A proton beam with a velocity of the order of 10 9 cm/s is generated to interact with a charge neutral hydrogen-boron medium such as H 3 B. The created charged particles are confined by magnetic fields. This concept was the basis for a novel non-thermal fusion reactor, published recently in Laser and Particle Beams [1]. The fusion is initiated by protons followed by a process of chain reactions in a neutral medium density of the order of 10 19 cm −3 , heated by the pB 11 fusion created alphas up to a temperature of about one electron volt. In this system, the radiation losses by bremsstrahlung are negligible and the plasma thermal pressure is low. The ionization of the gaseous medium is caused by the alpha elastic nuclear collisions with the hydrogen atoms and their thermal heating and it is < 10 −4. An external electric field is applied to avoid the energy losses of the protons particles by friction, due to their interaction with the electrons of the medium, to keep the proton-boron fusion at the maximum cross section of about 600 keV at the center of mass frame of reference. The alphas created in the pB 11 fusion undergo nuclear elastic collisions with the hydrogen protons of the medium and causing a pB 11 chain reaction. In this paper the equation of motion of these proton and alphas are solved numerically for the one-dimensional (1D) case, and their possible solutions are analyzed and discussed. Specifically, it is shown how the electric field can mitigate the stopping power for the proton11-proton nuclear fusion. Our results show that starting from a bunch of 10 13 protons in our volume, an alpha number of particles of 6 × 10 16 was accepted after a 5 ms cycle of applying our specially designed electric field. Consequently, the medium temperature was raised to 1.3 eV. The aim of this paper is to present a new concept by addressing only the main physical processes and not to present a complete engineering design. The configuration for mitigating the stopping power and the numerical solution in this paper is novel and promises few applications with a viable proton-boron11 fusion reactions.