Cerenkov and transition radiation in space-time periodic media

Abstract

EFFECTS OF DIELECTRIC CONTAINERS 3719though it could be a necessary correction for techniques employing different geometries. The procedure represented by the application of Eq. (7) corrects for the combined effect of the container wall and the holes in the cavity. Plasma density measurementsThe motivation for the present work was the requirement for accurate electron densities in the positive column of a glow discharge in helium over a range of discharge currents and gas pressures. 8 Using a quartz tube with 0. 4 -mm -thick walls, the resonance frequency shifts t:.fd were first determined for the six dielectric slugs described above. The quartz tube was then made part of the positive column of the helium discharge and the frequency shifts C:.fP were then observed for the desired set of pressures and currents. The integrals gd and gP of Eq. (7) were machine calculated, now using for convenience the theoretical distributions Ei(r) of Eq. (8). Of the set of values of fd, the one chosen in a particular density determination made the ratio t:.f/ C:.fP nearest unity. Equation (7) then yielded the corresponding electron density. The densities obtained were about 16% larger than would have been obtained without the refined calibration procedure described above. Microwave bridge measurementFrequently, plasma densities are measured in a microwave bridge circuit 4 rather than by a frequency shift of a resonator, and the field attenuation and distortions as introduced by the dielectric container walls (plus that of the holes in the waveguides, or of the distorted antenna radiation fields) are sources of errors of the same magnitude as in the above case. For example, it was found that a 1-mm-thick Pyrex tube (same dimensions as above) inserted in an X-band waveguide reduced the measured phase shifts of the dielectric samples by 74%! A quartz tube of the same wall thickness introduced similarly 32% error. Such errors can be avoided by the simple calibration procedure outlined above. CONCLUSIONIt has been shown that plasma containers made from quartz or Pyrex will attenuate microwave fields appreciably and that holes cut into resonance cavities will distort fields, with each effect leading to significant errors in microwave density measurements. However, when proper calibration procedures are employed, such errors can be minimized. It is thus recommended that the calibration procedure described above be followed when large errors in electron density measurements are to be avoided. Chern. Phys. 56, 1077Phys. 56, (1972 J. Chern. Phys. 56, 1411. Cerenkov and transition radiation in space-time periodic media Charles ElachiJet Propulsion Laboratory and California Institute of Technology, Pasadena, California 91109 (Received 17 March 1972) The solution to the problem of determining the radiation emitted by a uniformly moving charged particle in a sinusoidally space-time periodic medium is obtained. The space-time periodicity can be considered as due to a strong pump wave and is expressed as a traveling-wave-type change in th...

Asymptotic theory of mode coupling in a space-time periodic medium—Part I: Stable interactions

“…The permittivity has a progressive wave modulation of sinusoidal form in the z direction. The index of modulation, the spatial periodicity, the temporal periodicity, and the phase velocity of the progressive wave modulation are given by q, 2 n / K , 2~1 5 where u = U~( E~O E O E , )~~~, the normalized phase velocity of the progressive wave modulation. We assume that the index of modulation q is small and we find it convenient to exhibit the smallness of q by the introduction of a formal expansion parameter 6 which is equal to unity in all the final formulas.…”

Microwave Pioneers: Charles Elachi, “Dare Mighty Things”

“…Meanwhile, on the Caltech campus, Elachi hooked up with notable Radiophysics and Electrical Engineering Professor, Charles Papas, and started working on electromagnetic wave interactions in periodic media. He earned his Master's degree in 1969 and his Ph.D. in 1971 [1]- [4]. By 1970, he had also managed to land a part-time paying job at JPL, which he gladly substituted for his university fellowship.…”