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LCLS II Subharmonic Beam Loading

LCLS II Subharmonic Beam Loading. G. A. Krafft. Subharmonic Beam Loading. Under condition of constant incident RF power, there is a voltage fluctuation in the fundamental accelerating mode when the beam load is sub harmonically related to the cavity frequency

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LCLS II Subharmonic Beam Loading

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  1. LCLS IISubharmonicBeam Loading G. A. Krafft

  2. SubharmonicBeam Loading • Under condition of constant incident RF power, there is a voltage fluctuation in the fundamental accelerating mode when the beam load is sub harmonically related to the cavity frequency • Have some old results, from the days when we investigated FELs in the CEBAF accelerator • These results can be used to quantify the voltage fluctuations expected from the subharmonicbeam load in LCLS II

  3. CEBAF FEL Results Bunch repetition time τ1 chosen to emphasize physics Krafft and Laubach, CEBAF-TN-0153 (1989)

  4. Model • Single standing wave accelerating mode. Reflected power absorbed by matched circulator. • Beam current • (Constant) Incident RF (β coupler coupling)

  5. Analytic Method of Solution • Green function • Geometric series summation • Excellent approximation

  6. Phasor Diagram of Solution

  7. Single SubharmonicBeam

  8. Beam Cases • Case 1 • Case 2 • Case 3

  9. Case 1 Straight Current HXR Current SXR Current Total Voltage 2 µsec 100 µsec

  10. Case 1 ΔE/E=10-4 . . . Volts t/20 nsec

  11. Case 2 ΔE/E=10-4 . . . Volts t/20 nsec

  12. Case 3 ΔE/E=10-4 Volts t/20 nsec

  13. Summaries of Beam Energies • Case 1 • Case 2 • Case 3 For off-crest cavities, multiply by cosφ

  14. Summary • Fluctuations in voltage from constant intensity subharmonicbeams can be computed analytically • Basic character is a series of steps at bunch arrival, the step magnitude being (R/Q)πfcq • Energy offsets were evaluated for some potential operating scenarios. Spread sheet provided that can be used to investigate differing current choices

  15. Case I’ Zero Crossing Left Deflection Right Deflection Total Voltage 20 µsec 100 µsec

  16. Case 2 (100 kHz contribution minor) Zero Crossing Left Deflection Right Deflection Total Voltage 2 µsec 100 µsec

  17. Case 3 Zero Crossing Left Deflection Right Deflection Total Voltage 20 µsec 100 µsec

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