TABLES OF LOWEST SPHERICAL CAVITY RESONANT MODES
Properties of H Wave Modes:-
For resonance BesselJ(p+1/2, R) = 0 where
R = 
Resonant
frequency (f Hz) = 
where
R has one of the values in the table below.
Rotational angular frequency (Ω
radians/sec) = 
=
Phase velocity = Ω rad.
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STATIONARY AND SPINNING MODES |
SPINNING MODE ONLY |
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|
MODE |
For 83.4 cm diameter cavity oscillating in first radial mode
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p (θ term) |
Radial Harmonics(R) |
n (ф term) |
Resonant Frequency (MHz) |
Rotational Speed |
Phase Velocity |
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1 |
2 |
3 |
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0 |
Not Allowed |
0 |
-- |
Not Allowed |
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0 |
Not Allowed |
1 |
-- |
Not Allowed |
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1 |
4.49 |
7.721 |
10.9 |
0 |
514.1 |
Not Allowed |
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1 |
4.49 |
7.72 |
10.9 |
1 |
514.1 |
514.1 |
4.49c |
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|
1 |
Not Allowed |
2 |
-- |
Not Allowed |
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2 |
5.76 |
9.1 |
12.3 |
0 |
659.5 |
Not Allowed |
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2 |
5.76 |
9.1 |
12.3 |
1 |
659.5 |
659.5 |
5.76c |
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2 |
5.76 |
9.1 |
12.3 |
2 |
659.5 |
329.7 |
2.88c |
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2 |
Not Allowed |
3 |
-- |
Not Allowed |
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Properties of E Wave Modes:-
For resonance BesselJ(p+1/2, R)-
BesselJ(p-1/2,R) = 0 where R =
Resonant frequency (f Hz) = where
R has one of the values in the table below.
Rotational angular frequency (Ω
radians/sec) = =
Phase velocity = Ω rad.
|
STATIONARY AND SPINNING MODES |
SPINNING MODE ONLY |
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|
MODE |
For 83.4 cm diameter cavity oscillating in first radial mode
|
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|
p (θ term) |
Radial Harmonics(R) |
n (ф term) |
Resonant Frequency (MHz) |
Rotational Speed |
Phase Velocity |
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|
1 |
2 |
3 |
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|
0 |
Not Allowed |
0 |
-- |
Not Allowed |
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|
0 |
Not Allowed |
1 |
-- |
Not Allowed |
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1 |
2.74 |
6.12 |
9.32 |
0 |
313.7 |
Not Allowed |
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|
1 |
2.74 |
6.12 |
9.32 |
1 |
313.7 |
313.7 |
2.74c |
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|
1 |
Not Allowed |
2 |
-- |
Not Allowed |
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2 |
3.87 |
7.44 |
10.72 |
0 |
443.1 |
Not Allowed |
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2 |
3.87 |
7.44 |
10.72 |
1 |
443.1 |
443.1 |
3.87c |
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2 |
3.87 |
7.44 |
10.72 |
2 |
443.1 |
221.55 |
1.935c |
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2 |
Not Allowed |
3 |
-- |
Not Allowed |
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GENERAL NOTES:-
1 This mode is TE120 (i.e. Derived from the numbers in the p column, the R column heading and the n column). 7.72 is the second value of R that makes the BesselJ function zero.
2. The symbols used above are as follows:-
p, n---- Can take the values 0, 1, 2, 3……etc and are the integers defining the harmonic solutions. (Sometimes called the eigenvalues).
c------- The velocity of light.
ω------ The resonant angular frequency.
Ω------ The rotational angular frequency.
f
The resonant frequency. (Where f = 
) . For the
spinning field this will be the frequency measured by a probe and will be 
.
rad----- The radius of the spherical cavity.
φ------- The coordinate measuring the angle of rotation about the z axis measured from the x axis (in the initial direction of the y axis).
θ------- The coordinate angle to the z axis.