Measurements of plasma parameters and thrust imparted from the compact helicon source having an annular permanent magnet in addition to the previously reported magnet configuration are performed, where two different diameter annular permanent magnets of the 5.4-cm-diam and the 8-cm-diam are tested. The source diameter, the working argon gas pressure, and the 13.56 MHz rf power are chosen as 6.6 cm, 0.85 mTorr, and 500-2000 W, respectively. Both the plasma density in the magnetic nozzle and the measured thrust for the 8-cm-diam annular magnet are higher than that for the 5.4-cm-diam one. The thrust can be increased by the effective rf power, and reaches a maximum of about 9 mN and 6 mN for the 8-cm-diam and the 5.4-cm-diam annular magnet, respectively. As some of the plasma flow is trapped by the closed field lines near the annular magnets, the obtained thrust is lower than the configuration with no annular magnet.