Micro particles that are introduced into a plasma environment charge up to a high negative value due to ion and electron bombardment. As a result of the strong Coulomb interaction between the particles often so-called "Coulomb crystals" are built up. These systems show a variety of wave phenomena like dust acoustic waves, dust shear waves, etc. that have been investigated partially only. We are interested in particular in wave propagation in a magnetized Coulomb crystal, where each dust particle incompletely gyrates in a magnetic field.
The dispersion relation has two branches under the magnetic field conditions. The high frequency branch has a low-frequency cut-off at the cyclotron frequency and a resonance at the hybrid frequency, that is determined by the cyclotron and the dust plasma frequency. An expression for the wave dispersion has been derived analytically, showing clearly that the longitudinal and transverse waves in a Coulomb crystal are coupled due to the Lorenz force. In addition corresponding simulations have been carried out where the particles are restricted to a plane with the magnetic field pointing perpendicular to the particle layer. By the use of periodic boundary conditions within the plane the system is made virtually infinite. When the simulated system reaches its thermodynamical equilibrium, the spectrum of the thermally excited waves is calculated from particle velocities by a Fourier transformation method. The results show good agreement with the analytical predictions.
In this presentation, we report on the detailed properties of the wave propagation in a magnetized Coulomb crystal that we obtained from computer simulations as well as from theoretical analysis.