FPGA embedded Cavity multi harmonic servo loops beam

FPGA embedded Cavity multi harmonic servo loops, beam loading compensation and new longitudinal blow up methods John C. Molendijk: Overview of the PSB LLRF and implications for OP Part 2

Introduction • • PSB Finemet system post LS 2 Beam loading / beam induced voltage VXS Low Level RF Servo loops • Block Diagram • V-Gap Regulation loops • V-Gap Magnitude / Phase Control • Loop Stability • Longitudinal Blow-up • Sector Vector sum Phasing

PSB Finemet post LS 2 Finemet system: • For each ring: One “cavity” in PSB Sectors: • • S 13 • S 7 • S 5 12 Cells / sector: • • <= 666 V-pk / Cell • <= 8 k. V-pk / Sector • V-RF per ring 3 * 8 k. V = 24 k. V-pk* • One Cell redundancy / Sector 24 k. V-pk* = Nominal voltage optimal freq-range

Beam loading / beam induced voltage Finemet system: • High(er) impedance up-to 18 MHz • Beam current harmonics* • Induce parasitic fields • Each h in this range needs active damping / impedance reduction harmonics* = h x f-rev with h

VXS LLRF R 4 Digital Low Level RF: • One VXS* crate / ring • Modular architecture • Beam loops in DSP • Cavity Servoloops in FPGA Firmware VXS* = VME Switched Serial R 0 Test system R 3 R 2 R 1

VXS LLRF Digital Low Level RF: • Radial Loop / Freq. prog. • Phase loops / synchros • Cavity Servo loops, S 13, S 7, S 5 LLRF R 4 V-Gap RF Drives h=64 RF Train h=1, 8 RF Trains

Servo-loops – Block Diagram OASIS RCAV OASIS WCAV

Servo-loops – V-Gap Regulation loops Cartesian (I, Q) Feedback 16 x OASIS RCAV OASIS WCAV Multi Harmonic Local Oscillator

Servo-loops – V-Gap Magnitude / Phase Control V-Gap Voltage Set-point Fixed Value / Function generator OASIS RCAV Cavity Phase calculator & rotator ∑ of: + Fixed Ph. Offset + Ideal Delay comp. + Function Generator OASIS WCAV V-Gap Phase ∑ to Loop φ compensation • Keep Loop phase independent Operator has control over V-Gap Voltage & Phase functions

Servo-loops – V-Gap Magnitude / Phase Control V-Gap Voltage Set-point Function generator BAx. VRFH 1_S 13 V-Gap Phase Set-point Function generator BAx. PRFH 2_S 13

Servo-loops – V-Gap Magnitude / Phase Control DAC Drive h=1, h=2 V-Gap h=1, h=2 OASIS WCAV

Servo-loops – Loop stability Embedded Network Analyzer To measure closed loop TF Loop Filter RF Switch OASIS RCAV Loop Phase Calculator & phase rotator • Static loop Delay Comp. • Phase Comp. Table OASIS WCAV Error signal = SP – V-Gap No operator settings apart from RF Switch

Servo-loops – Loop stability Real-life Delay RF Drive -> V-Gap: 1860 • Highly frequency dependent • Fixed Delay compensation hωτ not adequate • Phase compensation table t [ns] required φ= f(h*frequency) 1800 1780 2. 5 5. 0 7. 5 10 f [MHz] 12. 5 15 17. 5

Servo-loops – Loop stability +180° Loop Phase Compensation table: • Memory with φ and dφ/df values • PSB each cell covers 16384 Hz • dφ/df values used to interpolate φ [deg] 0° -180° 5. 0 10 15 20 f [MHz] φ [deg s]

Servo-loops – Loop stability Open Loop h=1 Without Phase Compensation With Phase Compensation 1. 8 MHz 0. 995 MHz Gap return rotates Stable Gap return V-Gap I/Q BAx. RCAV Drive I/Q Bax. WCAV Pre-distorted Drive

Servo-loops – Loop Stability Real-life Gain RF Drive -> V-Gap: • Highly frequency dependent • Use gain compensation table: • Closed-loop gain = constant • Loop BW = constant 1. 0 Gain [lin] 0. 5 0 5. 0 10 f [MHz] 15 20

Servo-loops – Loop stability Loop Gain Compensation table: • Memory with G and d. G/df values • PSB each cell covers 16384 Hz • d. G/df values used to interpolate +1 G -0. 5 5. 0 10 15 20 f [MHz] G [s]

Servo-loops – Longitudinal Blow-up OASIS RCAV Note: • Phase modulation on the cavity rotator / MH LO, • Invisible* to the Phase loop. OASIS WCAV Sinusoidal / Noise Blow-up generator Invisible* : Provided the beam barycenter doesn’t move as a whole

Servo-loops – Longitudinal Blow-up. Phase-mod. on complete RF bucket shape Sinusoidal generator Noise buffer 0. 671 s Source Selector Phase-mod. on a selection of (one or more) harmonics

Servo-loops – Longitudinal Blow-up Frequency Function Sinusoidal generator Phase φ Modulation Depth Start Timing Stop Timing

Servo-loops – Sector Vector sum phasing Sector Phasing through Azimuth register of the Multi-h oscillator OASIS RCAV OASIS WCAV Azimuth Theoretical Sector phases h=1: S 13 = 0° S 7 = 135° S 5 = 180° Setup by RF specialist No effect on RF bucket-shape nor loop phase

Conclusion • The wide-band Finemet cavities enable tuning free operation • Beam-loading compensation is a must over the usable cavity bandwidth The FPGA embedded Servo loops allow in principle to control 16 harmonics • A versatile Blow-up mechanism is integrated with extended capabilities • • In principle independent of the Beam Phase loop

Further Reading • • High Level RF – Voltage Limitations PSB Cycle Timing Servo-loops - Concepts Servo-loops - Delay

High Level RF – Voltage Limitations Freq [MHz] V-pk Nom 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 V-pk Abs 8000 7551 7102 6653 6204 5755 5307 4857 4409 3959 3510 3062 2612 2164 1714 Relative weight 1. 190476 8400 1. 261193 7929 1. 341022 7457 1. 431434 6986 6514 1. 535155 6043 1. 654807 5572 1. 794688 5100 1. 960784 4629 2. 160294 4157 2. 405581 3686 2. 712968 3215 3. 11042 2743 3. 645643 2272 4. 401408 1800 5. 555556

PSB Cycle Timing

Servo-loops - Concepts

Servo-loops - Concepts

Servo-loops - Concepts

Servo-loops - Concepts

Servo-loops - Delay: • Drive to V-Gap loop phase rotation must be << to allow loop closure • For a constant t easy to compensate by rotation proportional to the frequency.