Semi-local Floquet theory for active azimuthal magnetic modulation of Hall-thruster high-frequency instabilities

Abstract

A semi-local Floquet extension of a uniform-field kinetic electron drift instability (EDI) dispersion relation is developed to assess prescribed azimuthal magnetic-field modulation as a linear pre-screening tool for Hallthruster high-frequency instabilities. The uniform kinetic response is used as a local spectral kernel, while a sinusoidal magnetic modulation couples Floquet sidebands and replaces the scalar dispersion condition by a finite matrix dispersion problem. The numerical procedure combines scalar uniform-field predictors, determinant correction, singular-value diagnostics, sideband-weight analysis, and truncation checks. Because a single Floquet root contains multiple physical wave numbers, stability is assessed with the upper growth envelope over the Bloch zone rather than with an individual projected azimuthal wave-number branch. Parameter scans over modulation wavelength and amplitude show that sinusoidal azimuthal magnetic modulation broadens the coupled spectrum and redistributes unstable growth among low-wave-number modified-two-stream-like and cyclotron-resonant ranges. Some long-wavelength, moderate-to-large-amplitude cases reduce integrated positive growth measures, but these reductions are not accompanied by robust suppression of the peak growth envelope. No tested case produces a finite stable Bloch interval. Within the present cold-ion semi-local Floquet model, prescribed azimuthal magnetic modulation is therefore better interpreted as a spectral-redistribution mechanism than as a robust linear stabilization mechanism by itself.