In last sixty years, the scientists spent the tens billion dollars attempting to develop useful thermonuclear energy. But they cannot yet reach a stable thermonuclear reaction. They still are promising publically, after another 15 – 20 years, and more tens of billions of US dollars to finally design the expensive workable industrial installation, which possibly will produce electric energy more expensive than current heat, wind and hydro-electric stations can in 2015. The author offers a new, small cheap cumulative inertial thermonuclear reactor, which increases the pressure and temperature of its nuclear fuel by thousands of times, reaches the required ignition stage and, ultimately, full constant contained thermonuclear reaction. Cumulative A-B Reactor contains several innovations to achieve its product Chief among them is using moving explosives (rocket thrust), which allows to accelerate the special piston to very high speed (more 30 km/s) which (as shown by integral computations) compresses the fuel capsule a million times and heats up the millions degrees of temperature.