skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: On steady flows in smooth-walled magnetrons: Fundamental modes and no-cutoff flows in planar geometry

Abstract

The Maxwell equations coupled with the ideal fluid equations for a warm isothermal non-neutral plasma are applied without approximation to predict three modes of time-independent electron flow in smooth-walled planar magnetrons, at any temperature. For all three modes, the equations predict that the fluid flow velocity tangent to the cathode is the Brillouin velocity. One of the modes is the well-known magnetic insulation mode, in which the magnetic field is larger than the Hull cutoff field [Phys. Rev. 18, 31 (1921)], the anode current is essentially zero, and virtually all the electrons reside in a sheath near the cathode. The other two modes exhibit fairly large anode currents. One of these modes is the well-known Child-Langmuir flow [Phys. Rev. 32, 492 (1911); ibid. 21, 419 (1923)], in which the magnetic field is smaller than the Hull cutoff field. The other high-current mode, in which the magnetic field is larger than the Hull cutoff field, has not been discussed previously; in this paper, it is called the 'no-cutoff' (NC) mode. Experiments using a thin smooth-walled magnetron were conducted, during which large anode currents were observed even for magnetic fields much larger than the Hull cutoff field. It is shown that NCmore » mode parameters can be adjusted to produce a complete agreement with the experimental results, but that this requires the transverse flow velocity near the cathode to be superthermal and even mildly relativistic for the larger magnetic fields. Matching the experimental values also predicts a number density that is larger near the anode than near the cathode, but is small enough that space-charge effects are negligible in most cases.« less

Authors:
; ; ;  [1];  [2];  [3]
  1. Physics Department, New Mexico State University, Las Cruces, New Mexico 88003 (United States)and Raytheon Missile Systems, 1151 E. Hermans Road, Tucson, Arizona 85706 (United States)
  2. (United States) and Raytheon Missile Systems, 1151 E. Hermans Road, Tucson, Arizona 85706 (United States)
  3. (United States)
Publication Date:
OSTI Identifier:
20782359
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 12; Journal Issue: 11; Other Information: DOI: 10.1063/1.2122427; (c) 2005 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ANODES; APPROXIMATIONS; CATHODES; CHARGED-PARTICLE TRANSPORT; ELECTRIC CURRENTS; ELECTRON TEMPERATURE; ELECTRONS; GEOMETRY; IDEAL FLOW; ION TEMPERATURE; MAGNETIC FIELDS; MAGNETIC INSULATION; MAGNETRONS; MAXWELL EQUATIONS; PLASMA DENSITY; PLASMA INSTABILITY; PLASMA SHEATH; RELATIVISTIC PLASMA; RELATIVISTIC RANGE; SPACE CHARGE

