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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Shuichi Noguchi, KEK6-th ILC School, November Shuichi Noguchi, KEK6-th ILC School, November Boundary Condition r = a z m n y mn

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

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

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

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

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

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

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

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

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

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

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

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