  A free-boundary Tokamak Equilibrium Solver (TES), developed for advanced
study of tokamak equilibra, is described with two distinctive features. One is
a generalized method to resolve the intrinsic axisymmetric instability, which
is encountered after all in equilibrium calculation with a free-boundary
condition. The other is an extension to deal with a new divertor geometry such
as snowflake or X divertors. For validations, the uniqueness of a solution is
confirmed by the independence on variations of computational domain, the
mathematical correctness and accuracy of equilibrium profiles are checked by a
direct comparison with an analytic equilibrium known as a generalized Solovev
equilibrium, and the governing force balance relation is tested by examining
the intrinsic axisymmetric instabilities. As a valuable application, a
snowflake equilibrium that requires a second order zero of the poloidal
magnetic field is discussed in the circumstance of KSTAR coil system.
