“…For twospecies VMB system, we can observe some phenomena of wave propagation and magnetic field domination on long time behaviors of charge transport of charge transport due to the effect of magnetic filed and mutual interaction between the particles of two species. Indeed, for the global solution (f 1 , f 2 , E, B) to the linearized two-species VMB system, we can show that the distribution function f 1 , corresponding to the total summation of the distribution functions between the two species, is governed by the linearized Boltzmann equation and its optimal time decay rate (1 + t) − 3 4 in L 2 -norm has been already established for instance in [20,25]. Meanwhile, the magnetic field B is also shown to tend to zero at the optimal time decay rates (1 + t) − 3 4 in L 2 -norm, but the distribution function f 2 , corresponding to the difference of the distribution functions between the two species, and the electric field E decay at the faster optimal time rate (1 + t) − 5 4 in L 2 -norm.…”