TEAM Workshop Problem No. 18
Waveguide Loaded Cavity
Canonical Problem
(First Version July 25, 1992)
Geometry:
Fig.1 Square cavity coupled to a rectangular waveguide through a centered
inductive iris. The inner height of the structure is b.
Statement of the problem:
Find the resonant frequency, the Q-factor and the complex reflection
coefficient of a square-shaped TE 101 - cavity coupled to a rectangular
waveguide through a centered symmetrical inductive iris. The geometry of the
arrangement and the co-ordinate system are shown in Fig. 1 above. The height
of the structure is everywhere b. The wavwguide extends to infinity
in positiv z-direction. Hence, it is considered to be matched at all
frequencies and for all models.
The waveguide is air-filled and carries a TE 10 wave incident from
z=+???. The iris has a thickness t=a/32 (note that this
differs slightly from the dimensions given in the reference above).
Consider the following three cases:
All walls are perfectly conducting (???=???) (2D problem)
All walls are made of coin silver (???=4.7E7 S/m) 3D problem)
All walls are made of electrolytic cooper (???=5.75E7 S/m) (3D
problem)
Assume that in all cases the wall thickness is much larger than th eskip
depth.
Observables to be determined:
For the three cases specified above, find
the resonant frequency of the TE 101 - mode,
the total Q-factor of the cavity. (This factor will be external
Q in the lossless case, and the loaded Q in the lossy
cases),
the complex reflection coefficient (absolute magnitude and phase) at
a distance D=2a from the iris wall (z=3a+
t) within ??? 10% of the resonant frequency,
for WR(90) (a=0.9 in., b=0.4 in.) and WR(28) (a=0.28
in., b=0.14 in.) and for the following normalized widths of the iris:
d/a=0.5, 0.65, 0.70, and 0.75.
Extra credit:
At the resonant frequency, provide:
2D plots of Ey within the cavity and the waveguide between
z=0 and z=2a+t.
1D plots of Ey across the iris at
z=a+t/2.
Plots of the surface current density on the cavity walls, both sides
of the iris, and on the waveguide walls up to a distance z=2a+t.
Wolfgang J. R. Hoefer
Reference:
N.M. Kroll and X-T Lin, "Efficient Computer Determination of the
Properties of Waveguide Loaded Cavities", SLAC-PUB-5296, July 1990, pp.
1-16.
