  A new tool (GSEQ-FRC) for solving two-dimensional (2D) equilibrium of
field-reversed configuration (FRC) based on fixed boundary and free boundary
conditions with external coils included is developed. Benefiting from the
two-parameter modified rigid rotor (MRR) radial equilibrium model and the
numerical approaches presented by [Ma et al, Nucl. Fusion, 61, 036046, 2021],
GSEQ-FRC are used to study the equilibrium properties of FRC quantitatively and
will be used for fast FRC equilibrium reconstruction. In GSEQ-FRC, the FRC
equilibrium can be conveniently determined by two parameters, i.e., the ratio
between thermal pressure and magnetic pressure at the seperatrix $\beta_s$, and
the normalized scrape of layer (SOL) width $\delta_s$. Examples with fixed and
free boundary conditions are given to demonstrate the capability of GSEQ-FRC in
the equilibrium calculations. This new tool is used to quantitatively study the
factors affecting the shape of the FRC separatrix, revealing how the FRC
changes from racetrack-like to ellipse-like.
