Theory of dissipative density-gradient-driven turbulence in the tokamak edge

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Abstract
A theory of resistive, density‐gradient‐driven turbulence is presented and compared with tokamak edge fluctuation measurements. In addition to linear driving, the theory accounts for relaxation of the density gradient through a nonlinear process associated with emission from localized density fluctuation elements. From a fluid model for isothermal electrons in toroidal geometry, equations are obtained and solved analytically, retaining both coherent and incoherent contributions. The effect of collisions on the density blobs is treated. A Reynolds number parameterizes the magnitude of the turbulent scattering relative to the collisional viscous diffusion. The analytic results indicate that the spectrum is characterized by linewidths which increase as a function of the Reynolds number and may reach Δω/ω≳1. Energy lies predominantly in the small wavenumbers (k⊥ ρs∼0.1). For larger wavenumbers and frequency, the spectrum decays as k−17/6 and ω−2. The fluctuation level scales as 1/k⊥Ln and may reach −30% for parameters typical of the pretext edge. Particle diffusion is Bohm‐like in magnitude but does not follow Bohm scaling, going instead as n2/3T1/6e. The density fluctuations exhibit nonadiabatic character caused by the incoherent mode coupling. An expression for the departure from adiabaticity is given.