Localized optical vortex solitons in pair plasmas

The dynamics of short intense electromagnetic pulses propagating in a relativistic pair plasma is governed by a nonlinear Schrödinger equation with a new type of focusing-defocusing saturable nonlinearity. In this context, we provide an existence theory for ring-profiled optical vortex solitons. We prove the existence of both saddle point and minimum type solutions. Via a constrained minimization approach, we prove the existence of solutions where the photon number may be prescribed, and we get the nonexistence of small-photon-number solutions. We also use the constrained minimization to compute the soliton’s profile as a function of the photon number and other relevant parameters.

Density jump for parallel and perpendicular collisionless shocks

In a collisionless shock, there are no binary collisions to isotropize the flow. It is therefore reasonable to ask to which extent the magnetohydrodynamics (MHD) jump conditions apply. Following up on recent works which found a significant departure from MHD in the case of parallel collisionless shocks, we here present a model allowing to compute the density jump for collisionless shocks. Because the departure from MHD eventually stems from a sustained downstream anisotropy that the Vlasov equation alone cannot specify, we hypothesize a kinetic history for the plasma, as it crosses the shock front. For simplicity, we deal with non-relativistic pair plasmas. We treat the cases of parallel and perpendicular shocks. Non-MHD behavior is more pronounced for the parallel case where, according to MHD, the field should not affect the shock at all.

Simulation study of the formation of a non-relativistic pair shock

We examine with a particle-in-cell (PIC) simulation the collision of two equally dense clouds of cold pair plasma. The clouds interpenetrate until instabilities set in, which heat up the plasma and trigger the formation of a pair of shocks. The fastest-growing waves at the collision speed $c/5$, where $c$ is the speed of light in vacuum, and low temperature are the electrostatic two-stream mode and the quasi-electrostatic oblique mode. Both waves grow and saturate via the formation of phase space vortices. The strong electric fields of these nonlinear plasma structures provide an efficient means of heating up and compressing the inflowing upstream leptons. The interaction of the hot leptons, which leak back into the upstream region, with the inflowing cool upstream leptons continuously drives electrostatic waves that mediate the shock. These waves heat up the inflowing upstream leptons primarily along the shock normal, which results in an anisotropic velocity distribution in the post-shock region. This distribution gives rise to the Weibel instability. Our simulation shows that even if the shock is mediated by quasi-electrostatic waves, strong magnetowaves will still develop in its downstream region.