High density helicon plasma is produced by a 13.56 MHz rf discharge under an IGBT-pulsed expanding and strong magnetic field, where the compact solenoid (inner diameter of 10 cm and 616 turn) is used for the formation of the magnetic field. The solenoid current is pulsed by the IGBT device with a pulse width of 20-40 msec. The solenoid current and the resultant magnetic field strength are proportional to the charging voltage to the capacitor. In the presently used solenoid and circuit, the maximum current and the resultant field strength are about 56 A and 3 kGauss, respectively. For the rf power of about 700 W, the high density plasma of about 4 × 1012 cm-3 is achieved. Above the field strength of about 1.6 kGauss, the source plasma density is constant, while the downstream density increases due to the suppression of the radial loss of the plasma particles.