Role of Magnetosonic Solitons in Perpendicular Collisionless Shock Reformation

The nature of the magnetic structure arising from ion specular reflection in shock compression studies is examined by means of 1D particle-in-cell simulations. Propagation speed, field profiles, and supporting currents for this magnetic structure are shown to be consistent with a magnetosonic soliton. Coincidentally, this structure and its evolution are typical of foot structures observed in perpendicular shock reformation. To reconcile these two observations, we propose, for the first time, that shock reformation can be explained as the result of the formation, growth, and subsequent transition to a supercritical shock of a magnetosonic soliton. This argument is further supported by the remarkable agreement found between the period of the soliton evolution cycle and classical reformation results. This new result suggests that the unique properties of solitons can be used to shed new light on the long-standing issue of shock nonstationarity and its role on particle acceleration.

Figure 1

(a) Normalized magnetic field contours. The upper left corner (left of the black dotted line) is the vacuum region. The lower right corner is the upstream plasma. The magnetic bump, visible as a narrow peak to the right of the shock front, grows with time. (b) Mach number vs time. $M$ increases almost linearly from 1.8 to 3.5 for $0.95\le \tilde{t}\le 2.4$. Past $\tilde{t}\sim 2.4$, $M$ begins to plateau.

Figure 2

Normalized magnetic field profiles at various times showing the onset and growth of a magnetic structure ahead of the shock front.

Figure 3

Time evolution of the pulse’s parameters. Red open circles show the renormalized abscissa of the magnetic pulse maximum (lower horizontal axis), with $\delta \tilde{x}=\tilde{x}-\tilde{x}(\tilde{t}=1.485)$. Grey crosses indicate the pulse amplitude ${\tilde{B}}_m$ (upper horizontal axis). The black dash-dotted curve $s=\tilde{t}+c$ has a slope equal to 1, typical of magnetosonic solitons.

Figure 4

Field profiles at three different instants during the magnetosonic pulse growth: [(a),(b)] $\tilde{t}=1.58$, [(c),(d)] $\tilde{t}=1.87$, and [(e),(f)] $\tilde{t}=2.16$. [(a), (c), and (e)] Normalized magnetic field (black), transverse electric field (green), electric potential (blue), and density (red) and [(b), (d), and (f)] normalized electron (blue), ion (red) and total (black) transverse current densities.

Figure 5

(a) Magnetic field profile and [(b),(c)] ion phase space distribution after the magnetosonic pulse became supercritical ($\tilde{t}=2.59$).