Effect of trapping on vortices in plasma

Microscopic trapping of electrons is considered in one- and two-dimensional potential wells (shallow and deep) and its effect on vortex formation is investigated by deriving modified Hasegawa Mima (HM) equations. Inhomogenieties in the number density and magnetic field are taken into account. The modified HM equations are analysed by considering bounce frequencies of the trapped particles. Solitary vortices are obtained via Kortweg deVries (KdV) type of equations and both exact and Sagdeev potential solutions are obtained. In general it is observed that trapping produces stronger non-linearities and this leads to the modification of the original HM equation.