Acceleration of trapped particles by a Langmuir wave in an inhomogeneous plasma

The acceleration of trapped particles by a Langmuir wave in an inhomogeneous plasma is investigated for different density profiles. In particular the important case of a wave moving towards its refiexion point is considered both analytically and numerically. To obtain estimates of the energy gain of the trapped particles, their stability is investigated. Our findings differ from those of previous authors. The effect of wave damping, and a slowly varying frequency (whistler-like phenomena), on the stability of trapping is estimated.