Low Level RF for superB Olivier BOURRION LPSC Grenoble December 1, - PowerPoint PPT Presentation

LLRF motivation reminder Feedback techniques Loop implementation Summary Low Level RF for superB Olivier BOURRION LPSC Grenoble December 1, 2010 Olivier BOURRION LLRF for superB 1 / 30

LLRF motivation reminder Feedback techniques Loop implementation Summary Table of Contents LLRF motivation reminder 1 Feedback techniques 2 Direct RF feedback One turn delay feedback Loop implementation 3 Loop details Hardware plateform A few technical details Summary 4 Olivier BOURRION LLRF for superB 2 / 30

LLRF motivation reminder Feedback techniques Loop implementation Summary Table of Contents LLRF motivation reminder 1 Feedback techniques 2 Direct RF feedback One turn delay feedback Loop implementation 3 Loop details Hardware plateform A few technical details Summary 4 Olivier BOURRION LLRF for superB 3 / 30

LLRF motivation reminder Feedback techniques Loop implementation Summary Cavity model I G Generator current V c I T I B Beam current I T Cavity current I G C L R I B ( − → I T = − → I G + − → I B ) I 0 I 0 Loss current in shunt R ω r s resistance Q l Z ( s ) = s 2 + ω r V C Cavity voltage s + ω 2 r Q l Q l Loaded quality factor High intensity beam → cavity voltage perturbated by I B Objective: maintain constant V C I G contribution should compensate I B Modulation of I B → modulation I G Olivier BOURRION LLRF for superB 4 / 30

LLRF motivation reminder Feedback techniques Loop implementation Summary Cavity tuning / phasor diagram IT IB φ L Loading angle φ Z Cavity tuning angle φ B Stable phase angle (above transition I B points upward) f Z IG f L f B I0 Vc From diagram study: tan φ Z = tan φ 0 + I B I 0 (tan φ 0 sin φ B + cos φ B ) Maintaining generator current in phase with cavity voltage → tan φ Z = I B I 0 cos φ B Cavity tuning angle increase with current Z sh I Frequency shift due to cavity tuning δ f = − f RF N c Q V RF In LER: 233 kHz In HER: 252 kHz Values close to ω rev − ω s (227 kHz- 2.65 kHz) Olivier BOURRION LLRF for superB 5 / 30

LLRF motivation reminder Feedback techniques Loop implementation Summary Instabilities and cavity impedance Instabilities growth rates proportionnal to the cavities impedance: ≈ eI B F rf α τ − 1 [ Re Z c ( ω rf + l ω rev + ω s ) − Re Z c ( ω rf − l ω rev − ω s )] l 2 EQ s Applying this to the detunned cavity impedance yields: Cavity impedance Growth rate NF 900000 40 800000 30 700000 20 600000 growth (ms-1) 10 500000 400000 0 300000 -10 200000 -20 100000 0 -30 4.74e+ 08 4.75e+ 08 4.76e+ 08 4.77e+ 08 4.78e+ 08 -10 -8 -6 -4 -2 0 2 4 6 8 10 freq (Hz) mode mode -1 growth rate is 33 ms -1 (baseline LER) Comparable to synchrotron frequency (1 /τ − 1 ) /ω s ∼ 0 . 5 Exceed the radiation damping rate (LER damping time =20.3 ms) (1 /τ − 1 ) / (1 /τ d ) ∼ 670 Olivier BOURRION LLRF for superB 6 / 30

LLRF motivation reminder Feedback techniques Direct RF feedback Loop implementation One turn delay feedback Summary Table of Contents LLRF motivation reminder 1 Feedback techniques 2 Direct RF feedback One turn delay feedback Loop implementation 3 Loop details Hardware plateform A few technical details Summary 4 Olivier BOURRION LLRF for superB 7 / 30

LLRF motivation reminder Feedback techniques Direct RF feedback Loop implementation One turn delay feedback Summary Direct RF feedback (1/2) IB Expected impedance reduction IG Cavity model Vp + A Z ( ω ) Zc Z fbk ( ω ) = 1 + GAe − jT ∆ ω Z ( ω ) Loop delay + G e � Tp Vref In theory the highest gain GA is desired: Maintain loop stability → Phase Margin is impacted by loop delay Canonical value of PM = π/ 4 yields π 4 T + 2 ω r GAR ≤ Q = G max AR ω r 1 + ω r 4 T π Impedance reduction limited by the loop delay T Olivier BOURRION LLRF for superB 8 / 30

LLRF motivation reminder Feedback techniques Direct RF feedback Loop implementation One turn delay feedback Summary Direct RF feedback (2/2) Plots with loop gain = 1 . 3 × G max AR (flat response) and T=440 ns (PEP2 delay value) Cavity impedance Growth rate direct 70000 2.0 1.5 60000 1.0 impedance (ohms) 50000 growth (ms-1) 0.5 40000 0.0 -0.5 30000 -1.0 20000 -1.5 10000 -2.0 4.74e+ 08 4.75e+ 08 4.76e+ 08 4.77e+ 08 4.78e+ 08 -10 -8 -6 -4 -2 0 2 4 6 8 10 freq (Hz) mode Maximum impedance decreased by a factor of 12.8 -1 Mode is damped by a factor of 20 Side effect: other modes growth rates are increased! More impedance reduction is needed Olivier BOURRION LLRF for superB 9 / 30

