Abstract
The expansion of a dense plasma through a more rarefied ionized medium has been studied by means of two-dimensional particle-in-cell simulations. The initial conditions involve a density jump by a factor of 100, located in the middle of an otherwise equally dense electron–proton plasma with uniform proton and electron temperatures of 10 eV and 1 keV, respectively. Simulations show the creation of a purely electrostatic collisionless shock together with an ion-acoustic soliton tied to its downstream region. The shock front is seen to evolve in filamentary structures consistently with the onset of the ion–ion instability. Meanwhile, an un-magnetized drift instability is triggered in the core part of the dense plasma. Such results explain recent experimental laser–plasma experiments, carried out in similar conditions, and are of intrinsic relevance to non-relativistic shock scenarios in the solar and astrophysical systems.
Highlights
Involving laser pulses that impact on solid targets [4] have demonstrated the rarefied plasma to play an important role in the plasma dynamics
The rarefaction wave was destabilized in the simulation by an electrostatic drift instability [26, 27], which triggered the formation of plasma structures that resembled the ion-acoustic waves observed in the experiment
The drift instability mentioned above triggers a strongly modulated electric field distribution, in correspondence to the core of the dense plasma (see −20 x 10 in figure 7(a)), which reaches a maximum amplitude of 2 × 107 V m−1, i.e. strong enough to induce the proton deflections detected in the experiment
Summary
We will discuss the simulated plasma dynamics following the evolution in time of the electron and proton phase spaces and the related electric field distributions. A broad peak in the electric field is present only in the ‘foreshock’ region (i.e. that spatial interval, just in front of the shock, in which the ambient plasma is perturbed by the presence of the shock, approximately at x = 28); such an electric field is related, as will be extensively discussed, to the onset of an instability, which is transverse to the shock front, driven by the two counter-propagating proton beams The absence of such Ey components, in correspondence to the shock and the soliton, is a good indication that the plasma flow direction (i.e. the direction along which the strongest currents are expected to be) is mostly parallel to Ex and those structures are purely electrostatic. The drift instability mentioned above triggers a strongly modulated electric field distribution, in correspondence to the core of the dense plasma (see −20 x 10 in figure 7(a)), which reaches a maximum amplitude of 2 × 107 V m−1, i.e. strong enough to induce the proton deflections detected in the experiment
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