Weak turbulence theory of collisionless trapped electron driven drift instability in tokamaks

Publisher Website
Google Scholar
Abstract
The toroidal collisionless trapped electron modes are analyzed in the weak turbulence regime treating both ions and trapped electrons nonlinearly in the presence of ion and electron temperature gradients. The spectral intensity of the density fluctuations in the nonlinearly saturated state is analytically obtained from the steady‐state solution of the wave‐kinetic equation. Distant nonlinear interactions between low‐kθ and high‐kθ modes of similar frequencies via trapped electron scattering (the resonance between the beat wave and the trapped electron precession drift frequencies) suppress the low‐kθ [kθρs ≪(Ln/R)1/2] modes while close interactions via ion Compton scattering (nonlinear ion Landau damping) produce a monotonically decreasing spectrum from kθρs ≂(Ln/R)1/2 to kθρs≂1 according to an approximate power law k−3θ. Various fluctuation amplitudes at saturation and the fluctuation‐induced anomalous particle and heat fluxes are found to be smaller than the mixing length estimates. The plasma confinement is predicted to improve with higher Ti/ Te, more peaked density profile, larger aspect ratio, and higher plasma current. Also, a significant dependence of transport on the electron temperature gradient is found which could contribute to the rigidity of the electron temperature profile often experimentally observed.