Electrostatic fluctuation in Low-β plasmas

The thesis gives an overview, which by no means is complete, to two dimensional plasma flows. The plasma is taken to be strongly magnetized such that magnetic fields generated by internal currents are small compared to the background magnetic field. This requires that the magnetic pressure exerted by the ambient magnetic field is large compared to the pressure due to thermal fluctuations, i.e. low-β plasma. The author also assume low frequency electrostatic fluctuations with ω<<ωci where ωci is the ion gyro frequency. A brief introduction to nonlinear phenomena in two dimensional plasma flows has been presented. Particular attention was given to simple models describing flute and drift modes. Although the derivations of the model equations are based on different assumptions regarding the plasma conditions, the resulting equations exhibit similar behavior in some respects. For instance, both the simple guiding center model and the Hasegawa-Mima model have stable dipolar structures. The inverse cascade was also found in both models. However, it is evident that there are significant differences, first of all the Hasegawa-Mima model assumes a background density gradient which makes it an inhomogeneous model. Secondly, in this model the electrons respond instantaneously to variations in the ion density by moving along the magnetic field, thereby introducing Debye shielding