus an
integral over a continuum of wave-like modes. A rigorous treatment
shows that the continuum can be approximated effectively by a single
mode that satisfies the external wave dispersion relation, thus making
the perturbation a weighted sum of three modes. We find numerically
the solution for the complex instability frequency, and for the
corresponding 3 mode amplitudes determining the perturbation
eigenmode. This multimode analysis refines the accuracy of the prior
shiftmode results, giving slightly higher growth rates at most
parameters, as expected from the extra mode shape freedom. Oscillating
modes near stability boundaries have larger eigenmode distortions
which helps explain PIC simulations that observe spatial narrowing of
the perturbation, and instability at up to $\sim20$\% beyond the prior
shiftmode thresholds.
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