Guiding center Equation in polar coordinates: $$ \partial_t f(t,r,\theta) - \frac{\partial_{\theta}\Phi(r, \theta)}{r} \partial_r f(t,r,\theta) + \frac{\partial_{r}\Phi}{r} \partial_{\theta} f = 0. $$ Diocotron instability {cite}Crouseilles14