  A two-flavor color superconducting (2SC) Nambu--Jona-Lasinio (NJL) model is
introduced at finite temperature T, chemical potential mu and in the presence
of a constant magnetic field eB. The effect of (T,mu,eB) on the formation of
chiral and color symmetry breaking condensates is studied. The complete phase
portrait of the model in T-mu, mu-eB, and T-eB phase spaces for various fixed
eB, T, and mu is explored. A threshold magnetic field eB_t~ 0.5 GeV^2 is found
above which the dynamics of the system is solely dominated by the lowest Landau
level (LLL) and the effects of T and mu are partly compensated by eB.
