Explosive Particle Dispersion in Plasma Turbulence

Particle dynamics are investigated in plasma turbulence, using self-consistent kinetic simulations, in two dimensions. In the steady state, the trajectories of single protons and proton pairs are studied, at different values of plasma $\beta$ (ratio between kinetic and magnetic pressure). For single-particle displacements, results are consistent with fluids and magnetic field line dynamics, where particles undergo normal diffusion for very long times, with higher $\beta$’s being more diffusive. In an intermediate time range, with separations lying in the inertial range, particles experience an explosive dispersion in time, consistent with the Richardson prediction. These results, obtained for the first time with a self-consistent kinetic model, are relevant for astrophysical and laboratory plasmas, where turbulence is crucial for heating, mixing, and acceleration processes.

Figure 1

Structure function of the magnetic field as a function of the spatial increment $\delta$, for all the runs. Solid (green) and dashed (blue) lines represent the fit with Eq. (5), for run II and III, respectively. Exponents $\gamma$ are given in Table 1.

Figure 2

Puffs of particles as a function of time, starting from the steady state, located at different regions of 2D plasma turbulence. $j_z$ is shown at two times, $t{\mathrm{\Omega }}_{cp}=50$ and 250 (shaded surfaces). The inset shows the initial spreading of a population (small subset), up to $t{\mathrm{\Omega }}_{cp}\sim 75$ (small spheres), together with the position of some gyrocenters (big spheres). Explosive dispersion is observed.

Figure 3

Running diffusion coefficients $\frac{1}{2}(\partial ⟨\mathrm{\Delta }{s}^2⟩/\partial \tau )$ for all the runs. Stars indicate $D_s$, computed as a fit for very large times $\tau {\mathrm{\Omega }}_{cp}>90$. The inset shows the mean square displacement $⟨\mathrm{\Delta }{s}^2⟩$ in the very initial stage (run II).

Figure 4

(a) Mean squared gyrocenter separation as a function of time. Inertial range fits $\sim {\tau }^{\mu }$ are reported (black dashed lines) (see Table 1 for $\mu$). The horizontal (orange) dotted line represents ${\lambda }_C$, while arrows indicate ${\tau }_{\ell g}$. (b) Particle separation probability $P(r,\tau )$ as a function of $r$, at different $\tau$. Results are shown for the intermediate $\beta$ (run II) but are similar for all the runs. The Richardson fit is reported with dashed (black) lines. Inset in (b): Rescaled $P(r,\tau )$ for the same times (symbols) and Richardson expectation ($-r^{\gamma }$) (dashed line). The generalized law is clearly observed for $t\sim {\tau }_{\ell g}$, being lost when $t\gg {\tau }_{\ell g}$ (red triangles).