The space charge layer of the electrical probe taking into account the collisions

The space charge layer of a cylindrical probe has been considered under moderate pressures. A precise solution of Poisson’s equation has been obtained in the approximation of strong field taking into account collisions with atoms. The approximate expression for a space charge layer in the cylindrical geometry without collisions has been suggested; the expression yields an error of up to 1% at 1$\le (r_{sh})/(r_{p})\le$ 200. A simplified approximate expression for a space charge layer under moderate pressures, which is suitable for practical calculations, has also been proposed.