  For a particle in the magnetic field of a cloud of monopoles, the naturally
associated 2-form on phase space is not closed, and so the corresponding
bracket operation on functions does not satisfy the Jacobi identity. Thus, it
is not a Poisson bracket; however, it is twisted Poisson in the sense that the
Jacobiator comes from a closed 3-form.
  The space $\mathcal D$ of densities on phase space is the state space of a
plasma. The twisted Poisson bracket on phase-space functions gives rise to a
bracket on functions on $\mathcal D$. In the absence of monopoles, this is
again a Poisson bracket. It has recently been shown by Heninger and Morrison
that this bracket is not Poisson when monopoles are present. In this note, we
give an example where it is not even twisted Poisson.
