High-energy acceleration phenomena in extreme-radiation–plasma interactions

We simulate, using a particle-in-cell code, the chain of acceleration processes at work during the Compton-based interaction of a dilute electron-ion plasma with an extreme-intensity, incoherent $\gamma$-ray flux with a photon density several orders of magnitude above the particle density. The plasma electrons are initially accelerated in the radiative flux direction through Compton scattering. In turn, the charge-separation field from the induced current drives forward the plasma ions to near-relativistic speed and accelerates backwards the nonscattered electrons to energies easily exceeding those of the driving photons. The dynamics of those energized electrons is determined by the interplay of electrostatic acceleration, bulk plasma motion, inverse Compton scattering and deflections off the mobile magnetic fluctuations generated by a Weibel-type instability. The latter Fermi-like effect notably gives rise to a forward-directed suprathermal electron tail. We provide simple analytical descriptions for most of those phenomena and examine numerically their sensitivity to the parameters of the problem.

Figure 1

Time evolution of the transversely averaged electron density ($n_e/n_0$). The plasma initially occupies the region $0\le x{\omega }_{\mathrm{p}}/c\le 3800$. The photon flux is impinging from the left-hand side and the green dashed line indicates the trajectory of the radiation front. The simulation parameters are ${\overline{\epsilon }}_{\gamma }=4$, ${\alpha }_{\gamma }=1.05\times {10}^4$, and $m_i/m_e=184$.

Figure 2

Electron $\xi -p_x$ phase space at time $\overline{t}=3500$, with the corresponding laboratory-frame $x$ position and comoving $\xi$ position indicated on the bottom and top axes, respectively. The photon front is then located at $\overline{x}=3500$ ($\overline{\xi }=0$). The simulation parameters are ${\overline{\epsilon }}_{\gamma }=4$, ${\alpha }_{\gamma }=1.05\times {10}^4$ and $m_i/m_e=184$. The black box near the photon front delineates the region where early-time interactions effectively thermalize the plasma bulk. The red line represents the typical trajectory of an electron backward-accelerated by the charge-separation field in the energetic tail.

Figure 3

Electron $p_x-p_y$ phase space near the photon front ($0<\overline{\xi }<50$) at $\overline{t}=1050$, with ${\overline{\epsilon }}_{\gamma }=4$, ${\alpha }_{\gamma }=1.05\times {10}^4$ and $m_i/m_e=184$. The orange region that extends up to $p_x\simeq {\epsilon }_{\gamma }/c$ represents the electrons scattered once by the photons, while the green component extending to ${\overline{p}}_x\simeq 2{\overline{\epsilon }}_{\gamma }$ corresponds to twice scattered electrons. The unscattered dense component is visible in red. The simulation parameters are those of Fig. 2.

Figure 4

Top: Electron $\xi -p_x$ phase space, near the photon front (as indicated). The blue, red and green lines represent three representative electron trajectories. The colored arrows pinpoint the locations of individual Compton scattering events. Bottom: Corresponding trajectories in $p_x-p_y$ space. Plain arrows indicate the direction of motion while filled arrows trace the jumps due to Compton scatterings. The simulation parameters are those of Fig. 2.

Figure 5

Blue: Longitudinal profile of the transversely averaged $\langle E_x\rangle$ field extracted at $\overline{t}=3500$ from the same PIC simulation as in Fig. 2. Orange: same quantity but smoothed over 100 grid points along $\xi$. Green: Approximate $\langle E_x\rangle$ field as given by Eq. (1) and fitting the local electron distribution function to a bi-Maxwellian distribution. See text for details.

Figure 6

Ion $\xi -p_x$ phase space at time $\overline{t}=3500$ from the same simulation as in Fig. 2. The overall profile in mean momentum $p_x$ is shaped by the electric drag, as discussed in the text.

Figure 7

(a) Out-of-plane magnetic field ($e{B}_z/m_e{\omega }_{\mathrm{p}}c$) and (b) electron density ($n_e/n_0$) distributions near the photon front. The simulation parameters are those of Fig. 2.

Figure 8

(a) Longitudinal and (b) transverse momentum distributions of the plasma (blue) electrons and (orange) ions, as extracted at $\overline{\xi }=1500$ from the same simulation as in Fig. 2, and averaged over the transverse dimension. The electron (ion) momenta are normalized to $m_{e}c$ (respectively, $m_{i}c$). The brown curves closely matching the simulated electron distribution in both panels is the sum of the three drifting bi-Maxwellian components plotted in green, red and purple. See Eq. (14) and text for details.

