Nonequilibrium macroparticle charging in low-density discharge plasmas

Nonequilibrium macroparticle (MP) charging was studied theoretically in the case of small MP radius to the Debye length ratio. The different cases were considered: 1) nonstationary MP charging in plasmas with large MP density to the ion density ratio κ and 2) MP charging in nonuniform plasmas. In the first case, the large fraction of plasma charges captured by MP´s was taken into account. In the second case, the charging of MP´s moving in plasmas with nonuniform density distributions was considered. It was obtained that the MP charge decreases with parameter κ and increases and saturates with radius (for MP radii larger than some critical radius R_cr) and these effects strongly depend on the MP residence time in the discharge plasma. In the case of plasma density N_i=10¹² m ^-3 and for κ in the range 10^-4-10^-1 , the value of R decreases from 30 to 0.4 μm if the MP residence time is t~0.1 ms, and R_cr decreases from 20 to 0.1 μm if t~10 ms, while in the steady-state case, R_cr changes more significantly from 10 to 10^-2 μm. Qualitative agreement with experiments of MP charge behavior with the MP radius and the effect of MP charge saturation with the radius was obtained. MP´s traveling through a nonuniform plasma, when the plasma density changed as N_i~1/x^m (where m is the nonuniformity parameter) were considered. It was obtained that if the distance during which charging occurred is larger than the characteristic linear scale of the plasma density changes, the MP´s may not have time to reach their equilibrium charge value at any location that they pass through. In the case of MP traveling in the plasma jet, the MP does not reach the equilibrium charge if m⩾2 and ~1 cm