Investigation of the charge and potential of a dust grain in a low-pressure plasma with allowance for ionization in the intergrain space

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The formation of the ion flow to a dust grain and the distribution of the electric potential in a low-pressure dusty plasma are investigated theoretically with allowance for ionization in the intergrain space. Poisson’s equation similar to the Langmuir plasma-sheath equation is solved numerically with the use of partial analytic solutions at the boundary of the Seitz-Wigner cell and in thin layers in the intergrain space. The charge and potential of a dust grain are found as functions of the grain radius and cell size. The grain potential and the total cell potential energy as functions of the cell size display weak minima, whose positions correspond to the observed intergrain distance in dusty crystals.