Theory of self-organized critical transport in tokamak plasmas

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Abstract
A theoretical and computational study of the ion temperature gradient (ITG) and ηi instabilities in tokamak plasmas has been carried out. In a toroidal geometry the modes have a radially extended structure and their eigenfrequencies are constant over many rational surfaces that are coupled through toroidicity. These nonlocal properties of the ITG modes impose a strong constraint on the drift mode fluctuations and the associated transport, showing self‐organized criticality. As any significant deviation away from marginal stability causes rapid temperature relaxation and intermittent bursts, the modes hover near marginality and exhibit strong kinetic characteristics. As a result of this, the temperature relaxation is self‐similar and nonlocal, leading to radially increasing heat diffusivity. The nonlocal transport leads to Bohm‐like diffusion scaling. Heat input regulates the deviation of the temperature gradient away from marginality. We present a critical gradient transport model that describes such a self‐organized relaxed state. Some of the important aspects in tokamak transport like Bohm diffusion, near marginal stability, radially increasing fluctuation energy and heat diffusivity, intermittency of the wave excitation, and resilient tendency of the plasma profile can be described by this model, and these prominent features are found to belong to one physical category that originates from the radially extended nonlocal drift modes. The obtained transport properties and scalings are globally consistent with experimental observations of low confinement mode (L‐mode) discharges. The nonlocal modes can be disintegrated into smaller radial islands by a poloidal shear flow, suggesting that the transport changes from Bohm‐like to near gyro‐Bohm.