Analytical solution for capacitive RF sheath

Journal Article · Thu Dec 01 04:00:00 EST 1988 · IEEE Trans. Plasma Sci.; (United States)

DOI:https://doi.org/10.1109/27.16552· OSTI ID:6403174

Lieberman, M A ^[1]

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1. Dept. of Electrical Engineering and Computer Sciences and the Electronics Research Lab., Univ. of California, Berkeley, CA (US)

A self-consistent solution for the dynamics of a high voltage, capacitive RF sheath driven by a sinusoidal current source is obtained under the assumptions of time-independent, collisionless ion motion and inertialess electrons. Some results are that 1) the ion sheath thickness s/sub m/ is ..sqrt..50/27 larger than a Child's law sheath for the same dc voltage and ion current density; 2) the sheath capacitance per unit area for the fundamental voltage harmonic is 1.226 epsilon/sub O//s/sub m/, where epsilon/sub O/ is the free space permittivity; 3) the ratio of the dc to the peak value of the oscillating voltage is 54/125; 4) the second and third voltage harmonics are, respectively, 12.3 and 4.2 percent of the fundamental; and 5) the conductance per unit area for stochastic heating by the oscillating sheath is 2.98 (lambda/sub D//s/sub m/)/sup 2/3/ (e/sup 2/n/sub O//m..mu../sub e/), where n/sub O/ is the ion density and lambda/sub D/ is the Debye length at the plasma-sheath edge, and ..mu../sub e/ = (8eT/sub e//..pi..m)/sup 1/2/ is the mean electron speed.

• OSTI ID: 6403174
• Journal Information: IEEE Trans. Plasma Sci.; (United States), Journal Name: IEEE Trans. Plasma Sci.; (United States) Vol. 16:6; ISSN ITPSB
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420800* -- Engineering-- Electronic Circuits & Devices-- (-1989)
ANALYTICAL SOLUTION
CHARGED PARTICLES
CONTAINERS
CURRENT DENSITY
CURRENTS
DIRECT CURRENT
ELECTRIC CURRENTS
ELECTRIC POTENTIAL
ELECTRODYNAMICS
ELECTRONS
ELEMENTARY PARTICLES
FERMIONS
HEATING
IONS
LEPTONS
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SLEEVES