Bootstrap Current in Spherical Tokamaks

Abstract Variational principle for the neoclassical theory has been developed by including amomentum restoring term in the electron-electron collisional operator, which gives an additionalfree parameter maximizing the heat production rate. All transport coefficients are obtained in-cluding the bootstrap current. The essential feature of the study is that the aspect ratio affects thefunction of the electron-electron collision operator through a geometrical factor. When the aspectratio approaches to unity,the fraction of circulating particles goes to zero and the contribution toparticle flux from the electron-electron collision vanishes. The resulting diffusion coefficient is inrough agreement with Hazeltine. When the aspect ratio approaches to infinity,the results are inagreement with Rosenbluth. The formalism gives the two extreme cases a connection. The theoryis particularly important for the calculation of bootstrap current in spherical tokamaks and thepresent tokamaks, in which the square root of the