Beam–Plasma Interaction in Two-Dimensional Yukawa Lattices

The beam-plasma instability displays new properties when either the beam or the plasma, or both, are strongly interacting. We have considered theoretically the case when the plasma is in the crystalline phase and forms a lattice, and the beam is moving in the lattice plane. We consider a 2-D plasma crystal in which both the grains and the beam particles interact through a realistic Yukawa potential. The beam particles are assumed to be weakly coupled to each other and to the lattice. Using the full phonon spectrum for a 2-D hexagonal Yukawa lattice, we determine and compare the transverse and longitudinal growth rates. The relationship between the beam speed and the longitudinal and transverse sound speeds, and the direction of the beam with respect to the principle axes of the lattice determine the qualitative behavior of the growth rates. For beam speeds between the longitudinal and transverse sound speeds, the transverse instability could be more important, because it appears at lower wavenumbers