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Tuning of Mode Cavities Using Equivalent Circuits

Tuning of Mode Cavities Using Equivalent Circuits. Mike Jenkins Lancaster University and Cockcroft Institute. Outline. mode cavities Equivalent circuits 5 cell equivalent circuit model. Mode C avities.

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Tuning of Mode Cavities Using Equivalent Circuits

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  1. Tuning of Mode Cavities Using Equivalent Circuits Mike Jenkins Lancaster University and Cockcroft Institute

  2. Outline • mode cavities • Equivalent circuits • 5 cell equivalent circuit model

  3. Mode Cavities • At Cockcroft Institute we are currently looking into mode cavities for security applications • mode structures are of interest for this application due to high field stability • They are hard to tune as every other cell has no field in it

  4. Equivalent Circuits Electrical properties of RF cavities can be modelled by an RLC circuit. L C R

  5. 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

  6. Bi Periodic Equivalent Circuit Apply Kirchhoff’s voltage summation rule to each current loop giving an equation for each cell

  7. Bi Periodic Equivalent Circuit

  8. Bi Periodic Equivalent Circuit Where

  9. Effect of Beam Pipe • Currently γ describes the effect of the beam pipe. • We want to have a flatπ/2 mode • This allows us to determine that

  10. Eigenvalue Problem Where

  11. Modelling Out of Tune Cavities • We now have an equation describing the field in each cell which depends only on Ω and k • Using these equations we can model an out of tune cavity using perturbation theory to represent errors in the cell capacitances

  12. 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

  13. Testing the Equivalent Circuit Model Perturbed Case First Correction Tuned

  14. Extending the Model • The current equivalent circuit model is working well for a structure • The security linac we are working on is a not structure, each accelerating cell is different • Need a more general model possibly with different coupling

  15. Summary • We are developing compact mode linacs for security applications • A new tuning method for these structures is being developed using equivalent circuit and perturbation techniques • Initial testing of the tuning method on simplified structure shows promising results

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