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Title: Stability of Brillouin flow in the presence of slow-wave structure

Abstract

Including a slow-wave structure (SWS) on the anode in the conventional, planar, and inverted magnetron, we systematically study the linear stability of Brillouin flow, which is the prevalent flow in crossed-field devices. The analytic treatment is fully relativistic and fully electromagnetic, and it incorporates the equilibrium density profile, flow profile, and electric field and magnetic field profiles in the linear stability analysis. Using parameters similar to the University of Michigan's recirculating planar magnetron, the numerical data show that the resonant interaction of the vacuum circuit mode and the corresponding smooth-bore diocotron-like mode is the dominant cause for instability. This resonant interaction is far more important than the intrinsic negative (positive) mass property of electrons in the inverted (conventional) magnetron geometry. It is absent in either the smooth-bore magnetron or under the electrostatic assumption, one or both of which was almost always adopted in prior analytical formulation. This resonant interaction severely restricts the wavenumber for instability to the narrow range in which the cold tube frequency of the SWS is within a few percent of the corresponding smooth bore diocotron-like mode in the Brillouin flow.

Authors:
; ; ; ;  [1];  [2]
  1. Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, Michigan 48109-2104 (United States)
  2. Air Force Research Laboratory, Kirtland Air Force Base, Albuquerque, New Mexico 87117 (United States)
Publication Date:
OSTI Identifier:
22599860
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 23; Journal Issue: 9; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANODES; BRILLOUIN THEOREM; CROSSED FIELDS; DENSITY; ELECTRIC FIELDS; ELECTRONS; EQUILIBRIUM; GEOMETRY; INSTABILITY; INTERACTIONS; MAGNETIC FIELDS; MAGNETRONS; MASS; RELATIVISTIC RANGE; STABILITY; TUBES

Citation Formats

Simon, D. H., Lau, Y. Y., Greening, G., Wong, P., Gilgenbach, R. M., and Hoff, B.. Stability of Brillouin flow in the presence of slow-wave structure. United States: N. p., 2016. Web. doi:10.1063/1.4961917.
Simon, D. H., Lau, Y. Y., Greening, G., Wong, P., Gilgenbach, R. M., & Hoff, B.. Stability of Brillouin flow in the presence of slow-wave structure. United States. doi:10.1063/1.4961917.
Simon, D. H., Lau, Y. Y., Greening, G., Wong, P., Gilgenbach, R. M., and Hoff, B.. 2016. "Stability of Brillouin flow in the presence of slow-wave structure". United States. doi:10.1063/1.4961917.
@article{osti_22599860,
title = {Stability of Brillouin flow in the presence of slow-wave structure},
author = {Simon, D. H. and Lau, Y. Y. and Greening, G. and Wong, P. and Gilgenbach, R. M. and Hoff, B.},
abstractNote = {Including a slow-wave structure (SWS) on the anode in the conventional, planar, and inverted magnetron, we systematically study the linear stability of Brillouin flow, which is the prevalent flow in crossed-field devices. The analytic treatment is fully relativistic and fully electromagnetic, and it incorporates the equilibrium density profile, flow profile, and electric field and magnetic field profiles in the linear stability analysis. Using parameters similar to the University of Michigan's recirculating planar magnetron, the numerical data show that the resonant interaction of the vacuum circuit mode and the corresponding smooth-bore diocotron-like mode is the dominant cause for instability. This resonant interaction is far more important than the intrinsic negative (positive) mass property of electrons in the inverted (conventional) magnetron geometry. It is absent in either the smooth-bore magnetron or under the electrostatic assumption, one or both of which was almost always adopted in prior analytical formulation. This resonant interaction severely restricts the wavenumber for instability to the narrow range in which the cold tube frequency of the SWS is within a few percent of the corresponding smooth bore diocotron-like mode in the Brillouin flow.},
doi = {10.1063/1.4961917},
journal = {Physics of Plasmas},
number = 9,
volume = 23,
place = {United States},
year = 2016,
month = 9
}
  • A linear stability approach free from the singularities of the cold fluid theory is applied to laminar {ital E}{times}{ital B} flows in slow wave cavities. Employing time scale separation in the appropriate frame of reference, one avoids singularities in the guiding center motion near the drift and drift-cyclotron resonances {omega}{minus}{ital ku}{sub 0}({ital x})={ital n}{Omega}, {ital n}=0,{plus_minus}1. Instead of an {ital a} {ital priori} Fourier mode expansion, a boundary value problem is solved with a traveling wave boundary condition at the wall. The space-charge potential is obtained in closed form using the Green`s function approach. Due to the incompressibility of themore » flow, charge perturbations and energy exchange take place at the free flow boundaries (surface perturbations). A local expansion of the Green`s function in terms of the perturbation amplitude and its derivative at the boundary yields the self-consistent closure. The loaded cavity mode profiles are everywhere free from singularities, exhibiting local maxima at the flow boundaries, not at the resonant layer(s). The small signal growth is biexponential {proportional_to}{ital e}{sup {Gamma}{ital t}{sup 2}}, where {Gamma} scales as the diocotron frequency squared {Omega}{sup 2}{sub {ital D}}={omega}{sup 4}{sub {ital p}}/{Omega}{sup 2}, and is independent of the frequency detuning from resonance. The method is compared to the normal mode analysis and the vacuum mode expansion technique. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.« less
  • Three-dimensional simulations show that stimulated Brillouin backscattered (SBS) light can be deflected in a direction opposite to transverse plasma flow. When the backscatter gain occurs predominantly in the region beyond where the incident light is deflected by transverse flow, and when the backscatter gain from the deflected incident light region is detuned from the undeflected incident light region by axial flow gradients, the SBS deflection correlates well with the steering of the incident beam. The level of Brillouin backscatter gain in the presence of transverse flow is less than that in the absence of transverse flow because of convective damping,more » where ion acoustic waves are swept out of the high intensity regions(s) of a beam. {copyright} {ital 1999 American Institute of Physics.}« less
  • Previous treatments of relativistic Brillouin flow stability are extended to the case of nonzero anode resistivity, for the case of wave propagation across the equilibrium magnetic field. It is found that transverse magnetic (TM) waves are unstable at frequencies below the equilibrium cyclotron frequency, unlike the case for a perfectly conducting anode. Transverse electric (TE) waves, always oscillatory in the case of a perfectly conducting anode, are damped; an explicit expression for the damping rate, valid for large conductivities, is given.
  • The Brillouin flow is the prevalent flow in crossed-field devices. We systematically study its stability in the conventional, planar, and inverted magnetron geometry. To investigate the intrinsic negative mass effect in Brillouin flow, we consider electrostatic modes in a nonrelativistic, smooth bore magnetron. We found that the Brillouin flow in the inverted magnetron is more unstable than that in a planar magnetron, which in turn is more unstable than that in the conventional magnetron. Thus, oscillations in the inverted magnetron may startup faster than the conventional magnetron. This result is consistent with simulations, and with the negative mass property inmore » the inverted magnetron configuration. Inclusion of relativistic effects and electromagnetic effects does not qualitatively change these conclusions.« less