Velocity correlations in two-dimensional electrostatic turbulence in low-beta plasmas

The Eulerian and Lagrangian correlation functions in low-frequency electrostatic turbulence in strongly magnetized plasmas are studied in two spatial dimensions. In this limit the ion velocity in the direction perpendicular to a homogeneous magnetic field is approximated by the E x B/B-2 velocity. For strictly flute-type fluctuations, a similar model is also used for the electron dynamics. Allowing, on the other hand, for a small B-parallel component of the perturbations, an isothermal Boltzmann distribution for the electrons can be justified while the two-dimensional ion description is retained. The present analysis is based on an approximation of the actual two-dimensional flow in terms of an autonomous system consisting of many overlapping and mutually convecting vortices. Simple analytical expressions for the full space-time-varying Eulerian correlation are derived solely in terms of plasma parameters. It is demonstrated that an extension of the arguments giving the foregoing results also allows for derivation of analytical express:ions for the Lagrangian correlation function. The results are supported by a Monte Carlo simulation based on the model.