Stability of Brillouin flow in the presence of slowwave structure
Abstract
Including a slowwave 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 crossedfield 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 smoothbore diocotronlike 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 smoothbore 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 diocotronlike mode in the Brillouin flow.
 Authors:
 Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, Michigan 481092104 (United States)
 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 slowwave 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 slowwave 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 slowwave structure". United States.
doi:10.1063/1.4961917.
@article{osti_22599860,
title = {Stability of Brillouin flow in the presence of slowwave 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 slowwave 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 crossedfield 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 smoothbore diocotronlike 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 smoothbore 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 diocotronlike 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
}

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