DRIVEN, DISSIPATIVE, ENERGY-CONSERVING MAGNETOHYDRODYNAMIC EQUILIBRIA.2. THE SCREW PINCH

A cylindrically symmetric, electrically driven, dissipative, energy-co nserving magnetohydrodynamic equilibrium model is considered. The high -magnetic-field Braginskii ion thermal conductivity perpendicular to t he local magnetic field and the complete electron resistivity tensor a re included in an energy equation and in Ohm's law. The expressions fo r the resistivity tensor and thermal conductivity depend on number den sity, temperature, and the poloidal and axial (z-component) magnetic f ield, which are functions of radius that are obtained as part of the e quilibrium solution. The model has plasma-confining solutions, by whic h is meant solutions characterized by the separation of the plasma int o two concentric regions separated by a transition region that is an i nternal boundary layer. The inner region is the region of confined pla sma, and the outer region is the region of unconfined plasma. The inne r region has average values of temperature, pressure, and axial and po loidal current densities that are orders of magnitude larger than in t he outer region. The temperature, axial current density and pressure g radient vary rapidly by orders of magnitude in the transition region. The number density, thermal conductivity and Dreicer electric field ha ve a global minimum in the transition region, while the Hall resistivi ty, Alfven speed, normalized charge separation, Debye length, (omegata u)ion and the radial electric field have global maxima in the transiti on region. As a result of the Hall and electron-pressure-gradient effe cts, the transition region is an electric dipole layer in which the no rmalized charge separation is localized and in which the radial electr ic field can be large. The model has an intrinsic value of beta, about 13.3 %, which must be exceeded in order that a plasma-confining solut ion exist. The model has an intrinsic length scale that, for plasma-co nfining solutions, is a measure of the thickness of the boundary-layer transition region. If appropriate boundary conditions are given at R = 0 then the equilibrium is uniquely determined. If appropriate bounda ry conditions are given at any outer boundary R = a then the equilibri um exhibits a bifurcation into two states, one of which exhibits plasm a confinement and carries a larger axial current than the other, which is almost homogeneous and cannot confine a plasma. Exact expressions for the two values of the axial current in the bifurcation are derived . If the boundary conditions are given at R = a then a solution exists if and only if the constant driving electric field exceeds a critical value. An exact expression for this critical electric field is derive d. It is conjectured that the bifurcation is associated with an electr ic-field-driven transition in a real plasma, between states with diffe rent rotation rates. energy dissipation rates and confinement properti es. Such a transition may serve as a relatively simple example of the L-H mode transition observed in tokamaks.