The interaction between charged dust particles in a plasma

A solution to the Poisson-Boltzmann equation for a cloud of charges surrounding two charged dust particles, considered as Debye atoms forming a Debye molecule, is studied by numerical methods. It is demonstrated that attractive forces between the particles arise when two conditions are satisfied. First, the Debye screening radius, corresponding to the electron density at a half average spacing between particles, must be equal to approximately half of this distance. In this case, the attraction arises at a distance equal approximately to the average spacing between particles. Second, charges of one sign must be concentrated predominantly on the particles. Should the particles possess only a small fraction of charges of one sign, they will repulse at any distance. Estimates of the electrostatic pressure and surface tension in a gas of dust particles are obtained.