Drift-ordered fluid equations for field-aligned modes in low-β collisional plasma with equilibrium pressure pedestals

Starting from the complete short mean-free path fluid equations describing magnetized plasmas, assuming that plasma pressure is small compared to magnetic pressure, considering field-aligned plasma fluctuations, and adopting an ordering in which the plasma species flow velocities are much smaller than the ion thermal speed, a system of nonlinear equations for plasma density, electron and ion temperatures, parallel ion flow velocity, parallel current, electrostatic potential, perturbed parallel electromagnetic potential, and a perturbed magnetic field is derived. The equations obtained allow sharp equilibrium radial gradients of plasma quantities, and are shown to contain the neoclassical (Pfirsch-Schlueter) results for plasma current, parallel ion flow velocity (with the correct temperature gradient terms), and parallel gradients of equilibrium electron and ion temperatures. Special care is taken to ensure the divergence-free character of perturbed magnetic field and total plasma current, as well as local particle number and total energy conservation