The noninductive part of the measured current profile has been determined for DIII-D plasmas. A technique for determining the flux surface average of the quantity K~B and a model for the resistivity separates the current profile into inductive and noninductive portions. Analysis (1) where the cylindrical coordinate system (R, Z, @) is used, P = -fo BzR'dR' is the total poloidal flux per radian inside a major radius R, and F(p) = RB~. Furthermore, it is assumed that toroidally symmetric, nested fiux surfaces exist and can be labeled by either i/I or the en- gives a measurement at a fixed point.In a general toroidal geometry, the equation relating the current density to the electric field is (i B) = n '(E B) + (iNi B), (2) where (A) is the flux surface average of A, 71 is the parallel resistivity, and jNi represents any sources of noninductive current drive (including both bootstrap current and auxiliary driven currents). The flux surface average of the quantity (E B) can be shown to be [6] (E B) =

Stable and stationary states with hollow current density profiles have been achieved in Tore Supra with lower hybrid current drive (LHCD) during reduced toroidal magnetic field operation (B t 2 T) and in weak LH absorption regimes. For these plasma conditions, offaxis LH power deposition profiles are obtained in a reproducible manner when the internal LH caustics prevent central absorption of the waves. In the multipass LH wave propagation regime, the validity of the statistical treatment of stochastic wave diffusion is shown both theoretically and experimentally. When a large fraction of the plasma current (above 50%) is non-inductively sustained by the LH waves, the magnetic shear is reversed in the plasma core, i.e. inside a normalized plasma radius of the order of 0.4. The resulting hollow current density profiles have led to an enhancement of the total electron thermal energy content, up to a factor of 1.6 compared with L-mode discharges. The confinement improvement is attributed to a strong reduction of the electron thermal diffusivity in the central reversed shear region, nearly down to its neoclassical level.

It is well known that absolute instabilities can be located by prescribed mappings from the complex frequency plane to the wave-number plane through the dispersion relation D(w, k) = 0. However, in many systems of physical interest the dispersion relation is polynominal in w while transcendental in k, and the implementation of this mapping procedure is particularly difficult. If one maps consecutive deformations of the Fourier integral path (originally along the real k-axis) into the w-plane, points having (8D/8k) = 0 are readily detected by the distinctive feature of their local maps. It is shown that a simple topological relationship between these points and the image of the real k-axis determines the stability characteristics of the system, without mapping from the w-plane back into the k-plane.

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