Ii. Beilis et al., NONEQUILIBRIUM MACROPARTICLE CHARGING IN LOW-DENSITY DISCHARGE PLASMAS, IEEE transactions on plasma science, 25(2), 1997, pp. 346-352
Nonequilibrium macroparticle (MP) charging was studied theoretically i
n the case of small MP radius to the Debye length ratio. Two different
cases were considered: 1) nonstationary MP charging in plasmas with l
arge MP density to the ion density ratio k and 2) MP charging in nonun
iform plasmas. In the first case, the large fraction of plasma charges
captured by MP's was taken into account. In the second case, the char
ging of MP's moving in plasmas with nonuniform density distributions w
as considered. It was obtained that the MP charge decreases with param
eter k and increases and saturates with radius (for MP radii larger th
an some critical radius R-cr) and these effects strongly depend on the
MP residence time in the discharge plasma. In the case of plasma dens
ity N-i = 10(12) m(-3) and for k in the range 10(-1)-10(-1), the value
of R-cr decreases from 30 to 0.4 mu m if the MP residence time is t s
imilar to 0.1 ms, and R-cr decreases from 20 to 0.1 mu m if t similar
to 10 ms, while in the steady-state case, R-cr changes more significan
tly from 10 to 10(-2) mu m. Qualitative agreement with experiments of
MP charge behavior with the MP radius and the effect of MP charge satu
ration with the radius was obtained. MP's traveling through a nonunifo
rm plasma, when the plasma density changed as N-i similar to 1/x(m) (w
here m is the nonuniformity parameter) were considered. It was obtaine
d that if the distance during which charging occurred is larger than t
he characteristic linear scale of the plasma density changes x(o), 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 p
lasma jet, the MP does not reach the equilibrium charge if m greater t
han or equal to 2 and x(o) similar to 1 cm.