Vlasov equation

Collisionless case of the Boltzman equation for the Lorentz Force

\frac{\partial f}{\partial t} + \vec{v} \cdot \nabla_{\vec{x}} f + \frac{q}{m} (\vec{E} + \vec{v} \times \vec{B}) \cdot \nabla_{\vec{v}} f = 0