Radial Transport Of Toroidal Momentum Research Articles

Neoclassical, semi-collisional tearing mode theory in an axisymmetric torus

A set of layer equations for determining the stability of semi-collisional tearing modes in an axisymmetric torus, incorporating neoclassical physics, in the small ion Larmor radius limit, is provided. These can be used as an inner layer module for inclusion in numerical codes that asymptotically match the layer to toroidal calculations of the tearing mode stability index, $\unicode[STIX]{x1D6E5}^{\prime }$. They are more complete than in earlier work and comprise equations for the perturbed electron density and temperature, the ion temperature, Ampère’s law and the vorticity equation, amounting to a twelvth-order set of radial differential equations. While the toroidal geometry is kept quite general when treating the classical and Pfirsch–Schlüter transport, parallel bootstrap current and semi-collisional physics, it is assumed that the fraction of trapped particles is small for the banana regime contribution. This is to justify the use of a model collision term when acting on the localised (in velocity space) solutions that remain after the Spitzer solutions have been exploited to account for the bulk of the passing distributions. In this respect, unlike standard neoclassical transport theory, the calculation involves the second Spitzer solution connected with a parallel temperature gradient, because this stability problem involves parallel temperature gradients that cannot occur in equilibrium toroidal transport theory. Furthermore, a calculation of the linearised neoclassical radial transport of toroidal momentum for general geometry is required to complete the vorticity equation. The solutions of the resulting set of equations do not match properly to the ideal magnetohydrodynamic (MHD) equations at large distances from the layer, and a further, intermediate layer involving ion corrections to the electrical conductivity and ion parallel thermal transport is invoked to achieve this matching and allow one to correctly calculate the layer $\unicode[STIX]{x1D6E5}^{\prime }$.

Turbulence induced radial transport of toroidal momentum in boundary plasma of EAST tokamak

Turbulence induced toroidal momentum transport in boundary plasma is investigated in H-mode discharge using Langmuir-Mach probes on EAST. The Reynolds stress is found to drive an inward toroidal momentum transport, while the outflow of particles convects the toroidal momentum outwards in the edge plasma. The Reynolds stress driven momentum transport dominates over the passive momentum transport carried by particle flux, which potentially provides a momentum source for the edge plasma. The outflow of particles delivers a momentum flux into the scrape-off layer (SOL) region, contributing as a momentum source for the SOL flows. At the L-H transitions, the outward momentum transport suddenly decreases due to the suppression of edge turbulence and associated particle transport. The SOL flows start to decelerate as plasma entering into H-mode. The contributions from turbulent Reynolds stress and particle transport for the toroidal momentum transport are identified. These results shed lights on the understanding of edge plasma accelerating at L-H transitions.

Neoclassical theory of rotation and electric field in high collisionality plasmas with steep gradients

The equation describing the radial transport of toroidal momentum in a collisional subsonic plasma with steep gradients has been obtained via a systematic expansion of the two-fluid equations. The diffusion rate is classical; the poloidal rotation, driven by the temperature gradient, generates, in turn, a toroidal flow gradient, also in Ohmic discharges. Moreover, important modifications of the parallel momentum equation are found to arise if Λ1≡(νi/Ωi)(q2R2/rLT) is ⩾O(1/3); the poloidal rotation velocity is then no longer unique but obeys a cubic equation which may allow for bifurcated equilibria under certain conditions. The toroidal velocities predicted for Ohmic discharges compare well with those measured in PLT [Princeton Large Torus; S. Suckewer et al., Nucl. Fusion 21, 1301 (1981)]; the relevance of the extended equation providing the poloidal rotation velocity to selected experimental edge plasmas is discussed.

Momentum transport and flow damping in the reversed-field pinch plasma

A biased electrode is used in the Madison Symmetric Torus (MST) reversed-field pinch [Fusion Technol. 19, 131 (1991)] to manipulate plasma flow in order to study flow damping and momentum transport. Finite radial conductivity allows a radial current, which provides the toroidal torque that spins up the plasma. The applied torque is balanced by a viscous force that opposes toroidal flow acceleration. From the plasma flow damping the viscosity is inferred to be anomalous. The radial transport of toroidal momentum is comparable to that of particles and energy, and is consistent with transport by stochastic magnetic field lines.

Gyroviscous momentum transfer and toroidal rotation in Tokamaks with unbalanced NBI

Gyroviscous theory for the radial transport of toroidal momentum and the related theory for the poloidal variation of the angular rotation frequency in a Tokamak with strong rotation due to NBI are reviewed. Supporting theoretical and experimental evidence are cited. Stacey confirms that gyroviscosity can account for the momentum confinement times measured in Tokamak plasmas with directed NBI. A recent paper by Connor et al. (1987, ibid., vol.29, p.919, 1987) which arrived at a different conclusion and which criticized his theory is discussed.