Theory of Mach cones in magnetized dusty plasmas

Theoretical models for Mach cones in magnetized dusty plasmas of Saturn's rings are presented. Dispersion properties of different types of longitudinal and transverse waves (viz. dust–acoustic waves, fast and slow dust–magnetoacoustic waves) in magnetized dusty plasmas are presented. Numerical results are presented for Vd/Vp (> 1), which determines the existence of Mach cones as well as their opening angles [θ = sin-1(Vp/Vd)], where Vd is the dust boulder speed and Vp ( = ω/k) is the phase speed of short or long wavelength disturbances in magnetized dusty plasmas. It is found that short wavelength (in comparison with the ion gyroradius) modified dust–acoustic waves and long wavelength slow dust–magnetoacoustic waves (DMW) are viable candidates for the formation of Mach cones in the equatorial plane of Saturn's rings. They should be observed by on board instruments of the CASSINI spacecraft that is supposed to enter Saturn's orbit in July 2004.