Radiation converter physics and a method for obtaining the upper limit for gain in heavy ion fusion

Converting the kinetic energy of heavy ion beams into radiation energy at high efficiency is important for heavy ion fusion. High conversion efficiency can be achieved if the radiating material consists mainly of a low Z element, for example, beryllium, mixed with a small amount of high Z element, for example, lead. For stopping incoming beams with a given energy, low Z material has higher stopping power and hence has less total internal energy than a high Z material. A high Z material is used for efficient radiation; the exact amount used is determined by the requirement that the Planck mean free path is approximately equal to the dimension of the radiation converter. Too much high Z material would hence prevent radiation from escaping from the interior region of the radiating material. To reduce the hydrodynamic loss in the radial direction, the radiating material is placed inside a casing made of high Z material. Calculations show that the energy absorbed by the casing is tolerable and that the interface between the casing and the radiating material is almost stationary. Various scaling laws for the converter are developed. Simulations with the LASNEX hydrodynamic code show that carefully designed converters can have conversion efficiencies as high as 70% (80%) for incoming beams with 10 GeV (5 GeV) energy. Because the converters have high efficiency and ion range shortening in beryllium is not substantial, range shortening is not a major issue. Once the diagram for the conversion efficiency versus the converter radius is obtained for various beam ion energies, the trajectory is located on this diagram that gives the upper limit for conversion efficiency (and hence for gain) while satisfying the engineering limit of the quadrupole pole-tip magnetic fields of the final-focusing system for heavy ion beams (for ballistic transport through a hard-vacuum reactor chamber). Finally, converter configurations are presented that can deflect the direction of radiation, thereby eliminating the need for ion beam bending