Transport of intense particle beams in large-scale plasmas

Transport of particle beams in plasmas is widely employed in fundamental research, industry, and medicine. Due to the high inertia of ion beams, their transport in plasmas is usually assumed to be stable. Here we report the focusing and flapping of intense slab proton beams transporting through large-scale plasmas by using a recently developed kinetic particle-in-cell simulation code. The beam self-focusing effect in the simulation is prominent and agrees well with previous experiments and theories. Moreover, the beam can curve and flap like turbulence as the beam density increases. Simulation and analysis indicate that the self-generated magnetic fields, produced by movement of collisional plasmas, are the dominant driver of such behaviors. By analyzing the spatial growth rate of magnetic energy and energy deposition of injected proton beams, it is found that the focusing and flapping are significantly determined by the injected beam densities and energies. In addition, a remarkable nonlinear beam energy loss is observed. Our research might find application in inertial confinement fusion and also might be of interest to the laboratory astrophysics community.

Figure 1

(a) Schematic representation of the simulation model. Plasma is uniformly distributed within the red dashed box. Planes I and II are positions where the beam energy is measured. The black grids present the simulation cells. (b) Beam transport with the self-generated magnetic constraint. The red and blue surfaces stand for the self-generated magnetic fields in the $x$ direction which are positive and negative, respectively. The green surface is the beam density distribution.

Figure 2

Distributions of beam densities and magnetic fields for proton beams with different densities at 12 ns. The beam distributions (in units of $n_0={10}^{14}{\mathrm{cm}}^{-3}$) have an injection energy of $0.4\mathrm{MeV}$; initial densities of (a) $1\times {10}^{14}$, (c) $1\times {10}^{15}$, (e) $5\times {10}^{15}$, and (g) $1\times {10}^{16}{\mathrm{cm}}^{-3}$; and current densities of (a) $1.4\times {10}^8$, (c) $1.4\times {10}^9$, (e) $7\times {10}^9$, and (g) $1.4\times {10}^{10}\mathrm{A}/{\mathrm{m}}^2$. The corresponding magnetic fields are shown in (b), (d), (f), and (h).

Figure 3

The $z$ component of the electric field with a beam density of $1\times {10}^{16}{\mathrm{cm}}^{-3}$ at 12 ns. Other conditions are the same as in Fig. 2. The black dots reveal the distribution of beam particles.

Figure 4

Evolution as a function of distance: (a) magnetic field energies and (b) spatial growth rates for proton beams with a fixed initial energy of $0.4\mathrm{MeV}$ but different densities, and (c) magnetic field energies and (d) spatial growth rates for a proton beam with a fixed density of ${10}^{16}{\mathrm{cm}}^{-3}$ but different initial energies.

Figure 5

Beam energy spectra for different densities measured on plane II at 13.33 ns. The black curve is the initial spectrum of these beams, detected on plane I. The dots at the bottom are the minimum energies detected.