Energy loss for the assemblies of charged projectiles in a dusty plasma

Expressions for the electrostatic potential and the energy loss are derived for a variety of arrays of dust grain projectiles, arranged at different orientations and separations and moving with a constant velocity along the z axis in an unmagnetized collisionless dusty plasma, using linear dielectric theory. By employing the dielectric constant of dust acoustic wave, the Debye and wake potentials are calculated for the projectiles. It is found that a projectile moving with high speed forms a negative wake behind and a shock in front of it. Further, for particular values of interspacing, the three different assemblies exhibit almost similar behavior of the energy loss and thus permit the possibility of all of them to move in unison to establish a dynamical equilibrium in a hexagonal geometry.