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Cyclotron waves in a non-neutral plasma column
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10.1063/1.4802101
/content/aip/journal/pop/20/4/10.1063/1.4802101
http://aip.metastore.ingenta.com/content/aip/journal/pop/20/4/10.1063/1.4802101

Figures

Image of FIG. 1.
FIG. 1.

Schematic diagram of the charge densities and rotation frequency in a non-neutral plasma column consisting of three species. Cylindrical conductors bound the plasma at and rw ; in many experiments, the inner conductor is not present. Centrifugal and/or charge separation 25 can cause the species to separate radially, in order of largest to smallest charge to mass ratio.

Image of FIG. 2.
FIG. 2.

Imaginary part of the admittance versus frequency for an wall perturbation, in the cold fluid limit, at different collision frequencies ν (measured in units of for the density profile of Eq. (79) with , where rw is the wall radius).

Image of FIG. 3.
FIG. 3.

Same as Fig. 2 but for fixed , at different profile widths (in units of rw ). The arrow shows the frequency for a step profile, Eq. (77) .

Image of FIG. 4.
FIG. 4.

Imaginary part of the admittance for an cold-fluid cyclotron mode in a plasma with an inner conductor of radius , for two values of the profile width (in units of rw ) and for , 1/100 and 1/1000 (in order from broadest to sharpest admittance curves). The arrow shows the frequency for a step profile, Eq. (84) .

Image of FIG. 5.
FIG. 5.

Schematic of a plasma for which there is a single upper hybrid cutoff. Varying ω moves the profile vertically and changes the location of the cutoff.

Image of FIG. 6.
FIG. 6.

Schematic of a plasma with parameters chosen so that there is a single resonance.

Image of FIG. 7.
FIG. 7.

(a) Rays (contours of constant ω) for Bernstein waves at a frequency corresponding to the profile in Fig. 6 . (b) Analogous ray (contour of constant ω) for Bernstein waves at a frequency corresponding to the profile in Fig. 5 .

Image of FIG. 8.
FIG. 8.

Comparison of cold fluid theory, Eq. (66) , to a solution to Eq. (85) when there is a resonance. Fluid solution and numerical solution are matched at . The resonance is located at the arrow.

Image of FIG. 9.
FIG. 9.

Admittance versus cyclotron radius at fixed frequency and uniform profile, , , and density given by Eq. (79) . Dots: numerical solution of Eq. (85) . Solid lines: WKB approximation, Eq. (151) . Singularities in Y occur at the frequencies of Bernstein modes.

Image of FIG. 10.
FIG. 10.

Perturbed potential of Bernstein modes for two different temperatures but the same frequency, and assuming uniform , with , and density given by Eq. (79) . Solid lines: numerical solution of Eq. (85) . Dashed lines: WKB approximation, Eqs. (147) , (150) , (138) , (101) , and (107) . The dashed vertical line shows the location of the upper hybrid cutoff. (a) and (b) The WKB approximation improves for smaller rc , and breaks down as expected near r = 0 and .

Image of FIG. 11.
FIG. 11.

Admittance versus frequency for uniform α, density given by Eq. (79) , and for , at three temperatures, with corresponding cyclotron radii rc measured in units of rw . As rc decreases, the admittance approaches cold fluid theory, Eq. (70) . For larger rc , Bernstein mode peaks are evident. Curves: WKB theory given by Eq. (151) , (138) , and (127) . Dots: numerical solution of Eq. (85) , shown only in the regime of validity for Bernstein solutions of Eq. (85) , . The arrow at shows the prediction of Eq. (77) for the frequency of the surface cyclotron wave.

Image of FIG. 12.
FIG. 12.

Frequency spectrum of internal Bernstein modes for two values of the cyclotron radius (measured in units of rw ). Plasma parameters are chosen, so that there is a single cutoff: the profile is assumed to be uniform, and density is given by Eq. (79) . Crosses: numerical solution of Eq. (85) , valid for the low order modes with . Dots: WKB approximation, Eq. (155) , valid for .

Image of FIG. 13.
FIG. 13.

The five lowest order internal Bernstein potential eigenmodes for for the same plasma parameters as in Fig. 12 , taking .

Image of FIG. 14.
FIG. 14.

α and β profiles for a case with two upper hybrid cutoffs.

Image of FIG. 15.
FIG. 15.

β and representative α profiles (in units of ) for a single species plasma with monotonically decreasing density . Frequencies are chosen so that there is one cutoff and one or more resonances. (a) and (b) .

Image of FIG. 16.
FIG. 16.

Admittance versus frequency for an wall perturbation in a single species plasma with the same plasma density as in Fig. 15 , taking and . Curve: WKB solution. Dots: solution to Eq. (85) .

Tables

Generic image for table
Table I.

Orbit coefficients in Eqs. (13) and (14) .

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/content/aip/journal/pop/20/4/10.1063/1.4802101
2013-04-25
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Cyclotron waves in a non-neutral plasma column
http://aip.metastore.ingenta.com/content/aip/journal/pop/20/4/10.1063/1.4802101
10.1063/1.4802101
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