  We demonstrated that a weak magnetic field can increase the permittivity,
leading to a reduction in the potential barrier within the Debye sphere
consisting of electrons and a nucleus. By solving the Boltzmann equation with
the inclusion of the magnetic field, we obtained the magnetized permittivity.
The resulting enhanced permittivity field inversely decreases the potential
barrier, thereby increasing the reaction rate between two fusing nuclei. We
compared this Boltzmann kinetic approach with the Debye potential method. We
found that they are qualitatively consistent. Further, we also derived the
magnetized Debye potential composed of the conventional term with a new
magnetic effect. Both approaches indicate that magnetized plasmas, which have
existed since the Big Bang, have ultimately influenced permittivity, potential
barrier, and nucleosynthesis.
