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Bootstrap Current in Spherical Tokamaks

Variational principle for the neoclassical theory has been developed by including a momentum restoring term in the electron-electron collisional operator, which gives an additional free parameter maximizing the heat production rate. All transport coefficients are obtained including the bootstrap current. The essential feature of the study is that the aspect ratio affects the function of the electron-electron collision operator through a geometrical factor. When the aspect ratio approaches to unity, the fraction of circulating particles goes to zero and the contribution to particle flux from the electron-electron collision vanishes. The resulting diffusion coefficient is in rough agreement with Hazeltine. When the aspect ratio approaches to infinity, the results are in agreement with Rosenbluth. The formalism gives the two extreme cases a connection. The theory is particularly important for the calculation of bootstrap current in spherical tokamaks and the present tokamaks, in which the square root of the inverse aspect ratio, in general, is not small.