Particle dynamics governed by radiation losses in extreme-field current sheets

Particles moving in current sheets under extreme conditions, such as those in the vicinity of pulsars or those predicted on upcoming multipetawatt laser facilities, may be subject to significant radiation losses. We present an analysis of particle motion in model fields of a relativistic neutral electron-positron current sheet in the case when radiative effects must be accounted for. In the Landau-Lifshitz radiation reaction force model, when quantum effects are negligible, an analytical solution for particle trajectories is derived. Based on this solution, for the case when quantum effects are significant an averaged quantum solution in the semiclassical approach is obtained. The applicability region of the solutions is determined and analytical trajectories are found to be in good agreement with those of numerical simulations which account for radiative effects. Based on these results we demonstrate that radiation reaction itself can provide a mechanism of pinching even within a given field consideration.

Figure 1

A sample trajectory of the positron in the $xz$ plane is in blue. Red-green color shows value of $B_y$.

Figure 2

Phase space of Eqs. (1). Certain points are marked, according trajectories are shown in Table 1.

Figure 3

A typical trajectory of a positron experiencing radiative friction in a current sheet. (a) $x\left(t\right)$ dependence (b) Trajectory in $xz$ plane. Colors represent the trajectory transitioning through different trajectory types. Blue (black) dashed line — type A-B, green (gray) solid line — type C, red (black) solid line — type D. Current separatrix height $x_{\mathrm{sep}}$ (10) on panel (a) is shown by the dotted black line.

Figure 4

The discrepancy between theory and numerical solution $\delta$ as a function of $p/mc$ and ${\phi }_{\max }$, where $cos{\phi }_{\max }=\eta$. The blue long-dashed line marks the upper edge of the region of weak radiative friction. The green short-dashed line and the solid red line mark the value of the quantum parameter $\chi$ equal to 0.2 and 1, respectively.

Figure 5

An example $\eta \left(t\right)$ using different models. Classical LL model — green dashed line, Corrected LL model — red solid line, Semiclassical case (averaged) — blue dotted line, Semiclassical case (100 particles) — black. The initial parameters used are $p/mc\approx 176, {\phi }_{\max }={20}^{\circ }$.

Figure 6

An example numerical solution of the system (4). The evolution of (a) particle trajectory amplitude $X$ (blue dashed line), current $I_z$ (green dash-dotted line), and linear current density $i_z$ (thick red line), (b) Lorentz-factor gamma. The parameters used are $D=0.01$ and the initial conditions are ${\gamma }_0=200, x_0=0$ and ${\phi }_0=0.5^{\circ }$.