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Stability of uniform plasmas with respect to longitudinal oscillations

Noerdlinger, Peter D. (1960) Stability of uniform plasmas with respect to longitudinal oscillations. Physical Review, 118 (4). pp. 879-885. ISSN 0031-899X.

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It is possible to relate the dispersion formula for longitudinal oscillations in an infinite, uniform, collision-free plasma with no magnetic field to the complex potential of a line charge distribution on the real axis of the phase velocity (u=ω/k) plane. If the initial velocity distribution integrated over directions orthogonal to the direction of propagation is f0(v) the plasma is stable if and only if U(u)=P∫-∞∞f0′(v)dv/v-u is negative at the minima of f0(v) on the real axis, with unimportant exceptions. In particular it is shown that single-peaked distributions are stable, while those with very sharp (e.g., nondifferentiable) minima or with a zero of f0 between two peaks are not. The charge analogy yields information on the wavelengths for which oscillations can grow and on rates of growth. Examples are given, including the case of two identical interpenetrating hot plasmas. A limited generalization to transverse oscillations is given.

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Additional Information:©1960 The American Physical Society. Received 2 December 1959. The author is indebted to Dr. Leverett Davis, Jr., for many valuable discussions and suggestions. [P.D.N. was a] Howard Hughes Fellow; work done in part on National Science Foundation Summer Fellowship.
Issue or Number:4
Record Number:CaltechAUTHORS:NOEpr60
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7154
Deposited By: Tony Diaz
Deposited On:11 Jan 2007
Last Modified:02 Oct 2019 23:39

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