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The Hamiltonian formulation of a plasma four-field fluid model that describescollisionless reconnection is presented. The formulation is noncanonical with acorresponding Lie-Poisson bracket. The bracket is used to obtain newindependent families of invariants, so-called Casimir invariants, three ofwhich are directly related to Lagrangian invariants of the system. The Casimirsare used to obtain a variational principle for equilibrium equations thatgeneralize the Grad-Shafranov equation to include flow. Dipole and homogeneousequilibria are constructed. The linear dynamics of the latter is treated indetail in a Hamiltonian context: canonically conjugate variables are obtained;the dispersion relation is analyzed and exact thresholds for spectral stabilityare obtained; the canonical transformation to normal form is described; anunambiguous definition of negative energy modes is given; and thresholdssufficient for energy-Casimir stability are obtained. The Hamiltonianformulation also is used to obtain an expression for the collisionlessconductivity and it is further used to describe the linear growth and nonlinearsaturation of the collisionless tearing mode.

Hamiltonian formulation and analysis of a collisionless fluid reconnection model