Citation Formats

Goedecke, G.H., Davis, Brian T., Chen Chiping, Baker, C. Vincent, Intense Beam Theoretical Research Group, Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, and Raytheon Missile Systems, 1151 E. Hermans Road, Tucson, Arizona 85706. On steady flows in smooth-walled magnetrons: Fundamental modes and no-cutoff flows in planar geometry. United States: N. p., 2005. Web. doi:10.1063/1.2122427.
Goedecke, G.H., Davis, Brian T., Chen Chiping, Baker, C. Vincent, Intense Beam Theoretical Research Group, Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, & Raytheon Missile Systems, 1151 E. Hermans Road, Tucson, Arizona 85706. On steady flows in smooth-walled magnetrons: Fundamental modes and no-cutoff flows in planar geometry. United States. doi:10.1063/1.2122427.
Goedecke, G.H., Davis, Brian T., Chen Chiping, Baker, C. Vincent, Intense Beam Theoretical Research Group, Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, and Raytheon Missile Systems, 1151 E. Hermans Road, Tucson, Arizona 85706. Tue . "On steady flows in smooth-walled magnetrons: Fundamental modes and no-cutoff flows in planar geometry". United States. doi:10.1063/1.2122427.
@article{osti_20782359,
title = {On steady flows in smooth-walled magnetrons: Fundamental modes and no-cutoff flows in planar geometry},
author = {Goedecke, G.H. and Davis, Brian T. and Chen Chiping and Baker, C. Vincent and Intense Beam Theoretical Research Group, Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 and Raytheon Missile Systems, 1151 E. Hermans Road, Tucson, Arizona 85706},
abstractNote = {The Maxwell equations coupled with the ideal fluid equations for a warm isothermal non-neutral plasma are applied without approximation to predict three modes of time-independent electron flow in smooth-walled planar magnetrons, at any temperature. For all three modes, the equations predict that the fluid flow velocity tangent to the cathode is the Brillouin velocity. One of the modes is the well-known magnetic insulation mode, in which the magnetic field is larger than the Hull cutoff field [Phys. Rev. 18, 31 (1921)], the anode current is essentially zero, and virtually all the electrons reside in a sheath near the cathode. The other two modes exhibit fairly large anode currents. One of these modes is the well-known Child-Langmuir flow [Phys. Rev. 32, 492 (1911); ibid. 21, 419 (1923)], in which the magnetic field is smaller than the Hull cutoff field. The other high-current mode, in which the magnetic field is larger than the Hull cutoff field, has not been discussed previously; in this paper, it is called the 'no-cutoff' (NC) mode. Experiments using a thin smooth-walled magnetron were conducted, during which large anode currents were observed even for magnetic fields much larger than the Hull cutoff field. It is shown that NC mode parameters can be adjusted to produce a complete agreement with the experimental results, but that this requires the transverse flow velocity near the cathode to be superthermal and even mildly relativistic for the larger magnetic fields. Matching the experimental values also predicts a number density that is larger near the anode than near the cathode, but is small enough that space-charge effects are negligible in most cases.},
doi = {10.1063/1.2122427},
journal = {Physics of Plasmas},
number = 11,
volume = 12,
place = {United States},
year = {Tue Nov 15 00:00:00 EST 2005},
month = {Tue Nov 15 00:00:00 EST 2005}
}
  • We simulate both microscopic and macroscopic shear flows in two space dimensions using nonequilibrium molecular dynamics and smooth-particle applied mechanics. The time-reversible {ital microscopic} equations of motion are isomorphic to the smooth-particle description of inviscid {ital macroscopic} continuum mechanics. The corresponding microscopic particle interactions are relatively weak and long ranged. Though conventional Green-Kubo theory suggests instability or divergence in two-dimensional flows, we successfully define and measure a finite shear viscosity coefficient by simulating stationary plane Couette flow. The special nature of the weak long-ranged smooth-particle functions corresponds to an unusual kind of microscopic transport. This microscopic analog is mainly kinetic,more » even at high density. For the soft Lucy potential which we use in the present work, nearly all the system energy is potential, but the resulting shear viscosity is nearly all kinetic. We show that the measured shear viscosities can be understood, in terms of a simple weak-scattering model, and that this understanding is useful in assessing the usefulness of continuum simulations using the smooth-particle method. We apply that method to the Rayleigh-Benard problem of thermally driven convection in a gravitational field.« less
  • Global steady-state solutions of the plasma hydrodynamic equations in planar geometry are generalized to include heat conduction both in front and in back of the critical surface. Constraints on the plasma parameters which must be satisfied in order to obtain solutions which reflect the important characteristics of the full time-dependent problem are derived. This yields some insight into the dynamics of laser plasmas.
  • The Epstein model of a dielectric layer having a smooth profile is used to describe the complex permittivity - in the plane of the active layer of the three-dimensional wave-guide structure in a planar stripe-geometry laser. A three-layer model generally suitable for a double heterostructure is used along the normal to the plane of the active layer. Aspects associated with the description of properties of hybrid modes are analyzed and solutions are obtained for a non-Gaussian angular distribution caused by bending of the wavefront under the influence of the Im - profile (in a waveguiding or ''antiwaveguiding'' structure). A comparisonmore » is made between the spontaneous emission intensity profiles in various types of planar stripe-geometry heterojunction lasers and the characteristic Im - profile in the assumed Epstein model. It is shown that the theoretical model can be applied to calculations of the mode profile in heterojunction lasers with stripe contact widths of approximately 15 ..mu...« less
  • In dc magnetrons the electrons emitted from the cathode may return there due to the applied magnetic field. When that happens, they can be recaptured or reflected back into the discharge, depending on the value of the reflection coefficient (RC). A 2d3v (two-dimensional in coordinate and three-dimensional in velocity space) particle-in-cell-Monte Carlo model, including an external circuit, is developed to determine the role of the electron recapture in the discharge processes. The detailed discharge structure as a function of RC for two pressures (4 and 25 mtorr) is studied. The importance of electron recapture is clearly manifested, especially at lowmore » pressures. The results indicate that the discharge characteristics are dramatically changed with varying RC between 0 and 1. Thus, the electron recapture at the cathode appears to be a significant mechanism in magnetron discharges and RC a very important parameter in their correct quantitative description that should be dealt with cautiously.« less
  • 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