On some necessary conditions for p-11B ignition in the hot spots of a plasma focus

Recently, it has been predicted that hydrogen-boron (p-B-11) nuclear fusion may attain ignition in the hot spots observed in a plasma focus (PF) pinch, due to their huge values of particle density, magnetic field and (reportedly) ion temperature. Accordingly, large magnetic fields should raise electronic Landau levels, thus reducing collisional exchange of energy from ion to electrons and Bremsstrahlung losses. Moreover, large particle densities, together with ion viscous heating, should allow fulfilment of Lawson criterion and provide effective screening of cyclotron radiation. We invoke both well-known, empirical scaling laws of PF physics, Connor-Taylor scaling laws, Poynting balance of electromagnetic energy and the balance of generalised helicity. We show that the evolution of PF hot spots is a succession of relaxed states, described by the double Beltrami solutions of Hall-MHD equations of motion. We obtain some necessary conditions for ignition, which are violated in most realistic conditions. Large electromagnetic fields in the hot spot accelerate electrons at supersonic velocities and trigger turbulence, which raises electric resistivity and Joule heating, thus spoiling further compression. Ignition is only possible if a significant fraction of the Bremsstrahlung-radiated power is reflected back into the plasma. Injection of angular momentum decreases the required reflection coefficient.