Abstract
The nonlinear group velocity of an electron plasma wave is investigated numerically using a Vlasov code, and is found to assume values which agree very well with those predicted by a recently published theory [D. Bénisti et al., Phys. Rev. Lett.103, 155002 (2009)], which we further detail here. In particular we show that, once Landau damping has been substantially reduced due to trapping, the group velocity of an electron plasma wave is not the derivative of its frequency with respect to its wave number. This result is moreover discussed physically, together with its implications in the saturation of stimulated Raman scattering.
One of the authors (D.B.) wants to thank Professor A. Bers for the reference to Whitham’s book. Work at LLNL was performed under the auspices of the U.S. Department of Energy under Contract No. DEAC5207NA27344, LDRD tracking number 08ERD017.
I. INTRODUCTION
II. NUMERICAL SIMULATIONS AND COMPARISONS WITH THEORY
III. THEORY
A. Envelope equation for an electron plasma wave
1. Linear regime
2. Connection to variational approaches and nonlinear regime
B. Consequence for stimulated Raman scattering
IV. CONCLUSION
Key Topics
 Plasma waves
 69.0
 Number theory
 11.0
 Radiosurgery
 10.0
 Plasma electromagnetic waves
 9.0
 Lagrangian mechanics
 8.0
Figures
Sketch of the propagation of a plasma pulse whose group velocity is independent of its amplitude and whose damping rate rapidly decreases with . The shape of the pulse at time is given by the blue dashed line, and at time by the green solid line, while the shape of the damping rate is given by the red dasheddotted line. Due to damping the pulse maximum, , at time , is not located at time at the new maximum, , but at point on the left of . Hence, for this particular example, the group velocity is less than the speed of propagation of the pulse maximum. Moreover, at time , point was located at , i.e., on the left of point corresponding to the same pulse amplitude as point . Therefore, .
Sketch of the propagation of a plasma pulse whose group velocity is independent of its amplitude and whose damping rate rapidly decreases with . The shape of the pulse at time is given by the blue dashed line, and at time by the green solid line, while the shape of the damping rate is given by the red dasheddotted line. Due to damping the pulse maximum, , at time , is not located at time at the new maximum, , but at point on the left of . Hence, for this particular example, the group velocity is less than the speed of propagation of the pulse maximum. Moreover, at time , point was located at , i.e., on the left of point corresponding to the same pulse amplitude as point . Therefore, .
Dimensionless plasma wave amplitude, , as a function of at times (blue solid line) and (green dashed line), obtained from the Vlasov run for the 5 keV case of Table I.
Dimensionless plasma wave amplitude, , as a function of at times (blue solid line) and (green dashed line), obtained from the Vlasov run for the 5 keV case of Table I.
Our theoretical predictions for the group velocity (blue solid line), and , normalized to the thermal velocity (green dashed line) when the electron density is 10% of the critical one and when (a) , (b) , (c) , and (d) .
Our theoretical predictions for the group velocity (blue solid line), and , normalized to the thermal velocity (green dashed line) when the electron density is 10% of the critical one and when (a) , (b) , (c) , and (d) .
Our theoretical predictions for (blue solid line) and (green dashed line) for a plasma wave with .
Our theoretical predictions for (blue solid line) and (green dashed line) for a plasma wave with .
Orbit, calculated between times and of a particle acted upon by the force with and , and whose initial position and velocity are and . The blue solid line is the actual orbit of the trapped electron. The green curve is the symmetric image, with respect to the axis, of that part of the orbit lying on the halfplane, . The black dashed curve is the virtual separatrix corresponding to the amplitude at .
Orbit, calculated between times and of a particle acted upon by the force with and , and whose initial position and velocity are and . The blue solid line is the actual orbit of the trapped electron. The green curve is the symmetric image, with respect to the axis, of that part of the orbit lying on the halfplane, . The black dashed curve is the virtual separatrix corresponding to the amplitude at .
Tables
Values of the nonlinear group velocity, normalized to the thermal one, either calculated theoretically or numerically, and compared to , also normalized to the thermal velocity. All results correspond to a plasma whose electron density is 10% of the critical one.
Values of the nonlinear group velocity, normalized to the thermal one, either calculated theoretically or numerically, and compared to , also normalized to the thermal velocity. All results correspond to a plasma whose electron density is 10% of the critical one.
Article metrics loading...
Full text loading...
Most read this month
Most cited this month










Electron, photon, and ion beams from the relativistic interaction of Petawatt laser pulses with solid targets
Stephen P. Hatchett, Curtis G. Brown, Thomas E. Cowan, Eugene A. Henry, Joy S. Johnson, Michael H. Key, Jeffrey A. Koch, A. Bruce Langdon, Barbara F. Lasinski, Richard W. Lee, Andrew J. Mackinnon, Deanna M. Pennington, Michael D. Perry, Thomas W. Phillips, Markus Roth, T. Craig Sangster, Mike S. Singh, Richard A. Snavely, Mark A. Stoyer, Scott C. Wilks and Kazuhito Yasuike

Commenting has been disabled for this content