A pulse-power-driven, heavy-ion beam, ignition and inertial confinement system for thermonuclear microexplosions is proposed. The proposed method depends on already developed and tested techniques and has the potential of a high repetition rate, one of the requirements for a thermonuclear microexplosion reactor. In the proposed method, a space charge neutralized ion beam of modest intensity is projected into a long drift tube where it is radially confined by an applied axial magnetic field and axially compressed by a programmed variation of the diode voltage with time. Because the beam consists of a space charge neutralized flow of heavy ions, it behaves like a high atomic number plasma and, as such, rapidly looses internal energy by radiation during its axial compression. The axial compression proceeds isothermally until the beam becomes optically opaque where it reaches its maximum density. The axial beam compression greatly amplifies the final beam power over its initial value at the beam producing diode. In typical cases the initial beam power is ≃ 1010 W, and in a drift tube ≃ 100 meters long can be amplified ≃ 104 fold up to ≃ 1014 W; but much larger beam powers are also possible. The accelerating voltage is typically in the range of several 106V and the diode current several 103A. Because the collision mean free path in the beam is smaller than the beam length, some unavoidable deviation from the programmed diode voltage will not lead to a dispersion of the beam. For typical cases the beam has, at its maximum compression, an atomic number density of ≃ 1018 cm−3 and a radius of ≃ 1 cm. After being compressed to its final maximum density the beam can, from there on, be easily focused on to the thermonuclear target. The use of singly ionized heavy ions in combination with an accelerating voltage of several 106V has the further advantage that the ion velocities are of the order of several 108 cm sec−1, ideally matching the required optimal implosion velocity for the microexplosion target and thus implying a high beam energy conversion efficiency for ignition and confinement. For a final beam power of ≃ 1014W the diode cross-section is ≃ 102 cm2. With a diode cross-section ≃ 103 times larger, that is ≃ 10 m2, final beam powers up to ≃ 1017 W will be possible, opening the prospect for igniting the DD and perhaps the HB11 thermonuclear reactions.