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The Cavity Q for Ergodic Eigenmodes

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Memorandum rept.

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We consider here the problem of calculating the Q of a very overmoded, wavelength cavity size irregularly shaped resonant cavity due to absorption of the electromagnetic radiation at the walls. We assume further that the volume inside the cavity can be either vacuum, or else partially filled with anisotropic inhomogeneous dielectric or plasma. Both the scale length of the dielectric and the radius of curvature of the walls are assumed much larger than the radiation wavelength. However, near the cavity walls, a vacuum is assumed. Our main interest here is in applications concerning magnetically confined plasmas. For instance consider a tokamak containing a hot plasma which radiates at the cyclotron frequency and its harmonics. An important issue is how much of this cyclotron radiation is absorbed by the walls and how much is reabsorbed by the plasma. Generally this can be calculated with a ray tracing code where many rays are followed and the absorbtion and emission are calculated along each ray path. However if the plasma is optically thin, as it would be at the higher harmonics, and if the reflection coefficient at the wall is near unity the rays would have to be followed for long distances before one could see how much energy is deposited in the wall. In this paper we utilize the ergodic theorem to calculate the wall absorbtion for the case where the wave makes many bounces and before it is absorbed.

Subject Categories:

  • Test Facilities, Equipment and Methods
  • Fusion Devices (Thermonuclear)
  • Plasma Physics and Magnetohydrodynamics

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