Towards a simple model of compressible Alfvénic turbulence

A simple model of collisionless, dissipative, compressible magnetohtdrodynamics (Alfv{acute e}nic) turbulence in a magnetized system is investigated. In contrast to more familiar paradigms of turbulence, dissipation arises from Landau damping, enters via nonlinearity, and is distributed over all scales. The theory predicts that two different regimes or phases of turbulence are possible, depending on the ratio of steepening to damping coefficient (m{sub 1}/m{sub 2}). For strong damping ({vert_bar}m{sub 1}/m{sub 2}{vert_bar}{lt}1), a regime of smooth, hydrodynamic turbulence is predicted. For {vert_bar}m{sub 1}/m{sub 2}{vert_bar}{gt}1, steady state turbulence does not exist in the hydrodynamic limit. Rather, spikey, small scale structure is predicted. {copyright} {ital 1997} {ital The American Physical Society}