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Adiabatic description of capture into resonance and surfatron acceleration of charged particles by electromagnetic waves
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10.1063/1.3518360
/content/aip/journal/chaos/20/4/10.1063/1.3518360
http://aip.metastore.ingenta.com/content/aip/journal/chaos/20/4/10.1063/1.3518360
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Geometry of the system.

Image of FIG. 2.
FIG. 2.

Larmor rotation in the averaged system in the presence of a single wave.

Image of FIG. 3.
FIG. 3.

Schematic view of the phase portrait on the resonance plane.

Image of FIG. 4.
FIG. 4.

Trajectory of a particle moving along a Larmor circle and then captured into resonance, , , . (a) Projection on the resonance plane; gray curves show the fragments of trajectory just after capture and after some intermediate moment of time. (b) Evolution of energy; Inset: Projection of the trajectory on the velocity plane.

Image of FIG. 5.
FIG. 5.

Schematic view of a Larmor rotation in the presence of two parallel waves.

Image of FIG. 6.
FIG. 6.

Trajectory of a particle moving along a Larmor circle, captured into resonance, and later released, , , , . (a) Projection on the velocity plane. (b) A projection of a trajectory on the resonance plane. (c) Evolution of energy for the time interval around the capture.

Image of FIG. 7.
FIG. 7.

For the comparison with Fig. 6(c) purposes: evolution of energy for . Note the change of scale.

Image of FIG. 8.
FIG. 8.

Schematic plot of lines of constant area under separatrix. The segments of the inclined straight lines, , correspond to the captured motion.

Image of FIG. 9.
FIG. 9.

Evolution of the energy averaged over an ensemble of 10 000 particles in the field of two waves for different values of and , .

Image of FIG. 10.
FIG. 10.

Capture into resonance and release from resonance in the field of two parallel waves for different values of and , , . Left panels: evolution of components of velocity in time. Right panel: the dependence of the combined width of the resonance domain at the moment of release as a function of . The dashed line is the theoretical prediction; the bullets are results of numerical simulations.

Image of FIG. 11.
FIG. 11.

Scheme of particle Larmor rotation in the presence of two waves propagating at an angle to each other.

Image of FIG. 12.
FIG. 12.

The gain of energy during a single capture into resonance in the field of two waves propagating at an angle for different values of and ; , . Small panels: plots of energy vs time. Large panel: the cumulative plot of . The dashed lines are the theoretical prediction; the symbols are results of numerical simulations.

Image of FIG. 13.
FIG. 13.

Subsequent captures and releases, , , . (a) Projection on the physical plane. (b) Projection on the velocity plane. (c) Evolution of energy.

Image of FIG. 14.
FIG. 14.

For the comparison with Fig. 13 purposes: evolution of energy for . Note the change of scale.

Image of FIG. 15.
FIG. 15.

Evolution of the energy averaged over an ensemble of 10 000 particles in the field of two waves propagating at an angle for different values of ; , .

Image of FIG. 16.
FIG. 16.

Distribution of particles in the velocity plane after reaching the quasistationary state (after many captured and releases for each particle), , , .

Image of FIG. 17.
FIG. 17.

Capture into resonance for a single wave with different values of .

Image of FIG. 18.
FIG. 18.

Multiple captures into and releases from resonance for parallel waves for three different values of . In all the panels , , .

Image of FIG. 19.
FIG. 19.

(a) Evolution of (top panel), (middle panel), and the energy (bottom panel) of a relativistic particle. The solid lines are obtained by the direct simulations of Eq. (B1). The dashed line in the first panel shows the evolution of for nonrelativistic case. The dashed line in the bottom panel shows the asymptotic evolution of for relativistic case with . (b) Evolution of at the extended time interval.

Image of FIG. 20.
FIG. 20.

Particle in the field of two parallel waves with different amplitudes: , , , . (a) Evolution of energy. (b) Projection on the resonance plane.

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/content/aip/journal/chaos/20/4/10.1063/1.3518360
2010-12-07
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Adiabatic description of capture into resonance and surfatron acceleration of charged particles by electromagnetic waves
http://aip.metastore.ingenta.com/content/aip/journal/chaos/20/4/10.1063/1.3518360
10.1063/1.3518360
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