From the basic equations of magneto-hydrodynamics the energy conservation theorem for plasmas is derived for events periodic in time. In addition to the terms known from vacuum electrodynamics, there are the kinetic energies of the electrons and ions, and a term due to the oscillations of the electrons and ions in the magnetic field. — With the help of the solution for the radially oscillating cylinder, the impedance of a coil containing the plasma is derived from general energy considerations. The impedance [eq. (31)] is discussed and its mean value in the range between two eigenfrequencies of the plasma cylinder is given.
Non-linear energy conservation theorem in the framework of special relativity