LLRF motivation reminder Feedback techniques Direct RF feedback Loop implementation One turn delay feedback Summary Delay influence T=470 ns Cavity impedance Growth rate direct 80000 2.0 1.5 70000 1.0 60000 impedance (ohms) 0.5 growth (ms-1) 50000 0.0 40000 -0.5 30000 -1.0 20000 -1.5 10000 -2.0 4.74e+ 08 4.75e+ 08 4.76e+ 08 4.77e+ 08 4.78e+ 08 -10 -8 -6 -4 -2 0 2 4 6 8 10 freq (Hz) mode T=500 ns Cavity impedance Growth rate direct 80000 2.0 1.5 70000 1.0 60000 impedance (ohms) growth (ms-1) 0.5 50000 0.0 40000 -0.5 30000 -1.0 20000 -1.5 10000 -2.0 4.74e+ 08 4.75e+ 08 4.76e+ 08 4.77e+ 08 4.78e+ 08 -10 -8 -6 -4 -2 0 2 4 6 8 10 mode freq (Hz) Olivier BOURRION LLRF for superB 10 / 30

LLRF motivation reminder Feedback techniques Direct RF feedback Loop implementation One turn delay feedback Summary Comb filter feedback principle IB IG Overcome loop delay Vp Cavity model + A Zc limitation Correction applied with Loop delay + one turn delay G � Tp e Minimize impedance at certain frequencies Vref Phase 1 turn delay Comb filter equalizer Attenuation needed at synchrotron sidebands → dual peaked comb G (1 − e − jwT rev ) filter H comb ( jw ) = 1 − 2 K cos(2 πν s ) e − jwT rev + K 2 e − j 2 wT rev Response is modified by the complement to reach one turn delay H ( jw ) = H comb ( jw ) × e − jw ( T rev − T g ) Olivier BOURRION LLRF for superB 11 / 30

LLRF motivation reminder Feedback techniques Direct RF feedback Loop implementation One turn delay feedback Summary Comb filter details Revolution harmonics The closest K come to the unity, higher the gain, and narrower the bandwidth Olivier BOURRION LLRF for superB 12 / 30

LLRF motivation reminder Feedback techniques Direct RF feedback Loop implementation One turn delay feedback Summary Comb filter feedback limitations Out of klystron bandwidth, large dephasing → loop instability Precompensation of the dephasing → phase equalizer Gain margin of 10 dB for loop stability (when φ = π ) G max ≤ 1 + 2 K cos(2 πν s ) + K 2 6 Max gain on comb loop is function of K with K=63/64 G=0.655 with K=127/128 G=0.660 Reminder: longitudinal radiation damping rate: 0.0492 ms -1 Olivier BOURRION LLRF for superB 13 / 30

LLRF motivation reminder Feedback techniques Direct RF feedback Loop implementation One turn delay feedback Summary Simulations K=63/64 Cavity impedance Growth rate direct+ comb 600000 0.15 500000 0.10 400000 0.05 impedance (ohms) growth (ms-1) 300000 0.00 200000 -0.05 100000 -0.10 0 -0.15 4.74e+ 08 4.75e+ 08 4.76e+ 08 4.77e+ 08 4.78e+ 08 -10 -8 -6 -4 -2 0 2 4 6 8 10 freq (Hz) mode Cavity impedance Growth rate direct+ comb 450000 0.05 0.04 400000 0.03 350000 0.02 300000 impedance (ohms) growth (ms-1) 0.01 250000 0.00 200000 K=127/128 -0.01 150000 -0.02 33 ms -1 → 100000 -0.03 0.05 ms -1 50000 -0.04 0 -0.05 4.74e+ 08 4.75e+ 08 4.76e+ 08 4.77e+ 08 4.78e+ 08 -10 -8 -6 -4 -2 0 2 4 6 8 10 mode freq (Hz) Olivier BOURRION LLRF for superB 14 / 30

LLRF motivation reminder Loop details Feedback techniques Hardware plateform Loop implementation A few technical details Summary Table of Contents LLRF motivation reminder 1 Feedback techniques 2 Direct RF feedback One turn delay feedback Loop implementation 3 Loop details Hardware plateform A few technical details Summary 4 Olivier BOURRION LLRF for superB 15 / 30

LLRF motivation reminder Loop details Feedback techniques Hardware plateform Loop implementation A few technical details Summary LLRF feedback overview Tuner loop GFF Gap voltage loop Klystron loop Hardware platform delay sensitive setpoints Slow processing fast processing Olivier BOURRION LLRF for superB 16 / 30

LLRF motivation reminder Loop details Feedback techniques Hardware plateform Loop implementation A few technical details Summary Cavity tuning Tuner loop Minimizing of the phasing between cavity probe signal and cavity forward voltage Setpoint: load offset angle Angle offset loop PEP2 implementation arguments. Since all cavities have the same voltage applied, it may be necessary to: decrease the gap voltage by having non zero angle. Lowers voltage on fragile cavity compensate eventual misphasing between beam and generator current (relative beam phase due to geometry, waveguide length, ...) Back to loops overview Olivier BOURRION LLRF for superB 17 / 30