It is shown that the net momentum delivered by the large electric field inside a one-dimensional double layer is zero. This is demonstrated through an analysis of the momentum balance in the double layer at the boundary between the ionosphere and the aurora cavity. For the recently observed double layer in a current-free plasma expanding along a divergent magnetic field, an analysis of the evolution of the radially averaged variables shows that the increase of plasma thrust results from the magnetic-field pressure balancing the plasma pressure in the direction of acceleration, rather than from electrostatic pressure.

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The dynamics of plasma and neutral gas in pressure balance are solved self-consistently to reveal the impact of neutral depletion. Analytical relations that determine the electron temperature, the rate of ionization, and the plasma density are derived. Because of the inherent coupling of ionization and transport, an increase of the energy invested in ionization can nonlinearly enhance the transport process. We show that such an enhancement of the plasma transport due to neutral depletion can result in an unexpected decrease of the plasma density when power is increased, despite the increase of the flux of generated plasma.

This paper provides perspectives on recent progress in the understanding of the physics of devices where the external magnetic field is applied perpendicularly to the discharge current. This configuration generates a strong electric field, which acts to accelerates ions. The many applications of this set up include generation of thrust for spacecraft propulsion and the separation of species in plasma mass separation devices. These "E×B" plasmas are subject to plasma-wall interaction effects as well as various micro and macro instabilities, and in many devices, we observe the emergence of anomalous transport. This perspective presents the current understanding of the physics of these phenomena, state-of-the-art computational results, identifies critical questions, and suggests directions for future research.

The measured axial force imparted from a magnetically expanding current-free plasma has been shown recently [Takahashi, Phys. Rev. Lett. 107, 235001 (2011)] to equal the axial force on that plasma calculated by a two-dimensional fluid model. Here, we calculate the same axial force on the plasma by a quasi one-dimensional model of a magnetic nozzle. The quasi one-dimensional magnetic nozzle model provides us with an estimate of the force on the plasma that is similar to that found by the more accurate two-dimensional model. V

A two-dimensional steady-state model is developed, in which, even though ion inertia is retained, a variable separation allows us to analyse separately the axial and the radial transports. For the axial transport (along magnetic field lines) an integral dispersion relation is derived that includes a nonlinear form that is obtained from the ion-neutral collision operator. The dispersion relation is solved for various values of the Paschen parameter, and the electron temperature and the axial profiles of the plasma density and plasma potential are calculated. The solutions of the dispersion relation are shown to have three asymptotic limits: collisionless, linear diffusion and nonlinear diffusion. For the radial transport, the rate of which is determined by electron cross-field diffusion, the full equations are numerically solved. The calculations are compared to probe measurements performed at various locations inside our helicon source for various magnetic field intensities and wave powers. The proposition that the measured increase in the plasma density with the increase of the magnetic field intensity is a result of an improved confinement, is examined. For the parameters of the experiment described here, this proposition implies that the electron collisionality is much larger than expected from electron-ion and electron-neutral collisions. A different explanation for the dependence of the density on the magnetic field intensity is suggested, that the density increase that follows an increase of the magnetic field intensity results from an improved wave-plasma coupling via the helicon interaction, causing a larger fraction of the total wave power to be deposited inside the helicon source.

The Tonks-Langmuir, Godyak, and Schottky steady-state isothermal models are extended when the dynamics of the neutral gas is taken into account. Exact analytic quadratures for the electron temperature, densities, and potential profiles are obtained for these three models within the plasma approximation. It is shown that, contrary to the uniform neutral pressure case, the particle and the power balance are both necessary to determine the electron temperature when neutral dynamics is included. When neutral dynamics is governed by collisions with ions, the neutral density that results from ionization is predicted to have a minimum at the center of the discharge, as indeed is observed in experiment. It is found that even a small amount of ionization can result in a rather strong neutral depletion. However, when the drag on neutrals due to collisions with ions is negligible, the predicted profile of the neutral density that results from intense ionization is reversed and exhibits an unexpected maximum at the center of the discharge.

The two-dimensional (2D) steady state of plasma confined radially by an axial magnetic field is studied. An analytical solution of the 2D diffusion equation is found by a variable separation for constant transport coefficients, without the assumption that the flow is ambipolar. The analytical solution is employed for comparing ambipolar flow with the 'short-circuit' limit of a nonambipolar flow. The nonlinear one-dimensional (1D) cross-field diffusion problem is formulated, where the nonlinearity results from the dependence of the transport coefficients on the plasma and neutral densities. The different roles of collisions with plasma particles and with neutral particles are unfolded in the two types of flow, ambipolar and nonambipolar, in either flattening the density profile or making it more peaked. The effect of neutral depletion on the cross-field diffusion is explored.