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We study the one-dimensional, longitudinally boost-invariant motion of anideal fluid with infinite conductivity in the presence of a transverse magneticfield, i.e., in the ideal transverse magnetohydrodynamical limit. In anextension of our previous work Roy et al., [Phys. Lett. B 750, 45 (2015)], weconsider the fluid to have a non-zero magnetization. First, we assume aconstant magnetic susceptibility $\chi_{m}$ and consider an ultrarelativisticideal gas equation of state. For a paramagnetic fluid (i.e., with$\chi_{m}>0$), the decay of the energy density slows down since the fluid gainsenergy from the magnetic field. For a diamagnetic fluid (i.e., with$\chi_{m}<0$), the energy density decays faster because it feeds energy intothe magnetic field. Furthermore, when the magnetic field is taken to beexternal and to decay in proper time $\tau$ with a power law $\sim\tau^{-a}$,two distinct solutions can be found depending on the values of $a$ and$\chi_m$. Finally, we also solve the ideal magnetohydrodynamical equations forone-dimensional Bjorken flow with a temperature-dependent magneticsusceptibility and a realistic equation of state given by lattice-QCD data. Wefind that the temperature and energy density decay more slowly because of thenon-vanishing magnetization. For values of the magnetic field typical forheavy-ion collisions, this effect is, however, rather small. Only for magneticfields which are about an order of magnitude larger than expected for heavy-ioncollisions, the system is substantially reheated and the lifetime of the quarkphase might be extended.

Bjorken flow in one-dimensional relativistic magnetohydrodynamics with magnetization