Self-generated magnetic dipoles in weakly magnetized beam-plasma system

A self-generation mechanism of magnetic dipoles and the anomalous energy dissipation of fast electrons in a magnetized beam-plasma system are presented. Based on two-dimensional particle-in-cell simulations, it is found that the magnetic dipoles are self-organized and play important roles in the beam electron energy dissipation. These dipoles drift slowly in the direction of the return flow with a quasisteady velocity, which depends upon the magnetic amplitude of the dipole and the imposed external magnetic field. This dipole formation provides a mechanism for the anomalous energy dissipation of a relativistic electron beam, which would play an important role in collisionless shock and ion shock acceleration.

Figure 1

(a) The temporal evolution of the energy of $B_z$ for cases with external magnetic fields of ${\mathbf{B}}_0=0$ (green dashed line), ${\mathbf{B}}_0=0.15$ (black solid line), and ${\mathbf{B}}_0=1.0$ (blue dash-dotted line), and the energy of $E_x$ (magenta solid line) and $E_y$ (red solid line) for the ${\mathbf{B}}_0=0.15$ case. The inserted figure (b) shows the temporal evolutions in the linear stage.

Figure 2

Snapshots of the magnetic field $B_z$ at $t=14T_0$. (a), (c), and (e) are for ${\mathbf{B}}_0=0$, ${\mathbf{B}}_0=0.15$, and ${\mathbf{B}}_0=1.0$, respectively. (b), (d), and (f) are the sketches for the three cases, respectively. The blue and yellow regions in (b) and (d) denote the magnetic dipoles, and the red curves (circles) denote the irregular thermal motion (cyclotron motion) of electrons.

Figure 3

(a) Snapshot of the $B_z$ field distribution at $t=32T_0$ for the ${\mathbf{B}}_0=0.15$ case. (b) The profile of $B_z$ versus $\mathbf{x}$ for fixed $y=7.6{\lambda }_0$ (solid line) and $y=8.1{\lambda }_0$ (dashed line) at different times $t=28T_0$, $30T_0$, $32T_0$, and $34T_0$. (c) Measured average drift velocities and theoretical velocities of the dipoles for different amplitudes of the external magnetic field.

Figure 4

The trajectories of sampled beam electrons based on the $B_z$ structure. The red points are starting points.

Figure 5

(a) and (b) represent respectively the density distribution of the beam and background electrons at $32T_0$ in the marked dipole region respectively. (c) and (d) represent the detail electric field $E_x$ and $E_y$ in the same region respectively. (e) and (f) represent the corresponding average energy (unit: MeV) per electron for the beam and background electrons respectively.

Figure 6

(a) and (b) are snapshots of the magnetic field $B_z$ (units of 100 MG) for the cases without and with ${\mathbf{B}}_0$ at $t=80$ fs. The inset figure (g) in (b) is the amplification of the MD directed by the arrow. (c) and (d) are the electron energy density (units of $n_c{m}_e{c}^2$) distributions at $t=80$ fs. (e) and (f) are the electron energy density distributions at $t=330$ fs.