Magnetic moment of thermal plasma: Revisiting the Bohr-van Leeuwen theorem

Magnetic properties of thermal plasma can be explained by studying behaviors of charged particles constituting the plasma in the magnetic field. Due to the Bohr-van Leeuwen theorem, it has been believed that the thermal plasma do not have magnetic moment. Here, we revisit the foundation of the theory and show that the thermal plasma do have magnetic moment by solving the equation of motion of particles before averaging the magnetic moments in the phase space. This process was not included in the derivation of the Bohr-van Leeuwen theorem. It is suggested that the magnetic Kelvin force acting on the magnetized plasma should be include in the magneto hydrodynamic equation of motion. In the Lagrangean of the combined system of particles and electro-magnetic field, there is an interaction term qV.A (q: charge, V: velocity, A: vector potential) which corresponds to the potential energy of the magnetic moment. The total energy of the system is not influenced by the potential energy. This means that the thermal energy of particles is converted to the potential energy. This energy can be a source of solar activity including coronal heating associated with magnetic field. Coherent plasma motions can be driven by the Kelvin force along an inhomogeneous magnetic field without contradicting the Second Law of Thermodynamics. The magnetic moment plays key roles in the solar atmosphere.