A local equilibrium model for shaped tokamak plasmas with a separatrix based on the Solovev approach

A local equilibrium solution is presented for the up-down symmetric tokamak plasma in the vicinity of a separatrix. We present the solution as the sum of seven terms with seven free parameters based on the Solovev approach. The seven parameters can be completely determined the shaping factors of the separatrix and the pressure ratio and the magnetic shear on the flux surface containing 98% of the total poloidal magnetic flux. The equilibrium model can be used for investigation of phenomena localized near the separatrix like the peeling-ballooning modes, or used for flux tube plasma simulations accounting for separatrix effects.