Plasma dynamics at the Schwinger limit and beyond

Strong field physics close to or above the Schwinger limit are typically studied with vacuum as initial condition or by considering test particle dynamics. However, with a plasma present initially, quantum relativistic mechanisms such as Schwinger pair creation are complemented by classical plasma nonlinearities. In this work we use the Dirac-Heisenberg-Wigner formalism to study the interplay between classical and quantum mechanical mechanisms in the regime of ultrastrong electric fields. In particular, the effects of initial density and temperature on the plasma oscillation dynamics are determined. Finally, comparisons with competing mechanisms such as radiation reaction and Breit-Wheeler pair production are made.

Figure 1

The normalized vector potential $A_N$, the dashed lines, and electric field $E$, the solid lines, vs the normalized time $t_n={\omega }_{c}t$ for four different values of initial $E$ field $E=(0.01,0.1,1,4)$.

Figure 2

The total particle number density $n\left(t\right)$ over time for four different initial values of the electric field $E(t=0)=(0.01,0.1,1,4)$.

Figure 3

The number density $n\left(q\right)=\int d{p}_{\perp }{p}_{\perp }/\varepsilon [{\varepsilon }_{\perp }{\chi }_2+(q-A){\chi }_1]$ as a function of the canonical momentum $q$ is plotted for $E=4$ for two cases: $\mu =4$ and $T=0.02$ (top panel) and $\mu =-10$ and $T=5$ (bottom panel).

Figure 4

The electric field (upper panel), vector potential (middle panel), and number density (lower panel) for a plasma with an initial current. The dotted line (blue) corresponds to the initial parameters $E=0, \mu =3, T=0.2$, and $p_d=70$. The solid line (brown) corresponds to initial values $E=1, \mu =1.5, T=0.2$, and $p_d=0$.

Figure 5

The electric field damping (squares) and frequency increase (dots) for $E(t=0)=1, \mu =1.5$ and $T=0.2$, where a line equal to unity is drawn for comparison. The electric field dots are evaluated at successive peaks, and the frequencies are computed as $\omega =2\pi /T_p$, with the time period $T_p$ computed for successive peak values of the electric field. The frequencies are normalized against the frequency for the first oscillation period (with $T_p$ = 462).

Figure 6

The damping of the electric field $\mathrm{\Gamma }$ as a function of three different parameters. In the top panel we plot $\mathrm{\Gamma }$ vs $\mu$ for $E=1$ and $T=1$. For the second panel, we plot $\mathrm{\Gamma }$ vs the temperature $T$ for $E=1$ and $\mu =1.5$. For the third panel, we vary $T$ but compensate with varying $\mu$ to keep the number density fixed. Finally, in the bottom panel, we plot $\mathrm{\Gamma }$ vs initial electric field for $T=0.4$ and $\mu =1.5$.

Figure 7

Color mappings of the momentum distribution of the total particle density $n(p_z,p_{\perp })$ at three different times $t=(0,T_p/4,T_p/2)$ for $E_0=1, \mu =1.5$, and $T=0.2$.

Figure 8

The induced electric field (i.e., without including the external field of the initial Sauter pulse) (upper panel) and the induced number density (lower panel). The parameter values for the Sauter pulse are $A_0=10$ and $\tau =0.5$

Figure 9

The induced electric field (i.e., without including the external field of the initial Sauter pulse) (upper panel) and the induced number density (lower panel). The parameter values for the Sauter pulse are $A_0=10$ and $\tau =0.5$ and the enhanced value $\alpha =4$ for the fine-structure constant.

Figure 10

The electric field profile starting from a an initial value $E(t=0)=100E_{cr}$ using the actual value of $\alpha$. The result is compared with the curve computed in Ref. [30], using the same parameters. The data from [30] have been extracted using the online tool WebPlotDigitizer [49].