  The dissipation effects of primordial magnetic fields on the primordial
elemental abundances were investigated. When a magnetic field reconnects, its
energy is converted to the kinetic energy of charged particles, as observed for
solar energetic particles arriving on earth. This accelerates the cosmic
background nuclei, and energetic nuclei induce nonthermal reactions. A
constraint on the dissipation is derived from a theoretical calculation of the
nonthermal reactions during Big Bang nucleosynthesis. We found that
observations of the Li and D abundances can be explained if 0.01--0.1 % of the
cosmic energy density was utilized for nuclear acceleration after the
electron--positron annihilation epoch. Reconnections of such amplitudes of
magnetic fields generate outgoing jets, the bulk velocity of which evolves to
values appropriate for cosmic ray (CR) nuclear energies of 0.1--1 MeV necessary
for successful CR nucleosynthesis. Therefore, acceleration of cosmic background
nuclei during the dissipation of primordial magnetic fields is a possible
generation mechanism of soft CRs that has been suggested as a solution to the
cosmic Li problem. Among the solutions suggested without exotic physics, only
the dissipating magnetic field model suggested here explains observations of
both low Li and high D abundances. Our results demonstrate that signatures of
strong magnetic fields in the early universe have been observed in primordial
elemental abundances.
