Screening of the dust-particle charge in a plasma with an external ionization source

An asymptotic theory of the screening of the dust-particle charge in a plasma with an external ionization source has been developed. It has been shown analytically that the screening of the charge of a dust particle adsorbing the charge of charged plasma particles that fall on it is not generally described by the Debye theory. The screening radius is determined by the relation between the coefficients $\beta_{ei}$ and $\beta_L=4\pi ek_i$ ($k_i$ is the ion mobility) of the electron-ion and Langevin recombinations, respectively. When $\beta_L \gg \beta_{ei}$, the screening radius is much larger than the electron Debye radius. It has been shown that the contribution of the ion component of an isothermal plasma to screening is equal to the electron contribution if the coefficient of the electron-ion recombination is twice or more larger than the Langevin coefficient of the ion recombination, $\beta_{ei}\geq 2\beta_L$.