Temperature distribution of a tokamak with a constant heat conductivity

An analytical expression of the detached plasma radius in and ohmically heated tokamak plasma was obtained. The assumption was made that the (anomalous) heat conductivity is constant and independent of minor radius, r. The resultant nonlinear differential equation has a universal solution for the plasma temperature as a function of r. The shape is very similar to the so-called profile consistency model. As the average plasma density increases, the tokamak plasma which is first attached to either limiter or divertor detaches itself from the limiter and forms a toroidal plasma whose boundary is clearly marked by a radiative boundary layer where the power input to the plasma is radiated away. As the plasma density increases, the radius of the plasma shrinks until the surface safety factor becomes less that ∼2, whereupon the plasma disruption starts. The density limit calculated by this model agrees with the experimental observation. 1 ref., 1 fig., 1 tab