Potential distribution around a test charge in a positive dust-electron plasma

The electrostatic potential caused by a test-charge particle in a positive dust-electron plasma is studied, accounting for the dust-charge fluctuations associated with ultraviolet photoelectron and thermionic emissions. For this purpose, the set of Vlasov–Poisson equations coupled with the dust charging equation is solved by using the space–time Fourier transform technique. As a consequence, a modified dielectric response function is obtained for dust-acoustic waves in a positive dust-electron plasma. By imposing certain conditions on the velocity of the test charge, the electrostatic potential is decomposed into the Debye–Hückel (DH), wake-field (WF), and far-field (FF) potentials that are significantly modified in the limit of a large dust-charge relaxation rate both analytically and numerically. The results can be helpful for understanding dust crystallization/coagulation in twocomponent plasmas, where positively charged dust grains are present.