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

Abstract

By keeping account of the trapped electron ∇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 (ŝ<0) if, as usual, LTe=1∕∂rlnTe<0; there are no bounded solutions if ŝLTe<0. In the latter case, there is either a set of bounded damped solutions if ηi>0 or a set of bounded unstable solutions if ηi<0. The unstable modes have a radiating character and the growth rates are γ∼(2n+1)1+2q2∣ŝ∣∣LNωe*∕qR∣ (n is the Hermite polynomial solution index, q the safety factor, ŝ the magnetic shear parameter, R the major radius, ωe* the electron diamagnetic frequency, LN=1∕∂rlnNe, and ηi=LN∕LTi).The sidebands are responsible for unusually large ratios Qe∕TeΓe, where Qe and Γe are the anomalous electron energy flux and the particle flux. These results may explain the box-type Te 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.