Power dissipation and magnetic forces on MAGLEV rebars

Concrete guideways for proposed MAGLEV vehicles may be reinforced with electrically conducting and magnetizable steel rebars. Transient magnetic fields due to passing MAGLEV vehicles will then induce transient currents in the rebars leading to power dissipation and temperature rise as well as Lorentz and magnetization forces on the rebars. In order to evaluate if this heating and force on the rebars affects concrete life and performance, analysis is presented for an infinitely long conducting and magnetizable cylinder in imposed uniform axial or transverse magnetic fields. Exact and approximate solutions are presented for sinusoidal steady state and step transient magnetic fields inside and outside the cylinder, the induced current density, the vector potential for transverse magnetic fields, the time average dissipated power in the sinusoidal steady state, and the total energy dissipated for step transients. Forces are approximately calculated for imposed magnetic fields with a weak spatial gradient. The analysis is applied to representative rebar materials