A trapped magnetic field of greater than 3 T has been achieved in a single grain GdBa$2$Cu$3$O$\mathrm{<mrow\; data-mjx-texclass="ORD">7-</mrow>}$ (GdBaCuO) bulk superconductor of diameter 30 mm by employing pulsed field magnetization. The magnet system is portable and operates at temperatures between 50 K and 60 K. Flux jump behaviour was observed consistently during magnetization when the applied pulsed field, $Ba$, exceeded a critical value (e.g., 3.78 T at 60 K). A sharp d$Ba$/d$t$ is essential to this phenomenon. This flux jump behaviour enables the magnetic flux to penetrate fully to the centre of the bulk superconductor, resulting in full magnetization of the sample without requiring an applied field as large as that predicted by the Bean model. We show that this flux jump behaviour can occur over a wide range of fields and temperatures, and that it can be exploited in a practical quasi-permanent magnet system.