The Vlasov–Poisson equations are an approximation of the Vlasov–Maxwell equations in the non-relativistic zero-magnetic field limit: ∂ ∂ f α α ∂ ∂ t + v α α ⋅ ⋅ ∂ ∂ f α α ∂ ∂ x + q α α E m α α ⋅ ⋅ ∂ ∂ f α α ∂ ∂ v = 0 ,