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Nonlinear Landau damping of purely perpendicular Bernstein modes

Published online by Cambridge University Press:  13 March 2009

Spilios Riyopoulos
Spilios Riyopoulos
Affiliation:
Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712-1060
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Abstract

The linear dispersion relation for Bernstein modes, obtained by the integration of Vlasov's equation along the unperturbed cyclotron orbits, predicts that the modes propagating perpendicularly to the magnetic field are undamped. However, when the frequency is close to a multiple of the cyclotron frequency, most of the particles become trapped for small wave amplitude and the unperturbed orbit approximation breaks down. The trapped particle trajectories are calculated analytically here using a resonant Hamiltonian approximation. Integration, consistent with the wave, along the orbits yields the nonlinear damping rate in a manner similar to that used by O'Neil for the damping of unmagnetized electrostatic modes. The results can be extended for the general case of almost perpendicular, short-wavelength electrostatic modes near cyclotron harmonics.

Type
Research Article
Information
Journal of Plasma Physics , Volume 36 , Issue 1 , August 1986 , pp. 111 - 125
Copyright
Copyright © Cambridge University Press 1986

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References

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