A high-efficiency proton-boron fusion scheme taking into account the effects of quantum degeneracy

The proton-boron (p-$^{11}$B) reaction is regarded as the holy grail of advanced fusion fuels, since the primary reaction produces three $\alpha$ particles with few neutrons and induced radio-activities from second order reactions. Compared to the Deuterium-Tritium reaction a much higher reaction temperature is required. Moreover, bremsstrahlung energy losses due to the high nuclear charge of boron deem it seemingly apparent than a fusion reactor based on Deuterium-Tritium plasma in equilibrium is to say the least very difficult.It is becoming more appealing to collide intense laser beams or accelerated proton beams with a boron target to produce p-$^{11}$B reactions. The fusion yield of p-$^{11}$B reactions is closely related to proton beam parameters and boron target conditions such as density, temperature, and ingredients. Quantum degeneracy will increase fusion yields by reducing the stopping power of injected protons. In this work, we suggest a high-efficiency scheme for beam-target p-$^{11}$B fusions via injecting a MeV proton beam into a highly compressed quantum degenerated boron target. Such a boron target can be achieved via quasi-isentropic compression of solid boron by using precisely shaped laser pulses. Our results indicate that for densities ranging from $10^3$ to $10^4\rho_s$, where $\rho_s$ is the density of solid boron, contributions of bound and free electrons to the stopping of protons can be completely disregarded and dramatically reduced respectively. The result is an increase in fusion yield by orders of magnitude. Furthermore, in order to achieve multiplication factor $F$ greater than one, with $F$ defined as the ratio of output fusion energy to the energy of injected protons, it is found there exits a minimum possible density of boron target, which is $2.15 \times 10^4 \rho_s$ when the kinetic energy of injected protons is $0.8$ MeV.