Effect of gauge fixing term in three dimensional stationary magnetic fields problem

Gauge fixing in 3-D stationary linear magnetic fields in a finite volume is achieved under some particular assumptions. Divergence of inner region A satisfies the Laplace equation by using a conventional gauge-fixing term to the gauge-invariant Lagrangian. Taking into account the assumed zero boundary condition for divA on the natural boundary condition surface, it is found that divA vanishes all over the region theoretically. Uniqueness of the solution is proved in another particular case. A numerical analysis is presented and the optimal value of the gauge-fixing parameter α is examined