Collisionless reversed magnetic shear trapped electron instability and contribution of sidebands to anomalous transport

By keeping account of the trapped electron del B and curvature drifts, it is found that the spatial decay of the collisionless electron drift wave is governed either by the trapped electron response or by the resonant interaction of ions with the sidebands of the primary oscillation. In the former case, pairs of spatially bounded unstable and damped solutions are obtained for negative magnetic shear (s < 0) if, as usual, L-Te=1/partial derivative(r) ln T-e< 0; there are no bounded solutions if (s) over capL(Te)< 0. In the latter case, there is either a set of bounded damped solutions if eta(i)>0 or a set of bounded unstable solutions if eta(i)< 0. The unstable modes have a radiating character and the growth rates are gamma similar to(2n+1) root 1+2q(2)vertical bar(s) over cap parallel to L(N)omega(e)(*)/qR vertical bar (n is the Hermite polynomial solution index, q the safety factor, (s) over cap the magnetic shear parameter, R the major radius, omega(e)(*) the electron diamagnetic frequency, L-N=1/partial derivative(r) ln N-e, and eta(i)=L-N/L-Ti).The sidebands are responsible for unusually large ratios Q(e)/T(e)Gamma(e), where Q(e) and Gamma(e) are the anomalous electron energy flux and the particle flux. These results may explain the box-type T-e profile observed in lower hybrid current drive reversed magnetic shear plasmas on the Japan Atomic Energy Research Institute Tokamak 60 Upgrade (JT-60U) [H. Ninomiya and the JT-60U Team, Phys. Fluids B 4, 2070 (1992)]. It is finally demonstrated that the ballooning hypothesis generally leads to conflicting requirements: it is thus hardly relevant for the electron drift branch! The "radiating" boundary condition that has formerly been imposed on the slab solution is finally discussed. (C) 2005 American Institute of Physics