Finite Beta Tokamak Equilibria By the Multipole Moments Method.

The characteristics of finite beta equilibria in tokamaks are discussedusing the virial theorem (the pressure balance) and multipole moments ofthe generalized pressure and current density. For the st and ard tokamakequilibrium, it is sufficient to find only a toroidal correction, i.e., thedisplacement of the magnetic axis from the axis of concentric cylinders.When the plasma pressure is allowed to rise even in the st and ard tokamakconfiguration, a strong deformation of the magnetic cross section, especiallynear the magnetic axis, takes place. We consider toroidal corrections notonly by geometrical factors but also the pressure factor. To carry outanalytical investigations, the inverse forms of equilibrium using an optimalpoloidal angle are utilized. Trial functions for the harmonic amplitudesgiven by the (epsilon) expansion are employed in the form of perturbationsresembling Chebychev polynomials. Perturbation terms with magnitudeof the order of SQRT.((beta) play a significant role if the plasma pressure, and (' )corresponding (beta), becomes large. The pressure balance condition yields the displacement of the magnetic axis from the concentric axis of circular cross-sections. The multipole moments will give the properties on non-circular cross-sections. Since the finite beta equilibrium is characterized by a large deformation of the flux cross section as well as a strong magnetic axis shift, it is essential to analyze it by the multipole moments. We produce the relations between the finite beta effect and the multipole moments through the pressure balance condition. Since the dipole moment of the current density is expected to be measured experimentally, finite beta tokamak equilibrium can be established from directly measurable parameters. The results obtained in this thesis cover the range from low beta to high beta asymptotically, so that they are useful in the study of the evolution of the equilibrium by rapid heating of plasma, such as the case in the Flux Conserving Tokamak. Finally, we demonstrate the use of the integral equations, namely the pressure balance equation, and the multipole moments of the generalized pressure in the solution of tokamak equilibria.PhDPlasma physicsUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/158314/1/8116302.pd