A magnetic field generator includes a power source and a coil connected to the power source to generate a time-varying magnetic field. Energy is applied to the coil so that the coil generates a time-varying magnetic field gradient with a magnitude of at least 1 milliTesla per meter and a rise-time of less than 10 microseconds. One or more of a capacitor, a multi-stage high-voltage switch, and/or a pulse-forming network may assist with the generation of the magnetic field gradient.