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Nonlinear Landau damping and formation of Bernstein-Greene-Kruskal structures for plasmas with q-nonextensive velocity distributions
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10.1063/1.4794320
/content/aip/journal/pop/20/3/10.1063/1.4794320
http://aip.metastore.ingenta.com/content/aip/journal/pop/20/3/10.1063/1.4794320
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Comparison of the “analytically” obtained and simulated values of the damping rate γ varying with q (k = 0.4, ).

Image of FIG. 2.
FIG. 2.

Plot of damping rate γ as a function of q for values of k = 0.4, 0.7, 1.2. One can see that as k increases, the values of |γ| are higher than those for a lower k.

Image of FIG. 3.
FIG. 3.

A run corresponding to Run I of Manfredi, 5 who had shown the oscillations to continue till t = 1600. We extended the run till t = 5000. The vertical grey line indicates the duration of Manfredi's simulations. Notice the continuation of the oscillations.

Image of FIG. 4.
FIG. 4.

For q = 1, at t = 5000, the phase-space vortex can be seen around at v = 3.21.

Image of FIG. 5.
FIG. 5.

Plot of relative entropy Srel with time. The vertical line represents the duration of Manfredi's simulation.

Image of FIG. 6.
FIG. 6.

Plots for the amplitude of the first harmonic of the electric field E 1 with time for Set I. One can notice that the oscillatory structures are not found for . Also, as damping rate increases, one can notice that the amplitude of oscillations decreases. This is similar to the result obtained by Valentini. 14 The vertical line represents the time of Valentini's simulations.

Image of FIG. 7.
FIG. 7.

Plot of relative entropy Srel with time for till t = 3000. The vertical line represents the time up to which Valentini's simulations were performed.

Image of FIG. 8.
FIG. 8.

Plot of distribution function for the run with q = 0.85, around , at t = 3000.

Image of FIG. 9.
FIG. 9.

Plots for the amplitude of the first harmonic of the electric field E 1 with time. The vertical line represents the time of Valentini's simulations. As we can see, the field has not saturated within this time.

Image of FIG. 10.
FIG. 10.

Plot of relative entropy Srel with time for . It can be seen that the entropy saturates within t = 3000. The vertical line represents the time up to which Valentini's simulations were performed.

Image of FIG. 11.
FIG. 11.

Plot of distribution function for the run with q = 1.15, around , at t = 3000.

Image of FIG. 12.
FIG. 12.

Plot of velocity distribution function at t = 3000 comparing cases with .

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/content/aip/journal/pop/20/3/10.1063/1.4794320
2013-03-12
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Nonlinear Landau damping and formation of Bernstein-Greene-Kruskal structures for plasmas with <em>q</em>-nonextensive velocity distributions
http://aip.metastore.ingenta.com/content/aip/journal/pop/20/3/10.1063/1.4794320
10.1063/1.4794320
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