Beam-Plasma Interaction in a 2D Complex Plasma

In a complex (dusty) plasma, penetrating ion or electron beams may lead to beam-plasma instabilities. The instability displays interesting new properties when either the plasma or the beam, or both, are strongly interacting$^{1}$. Foremost amongst them is the possible generation of \textit{transverse} instabilities. We consider the case when a 2D plasma is in the crystalline phase, forming a lattice, and the beam is moving in the lattice plane. 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$^{2}$. Using the full phonon spectrum for a 2D hexagonal Yukawa lattice$^{3}$, we determine and compare the transverse and longitudinal growth rates. The behavior of the growth rates depends on the direction of the beam and on the relationship between the beam speed $v$ and the longitudinal and transverse sound speeds $s_L$, $s_T$. For beam speeds between the longitudinal and transverse sound speeds, the transverse instability could be more important, because it appears at lower $k$ values. \newline $^{1}$ G. J. Kalman and M. Rosenberg, J. Phys. A: Math. Gen. \textbf{36} 5963 (2003) $^{2}$ M. Rosenberg, G. J. Kalman, S. Kyrkos and Z. Donko, J. Phys. A: Math. Gen. \textbf{39 }4613 (2006) $^{3}$ T. Sullivan, G. J. Kalman, S. Kyrkos, P. Bakshi, M. Rosenberg and Z. Donko, J. Phys. A: Math. Gen. \textbf{39} 4607 (2006)