Using an effective adiabatic index γeff to mimic the feedback of efficient shock acceleration, we simulate the temporal evolution of a young type Ia supernova remnant (SNR) with two different background magnetic field (BMF) topologies: a uniform and a turbulent BMF. The density distribution and magnetic-field characteristics of our benchmark SNR are studied with two-dimensional cylindrical magnetohydrodynamic simulations. When γeff is considered, we find that: (1) the two-shock structure shrinks and the downstream magnetic-field orientation is dominated by the Rayleigh–Taylor instability structures; (2) there exists more quasi-radial magnetic fields inside the shocked region; and (3) inside the intershock region, both the quasi-radial magnetic energy density and the total magnetic energy density are enhanced: in the radial direction, with γeff = 1.1, they are amplified about 10–26 times more than those with γeff = 5/3. While in the angular direction, the total magnetic energy densities could be amplified about 350 times more than those with γeff = 5/3, and there are more grid cells within the intershock region where the magnetic energy density is amplified by a factor greater than 100.