Pulsed field magnetization (PFM) of a high-J_c MgB_2 bulk disk has been investigated at 20 K, in which flux jumps frequently occur for high pulsed fields. Using a numerical simulation of the PFM procedure, we estimated the time dependence of the local magnetic field and temperature during PFM. We analyzed the electromagnetic and thermal instability of the high-J_c MgB_2 bulk to avoid flux jumps using the time dependence of the critical thickness, d_c(t), which shows the upper safety thickness to stabilize the superconductor magnetically, and the minimum propagation zone length, l_m(t), to obtain dynamical stability. The values of d_c(t) and l_m(t) change along the thermally-stabilized direction with increasing temperature below the critical temperature, T_c. However, the flux jump can be qualitatively understood by the local temperature, T(t), which exceeds T_c in the bulk. Finally, possible solutions to avoid flux jumps in high-J_c MgB_2 bulks are discussed.This work was supported by Open Partnership Joint Projects of Japan Society for the Promotion of Science (JSPS) Bilateral Joint Research Projects, and JSPS KAKENHI grant number 23560002 and 15K04646. Dr Mark Ainslie would like to acknowledge the support of a Royal Academy of Engineering Research Fellowship and a Royal Society International Exchanges Scheme grant, IE131084.This is the author accepted manuscript. The final version is available from IOP Publishing via http://dx.doi.org/10.1088/0953-2048/29/3/03400
