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Electrostatic Landau pole for -velocity distributions
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10.1063/1.2776897
/content/aip/journal/pop/14/9/10.1063/1.2776897
http://aip.metastore.ingenta.com/content/aip/journal/pop/14/9/10.1063/1.2776897
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

The integration path in Eq. (5) going around the two poles at and . In the limit , the contribution to the integral (10) of the second pole is half the residue of the integrand [see Eq. (11)].

Image of FIG. 2.
FIG. 2.

(Color online) Solid line: The analytical -dispersion relation, for evaluated by using our results [Eqs. (20) and (21)]. Dashed line: The unphysical singularity reported in many previous works appears at when one considers instead the frequency obtained from Eq. (22). Stars: The direct calculation of the dispersion relation, via the numerical evaluation of the Landau integral (9). The numerical results are in perfect agreement with the analytical result, and show no sign of a singularity at .

Image of FIG. 3.
FIG. 3.

Semilogarithmic plot of the initial distribution function , for (solid line). The dashed line represents a Maxwellian function in velocities.

Image of FIG. 4.
FIG. 4.

(Top) Spectral electric energy as a function of the frequency for . (Bottom) Time evolution of the electric field spectral component (mode ) in semilogarithmic plot.

Image of FIG. 5.
FIG. 5.

Time evolution of the electric field spectral component (mode ) in semilogarithmic plot, for a Maxwellian equilibrium distribution.

Image of FIG. 6.
FIG. 6.

In both plots the dashed line represents the analytical solution while the stars represent the numerical simulation. (Top) Oscillation frequency vs wave number . (Bottom) Damping rate (absolute value) vs wave number .

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/content/aip/journal/pop/14/9/10.1063/1.2776897
2007-09-27
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Electrostatic Landau pole for κ-velocity distributions
http://aip.metastore.ingenta.com/content/aip/journal/pop/14/9/10.1063/1.2776897
10.1063/1.2776897
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