  The two-dimentional (2D) separatrix shaping plays a crucial role in the
confinement of the Field Reversed Configuration (FRC), and the magnetic coils
serve as an effective means for its control. In this work we develop a method
to optimize the location, and current amplitude of the coils required for
achieving the target separatrix shape. By iteratively calculating the coil
currents, the plasma current, and the equilibrium magnetic flux, the
equilibrium separatrix progressively converges towards the desired shape. The
coil currents are determined through a matching method, and the NIMEQ code is
employed to compute the FRC equilibrium with a Rigid Rotor type of plasma
distribution. This approach enables the adaption of the equilibrium separatrix
into any desired shape, thus offering a potential coil optimization scheme for
the device design and the 2D shaping control of FRC plasma.
