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vlasov-poisson.md

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Vlasov--Poisson

$$ \partial_t f(t,\mathbf{x},\mathbf{v}) + \mathbf{v}\nabla_{\mathbf{x}} f(t,\mathbf{x},\mathbf{v}) + \frac{q}{m} \mathbf{E}(t,\mathbf{x}) \nabla_{\mathbf{v}} f(t,\mathbf{x},\mathbf{v}) = 0 $$

$$ -\Delta \phi(t,\mathbf{x}) = 1- \rho(t, \mathbf{x}) $$

  • Dimensions: 1d1v, 2d2v, 3d3v
  • Identifier in SeLaLib: vp
  • Typical initial conditions: