Relativistic Dispersion Relation of Electron Cyclotron Waves

2008 ◽  
Vol 53 (1) ◽  
pp. 130-138 ◽  
Author(s):  
Daniela Farina
Keyword(s):  
Dispersion Relation ◽  
Electron Cyclotron ◽  
Relativistic Dispersion ◽  
Electron Cyclotron Waves

Thermal effects on parallel-propagating electron cyclotron waves

1987 ◽  
Vol 37 (1) ◽  
pp. 149-162 ◽  
Author(s):  
P. A. Robinson
Keyword(s):  
Dispersion Relation ◽  
Thermal Effects ◽  
Cold Plasma ◽  
Stop Band ◽  
Plasma Temperature ◽  
Relativistic Effects ◽  
Electron Cyclotron ◽  
New Family ◽  
Electron Cyclotron Waves ◽  
Cyclotron Line

Thermal effects on the dispersion of right-handed (RH) electron cyclotron waves propagating parallel to a uniform, ambient magnetic field are investigated in the strictly non-relativistic (‘classical’) and weakly relativistic approximations for real frequency and complex wave vector. In each approximation, the two branches of the RH mode reconnect near the cyclotron frequency as the plasma temperature is increased or the density is lowered. This reconnection occurs in a manner different from that previously assumed at parallel propagation and from that at perpendicular propagation, giving rise to a new mode near the cold plasma cut-off frequency ωxC. For both parallel and perpendicular propagation, it is noted that reconnection occurs approximately when the cyclotron line-width equals the width of the stop-band in the cold plasma dispersion relation. Inclusion of weakly relativistic effects is found to be necessary for quantitative calculations and for an accurate treatment of the new mode near ωxC. Weakly relativistic effects also modify the analytic properties of the dispersion relation so as to introduce a new family of weakly damped and undamped solutions.

Plasma Current Sustainment and Ramp-Up by Electron Cyclotron Waves in the WT-2 Tokamak

1986 ◽  
Vol 55 (12) ◽  
pp. 4259-4271 ◽  
Author(s):  
Akira Ando ◽  
Kazuo Ogura ◽  
Hitoshi Tanaka ◽  
Motomi Iida ◽  
Shunsuke Ide ◽  
...  
Keyword(s):  
Electron Cyclotron ◽  
Plasma Current ◽  
Electron Cyclotron Waves

Expansions of the mildly relativistic dispersion function for nearly perpendicular electron cyclotron ray tracing

1999 ◽  
Vol 61 (1) ◽  
pp. 121-128 ◽  
Author(s):  
I. P. SHKAROFSKY
Keyword(s):  
Ray Tracing ◽  
Computer Programs ◽  
Higher Order ◽  
Electron Cyclotron ◽  
Dispersion Function ◽  
Relativistic Dispersion ◽  
Plasma Dispersion ◽  
Derivatives Of ◽  
Cyclotron Harmonic ◽  
Experienced Difficulty

To trace rays very close to the nth electron cyclotron harmonic, we need the mildly relativistic plasma dispersion function and its higher-order derivatives. Expressions for these functions have been obtained as an expansion for nearly perpendicular propagation in a region where computer programs have previously experienced difficulty in accuracy, namely when the magnitude of (c/vt)2 (ω−nωc)/ω is between 1 and 10. In this region, the large-argument expansions are not yet valid, but partial cancellations of terms occur. The expansion is expressed as a sum over derivatives of the ordinary dispersion function Z. New expressions are derived to relate higher-order derivatives of Z to Z itself in this region of concern in terms of a finite series.

Ion-cyclotron modes in weakly relativistic plasmas

1994 ◽  
Vol 51 (3) ◽  
pp. 371-379 ◽  
Author(s):  
Chandu Venugopal ◽  
P. J. Kurian ◽  
G. Renuka
Keyword(s):  
Dispersion Relation ◽  
High Frequency ◽  
Low Frequency ◽  
Dispersion Relations ◽  
The Other ◽  
Larmor Radius ◽  
Relativistic Plasmas ◽  
Ion Plasma ◽  
Maxwellian Plasma ◽  
Relativistic Dispersion

We derive a dispersion relation for the perpendicular propagation of ioncyclotron waves around the ion gyrofrequency ω+ in a weaklu relaticistic anisotropic Maxwellian plasma. These waves, with wavelength greater than the ion Larmor radius rL+ (k⊥ rL+ < 1), propagate in a plasma characterized by large ion plasma frequencies (). Using an ordering parameter ε, we separated out two dispersion relations, one of which is independent of the relativistic terms, while the other depends sensitively on them. The solutions of the former dispersion relation yield two modes: a low-frequency (LF) mode with a frequency ω < ω+ and a high-frequency (HF) mode with ω > ω+. The plasma is stable to the propagation of these modes. The latter dispersion relation yields a new LF mode in addition to the modes supported by the non-relativistic dispersion relation. The two LF modes can coalesce to make the plasma unstable. These results are also verified numerically using a standard root solver.

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