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Introduction “ Two modes ” model Method of the calculation for the transient response

Measurement & Calculation of the Lorentz Detuning for the transient response of the resonant cavity. Introduction “ Two modes ” model Method of the calculation for the transient response Case of Flat-top Comparison between experiment and calculation Next Measurement Plan Summary.

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Introduction “ Two modes ” model Method of the calculation for the transient response

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  1. Measurement & Calculation of the Lorentz Detuningfor the transient response of the resonant cavity Introduction “Two modes” model Method of the calculation for the transient response Case of Flat-top Comparison between experiment and calculation Next Measurement Plan Summary Y. Yamamoto, H. Hatori, H. Hayano, E. Kako, S. Noguchi, M. Sato, T. Shishido, K. Watanabe(KEK), H. Hara, K. Sennyu(MHI) SCRF Meeting @FNAL 21-25/Apr/2008

  2. Improvement in the KEK TESLA-like Cavities Ｆｒ Ｆｚ Cell Taper 13 deg. →10 deg. TTF Cavity Beam Tube f78 → f84 KEK TESLA-like Cavity Thick Titanium Baseplate, Thick Nb Beam Tube & Thick Nb End-cell Input Port f40 → f60 KEK TESLA-like Cavity TTF Cavity Stiffness of Cavity Fixing Support80 kN/mm13 kN/mm Lorentz Detuning-480 Hz-1050 Hz(31.5 MV/m) TESLA Technology Collaboration Meeting

  3. Introduction The shape of the resonant cavity is generally deformed by the Lorentz force. The frequency of the cavity is changed according to the square of the field strength. The cavity is detuned, and the field may not be constant during the flat-top of the pulse. It is necessary to compensate or lower the detuning by the Lorentz force. The methods to do it are following… (1) Using Piezo (2) Setting the initial offset of the frequency to the cavity (3) Increasing the mechanical strength of the cavity STF base-line cavity is mechanically stronger than TESLA’s one! SCRF Meeting @FNAL 21-25/Apr/2008

  4. Mechanical Oscillation (Two Modes Model) Very roughly speaking, the fast mode is mainly contributed to the Lorentz Detuning before 500μsec and the slow mode after 500 μsec. Oscillation Amplitude (Xk) Slow mode Offset Compensation Fast mode Stationary Amplitude Piezo Compensation Eacc Time 1.5 msec. The behavior of the filling is considered not to be different between on resonance and the slight detuning. SCRF Meeting @FNAL 21-25/Apr/2008

  5. Two Modes Model In this model, the Lorentz detuning is generated by two modes. One is the “fast mode” and the other is “slow”. 90Hz 300Hz In the simulation 500μsec 5msec(=200Hz) slow mode (sine) fast mode (linear) From the mechanical calculation Actually, so many modes exist in 9-cell cavity! But, these modes are mainly effective. slow mode fast mode SCRF Meeting @FNAL 21-25/Apr/2008

  6. Cavity Voltage Equation From J. Slater Equi-angular Spiral If the factor in each term is constant in time, this equation can be solved analytically. But, if not so… SCRF Meeting @FNAL 21-25/Apr/2008

  7. Voltage Solution Within the very short period (Δt), the following equation is filled and solved analytically. 1μsec SCRF Meeting @FNAL 21-25/Apr/2008 Generally normalized by 1

  8. Expressions and values for the calculation Used expressions Used numerical values filling time : Tf = 2QL/ω0 f0 = 1300.25MHz QL = 1.15x106 (from horizontal test for STF B.L. #3 cavity) Δt = 1μsec (sufficiently short) Δf = sine + linear (t<500μsec) → sine (t>500μsec) tanΨ=-2QLΔf/f0 After 500µsec, the fast mode disappears, because the damping is very fast. SCRF Meeting @FNAL 21-25/Apr/2008

  9. Example of Flat-top calculation fast mode + slow mode After 500µsec, the fast mode disappears. Input data (frequency) slow mode (sine) tanΨ=-2QLΔf/f0 Input data (degree) Output data (VC) Output data (ΨCavity) SCRF Meeting @FNAL 21-25/Apr/2008

