Structure of a microparticle crystal in a radio-frequency discharge plasma

By employing the particle-in-cell method we study the distributions of the electric field strength and of the electron and ion concentrations in the microparticle crystal in the electrode sheath in a radio-frequency discharge in helium. The coordinates and charges of the microparticles are found from the balance condition for the forces acting on the particles and the balance of electron and ion fluxes to the particles. With periodic boundary conditions introduced, we investigate the three-dimensional problem for the unit cell of the microparticle crystal. We examine the dependence on gas pressure and discharge voltage of the main crystal parameters: the critical particle separation (at which a phase transition from a monolayer crystal to a double-layer crystal occurs), the particle potentials, and the distances between the layers in the double-layer crystal. We obtain the critical values of the friction coefficient for the particles in the gas, i.e., values below which the crystal becomes unstable against the development of particle oscillations in the transverse direction, and compare the experimental data on crystal structure and stability with the theoretical results. Finally, we set up an approximate model that makes it possible to calculate the main parameters of the microparticle crystal.