Aspect ratio scaling of toroidal plasma equilibria and the tokamak bootstrap effect

The aspect ratio scaling of toroidal plasma equilibria is examined using a parametrization of an exact Solov close-quote ev solution to the Grad endash Shafranov equation in Boozer coordinates. The equilibrium analysis suggests that simultaneous enhancements in magnetohydrodynamic (MHD) stability and the bootstrap effect are possible in tight aspect ratio (A→1) tokamaks. The fundamental physical mechanism causing the enhancements is shown to be the natural increase of the MHD safety factor q in tight aspect ratio toroidal geometries. The results of the scaling model suggest that the lowest bootstrap current fractions are obtained in tokamaks with aspect ratios A∼3. It is also shown that a tight aspect ratio bootstrapped tokamak can be a weakly paramagnetic device. copyright 1997 American Institute of Physics