  10. Case of Flat-top (offset +160Hz) SCRF Meeting @FNAL 21-25/Apr/2008

  11. One pulse during High-Power Test (+160Hz Offset) SCRF Meeting @FNAL 21-25/Apr/2008

  12. Comparison between experiment and calculation ① Preliminary No offset +160Hz offset 1500µsec 500µsec 500µsec Before 500µsec, the response speed of the phase detector is probably significant. After that, it is consistent between the experiment and the calculation. “Two modes model” is valid! SCRF Meeting @FNAL 21-25/Apr/2008

  13. Comparison between experiment and calculation ② Preliminary +300Hz offset -160Hz offset 500µsec 500µsec “Two modes model” is valid! SCRF Meeting @FNAL 21-25/Apr/2008

  14. For the real operation (with Piezo), the calculation is modified for a few parameters. Eacc = 18.5 → 35MV/m QL = 1.15x106 →3x106 Sorry! There is not the experimental data around 35MV/m. The result around 30MV/m will be obtained in STF-Phase 1.0 on June or July. SCRF Meeting @FNAL 21-25/Apr/2008

  15. Example of Piezo Compensation (#1) SCRF Meeting @FNAL 21-25/Apr/2008

  16. Criteria of Piezo parameters (#1) 300Hz/μm for Δfcavity SCRF Meeting @FNAL 21-25/Apr/2008

  17. Example of Piezo Compensation (#2) SCRF Meeting @FNAL 21-25/Apr/2008

  18. Criteria of Piezo parameters (#2) 300Hz/μm for Δfcavity SCRF Meeting @FNAL 21-25/Apr/2008

  19. Next Measurement Plan • Comparing between Two types of Piezo actuator • High voltage type • 2μm/1000V@2K • Low voltage type • 2μm/150V@2K • Measurement of the Lorentz detuning around 30MV/m • STF #2 B.L. cavity achieved 29.4MV/m in the V.T. • Measurement of the detuning angle during the RF decay • This was already demonstrated in the horizontal test of LL cavity. • Checking the response of the phase detector 300Hz/μm for Δfcavity SCRF Meeting @FNAL 21-25/Apr/2008

  20. Suggestion to the compensation method for the Lorentz Detuning • Put the initial offset for the cavity frequency • During the filling time, the cavity frequency is gradually decreased by the Lorentz detuning. • Work piezo with the small oscillation • Avoid to break out the Piezo by the large oscillation • Longer lifetime of Piezo • Increase the mechanical strength of the cavity • It is difficult to deform the cavity. SCRF Meeting @FNAL 21-25/Apr/2008

  21. Summary • “Two modes model” is valid for the transient response of the cavity in the horizontal test at STF Phase-0.5. • It is effective to increase the mechanical strength of the cavity for the reduction of the Lorentz detuning. • It is similarly effective to set the initial offset to the cavity frequency around the high field. • In STF Phase-1.0, we will compare between the experimental data around 30MV/m and the simulation. • We will re-examine “two modes model” for more optimization. SCRF Meeting @FNAL 21-25/Apr/2008

  22. Backup Slides SCRF Meeting @FNAL 21-25/Apr/2008

  23. Mechanical Detuning Equation It is expected that there are two modes from the calculation of the mechanical oscillation. One is the fast mode and the other is slow. SCRF Meeting @FNAL 21-25/Apr/2008

  24. Two Dominant Mechanical Modes F ~ + Need Stiff Jacket-Tuner Need Stiff Cavity F ~200Hz ~２５00Hz Fundamental mode (Slow mode) 2-nd order mode (Fast mode) SCRF Meeting @FNAL 21-25/Apr/2008

  25. Case of Flat-top ① (no offset) Phaser diagram SCRF Meeting @FNAL 21-25/Apr/2008

  26. Case of Flat-top ③ (offset +300Hz) SCRF Meeting @FNAL 21-25/Apr/2008

  27. Case of Flat-top ④ (offset -160Hz) SCRF Meeting @FNAL 21-25/Apr/2008

  28. One pulse during High-Power Test (No Offset) Ψcavity This pulse is used for the comparison later. 5˚ Pkly PRef 18.5MV/m Vcavity SCRF Meeting @FNAL 21-25/Apr/2008

  29. One pulse during High-Power Test (+300Hz Offset) SCRF Meeting @FNAL 21-25/Apr/2008

  30. One pulse during High-Power Test (-160Hz Offset) SCRF Meeting @FNAL 21-25/Apr/2008

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