Electron sheaths in a crossed-field gap -- Equilibrium solution and transition to turbulence

Conference · Sun Dec 31 04:00:00 EST 1995

OSTI ID:170192

Christenson, P J; Lau, Y Y ^[1]

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1. Univ. of Michigan, Ann Arbor, MI (United States). Dept. of Nuclear Engineering

There is renewed interest in the equilibrium solutions and the transition to turbulence of electron sheaths in a crossed-field gap. IN this paper, the authors present an analytic theory of the critical current beyond which transition from laminar to turbulent behavior occurs, under the assumption that the electrons are released from the cathode with a nonzero mono-energetic velocity. This analytic theory is found to be in excellent agreement with the results obtained from a particle simulation code. They also find that the behavior of the sheaths is quite different, depending on whether B > B{sub H} or B < B{sub H}. Here B is the external magnetic field and B{sub H} is the Hull cutoff value. For example, in all cases they have studied for the regime B > B{sub H}, where many cross-field amplifiers of practical significance operate, they find that there is no electrostatic potential minimum in the equilibrium solution, in sharp contrast to the B < B{sub H} regime. However, a potential minimum always appears in front of the cathode whenever the injected current exceeds the critical value, according to the simulations of various B > B{sub H} cases. The spatial extent and the frequency of oscillations of this microsheath depend on the injected current and on the initial velocity. This study seems to have added substance to the notion, widely held in the community of ultra-low noise crossed-field amplifiers, that a necessary condition for quiescent behavior in a crossed-field gap is that electron emission be limited.

• OSTI ID: 170192
• Report Number(s): CONF-950612--; ISBN 0-7803-2669-5
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
ANALYTICAL SOLUTION
CROSSED FIELDS
ELECTRIC POTENTIAL
MATHEMATICAL MODELS
MICROWAVE AMPLIFIERS
PLASMA SHEATH
TURBULENCE