You should first estimate the required magnetic field (Tesla) and volume. This, along with the number of turns on the coil will help in designing the H-bridge driver. In general, because V = L dI/dt, getting the required peak coil current I with the applied voltage rating of the driver depends on the coil inductance, which depends on number of coil turns, volume, etc. The maximum field is proportional to the amp turns (NI) in the coil. Inductance, which is proportional to N2, limits the maximum current. In general, lower frequency is better, because dI/dt is lower. Why do you need >100 kHz for this?
The driver could be either integrated H-bridge circuits (e.g., LMD182XX), or IGBTs, depending on the voltage and current requirements. Really high coil currents will need water cooled coils. Sometimes, ferrite can be used to increase the magnetic field, and Litz wire can be used to reduce coil eddy current losses.
Please describe maximum field, coil geometry, and volume.
Bob S