Figure 9

(top) Longitudinal profiles of the root-mean-square electric ($E_x$, $E_y$) and magnetic ($B_z$) fields (averaged over the transverse directions and normalized to $m_{e}c{\omega }_{\mathrm{p}}/e$) at $\overline{t}=3500$. (bottom) Corresponding 2D $B_z$ field distribution. The simulation parameters are those of Fig. 2.

Figure 10

Evolution of the root-mean-square magnetic field ${\langle B_z^2\rangle }^{1/2}$ (averaged over the transverse dimension and normalized to $m_{e}c{\omega }_{\mathrm{p}}/e$) as a function of longitudinal position and time. The moving CFI-driven magnetic structures appear as the coherent streaks developing at late times. Same simulation parameters as in Fig. 2.

Figure 11

Electron density distribution $f_e\left({\gamma }^{\left(0\right)}\right)$ measured in the simulation along an unscattered trajectory ${\gamma }^{\left(0\right)}\left(\xi \right)$ as discussed in the text (blue), compared with its analytical approximation, Eq. (20) (red). The parameter ${\beta }_x^{\left(0\right)}$ is fixed here to $-0.6$, and the amplitude is rescaled to match the simulation data.

Figure 12

Three representative electron trajectories from the simulation with ${\overline{\epsilon }}_{\gamma }=4$, ${\alpha }_{\gamma }=1.05\times {10}^4$ and $m_i/m_e=184$. Plain and filled arrows respectively indicate direction of motion and Compton scattering events.

Figure 13

Charge-separation electric field, $\langle E_x\rangle$, in the (blue) $m_i/m_e=184$ and (orange) $m_i=+\infty$ cases, averaged over the $y$ direction. The other main parameters are ${\overline{\epsilon }}_{\gamma }=4$ and ${\alpha }_{\gamma }=1.05\times {10}^4$. Near the photon front, the two longitudinal profiles of $\langle E_x\rangle$ almost coincide, while further away $\langle E_x\rangle$ increases more slowly with distance when $m_i/m_e=184$.

Figure 14

Electron $\xi -p_x$ phase space, using immobile ions along with ${\overline{\epsilon }}_{\gamma }=4$ and ${\alpha }_{\gamma }=1.05\times {10}^4$.

Figure 15

Electron $\xi -p_x$ phase space at $\overline{t}=28000$ in a simulation using $m_i/m_e=1836$ along with ${\overline{\epsilon }}_{\gamma }=4$ and ${\alpha }_{\gamma }=1.05\times {10}^4$.

Figure 16

Same as Fig. 5 ($m_i/m_e=184$, ${\overline{\epsilon }}_{\gamma }=4$) but with a larger photon density (${\alpha }_{\gamma }=1.05\times {10}^5$).

Figure 17

Electron $\xi -p_x$ phase space. The simulation parameters are those of Fig. 5 except for a larger photon density (${\alpha }_{\gamma }=1.05\times {10}^5$).

Figure 18

Two representative electron $p_x-p_y$ trajectories from the simulation with ${\alpha }_{\gamma }=1.05\times {10}^5$, ${\overline{\epsilon }}_{\gamma }=4$ and $m_i/m_e=184$. As the ions, and therefore the microturbulence, move at relativistic bulk velocities, the loci of constant total momentum in the filament frame (${\overline{p}}^{*}$) are no longer circles, but ellipses. These are indicated in dotted lines, assuming that the filament frame moves at ${\beta }_{ix}=0.77$, as measured for ions around $\overline{\xi }\simeq 1000$.

Figure 19

Electron (top) and ion (bottom) $\xi -p_x$ phase spaces at $\overline{t}=11000$, from a simulation using a finite-length photon flux with ${\overline{\epsilon }}_{\gamma }=4$ and $m_i/m_e=184$. The yellow triangles indicate the photon density profile: it increases as $n_{\gamma }=1.05\times {10}^5{n}_0\overline{\xi }$ up to $\overline{\xi }<{\overline{\xi }}_{\max }=900$, and vanishes further away.

Figure 20

Electron $\xi -p_x$ phase space at $\overline{t}=3500$, from a simulation with ${\overline{\epsilon }}_{\gamma }=0.1$, ${\alpha }_{\gamma }=1.05\times {10}^4$ and $m_i/m_e=184$.

Figure 21

Electron $\xi -p_x$ phase space, from a simulation with ${\overline{\epsilon }}_{\gamma }=2$ and ${\alpha }_{\gamma }=1.05\times {10}^4$. Features similar to the reference configuration are found, yet in a parameter range precluding photon-photon pair production.