Plasma-grain interaction mediated by streaming non-Maxwellian ions

A comprehensive parametric study of plasma-grain interaction for non-Maxwellian streaming ions in steady-state employing particle-in-cell simulations is delineated. Instead of considering the intergrain interaction potential to be the linear sum of isolated grain potentials, we incorporate the numerical advancement developed fully for grain shielding by including nonlinear contributions from the plasma and shadowing effect. The forces acting on grains versus intergrain distance, streaming velocity of the ions, and impact of trapped ions density (number) are characterized for non-Maxwellian ions in the presence of charge-exchange collisions. It is found that the nonlinear plasma response considerably modifies the plasma-grain interaction. Unlike the stationary plasma case, for two identical grains separated by a distance in the presence of streaming ions, the electrostatic force is neither repulsive for all grain separations nor equivalent to the force due to one isolated grain. Inadequacy of the linear response formalism in dealing with the systems having very large grain charges is also discussed. The smallest intergrain separation for which the role of the shadow effect can be ignored is reported.

Figure 1

Schematic illustrating (a) a system of two stationary grains surrounded with ions isotropically and (b) an anisotropic system of two stationary grains in streaming ions in the presence of external driving field.

Figure 2

Intergrain (a) electrostatic forces, (b) plasma absorption induced forces, and (c) number of trapped and untrapped ions as a function of charges assigned to the the grains for $M_{\text{th}}=10$. The charge on unit of electron is denoted by $e_0$ here. The intergrain distance is fixed to $d/{\lambda }_D=6.06$.

Figure 3

Grain charge [in units of $-{10}^4{e}_0$, top row], Electrostatic force [in units of ${10}^{-7}\text{dyne}$, middle row], and Plasma induced absorption force [in units of ${10}^{-8}\text{dyne}$, bottom row] as a function of separation distance between the particles for $M_{\text{th}}=0, M_{\text{th}}=1, M_{\text{th}}=5, M_{\text{th}}=10$, and $M_{\text{th}}=15$. The golden colored $★$ symbol represents the corresponding data for single grain case ($d\sim \infty$). The black dashed horizontal line shown in the subplot (top row) display the initial grain charge of $28000e_0$ where $e_0$ is the charge on one electron. The black dashed lines in the middle and bottom rows indicate the line at the value zero.

Figure 4

Plot exhibiting the grain charge versus streaming speed for (a) upstream grain (two-grain case denoted here by 2G) for various intergrain separations $d/{\lambda }_D=2.02,6.06,10.1$ along with single grain case (denoted here by 1G $d/{\lambda }_D\sim \infty$) and (b) downstream grain for intergrain separations $d/{\lambda }_D=2.02,6.06,10.1$. Additionally, the data for the shifted Maxwellian distribution with collision (SM) and without collision (SM w/o coll.) are presented for $d/{\lambda }_D=6.06$. The plasma conditions are the same as described in the caption of Fig. 3.

Figure 5

Spatial profiles of the induced ion density for $M_{\text{th}}=0,1,5,10,15$ (column wise from left to right) for intergrain separations $d/{\lambda }_D=2.02$ in subplots (a)–(e) (the top-most row), $d/{\lambda }_D=6.06$ in subplots (f)–(j) (second row from top), $d/{\lambda }_D=10.1$ in subplots (k)–(o) (third row from top), respectively, for two grains, and in subplots (p)–(t) (the bottom-most row) for single-grain, all with non-Maxwellian drift distribution. The plasma conditions are the same as described in the caption of Fig 3.

Figure 6

Variation of the (a) trapped (top row) and (b) untrapped (bottom row) ion density along the flow direction for the two grains. First (upstream) grain is at origin and the second (downstream) grain is placed at different locations $d/{\lambda }_D\sim 2,4,6,8,10$ for $M_{\text{th}}=5$ (left column), $M_{\text{th}}=10$ (middle column), and $M_{\text{th}}=15$ (right column).

Figure 7

Plot exhibiting average number of (a) trapped ions as a function of separation distance between the particles for $M_{\text{th}}=0$ (red circle–solid line), $M_{\text{th}}=5$ (blue circle–big dashed line), $M_{\text{th}}=10.0$ (green circle–small dashed line), and $M=15$ (yelow circle–dotted line). Subplot (b) illustrates the variation of trapped ion density versus streaming speed for single-grain (red circle–solid line), two-grain at $d/{\lambda }_D=6$ for Shifted Maxwellian with collision (blue circle–big dashed line) and without collision (green circle–small dashed line), and two-grain with non-Maxwellian distributions (orchid circles–dotted line). The plasma conditions are the same as described in the caption of Fig. 3.