Stopping Power Enhancement From Discrete Particle-Wake Correlations in High Energy Density Plasmas

Three-dimensional (3D) simulations of electron beams propagating in high energy density (HED) plasmas using the quasi-static Particle-in-Cell (PIC) code QuickPIC demonstrate a significant increase in stopping power when beam electrons mutually interact via their wakes. Each beam electron excites a plasma wave wake of wavelength $\sim 2\pi c\mathrm{/}{\omega }_{pe}$, where $c$ is the speed of light and ${\omega }_{pe}$ is the background plasma frequency. We show that a discrete collection of electrons undergoes a beam-plasma like instability caused by mutual particle-wake interactions that causes electrons to bunch in the beam, even for beam densities $n_b$ for which fluid theory breaks down. This bunching enhances the beam’s stopping power, which we call “correlated stopping,” and the effect increases with the “correlation number” $N_b \equiv n_b (c/\omega_{pe})^3$. For example, a beam of monoenergetic 9.7 MeV electrons with $N_b=1\mathrm{/}8$, in a cold background plasma with $n_e={10}^{26}$ cm${}^{-3}$ (450 g cm${}^{-3}$ DT), has a stopping power of $2.28\pm 0.04$ times the single-electron value, which increases to $1220\pm 5$ for $N_b=64$. The beam also experiences transverse filamentation, which eventually limits the stopping enhancement.