We provide a new bound on the amplitude of primordial magnetic fields ( PMFs ) by using a novel mechanism , magnetic reheating .
The damping of the MHD fluid motions in a primordial plasma brings the dissipation of the PMFs .
In the early Universe with z \gtrsim 2 \times 10 ^ { 6 } , cosmic microwave background ( CMB ) photons are quickly thermalized with the dissipated energy and shift to a different Planck distribution with a new temperature .
In other words , the PMF dissipation changes the baryon-photon number ratio and we name such a process magnetic reheating .
From the current baryon-photon number ratio obtained from the BBN and CMB observations , we put a strongest constraint on the PMFs on small scales which CMB observations can not access , B _ { 0 } \lesssim 1.0 \mu { G } at the scales 10 ^ { 4 } h { Mpc } ^ { -1 } < k < 10 ^ { 8 } h { Mpc } ^ { -1 } .
Moreover , when the PMF spectrum is given in a blue power-law type , the magnetic reheating puts a quite strong constraint , for example , B _ { 0 } \lesssim 10 ^ { -17 } { nG } , 10 ^ { -23 } { nG } , and 10 ^ { -29 } { nG } at 1 comoving Mpc for n _ { B } = 1.0 , 2.0 , and 3.0 , respectively .
This constraint would give an impact on generation mechanisms of PMFs in the early Universe .