Velocity correlations in two-dimensional electrostatic plasma turbulence

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 × B/B²-velocity. For strictly flute type fluctuations a similar model is used also 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 argued 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 flow 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 allows also for derivation of analytical expressions for the Lagrangian correlation function. The results are supported by a Monte Carlo simulation based on the model.