Charged particle dynamics in turbulent current sheets

We study dynamics of charged particle in current sheets with magnetic fluctuations. We use the adiabatic theory to describe the nonperturbed charged particle motion and show that magnetic field fluctuations destroy the adiabatic invariant. We demonstrate that the evolution of particle adiabatic invariant's distribution is described by a diffusion equation and derive analytical estimates of the rate of adiabatic invariant's diffusion. This rate is proportional to power density of magnetic field fluctuations. We compare analytical estimates with numerical simulations. We show that adiabatic invariant diffusion results in transient particles trapping in the current sheet. For magnetic field fluctuation amplitude a few times larger than a normal magnetic field component, more than 50% of transient particles become trapped. We discuss the possible consequences of destruction of adiabaticity of the charged particle motion on the state of the current sheets.

Figure 1

Schematic view of the system. Gray region shows the current sheet (i.e., localized electric current density). Magnetic field $B_x$ varies across this current sheet with the spatial scale $L$. Gray arrow shows plasma flow coming from the deep tail region and bringing electromagnetic fluctuations.

Figure 2

Three particle trajectories in the $(x,p_x)$ plane and the corresponding time profiles of $I_z$: (a) $\beta =0$, (b) $\beta /\kappa =1$, (c) $\beta /\kappa =2.5$.

Figure 3

Profile of function $F\left(s\right)$.

Figure 4

Initial distribution $\mathrm{\Psi }\left(I_z\right)$, results of solution of Eq. (17) (dotted curves), and results of numerical integration of ${10}^6$ trajectories (solid curves) for two $\beta$ values: (a) $I_{z,\text{init}}=0.1$, (b) $I_{z,\text{init}}=0.5$.

Figure 5

Percentage of particles on transient trajectories after one interaction with CS for $\kappa =0.01$.