banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Electrostatic Landau pole for -velocity distributions
Rent this article for
View: 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 .


Article metrics loading...


Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Electrostatic Landau pole for κ-velocity distributions