The Greenwald density limit, found in all tokamak experiments, is reproduced for the first time using a phenomenologically correct model with parameters in the range of experiments. A simple model of equilibrium evolution and local power balance inside the island has been implemented to calculate the radiation-driven thermo-resistive tearing mode growth and explain the density limit. Strong destabilization of the tearing mode due to an imbalance of local Ohmic heating and radiative cooling in the island predicts the density limit within a few percent. The density limit is found to be a local edge limit and weakly dependent on impurity densities. Results are robust to a substantial variation in model parameters within the range of experiments.

Massive runaway positrons are generated by runaway electrons in tokamaks. The fate of these positrons encodes valuable information about the runaway dynamics. The phase space dynamics of a runaway position is investigated using a Lagrangian that incorporates the tokamak geometry, loop voltage, radiation and collisional effects. It is found numerically that runaway positrons will drift out of the plasma to annihilate on the first wall, with an in-plasma annihilation possibility less than 0.1%. The dynamics of runaway positrons provides signatures that can be observed as diagnostic tools.

The physical mechanism behind the tokamak density limit scaling is described in terms of a non-linear theory of tearing mode growth in cylindrical geometry coupled to a model for thermal transport in the island. Important new physics features of the model include: (1) island asymmetry due to finite island width in cylindrical geometry, (2) a model of radiation based on local coronal equilibrium including impurity radiation, (3) current perturbations due the perturbed resistivity, and (4) numerical solution of the cylindrical eigenfunctions and Δ′. The semi-analytic cylindrical model is then solved for a wide range of current profiles, magnetic field values, and plasma currents using reasonable assumptions for impurity densities and the Greenwald limit [M. Greenwald et al., Nucl. Fusion 28, 2199 (1988)] is reproduced. The limit is shown to be only weakly dependent on variations in the assumed parameters.