Effect of Alpha Particle Retention on the FRC Target during Stabilized Liner Compression

From the days of the Linus Program 1 at the Naval Research Laboratory, c. 1979, an attractive feature for the stabilized liner reactor concept has been the ability of alpha-particles from the D-T reaction to add energy to the liner implosion/expansion, reducing the required energy circulated back from the thermo-electric generator, thereby substantially decreasing the necessary nuclear gain and the reactor size. Such energy addition does not require thermalization of the alpha-particles in heating the D-T plasma, the fusion temperature of which is achieved simply by adiabatic compression. At megagauss magnetic field levels, attained by imploding liner flux compression, the gyro-radii of the alpha-particles are much smaller than the dimensions of the FRC target, so their energy density is retained as an effective pressure. With the peak value of the confining magnetic pressure limited by liner material compressibility and resistive heating, however, the alpha-particle pressure reduces that available for the D-T plasma, so the reaction rate is diminished as alpha-particles accumulate. For example 2 , if the necessary nuclear gain relative to the peak plasma energy is 6.8, the energy of the alphas will equal that of the plasma, implying a factor of four decrease in the reaction rate. The present paper provides an analytical solution to the compression of an FRC target by a stabilized liner when alpha particles are retained, offering scaling relations and estimates of the effect on the resulting FRC length.