Additive plasma pushing resulting from the propagation of a magnetosonic soliton in a finite size plasma

Solitons are solitary localized wave solutions to the Korteweg-de-Vries (KdV) equation which describes waves in weakly dispersive media for which dispersion balances out nonlinear effects. Soliton solutions exist both for ion-acoustic and magnetosonic (MS) waves in homogeneous plasmas. Besides their remarkable stability with respect to interactions, an interesting property of MS solitons is that they lead to plasma displacement. Indeed, owing to the odd longitudinal electric field associated with the pulse, compressive pulses push plasma along the direction of propagation while rarefaction pulses push plasma in the direction opposite to propagation. However, the form self-preserving nature of solitons breaks down in the presence of inhomogeneities. An interesting example illustrated here is the behavior of a MS soliton incident on a plasma-vacuum interface. We show that a compressive MS pulse turns into a rarefaction pulse upon reflection at the interface, and vice-versa. The nature of a MS pulse thus  alternates from compressive to rarefactive at each reflection when bouncing in a plasma slab, and the displacement induced by each of the pulse passages adds constructively. This interesting theoretical finding is illustrated and validated using particle-in-cell simulations.