A Statistical Study of Proton Microinstabilities and Nonlinear Effects in Space Plasmas

Using Particle-In-Cell (PIC) simulations and in-situ observations from the MMS and Wind spacecraft, we calculate and compare proton temperature-anisotropy driven linear-instability growth rate and non-linear time scale for every available pointwise sample. The linear growth rates are computed using a linear Vlasov solver. The non-linear time scales are directly evaluated from increments with spatial lags of the proton-inertial length, without using any particular cascade model. We observe that both linear and non-linear time scales are distributed intermittently in space, with enhanced values near current sheets. However, for the microinstabilities to have any dynamically significant effect, it is essential for the instabilities to grow sufficiently faster than the local (in space) non-linear processes. For only a small fraction of the available samples, linear time scales become faster than the computed non-linear time scales. These results imply that proton microinstabilities, when present, probably do not modify the large-scale dynamics in the evolution of a turbulent plasma.