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Cyclotron waves in a non-neutral plasma column

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10.1063/1.4802101

### Abstract

A kinetic theory of linear electrostatic plasma waves with frequencies near the cyclotron frequency of a given plasma species *s* is developed for a multispecies non-neutral plasma column with general radial density and electric field profiles. Terms in the perturbed distribution function up to are kept, as are the effects of finite cyclotron radius *r*_{c} up to . At this order, the equilibrium distribution is not Maxwellian if the plasma temperature or rotation frequency is not uniform. For , the theory reproduces cold-fluid theory and predicts surface cyclotron waves propagating azimuthally. For finite *r*_{c} , the wave equation predicts that the surface wave couples to radially and azimuthally propagating Bernstein waves, at locations where the wave frequency equals the local upper hybrid frequency. The equation also predicts a second set of Bernstein waves that do not couple to the surface wave, and therefore have no effect on the external potential. The wave equation is solved both numerically and analytically in the WKB approximation, and analytic dispersion relations for the waves are obtained. The theory predicts that both types of Bernstein wave are damped at resonances, which are locations where the Doppler-shifted wave frequency matches the local cyclotron frequency as seen in the rotating frame.

© 2013 AIP Publishing LLC

Received 22 February 2013
Accepted 04 April 2013
Published online 25 April 2013

Acknowledgments: The author thanks Professor C. F. Driscoll for useful discussions. This work was supported by National Science Foundation grant PHY-0903877, and Department of Energy Grants DE-SC0002451 and DE-SC0008693.

Article outline:

I. INTRODUCTION

II. PARTICLE ORBITS

III. EVOLUTION OF THE DISTRIBUTION FUNCTION

IV. GENERAL DISPERSION RELATION FOR LINEAR WAVES

V. CYCLOTRON MODES FOR SPECIES *s*

VI. COLD FLUID THEORY OF SURFACE CYCLOTRON MODES

A. Upper hybrid cutoff

B. Surface cyclotron waves for no inner conductor

C. Surface cyclotron waves for an inner conductor with radius *r* _{in} > 0

VII. FINITE TEMPERATURE EFFECTS, BERNSTEIN WAVES

VIII. WKB ANALYSIS OF FINITE TEMPERATURE CYCLOTRON MODES

A. Connection formula for an upper hybrid cutoff

B. Behavior near a resonance

IX. WKB SOLUTIONS: EXAMPLES

A. One upper-hybrid cutoff

1. Internal Bernstein modes with

B. Two upper hybrid cutoffs

C. Admittance regimes for the cyclotron response in a single-species plasma

1. or : Fluid regime

2. : Bernstein mode regime

3. : Resonance regime

X. CONCLUSIONS AND DISCUSSION

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2013-04-25

2014-04-23

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