Wang Juan Lin Yihua Dec 25th,2010

1. Discussion of resonant cavity and the simulation by software COMSOL Wang Juan Lin Yihua Dec 25th,2010

2. Content • 1.Theoretical deduction of TM wave function • 2.Practical simulation of TE & TM wave in resonant cavity by COMSOL • 3.Some interesting questions in the process of simulation

3. I. Theoretical deduction

4. I. Theoretical deduction According to: Z=0: Z=d:

5. I. Theoretical deduction

6. I. Theoretical deduction Resonance frequency: In a cubical resonant cavity: Discussion of degree of degeneracy: Define: 1. , the degree of degeneracy is 1; 2. , the degree of degeneracy is 3; 3. , the degree of degeneracy is 6;

7. II. Practical simulation • TE (0,1,1) Mode:

8. II. Practical simulation Section: z=0 a=0, b=1 Section: x=0 b=1, c=1 Section: y=0 a=0, c=1

9. II. Practical simulation Section: y=0 a=0, c=1

10. II. Practical simulation • TE (2,1,1) Mode: Section: y=0 a=2, b=1

11. II. Practical simulation • Calculating the power flow:

12. II. Practical simulation • The power flow in TE (2,1,1) Mode:

13. Problem 1 1. When simulating electrical density in COMSOL:

14. Key point The power density in the pipe is 2~3 ranges larger than that in the resonant cavity:

15. Solution

16. Problem 2 There exists a “power hole” in the process of simulating electrical density:

17. Key point The sub sources interfered the inner distribution of electric density! Then the challenge comes: 1. How to smooth the edges to avoid the occurrence of sub sources? 2.How to “break” the symmetry of the wave source to avoid the same phase position?

18. Solution 1. How to smooth the edges to avoid the occurrence of sub sources?

19. Solution 2.How to “break” the symmetry of the wave source to avoid the same phase position?

20. Solution • The result:

21. Conclusion • Having known how to take advantage of simulation software to test the theoretical result; • Try to think hard to find ways to eliminate all the problems when putting the model into practice!

22. Thanks!