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Shuichi Noguchi, KEK6-th ILC School, November 20111 Shuichi Noguchi, KEK6-th ILC School, November 20111 RF Basics; Contents  Maxwell’s Equation  Plane.

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Presentation on theme: "Shuichi Noguchi, KEK6-th ILC School, November 20111 Shuichi Noguchi, KEK6-th ILC School, November 20111 RF Basics; Contents  Maxwell’s Equation  Plane."— Presentation transcript:

1 Shuichi Noguchi, KEK6-th ILC School, November 20111 Shuichi Noguchi, KEK6-th ILC School, November 20111 RF Basics; Contents  Maxwell’s Equation  Plane Wave  Boundary Condition  Wave Guide  Cavity & RF Parameters  Normal Mode Analysis  Perturbation Theory  Equivalent Circuit  Coupled Cavity Part-1

2 Shuichi Noguchi, KEK6-th ILC School, November 20112 Shuichi Noguchi, KEK6-th ILC School, November 20112 Literatures  J. C. Slator “Microwave Electronics” Rev. Mod. Phys. 18,(1946)

3 Shuichi Noguchi, KEK6-th ILC School, November 20113 Shuichi Noguchi, KEK6-th ILC School, November 20113 Maxwell’s Equation ( MKS ) Not a Beam Current Faraday Ampere

4 Shuichi Noguchi, KEK6-th ILC School, November 20114 Shuichi Noguchi, KEK6-th ILC School, November 20114 Pointing Vector & Power Flow From Maxwell’s Equation Energy Loss + Change of Electric and Magnetic Energy = Power Flow at Boundary S

5 Shuichi Noguchi, KEK6-th ILC School, November 20115 Shuichi Noguchi, KEK6-th ILC School, November 20115 Maxwell’s Equation -  Wave Equation Cartesian Coordinate Cylindrical Coordinate  = 0

6 Shuichi Noguchi, KEK6-th ILC School, November 20116 Shuichi Noguchi, KEK6-th ILC School, November 20116 Wave Equation

7 Shuichi Noguchi, KEK6-th ILC School, November 20117 Shuichi Noguchi, KEK6-th ILC School, November 20117 Wave Equation  Helmholtz Equation Particular Solution for our Application No TEM Modes in one closed Conductor

8 Shuichi Noguchi, KEK6-th ILC School, November 20118 Shuichi Noguchi, KEK6-th ILC School, November 20118 Maxwell’s Equation in Cartesian Coordinates

9 Shuichi Noguchi, KEK6-th ILC School, November 20119 Shuichi Noguchi, KEK6-th ILC School, November 20119 Maxwell’s Equation in Cylindrical Coordinates

10 Shuichi Noguchi, KEK6-th ILC School, November 201110 Shuichi Noguchi, KEK6-th ILC School, November 201110 Plane Wave in Uniform Medium

11 Shuichi Noguchi, KEK6-th ILC School, November 201111 Shuichi Noguchi, KEK6-th ILC School, November 201111 Plane Wave in Uniform Medium Frequency  Time Dependence exp( j  t ) No Boundary TEM Mode

12 Shuichi Noguchi, KEK6-th ILC School, November 201112 Shuichi Noguchi, KEK6-th ILC School, November 201112 Plane Wave Propagation Constant Attenuation Constant ( Real Part ) Phase Constant ( Imaginary Part )

13 Shuichi Noguchi, KEK6-th ILC School, November 201113 Shuichi Noguchi, KEK6-th ILC School, November 201113 Impedance ; E / H Intrinsic Impedance

14 Shuichi Noguchi, KEK6-th ILC School, November 201114 Shuichi Noguchi, KEK6-th ILC School, November 201114 Boundary Condition Medium 1  1,  1, Z 1 Medium 2  2,  2, Z 2 Medium 1Medium 2 ss JsJs E t1 E t2 H t1 H t2 E n1 E n2 H n1 H n2 E = H = 0 in Perfect Conductor ; E t =H n = 0 FaradayAmpere 0

15 Shuichi Noguchi, KEK6-th ILC School, November 201115 Shuichi Noguchi, KEK6-th ILC School, November 201115 Reflection & Transmission Medium 1  1,  1, Z 1 Medium 2  2,  2, Z 2 z x Dielectric Boundary

16 Shuichi Noguchi, KEK6-th ILC School, November 201116 Shuichi Noguchi, KEK6-th ILC School, November 201116

17 Shuichi Noguchi, KEK6-th ILC School, November 201117 Shuichi Noguchi, KEK6-th ILC School, November 201117 Metallic Boundary

18 Shuichi Noguchi, KEK6-th ILC School, November 201118 Shuichi Noguchi, KEK6-th ILC School, November 201118 Metallic Boundary z x DielectricMetallic E H

19 Shuichi Noguchi, KEK6-th ILC School, November 201119 Shuichi Noguchi, KEK6-th ILC School, November 201119 Power Loss & Surface Impedance

20 Shuichi Noguchi, KEK6-th ILC School, November 201120 Shuichi Noguchi, KEK6-th ILC School, November 201120 Wave Guide  Coaxial Line  Parallel Conductor  Strip Line  Circular Wave Guide  Rectangular Wave Guide  Ridged Wave Guide

21 Shuichi Noguchi, KEK6-th ILC School, November 201121 Shuichi Noguchi, KEK6-th ILC School, November 201121 Traveling Wave Mode

