Semi-local Floquet theory for active azimuthal magnetic modulation of Hall-thruster high-frequency instabilities
Abstract
We develop a semi-local Floquet model to screen active azimuthal magnetic modulation as a control approach for high-frequency drift instabilities in Hall thrusters. The uniform-field kinetic response supplies a local kernel for a finite sideband matrix, and stability is measured by the upper growth envelope over the Bloch zone. Root searches include both frequency branches, continuation, singular-value validation, and contour root counts. At the reference normalized parallel wave number k_z = 0.045, for sinusoidal profiles with periods of 10, 20, and 40 mm, every nonzero sampled modulation amplitude increases both the peak and integrated positive Bloch-zone growth. The uniform-field reference is already unstable, so these increases describe faster linear amplification rather than the onset of instability from a stable state. At a period of 20 mm and relative amplitude 0.5, the peak and integral increase by 26.74 and 26.44 percent, respectively; this large amplitude requires caution within the semi-local ordering. Selected projected wave-number windows still show reductions, but these coexist with enhanced global growth and do not establish stabilization. A supplementary parallel-wave-number scan finds weak global growth reduction at k_z = 0.09: at 20 mm and amplitude 0.3, the peak and integral decrease by 0.300 and 0.299 percent, respectively, while the spectrum remains unstable. The sign and magnitude of the modulation effect therefore depend on the tested plasma parameters; neither these small reductions nor the local projected changes establish improved nonlinear transport.
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BibTeX
@misc{zhao2026semilocal,
title = {{Semi-local Floquet theory for active azimuthal magnetic modulation of Hall-thruster high-frequency instabilities}},
author = {Yinjian Zhao and Changzheng Hu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.21265},
eprint = {2606.21265},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.21265},
}
RIS
TY - UNPB
TI - Semi-local Floquet theory for active azimuthal magnetic modulation of Hall-thruster high-frequency instabilities
AU - Yinjian Zhao
AU - Changzheng Hu
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2606.21265
UR - https://arxiv.org/abs/2606.21265
AB - We develop a semi-local Floquet model to screen active azimuthal magnetic modulation as a control approach for high-frequency drift instabilities in Hall thrusters. The uniform-field kinetic response supplies a local kernel for a finite sideband matrix, and stability is measured by the upper growth envelope over the Bloch zone. Root searches include both frequency branches, continuation, singular-value validation, and contour root counts. At the reference normalized parallel wave number k_z = 0.045, for sinusoidal profiles with periods of 10, 20, and 40 mm, every nonzero sampled modulation amplitude increases both the peak and integrated positive Bloch-zone growth. The uniform-field reference is already unstable, so these increases describe faster linear amplification rather than the onset of instability from a stable state. At a period of 20 mm and relative amplitude 0.5, the peak and integral increase by 26.74 and 26.44 percent, respectively; this large amplitude requires caution within the semi-local ordering. Selected projected wave-number windows still show reductions, but these coexist with enhanced global growth and do not establish stabilization. A supplementary parallel-wave-number scan finds weak global growth reduction at k_z = 0.09: at 20 mm and amplitude 0.3, the peak and integral decrease by 0.300 and 0.299 percent, respectively, while the spectrum remains unstable. The sign and magnitude of the modulation effect therefore depend on the tested plasma parameters; neither these small reductions nor the local projected changes establish improved nonlinear transport.
ER -