Program for Basic Coil Flux Plot?

To get a ballpark approximation, you could simplify to a 72" diameter circle and try to design for 200 Gauss. However, it will be extremely difficult to get a truly uniform field with a rectangular coil. In addition, since you are using capacitor discharge, the field will exponential.

Please know there are significant safety risks in designing something like this, since back-current from the pulse can burn out your capacitors quickly. If you are in the US I can suggest a few companies that design these things on a regular basis. They design them for safety and long life.

a solenoid can supply a pretty uniform flux density (B) if it is long enough. B is proportional to amp turns, 200G is a practical value one should be able to build. note the magnetic field around but outside the coil is zero. You may also think about buliding a Helmholtz coil.