22 Shuichi Noguchi, KEK6-th ILC School, November 201122 Shuichi Noguchi, KEK6-th ILC School, November 201122 Traveling Wave Mode

23 Shuichi Noguchi, KEK6-th ILC School, November 201123 Shuichi Noguchi, KEK6-th ILC School, November 201123 TE-Modes ; E z = 0

24 Shuichi Noguchi, KEK6-th ILC School, November 201124 Shuichi Noguchi, KEK6-th ILC School, November 201124

25 Shuichi Noguchi, KEK6-th ILC School, November 201125 Shuichi Noguchi, KEK6-th ILC School, November 201125 TE-mn Modes in Rectangular WG x z y a b From Boundary Condition

26 Shuichi Noguchi, KEK6-th ILC School, November 201126 Shuichi Noguchi, KEK6-th ILC School, November 201126 Wave Length in Medium Critical Wave Length Guide Wave Length If k < k c (  c ) wave can not propagate.

27 Shuichi Noguchi, KEK6-th ILC School, November 201127 Shuichi Noguchi, KEK6-th ILC School, November 201127 TE-mn Modes

28 Shuichi Noguchi, KEK6-th ILC School, November 201128 Shuichi Noguchi, KEK6-th ILC School, November 201128 TM-Modes ; H z = 0

29 Shuichi Noguchi, KEK6-th ILC School, November 201129 Shuichi Noguchi, KEK6-th ILC School, November 201129 TM-mn Modes

30 Shuichi Noguchi, KEK6-th ILC School, November 201130 Shuichi Noguchi, KEK6-th ILC School, November 201130 Power Loss

31 Shuichi Noguchi, KEK6-th ILC School, November 201131 Shuichi Noguchi, KEK6-th ILC School, November 201131 TEM-Modes ; E z, H z = 0

32 Shuichi Noguchi, KEK6-th ILC School, November 201132 Shuichi Noguchi, KEK6-th ILC School, November 201132 Maxwell’s Equation in Cylindrical Coordinates

33 Shuichi Noguchi, KEK6-th ILC School, November 201133 Shuichi Noguchi, KEK6-th ILC School, November 201133 Traveling Wave Modes

34 Shuichi Noguchi, KEK6-th ILC School, November 201134 Shuichi Noguchi, KEK6-th ILC School, November 201134 Traveling Wave Modes

35 Shuichi Noguchi, KEK6-th ILC School, November 201135 Shuichi Noguchi, KEK6-th ILC School, November 201135 TM-Modes ; H z = 0

36 Shuichi Noguchi, KEK6-th ILC School, November 201136 Shuichi Noguchi, KEK6-th ILC School, November 201136

37 Shuichi Noguchi, KEK6-th ILC School, November 201137 Shuichi Noguchi, KEK6-th ILC School, November 201137

38 Shuichi Noguchi, KEK6-th ILC School, November 201138 Shuichi Noguchi, KEK6-th ILC School, November 201138 Boundary Condition r = a z m n1234 02.40485.52018.653711.7915 13.83177.015610.173513.3237 25.13568.417211.619814.7960 36.38029.761013.015216.2235 47.588311.064714.372517.6160 y mn

39 Shuichi Noguchi, KEK6-th ILC School, November 201139 Shuichi Noguchi, KEK6-th ILC School, November 201139 TM-man Modes

40 Shuichi Noguchi, KEK6-th ILC School, November 201140 Shuichi Noguchi, KEK6-th ILC School, November 201140 TE-Modes

41 Shuichi Noguchi, KEK6-th ILC School, November 201141 Shuichi Noguchi, KEK6-th ILC School, November 201141 TEM-Modes ; E z = H z = 0

42 Shuichi Noguchi, KEK6-th ILC School, November 201142 Shuichi Noguchi, KEK6-th ILC School, November 201142 Coaxial Waveguide ab

43 Shuichi Noguchi, KEK6-th ILC School, November 201143 Shuichi Noguchi, KEK6-th ILC School, November 201143 Power

44 Shuichi Noguchi, KEK6-th ILC School, November 201144 Shuichi Noguchi, KEK6-th ILC School, November 201144 Resonator / Cavity

45 Shuichi Noguchi, KEK6-th ILC School, November 201145 Shuichi Noguchi, KEK6-th ILC School, November 201145 Can be solved Analytically or by Computer Codes  Boundary Condition  Short-Circuited Plane S  Open-Circuited Plane S’ S S’ Media ;   wall Cavity ; Perfect Conductor

46 Shuichi Noguchi, KEK6-th ILC School, November 201146 Shuichi Noguchi, KEK6-th ILC School, November 201146 Analytic Solution, Example L a

47 Shuichi Noguchi, KEK6-th ILC School, November 201147 Shuichi Noguchi, KEK6-th ILC School, November 201147 TM-01 l Modes

48 Shuichi Noguchi, KEK6-th ILC School, November 201148 Shuichi Noguchi, KEK6-th ILC School, November 201148 Cavity RF Parameters Geometric Factor

49 Shuichi Noguchi, KEK6-th ILC School, November 201149 Shuichi Noguchi, KEK6-th ILC School, November 201149 Transit Time Factor ( TTF ) TM010 Mode in Cylindrical Cavity

50 Shuichi Noguchi, KEK6-th ILC School, November 201150 Calculate Skin Depth & Surface Resistance using following Values.

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