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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 Wave Boundary Condition Wave Guide Cavity & RF Parameters Normal Mode Analysis Perturbation Theory Equivalent Circuit Coupled Cavity Part-1

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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)

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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

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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

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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

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

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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

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

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

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

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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

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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 )

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

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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 ss 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

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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

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

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

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

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

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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

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

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

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

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

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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

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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.

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

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

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

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

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

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

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

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

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

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

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

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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

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

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

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

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

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

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

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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

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

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

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

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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

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

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