Cumulative displacement induced by a magnetosonic soliton bouncing in a bounded plasma slab

Abstract

The passage of a magnetosonic (MS) soliton in a cold plasma leads to the displacement of charged particles in the direction of a compressive pulse and in the opposite direction of a rarefaction pulse. In the overdense plasma limit, the displacement induced by a weakly nonlinear MS soliton is derived analytically. This result is then used to derive an asymptotic expansion for the displacement resulting from the bouncing motion of a MS soliton reflected back and forth in a vacuum-bounded cold plasma slab. Particles' displacement after the pulse energy has been lost to the vacuum region is shown to scale as the ratio of light speed to Alfvén velocity. Results for the displacement after a few MS soliton reflections are corroborated by particle-in-cell simulations.

Energy and momentum conservation upon reflection of a solitary pulse in a bounded magnetized plasma

“…with B 1 > 0 the magnetic perturbation propagating in the ±x direction. This configuration is analog to that studied previously by the author and co-workers [18], where it was indeed shown that the nature of the magnetic perturbation changes from compression (B 1 > 0) to rarefaction (B 1 < 0) and vice-versa upon reflection of the pulse at the plasma-vacuum interface. We further choose to limit ourselves to the overdense regime (ω pe ω ce ), and assume that the following ordering holds…”

“…Building on this finding, it was then demonstrated that an IA soliton can be forced to bounce back and forth by applying suitable boundary conditions in a laboratory plasma [16,17]. A similar bouncing dynamics has more recently been observed by the the author and co-workers in particle-in-cell simulations of the propagation of a MS soliton in a magnetized plasma slab bounded by vacuum [18].…”

“…The compression pulse B + then matches the soliton solution for magnetosonic waves in an overdense plasma in the limit of a weakly nonlinear pulse 1 [45]. The longitudinal and transverse electric field E x and E y and the longitudinal and transverse electron and ion velocities v ex and v ix and v ey and v iy associated with this perturbation thus write [18]…”

“…Clearly, Ê+ p = Ê− p = Êp so that the pulse EM energy is, to lowest order in v A /c, the same for compression and rarefaction pulses. The ordering v A c also ensures that the kinetic energy is to lowest order equal to the ion kinetic energy along x [18] and…”

“…The slab model considered is analogous to that previously studied by the author and co-workers [18]. Briefly, it consists of a 1d simulation domain of length L along x.…”