TABLES  OF LOWEST CYLINDRICAL CAVITY RESONANT MODES

 

Properties of H Wave Modes:-

 

     For resonance BesselJ(m+1, R) –  x BesselJ(m, R) = 0 where

             

     Resonant frequency (f Hz)  =       where R and n have the values in the table below.

    

     Rotational angular frequency (Ω radians/sec) =   =

    

     Phase velocity = Ω rad.

 

STATIONARY AND SPINNING MODES

SPINNING

MODE ONLY

MODE

For 83.4 cm diameter, 50 cm high cavity oscillating in first radial mode

 

m

(ф term)

Radial Harmonics(R)

n

(z term)

Resonant Frequency (MHz)

Rotational Speed

(106rev/sec)

Phase Velocity2

1

2

3

0

Not Allowed

0

--

Not Allowed

0

3.83

7.02

10.17

1

531.3

Not Allowed

1

Not Allowed

0

--

Not Allowed

1

1.84

5.331

8.54

1

366.6

366.6

3.20c

1

1.84

5.33

8.54

2

635.9

635.9

5.55c

1

1.84

5.33

8.54

3

924.3

924.3

8.07c

2

Not Allowed

0

--

Not Allowed

2

3.05

6.71

9.97

1

460.4

230.2

2.01c

2

3.05

6.71

9.97

2

694.2

347.1

3.03c

2

3.05

6.71

9.97

3

965.4

482.7

4.22c

 

 


 

Properties of E Wave Modes:-

 

     For resonance BesselJ(m, R) = 0    where

 

     Resonant frequency (f Hz) =     where R and n have the values in the table below.

 

 

     Rotational angular frequency (Ω radians/sec) =   =

 

     Phase velocity = Ω rad

                                       

    

STATIONARY AND SPINNING MODES

SPINNING

MODE ONLY

MODE

For 83.4 cm diameter, 50 cm high cavity oscillating in first radial mode

 

m

(ф term)

Radial Harmonics(R)

n

(z term)

Resonant Frequency (MHz)

Rotational Speed

(106rev/sec)

Phase Velocity2

1

2

3

0

2.40

5.52

8.65

0

274.8

Not Allowed

0

2.40

5.52

8.65

1

406.8

Not Allowed

1

3.83

7.02

10.17

0

438.5

438.5

3.83c

1

3.83

7.02

10.17

1

531.3

531.3

4.64c

1

3.83

7.02

10.17

2

743.2

743.2

6.49c

1

3.83

7.02

10.17

3

1001.1

1001.1

8.74c

2

5.14

8.42

11.62

0

588.5

294.2

2.57c

2

5.14

8.42

11.62

1

660.6

330.3

2.88c

2

5.14

8.42

11.62

2

840.4

420.2

3.67c

2

5.14

8.42

11.62

3

1075.3

537.6

4.70c

 

 


GENERAL NOTES:-

 

1 This mode is TE121 (i.e. Derived from the numbers in the m column, the R column heading and the n column). 5.33 is the second value of R that makes the BesselJ function zero.

 

2 Unlike the spherical cavity, where the phase velocity depends only on the mode, in the cylindrical cavity it also depends on the cavity size.

 

3.  The symbols used above are as follows:-

m,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 .

h        -The height of the cylindrical cavity.

rad     -The radius of the cylindrical 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)

 

 

 

                                                 

 

 

 

 

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