On the relationship between Marfes and density limits

An analytic theory is presented describing the interrelationship between Marfes and density limits in a tokamak. It extends in several directions an earlier calculation carried out by Drake. A Marfe is an asymmetric, sometimes long-lived, burst of radiation from the edge of a tokamak. Its structure usually corresponds to m = 1, n = 0. The density limit, often known as the Murakami limit, or the Greenwald limit, is associated with a radiation collapse of the plasma edge. The plasma undergoes an m = 0, n = 0 contraction, which ultimately leads to a major disruption when the minor radius has shrunk sufficiently. The first part of the theory determines the condition under which a radiation contraction occurs. Depending upon the shape of the density profile, the collapse can be either an unstable, uncontrollable transition from one meta-stable slate to another, or more desirably, a stable, controllable detached equilibrium in which 100% of the plasma energy loss is radiated away. An explicit expression is derived for the Murakami, Greenwald density limit including its dependence on auxiliary power. The second part of the theory, pertaining to the Marfe, is a classical linear stability analysis of the equilibrium described above for the radiation collapse. Here too, an explicit expression is derived determining the condition under which a Marfe occurs before or after a radiation collapse. For one class of operation, the Marfe can be used as a precursor diagnostic to predict the imminent appearance of a density limit disruption. Alternatively, it may be important to completely avoid Marfes when attempting to operate in the radiation divertor mode