Activities of research and development on repetitive induction voltage modulators in the Tokyo Institute of Technology–High Energy Accelerator Research Organization group are presented along with a discussion of the magnetic response of ferro-magnetic materials to fast magnetization and a transient beam loading in the modulators. The modulator is composed of independently driven modules switched by field effect transistors. To make waveform control, the induced voltages are stacked and synthesized in the induction unit. A proof-of-principle experiment shows that the module elements are successfully operated up to megahertz levels with good reproducibility. For the evaluation of magnetic core response, magnetic characteristics are investigated over a wide range of parameters, and an empirical core loss scaling is derived at minor-hysteresis loops. Using the prototype induction module, we have also investigated the effect of beam loading. Results indicate that the effect depends not only on the impedance of the driving circuit but on nonlinearity of the magnetic-core response. This means that the response of the induction modulator depends on the time scale of domain motion and operating point in the B-H plane of magnetic materials. Based on the progress of the component technology in the induction accelerator and database of magnetic materials, a system design has been developed.