We report measurements of electron densities, n e , and temperatures, T e , in a magnetized expanding hydrogen plasma performed using Thomson scattering. The effects of applying an axial magnetic field and changing the background pressure in the plasma vessel on n e and T e along the expansion axis are reported. Magnetic field strengths (B field) up to 170 mT were applied, which are one order of magnitude larger than previously reported. The main effect of the applied B field is the plasma confinement, which leads to higher n e . At B fields larger than 88 mT the electron density along the expansion axis does not depend strongly on the magnetic field strength. However, T e is susceptible to the B field and reaches at 170 mT a maximum of 2.5 eV at a distance of 1.5 cm from the exit of the cascaded arc. To determine also the effect of the arc current through the arc, measurements were performed with arc currents of 45, 60, and 75 A at background pressures of 9.7 and 88.3 Pa. At constant magnetic field n e decreases from the exit of the arc along the expansion axis when the arc current is decreased. At 88.3 Pa n e shows a higher value close to the exit of the arc, but a faster decay along the expansion axis with respect to the 9.7 Pa case. T e is overall higher at lower pressure reaching a maximum of 3.2 eV at the lower arc current of 45 A. The results of this study complement our understanding and the characterization of expanding hydrogen plasmas.