Self-diffusion in two-dimensional quasimagnetized rotating dusty plasmas

The self-diffusion phenomenon in a two-dimensional dusty plasma at extremely strong (effective) magnetic fields is studied experimentally and by means of molecular dynamics simulations. In the experiment the high magnetic field is introduced by rotating the particle cloud and observing the particle trajectories in a corotating frame, which allows reaching effective magnetic fields up to 3000 T. The experimental results confirm the predictions of the simulations: (i) superdiffusive behavior is found at intermediate timescales and (ii) the dependence of the self-diffusion coefficient on the magnetic field is well reproduced.

Figure 1

Schematics of the “RotoDust” electrode configuration of the (a) BUD setup and the (b) TEX system.

Figure 2

Elementary steps of the derotation transformation demonstrated using two subsequent snapshots from experiment TEX11 (see Table 2, with recording rate 125 frames per second, image resolution $256\times 256$ pixels, and a field of view of $4.5\times 4.5$ mm). Raw images at times (a) $t_0$ and (b) $t_0+8$ ms, with superposed red circles showing the result of the particle detection. (c) and (d) Detected particles together with the center of rotation (COR, red circle) and the vector connecting the COR with the instantaneous center of mass (COM). (e) Overlay of the two sets of particle positions after the rough derotation described in step 5. (f) Overlay of the two sets of particle positions after the least-squares correction and removal of the outer particle ring relative to COR as described in step 6.

Figure 3

Pair correlation functions $g\left(r\right)$ from the experiment (BUD01, symbols) and MD simulation (line) with parameters $\mathrm{\Gamma }=150, \kappa =1.05, \beta =0.65$.

Figure 4

Mean-squared displacement from the experiment (BUD02, symbols) and MD simulation (line) with parameters $\mathrm{\Gamma }=70, \kappa =0.9, \beta =0.84$. Only every 100th experimental data point is plotted for better visibility. The shaded area indicates the range for the parameter fitting, where the finite size effect is negligible. The shaded area itself does depend on the system size, as described in the text. The dashed line marks the time instance $t=1000/{\omega }_{\mathrm{p}}$ used for further analysis.

Figure 5

Fixed-time ($t{\omega }_{\mathrm{p}}=1000$) diffusion coefficient, $D_0^{1000}$, from the $\beta =0$ reference simulations as a function of the effective Coulomb coupling parameter. The theoretical fit formula is adapted from Ref. [46] with $A=2.1444$ and $B=0.00778$.

Figure 6

Fixed-time ($t{\omega }_{\mathrm{p}}=1000$) diffusion coefficient relative to the nonmagnetized values, $D_0$, as a function of the dimensionless magnetization parameter $\beta$.