Observations on the ponderomotive force

Burton, D. A. and Cairns, R. A. and Ersfeld, B. and Noble, A. and Yoffe, S. and Jaroszynski, D. A.; Jaroszynski, Dino, ed. (2017) Observations on the ponderomotive force. In: Relativistic Plasma Waves and Particle Beams as Coherent and Incoherent Radiation Sources II. Proceedings of SPIE . Society of Photo-Optical Instrumentation Engineers, CZE. ISBN 9781510609693 (https://doi.org/10.1117/12.2270542)

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The ponderomotive force is an important concept in plasma physics and, in particular, plays an important role in many aspects of the theory of laser plasma interactions including current concerns like wakefield acceleration and Raman amplification. The most familiar form of this gives a force on a charged particle that is proportional to the slowly varying gradient of the intensity of a high frequency electromagnetic field and directed down the intensity gradient. For a field amplitude simply oscillating in time there is a simple derivation of this formula, but in the more general case of a travelling wave the problem is more difficult. Over the years there has been much work on this using Hamiltonian or Lagrangian averaging techniques, but little or no investigation of how well these theories work. Here we look at the very basic problem of a particle entering a region with a monotonically increasing electrostatic field amplitude and being reflected. We show that the equation of motion derived from a widely quoted ponderomotive potential only agrees with the numerically computed orbit within a restricted parameter range and that outside this range it shows features which are inconsistent with any ponderomotive potential quadratic in the field amplitude. Since the ponderomotive force plays a fundamental role in a variety of problems in plasma physics we think that it is important to point out that even in the simplest of configurations standard theories may not be accurate.