  A comprehensive study of a reduced version of Lust's equations, the extended
magnetohydrodynamic (XMHD) model obtained from the two-fluid theory for
electrons and ions with the enforcement of quasineutrality, is given. Starting
from the Hamiltonian structure of the fully three-dimensional theory, a
Hamiltonian two-dimensional incompressible four-field model is derived. In this
way energy conservation along with four families of Casimir invariants are
naturally obtained. The construction facilitates various limits leading to the
Hamiltonian forms of Hall, inertial, and ideal MHD, with their conserved
energies and Casimir invariants. Basic linear theory of the four-field model is
treated, and the growth rate for collisionless reconnection is obtained.
Results from nonlinear simulations of collisionless tearing are presented and
interpreted using, in particular normal fields, a product of the Hamiltonian
theory that gives rise to simplified equations of motion.
