We study the dynamical generation of masses for fundamental fermions in quenched quantum electrodynamics, in the presence of magnetic fields of arbitrary strength, by solving the Schwinger-Dyson equation (SDE) for the fermion self-energy in the rainbow approximation. We employ the Ritus eigenfunction formalism which provides a neat solution to the technical problem of summing over all Landau levels. It is well known that magnetic fields catalyze the generation of fermion mass m for arbitrarily small values of electromagnetic coupling alpha. For intense fields it is also well known that m propto sqrt eB. Our approach allows us to span all regimes of parameters alpha and eB. We find that m propto sqrt eB provided alpha is small. However, when alpha increases beyond the critical value alpha_c which marks the onslaught of dynamical fermion masses in vacuum, we find m propto Lambda, the cut-off required to regularize the ultraviolet divergences. Our method permits us to verify the results available in literature for the limiting cases of eB and alpha. We also point out the relevance of our work for possible physical applications.
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