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Energy Modulation in Linac 4: Some Preliminary Results

Energy Modulation in Linac 4: Some Preliminary Results. Anirban Krishna Bhattacharyya , Philippe Baudrenghien CERN-BE-RF-FB . Reported by Anirban Krishna Bhattacharyya CERN-BE-RF-FB. The Klystron Model. Klystron Transfer Function. Experimental Setup.

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Energy Modulation in Linac 4: Some Preliminary Results

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  1. Energy Modulation in Linac 4: Some Preliminary Results Anirban Krishna Bhattacharyya, Philippe Baudrenghien CERN-BE-RF-FB Reported by Anirban Krishna Bhattacharyya CERN-BE-RF-FB

  2. The Klystron Model A. K. Bhattacharyya - Energy Modulation in LINAC 4

  3. Klystron Transfer Function Experimental Setup Done at reduced power. Maximum power output from klystron 100 KW A. K. Bhattacharyya - Energy Modulation in LINAC 4

  4. Klystron Transfer Function Algorithm: Experimental Data + error Norm Optimizer - Transfer function equation Number of poles Number of zeros Input is only the expected number of poles and zeros A. K. Bhattacharyya - Energy Modulation in LINAC 4

  5. Klystron Transfer Function Transfer function Transfer function in RF Number of poles: 14 Number of zeros: 18 Error: 10% A. K. Bhattacharyya - Energy Modulation in LINAC 4

  6. Klystron Transfer Function Transfer function in IQ ω0 = 352.2 MHz Hs(jω) = H(jω+jω0) + H(jω-jω0) 1 2 -1 Hc(jω) = H(jω-jω0) - H(jω+jω0) 2j Transfer function from II/QQ Transfer function from IQ/QI Number of poles: 12 Number of zeros: 17 Number of poles: 22 Number of zeros: 22 Error: 4% Error: 18% A. K. Bhattacharyya - Energy Modulation in LINAC 4

  7. Klystron Gain Modulation The gain modulation of the Klystron with respect to the input power has to be scaled so that the characteristics remain same but the Klystron saturates for an input of 0 dBm. Method for scaling: Find point (Ρi,Gi) where Klystron saturates from experimental data. Experimental data • Let saturation limit of klystron be Psat. • Gain at saturation has to be 10log10(Psat /1 mW ). • Gains from experiments are scaled such that Gi = 10log10(Psat /1 mW ). • Using Z0=50Ω find voltage for Klystron saturation Voutsat=√(2PsatZ0). • Vinsat=Voutsat/10(Gi/20). • Scale x-axis such that Pi is equal to Vinsat. A. K. Bhattacharyya - Energy Modulation in LINAC 4

  8. Klystron Simulation Model Closed loop simulation A. K. Bhattacharyya - Energy Modulation in LINAC 4

  9. Klystron Tuner Loop A. K. Bhattacharyya - Energy Modulation in LINAC 4

  10. Model/Simulation Parameters PIMS 11/12 Debunching ZTT = 23.1 MΩ L = 1.3 m QL = 7100 Q0 = 17000 Φ = -20° Z0 = 50 Ω ZTT = 23.1 MΩ L = 1.55 m QL = 6000/8000/1200 Q0 = 19227 Φ = -20° Z0 = 50 Ω ZTT * L * QL Beam coupling = Q0 √((Q0-QL)*2*ZTT*L) QL Cavity Gain = Q0 √(QL*Z0) Triangular output voltage in the cavity 1 with Vmin = 4.08 MV and Vmax = 5.36 MV Triangular phase modulation in cavity 12 with swing from -81.45° to 81.45° and voltage of 0.7 MV ± 25%. Time periods: 20 μsec and 40 μsec. A. K. Bhattacharyya - Energy Modulation in LINAC 4

  11. Results Gain characteristics for Psat=1.1 MW Gain characteristics for Psat=1.3 MW A. K. Bhattacharyya - Energy Modulation in LINAC 4

  12. Results: Voltage Modulation Beam current: 40 mA Saturation power: 1.1 MW (10.488 kV) A. K. Bhattacharyya - Energy Modulation in LINAC 4

  13. Results: Voltage Modulation Beam current: 20 mA Saturation power: 1.1 MW (10.488 kV) A. K. Bhattacharyya - Energy Modulation in LINAC 4

  14. Results: Voltage Modulation Beam current: 40 mA Saturation power: 1.3 MW (11.402 kV) A. K. Bhattacharyya - Energy Modulation in LINAC 4

  15. Results: Voltage Modulation Beam current: 20 mA Saturation power: 1.3 MW (11.402 kV) A. K. Bhattacharyya - Energy Modulation in LINAC 4

  16. Results: Debuncher • Beam current: 40 mA • Saturation power: 1.1 MW (10.488 kV) • Q = 6000 A. K. Bhattacharyya - Energy Modulation in LINAC 4

  17. Results: Debuncher A. K. Bhattacharyya - Energy Modulation in LINAC 4

  18. Results: Debuncher • Beam current: 40 mA • Saturation power: 1.1 MW (10.488 kV) • Q = 8000 A. K. Bhattacharyya - Energy Modulation in LINAC 4

  19. Results: Debuncher A. K. Bhattacharyya - Energy Modulation in LINAC 4

  20. Results: Debuncher • Beam current: 40 mA • Saturation power: 1.1 MW (10.488 kV) • Q = 12000 A. K. Bhattacharyya - Energy Modulation in LINAC 4

  21. Results: Debuncher A. K. Bhattacharyya - Energy Modulation in LINAC 4

  22. Simplifications made These simplifications allow the controller gain to be pushed so that effective control can be obtained. However this is not real and hence will call for some sophisticated control strategy. No delay in the loop (in reality there is a total loop delay of 1100 ns) Cavity model has single peak in frequency response Cavities on tune for PIMS and detuned for Debuncher A. K. Bhattacharyya - Energy Modulation in LINAC 4

  23. Scopes of improvement Large error in Klystron transfer function estimation (18%), in spite of quite a large number of poles and zeros. Hence, use of fractional order systems, proposed as virtually an infinite number of poles and zeros can be tackled with a finite number of parameters. Inclusion of delays in the loop, and tuning of PID controller to achieve optimal performance. Inclusion of noise model from HV power supply. Inclusion of observer in feed back loop to reduce noise. Design and comparison of various predictive schemes for control The non-linearity in the system provides opportunity to design and implement non-linear control strategies. A. K. Bhattacharyya - Energy Modulation in LINAC 4

  24. Thank You A. K. Bhattacharyya - Energy Modulation in LINAC 4

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