The transport effects induced by resistive ballooning modes are estimated from a theory, and are found to be mainly thermal electron conduction losses. An expression for electron thermal diffusivity x e is derived. The theoretical predictions agree well with experimental values of x e obtained from power balance for the ISX-J3 plasmas at high poloidal beta.PACS numbers: 52.25.Fi, 52.30. + r, 52.55.Gb A deterioration in confinement is observed in ISX-B tokamak experiments 1 ' 2 with high neutral injection power at high poloidal plasma beta (p p ). From a theoretical point of view, resistive pressure-driven ballooning modes are a possible cause of this deterioration, linked to high-^ plasmas. There have been several linear studies 3 "" 5 of these instabilities in the past. Recently, numerical and analytical work has been done 6 to understand the linear and nonlinear properties of resistive ballooning modes in the framework of the incompressible resistive magnetohydrodynamic (MHD) equations. Below and near the critical j3 for ideal instabilities (j3^1), the fastest growing mode, with a given torodial mode number n, has a growth ratewhere S is the ratio of resistive time r R to poloidal AlfvSn time r hp , (3 0 = 2p{0) \±JB T 2 , p is the pressure, q is the safety factor, B T is the toroidal magnetic field, e is the inverse aspect ratio, L p =[(-dp/dp)/p{0)]-\ and p (with 0 ^p ^1) is a flux surface label. These modes are extended greatly along magnetic field lines, with a characteristic width given by -7(P 8 S)]-I/4 , w. ••WS*n*y n T hpwhere S=[p(dq/dp)/q] and a is the minor radius. Their linear properties are similar to resistive interchanges. 7 With use of the nonlinear resistive MHD equation in the ballooning representation, a calculation of the renormalized response has been performed. 6 This calculation shows that the dominant nonlinear effect is due to the pressure-convective nonlinearity, which reduces the turbulent pressure response p to <£, the electrostatic perturbation. This causes a reduction of the interchange destabilizing term, without changing the basic structure of the eigenfunction. A physical interpretation is that the resistive ballooning modes saturate when the pressure fluctuation mixes dp/dp over the radial extent A of each poloidal subharmonic; thus, p-Adp/dp. Since the pressure is mainly convected, p ~inq" 1 ) 2 ' Details on the stability theory of these modes will be given elsewhere. In this Letter we limit ourselves to the consideration of the induced transport effects and consequences for confinement in ISX--B. We consider two main effects of the saturated modes, the diffusion induced by the convective nonlinearity and the anomalous electron conduction induced by the magnetic field-line stochastization.The radial diffusion induced by the convective term is given by D*(\(n'q/p)y nf \ 2 /y n _ n ,) = y n A 2 .Using the reciprocity of 3; (ballooning) space and position s...

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The kilometer scale irregularities in the daytime equatorial electrojet are studied within the framework of a two‐fluid, nonlocal theory of the gradient drift instability. A separation of scales is introduced into the equations in order to model the effects of the subgrid, short‐wavelength (λ < 100 m) modes. The presence of the short‐scale turbulence is included in the large‐scale equations through the average nonlinear flux due to the small‐scale nonlinear terms. With the use of the linear ion continuity equation the nonlinear flux is expressed in terms of the large‐scale quantities and of the small‐scale density fluctuation spectrum. It is shown that the small‐scale turbulence contributes to the large‐scale equations through turbulent mobility and diffusion coefficients. For a particular choice for the small‐scale density fluctuation spectrum (modeled after some of the available rocket data), the turbulent mobility is determined as a function of altitude, and its peak equals a few times the classical Pedersen mobility value. The equilibrium solutions of the large‐scale equations are also derived in the presence of the short‐wavelength turbulence. The localization of the current layer is seen to shift toward higher altitudes, and the current density profile conforms well with some of the available experimental data. Neglecting at this point the large‐scale nonlinearities, the local and nonlocal linear growth rates of the long‐wavelength modes are also obtained and discussed. The renormalized linear nonlocal equations for the large scales are integrated numerically, and the effects of the turbulent mobility and of velocity shear are observed and discussed. Nonlocal modes with horizontal wavelengths in the kilometer range dominate the linear stage of the instability, thus providing a possible explanation for the experimentally observed predominance of such wavelengths in the electrojet's wave spectrum. The dispersive nature of the large‐scale modes is also discussed and reconsidered in the presence of the turbulent mobility term.

The linear global eigenmodes of the gradient drift instability in the daytime equatorial electrojet are investigated. A main feature of the analysis is the inclusion of ion‐neutral and electron‐neutral collision frequencies dependent on altitude. It is found that the basic characteristics and localization of the unstable modes are determined mainly by the profiles of the Pedersen and Hall mobilities, which are derived from the Cowling conductivity model and experimental data. The equilibrium density profile is parabolic, which is fairly representative of the actual measurements. The unstable modes are sensitive not to the details of this profile, but only to the average value of the gradient. The results are obtained from a direct numerical integration of the nonlocal linearized equations. They are further analyzed through an eikonal analysis, which provides both an interpretation of the transient modes observed by Fu et al. (1986) and some additional physical insight into the linear evolution of the global unstable modes. Finally, it is shown that the previously reported short‐wavelength stabilization effect due to velocity shear may be overshadowed by the presence of regions in which the transient modes can develop into absolute instabilities.

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