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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