The Behaviour of a Plasma Under the Influence of a Standing Electromagnetic Wave in the Absence of a Constant Magnetic Field†

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Abstract
The physics of the radial confinement of an ionized plasma in an electromagnetic field is examined for a cylindrical cavity excited in the TM010 and T.E011 modes. This analysis reveals that two confining forces are operating, which forces we call the electromagnetic force and the Mathieu force, since the equation of electron motion is a Mathieu equation. Equations giving the degree of confinement of a fully ionized plasma, and its dependence on input power, arc derived. Two typos of unstable solution to Mathieu's equation are shown to arise; one of these gives rise to a unidirectional force on the plasma while the other gives rise to an exponentially increasing amplitude of oscillation. It is thought that this latter solution may represent an additional mechanism of plasma heating, provided there are sufficient electron-ion collisions to dissipate an appreciable fraction of the energy of ordered motion of the electron into random motion.