[en] An axially symmetric plasma immersed in a poloidal magnetic field with closed lines is considered. Low-frequency electrostatic modes are studied kinetically for an ''intermediate collisionality'' ordering, in which the particle collision frequency is much smaller than the transit or bounce frequency, but much larger than the mode, magnetic drift, and diamagnetic drift frequencies. This ordering is appropriate for the Levitated Dipole Experiment (LDX) [J. Kesner , 17th IAEA Fusion Energy Conference, Yokahama, Japan (IAEA, Vienna, 1999)] and some other closed field line devices. ''High-frequency'' magnetohydrodynamic-like and ''low-frequency'' entropy modes are found and stability boundaries are determined. Collisional effects are considered and the corresponding ion gyro-relaxation effects are evaluated. These effects introduce dissipation (or inverse dissipation) and are shown to modify the stability picture considerably, while leaving large stability regions in the d, η parametric space, where η is the ratio of the gradients of temperature and density and d is the ratio of the diamagnetic and magnetic drift frequencies

[en] Neutral particles that are present at the edge of plasma magnetic confinement devices can play an important role in energy and momentum transport, and their effects should be accounted for. This work uses the drift ordering to derive a closed fluid description for a collisional, magnetized, partially ionized plasma. Charge-exchange, ionization and recombination processes are taken into account. It is assumed that electron distribution function is unaffected by atomic processes, so that electron-ion momentum and energy exchange are described by the usual expressions for a fully ionized plasma, and that neutral-neutral collisions are unimportant. The collisional fluid equations derived herein generalize the drift-ordered description of a fully ionized collisional plasma (Catto P J et al 2004 Phys. Plasmas 11 90), agree with the MHD-ordered description of a partially ionized plasma (Helander P et al 1994 Phys. Plasmas 1 3174) in the large-flow limit and can be used to describe both turbulent and collisional behavior of a partially ionized plasma.

[en] Dissipation-independent, or 'fast', magnetic reconnection has been observed computationally in Hall magnetohydrodynamics (MHD) and predicted analytically in electron MHD. However, a quantitative analytical theory of reconnection valid for arbitrary ion inertial lengths, d_i, has been lacking and is proposed here for the first time. The theory describes a two-dimensional reconnection diffusion region, provides expressions for reconnection rates, and derives a formal criterion for fast reconnection in terms of dissipation parameters and d_i. It also confirms the electron MHD prediction that both open and elongated diffusion regions allow fast reconnection, and reveals strong dependence of the reconnection rates on d_i

[en] A simple zero-dimensional model is proposed that synthesizes the complex dynamics of driven, two-dimensional, magnetically reconnecting systems within the resistive magnetohydrodynamics (MHD) framework. The model applies to the so-called asymptotic regime of the well-known magnetic island coalescence problem, where well-separated macroscopic 'ideal' and microscopic 'resistive' regions are assumed to exist. The dynamics of the ideal region is described in terms of the Lorentz and pressure gradient forces on current filaments, and conservation of magnetic flux; that of the resistive region is described in terms of plasma flow and magnetic field magnitudes at the current sheet boundaries. Matching of the two regions provides the evolution equation for the current sheet thickness. The results for the O-point position versus time, reconnection rate, current sheet thickness, etc., at different resistivities obtained from the model agree well with those from the fully nonlinear two-dimensional reduced MHD simulation

[en] Magnetic reconnection is of fundamental importance for laboratory and naturally occurring plasmas. Reconnection usually develops on time scales which are much shorter than those associated with classical collisional dissipation processes, and which are not fully understood. While such dissipation-independent (or 'fast') reconnection rates have been observed in particle and Hall magnetohydrodynamics (MHD) simulations and predicted analytically in electron MHD, a quantitative analytical theory of fast reconnection valid for arbitrary ion inertial lengths d(i) has been lacking. Here we propose such a theory without a guide field. The theory describes two-dimensional magnetic field diffusion regions, provides expressions for the reconnection rates, and derives a formal criterion for fast reconnection in terms of dissipation parameters and d(i). It also demonstrates that both open X-point and elongated diffusion regions allow dissipation-independent reconnection and reveals a possibility of strong dependence of the reconnection rates on d(i).

[en] Short mean free path descriptions of magnetized plasmas have existed for almost 50 years so it is surprising to find that further modifications are necessary. The earliest work adopted an ordering in which the flow velocity is assumed to be comparable to the ion thermal speed. Later, less well-known studies extended the short mean free path treatment to the normally more interesting drift ordering in which the pressure times the mean flow velocity is comparable to the diamagnetic heat flow. Such an ordering is required to properly retain the temperature gradient terms in the viscosity that arise from the gyrophase dependent and independent portions of the distribution function. The treatment herein corrects the expressions for the parallel and perpendicular collisional ion viscosities found in these later treatments which use an approximate truncated polynomial expression for the distribution function and neglect the nonlinear piece of the collision operator due to its bilinear form. The modified parallel and perpendicular ion viscosities contain additional terms quadratic in the heat flux. In addition, the electron parallel and gyroviscosities, which were not considered by previous drift ordered treatments, are evaluated. As in all drift orderings, the collision frequency is assumed small compared to the cyclotron frequency. However, the perpendicular scale lengths are permitted to be much less than (as well as comparable to) the parallel ones; as is the case in many magnetic confinement applications. As a result, the description is valid for turbulent and collisional transport, and also allows stronger poloidal density, temperature, and electrostatic potential variation in a tokamak than the standard Pfirsch-Schlueter ordering

[en] 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

No abstract available

[en] A generalization of the Braginskii ion fluid description [S. I. Braginskii, Sov. Phys. - JETP 6, 358 (1958)] to the case of an unmagnetized collisional plasma with multiple ion species is presented. An asymptotic expansion in the ion Knudsen number is used to derive the individual ion species continuity, as well as the total ion mass density, momentum, and energy evolution equations accurate through the second order. Expressions for the individual ion species drift velocities with respect to the center of mass reference frame, as well as for the total ion heat flux and viscosity, which are required to close the fluid equations, are evaluated in terms of the first-order corrections to the lowest order Maxwellian ion velocity distribution functions. A variational formulation for evaluating such corrections and its relation to the plasma entropy are presented. Employing trial functions for the corrections, written in terms of expansions in generalized Laguerre polynomials, and maximizing the resulting functionals produce two systems of linear equations (for “vector” and “tensor” portions of the corrections) for the expansion coefficients. A general matrix formulation of the linear systems as well as expressions for the resulting transport fluxes are presented in forms convenient for numerical implementation. The general formulation is employed in Paper II [A. N. Simakov and K. Molvig, Phys. Plasmas 23, 032116 (2016)] to evaluate the individual ion drift velocities and the total ion heat flux and viscosity for specific cases of two and three ion species plasmas.

[en] A generalization of the Braginskii electron fluid description [S. I. Braginskii, Sov. Phys. JETP 6, 358 (1958)] to the case of an unmagnetized collisional plasma with multiple ion species is presented. A description of the plasma ions with disparate masses is also discussed