Surface States and the Charge of a Dust Particle in a Plasma

We investigate electron and ion surface states of a negatively charged dust particle in a gas discharge and identify the charge of the particle with the electron surface density bound in the polarization-induced short-range part of the particle potential. On that scale, ions do not affect the charge. They are trapped in the shallow states of the Coulomb tail of the potential and act only as screening charges. Using orbital-motion limited electron charging fluxes and the particle temperature as an adjustable parameter, we obtain excellent agreement with experimental data.

Figure 1

Left panel: Potential energy for an electron (ion) in the field of a MF particle ($R=4.7\mu \mathrm{m}$, $Z=6800$) [14] and $s$-type probability distributions shifted to the binding energy and maxima normalized to one. Dashed lines are the potentials used in the Schrödinger equations and thin lines are the bulk energy distribution functions for the hosting discharge. Right panel: Illustration of the surface model to be discussed in the main text. At quasistationarity, surface charges ${\sigma }_{e,i}$ bound at $r_e\approx R$ and $r_i\approx (2\pi {\sigma }_{\mathrm{cx}}{n}_g{)}^{-1}$, respectively, balance charging fluxes $s_{e,i}{j}_{e,i}$ with desorption fluxes ${\tau }_{e,i}^{-1}{\sigma }_{e,i}$.

Figure 2

Pressure dependence of the charge of a MF particle with $R=1\mu \mathrm{m}$ in the neon discharge of Ref. 5 (squares). Solid lines denote the (isothermal) charges deduced from the surface model whereas dotted and dashed lines are the charges obtained from $j_e^{\mathrm{OML}}=j_i^{\mathrm{OML}}+j_i^{\mathrm{CX}}$. The inset shows the radius dependence of the charge for $p=50\mathrm{Pa}$.

Figure 3

Radius dependence of the charge of a MF particle in the sheath of an argon discharge at $p=6.67\mathrm{Pa}$ [7] (squares). Solid (dashed) lines give the charges deduced from the surface model when the depletion of $n_e$ in the confining sheath is (is not) included in the OML electron charging flux.