isothermality. In the adiabatic limit, that is, the assumption of an isotropic pressure and isotropic temperature, a fluid with an adiabatic index , electrical resistivity , magnetic field , and electric field can be described by the continuity equation the equation of state the equation of motion the low-frequency Ampère's law Faraday's law and Ohm's law Taking the curl of this equation and using Ampère's law and Faraday's law results in the induction equation, where is the magnetic diffusivity. In the equation of motion, the Lorentz force term can be expanded using Ampère's law and a vector calculus identity to give where the first term on the right hand side is the magnetic tension force and the second term is the magnetic pressure force. Ideal MHD The simplest form of MHD, ideal MHD, assumes that the resistive term in Ohm's law is small relative to the other terms such that it can be taken to be equal to zero. This occurs in the limit of large magnetic Reynolds numbers during which magnetic induction dominates over magnetic diffusion at the velocity and length scales under consideration. Consequently, processes in ideal MHD that convert magnetic energy into kinetic energy, referred to as ideal processes, cannot generate heat and raise entropy. A fundamental concept underlying ideal MHD is the frozen-in flux theorem which states that the bulk fluid and embedded magnetic field are constrained to move together such that one can be said to be "tied" or "frozen" to the other. Therefore, any two points that move with the bulk fluid velocity and lie on the same magnetic field line will continue to lie on the same field line even as the points are advected by fluid flows in the system. The connection between the fluid and magnetic field fixes the topology of the magnetic field in the fluid—for example, if a set of magnetic field lines are tied into a knot, then they will remain so as long as the fluid has negligible resistivity. This difficulty in reconnecting magnetic field lines makes it possible to store energy by moving the fluid or the source of the magnetic field. The energy can then become available if the conditions for ideal MHD break down, allowing magnetic reconnection that releases the stored energy from the magnetic field. Ideal MHD equations In ideal MHD, the resistive term vanishes in Ohm's law giving the ideal Ohm's law,