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We consider the field-aligned acceleration of energetic\udions and electrons which takes place on auroral field lines due to their\udinteraction with time-varying density cavities stimulated by the strong\udoscillating field-aligned currents of kinetic Alfvén waves. It is shown\udthat when the field-aligned current density of these waves increases, such\udthat the electron drift speed exceeds the electron thermal speed, ion\udacoustic perturbations cease to propagate along the field lines and instead\udform purely-growing density perturbations. The rarefactions in these\udperturbations are found to grow rapidly to form density cavities, limited by\udthe pressure of the bipolar electric fields which occur within them. The\udtime scale for growth and decay of the cavities is much shorter than the\udperiod of the kinetic Alfvén waves. Energetic particles traversing these\udgrowing and decaying cavities will be accelerated by their time-varying\udfield-aligned electric fields in a process that is modelled as a series of\uddiscrete random perturbations. The evolution of the particle distribution\udfunction is thus determined by the Fokker-Planck equation, with an energy\uddiffusion coefficient that is proportional to the square of the particle\udcharge, but is independent of the mass and energy. Steady-state solutions\udfor the distribution functions of the accelerated particles are obtained for\udthe case of an arbitrary energetic particle population incident on a\udscattering layer of finite length along the field lines, showing how the\udreflected and transmitted distributions depend on the typical "random walk"\udenergy change of the particles within the layer compared to their initial\udenergy. When this typical energy change is large compared to the initial\udenergy, the reflected population is broadly spread in energy about a mean\udwhich is comparable with the initial energy, while the transmitted\udpopulation has the form of a strongly accelerated field-aligned beam. We\udsuggest that these processes are responsible for the occurrence of\udaccelerated field-aligned beams of ions and electrons that are commonly\udobserved on auroral field lines in planetary magnetospheres

Field-aligned particle acceleration on auroral field lines by interaction with transient density cavities stimulated by kinetic Alfvén waves