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Two-dimensional Vlasov simulation of electron plasma wave trapping, wavefront bowing, self-focusing, and sidelossa)
a)This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract number DE-AC52-07NA27344. This work was funded by the Laboratory Directed Research and Development Program at LLNL under project tracking code 08-ERD-031.
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10.1063/1.3577784
/content/aip/journal/pop/18/5/10.1063/1.3577784
http://aip.metastore.ingenta.com/content/aip/journal/pop/18/5/10.1063/1.3577784

Figures

Image of FIG. 1.
FIG. 1.

(Color online) Nonlinear frequency shifts vs square-root of wave amplitude , for laterally periodic boundary conditions. The squares are frequency shifts determined on axis. The blue triangles and red crosses are for different lateral positions. The blue data is for the wide driver case where the nonlinear shifts are dominant and the measurements were made for a time interval before a thermal transit time across the wave. The red crosses for a narrow driver run long enough so that the resonant electrons have the same distribution for all y. Thus, the frequency shift (red crosses) is nearly independent of the local field, .

Image of FIG. 2.
FIG. 2.

(Color online) Plot of electric field contours at fixed times (a) and (b) with showing evolution of wavefront bowing from linear theory.

Image of FIG. 3.
FIG. 3.

(Color online) Plot of electric field contours at fixed times (a) and (b) with and initially on axis showing nonlinear wavefront bowing.

Image of FIG. 4.
FIG. 4.

(Color online) Plot of electric field contours at and 200 showing wavefront bowing from a simulation with and peak wave amplitude on axis which then steadily decreases.

Image of FIG. 5.
FIG. 5.

(Color online) Plot of electric field contours at and 200 showing wavefront bowing from simulation with peak wave amplitude on axis which then decreases.

Image of FIG. 6.
FIG. 6.

(Color online) Plot of electric field contours at and 280 showing wavefront bowing from simulation with and peak wave amplitude on axis whose amplitude is relatively stationary near the axis.

Image of FIG. 7.
FIG. 7.

(Color online) Comparison of the EPW field history for periodic and outgoing boundary conditions for the wide lateral shape, . The driving external field is turned off at . (a) The history of the EPW field energy, WE , with periodic (black) and outgoing electron (red) boundary conditions. (b) The history of the peak EPW field with periodic (black) and outgoing electron (red) boundary conditions. (c) Transverse spatial dependence of Ex (xp , y) at five times for the periodic electron distribution boundary conditions. (d) Transverse spatial dependence of Ex (xp , y) at five times for the outgoing electron distribution boundary conditions. For (c) and (d), xp is the position at which Ex (x, y = 0) is maximum. Electric fields are normalized such that .

Image of FIG. 8.
FIG. 8.

(Color online) Comparison of the EPW field history for periodic and outgoing boundary conditions for a narrow lateral shape, . The driving external field is turned off at . (a) The history of the peak EPW field with periodic (black) and outgoing electron (red) boundary conditions. (b) The history of the EPW field envelope at with periodic (black) and outgoing electron (red) boundary conditions. (c) Transverse spatial dependence of Ex (xp , y) at five times indicated for the outgoing electron distribution boundary conditions. Here, xp is the position for which Ex (x, y = 0) is a maximum.

Image of FIG. 9.
FIG. 9.

(Color online) The EPW field for a lateral shape . The driving external field is turned off at . (a) The transverse shape of the EPW at the axial position, xp , where the field is a maximum for five times after the driving field is off. (b) Two-dimensional filled contour maps of the EPW field at the time of maximum focusing. (c) Two-dimensional filled contour maps of the EPW field after diffraction has overtaken focusing. There are 13 equally spaced contours in the range [−0.03, 0.03] for both figures (b) and (c).

Image of FIG. 10.
FIG. 10.

The distribution of electrons shown in Fig 9. F(Vx , Y) at the position of maximum potential for the EPW field and F(Vx , X) at y = 0: (a) and (b) , (c) and (d) , (e) and (f) . The distribution is integrated over the transverse velocity. The phase velocity is 3.6 Vte .

Image of FIG. 11.
FIG. 11.

(Color online) Lineouts of the distribution of electrons at the position of maximum potential for the EPW field shown inFig. 9. and various y positions, F(Vx ) vs Vx at (a) , (b) , (c) , and (d) . The distribution is integrated over the transverse velocity. The phase velocity is 3.6 Vte . Note, the distributions for and are nearly the same.

Image of FIG. 12.
FIG. 12.

(Color online) Time evolution of wave front curvature resulting from linear dispersion of EPWs.

Image of FIG. 13.
FIG. 13.

(Color online) Electrostatic field at time t max where the negative curvature bowing resulting from the linear evolution is maximum.

Image of FIG. 14.
FIG. 14.

(Color online) Critical curve in the plane delimiting the region corresponding to the linear regime with negative curvature of the wavefront for times from the nonlinear regime with positive curvature. Critical curves corresponding to the wavenumbers , 0.3, and 0.4 are shown, having used the Bohm–Gross dispersion and assumed an adiabatic generation of the EPWs.

Tables

Generic image for table
Table I.

Transit damping rates.

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/content/aip/journal/pop/18/5/10.1063/1.3577784
2011-05-09
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Two-dimensional Vlasov simulation of electron plasma wave trapping, wavefront bowing, self-focusing, and sidelossa)
http://aip.metastore.ingenta.com/content/aip/journal/pop/18/5/10.1063/1.3577784
10.1063/1.3577784
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