Boundary integral equation approach based on a polynomial expansion of the current distribution to reconstruct the current density profile in tokamak plasmas

Abstract

A new approach has been proposed to reconstruct the current density profile in tokamak plasmas. The boundary-only integral equation derived from the Grad–Shafranov equation, under the assumption of polynomial expansion of current density, will have no unknowns except for the polynomial expansion coefficients, once the magnetic flux and its derivative have been given along the plasma boundary with the aid of Kurihara's Cauchy-condition surface method based on magnetic sensor data. In addition to the discretized form of the equation, some constraints are taken into account: the total plasma current, zero-current along the plasma boundary and a scalar relationship derived from the MHD equilibrium to relate the current density to the magnetic flux. It is also assumed that the poloidal field, as a quantity closely related to the current density, can be measured at a certain number of points inside the plasma. The whole set of linear equations is solved using the singular value decomposition technique to determine the polynomial expansion coefficients. The validity of the present technique and the quality of the current density solution have been investigated through test calculations for some plasma configurations.