Entropy production rate in tokamaks with nonaxisymmetric magnetic fields

A variational principle based on an extremum of entropy production rate is derived for an integrable Hamiltonian system in the presence of two perturbations, which are resonant on neighboring or identical resonant surfaces. This method can be used to calculate the neoclassical transport in a magnetic fusion device with a nonaxisymmetric magnetic field. When applied to a tokamak with ripple, it provides an efficient means to discriminate between various regimes, depending on collisionality and ripple amplitude. This technique provides a means to test simplified collision operators suitable for gyrokinetic codes. It is found that these operators need only satisfy modest requirements in order to recover the correct neoclassical equilibrium, at least in the large aspect ratio limit. Finally, it appears that the toroidal viscous damping rate due to ripple is usually not negligible, thus removing the degeneracy between the radial electric field and the toroidal velocity.