Mike Jenkins Lancaster University and Cockcroft Institute
Outline
Equivalent Circuits Electrical properties of RF cavities can be modelled by an RLC circuit. R L C
Equivalent Circuits For multi cell structures: Model each cell as individual RLC circuits Cell to cell coupling represented by inductor or capacitor Effects of beam pipes on end cells described by addition of capacitor
Bi Periodic Equivalent Circuit Apply Kirchhoff’s voltage summation rule to each current loop giving an equation for each cell
Bi Periodic Equivalent Circuit
Effect of Beam Pipe
Eigenvalue Problem
Modelling Out of Tune Cavities
Testing the Equivalent Circuit Model To test the equivalent circuit model a 5 cell bi periodic structure was simulated in CST For an unperturbed structure it is field flat Added a known error into the model
Testing the Equivalent Circuit Model Perturbed Case First Correction Tuned
Extending the Model
Summary