Electron and ion resonance in a plasma

Consider a plasma of finite dimensions in a static magnetic field. Assume that the plasma is in equilibrium (not necessarily thermal equilibrium), and that some external force—say, a static electric field—is applied to the plasma at some angle to the magnetic field. Then, as Professor Allis pointed out, a sheath will form at the plasma boundaries, such that, within the plasma, the resulting space‐charge field will nearly cancel the applied field. If the applied field is suddenly removed, the sheath will collapse, and this will often lead to natural oscillations of the plasma. If there were no magnetic field, and if the plasma boundaries were planes, the oscillations would occur at the plasma frequency. In the presence of a magnetic field, these oscillations can be very complicated because they involve, in addition to the plasma frequency, the cyclotron frequencies of both electrons and ions. Such oscillations are the manifestation of the many degrees of freedom that a plasma in a magnetic field possesses. Clearly, the understanding of such oscillations is of fundamental importance to the understanding of plasmas.