Hamiltonian structure and stability analysis of a reduced four-field model for plasmas in the presence of a strong guide field

We analyze the collisionless and inviscid limit of a reduced fluid model for tokamak plasma dynamics. We show that the model under consideration possesses a noncanonical Hamiltonian structure with four infinite families of Casimir invariants. Sufficient conditions for energy stability are derived and formulated in terms of requirements on the current, electron pressure, and parallel ion velocity gradients, as well as on the ion temperature. In particular, the stability condition requires a gradient of the parallel flow in the presence of ion temperature and a negative upper bound on the current gradient, in the presence of pressure gradients and/or parallel velocity gradients. Examples of stable configurations are derived.