1. 14-Oct-02MI/RR Dampers - G. W. Foster Beam Dampers for Main Injector and Recycler Bill Ashmanskas, Bill Foster, Dave Wildman Warren Schappert, Jim Crisp, Dennis Nicklaus Oct ‘02

2. 14-Oct-02MI/RR Dampers - G. W. Foster Wide Variety of Beam Dampers Required in MI & Recycler 1)Transverse (X,Y) and Longitudinal 2)53 MHz, 2.5 MHz, 7.5 MHz, and DC Beam 3)Single Bunches, Full Batches, Short Batches 4)Injection, Ramping, and Stored Beam 5)Pbar and Proton Directions (  different timing)

3. 14-Oct-02MI/RR Dampers - G. W. Foster … plus unbunched DC Beam in Recycler…

4. 14-Oct-02MI/RR Dampers - G. W. Foster Damper Operating Modes X = Operation c = Commissioning & Tuneup BoosterMain Inj.RecyclerTevatron P bar P P P P 53 MHz Full Batches XXC 53 MHz Short Batches XX 53 MHz Coalesced Bunch XXXX 2.5 MHz Batch (4) XCXC 7.5 MHz Batch (12) XC DC Beam XC

5. 14-Oct-02MI/RR Dampers - G. W. Foster History of Dampers at FNAL Dampers are essential for maximum performance and forgiving operation. Over the years, many Beam Dampers have been built at Fermilab. Essentially all of these fell into disuse. Some of the most powerful (Superdampers) were deliberately removed from service and not replaced. In contrast, most other large labs have beam dampers on all coordinates on all machines.

6. 14-Oct-02MI/RR Dampers - G. W. Foster Difficulties in Maintaining Beam Dampers 1)Specialized custom built power amps –e.g. distributed tube amplifier for Superdampers 2)Limitations of Analog Signal Processing –Crates of specialized custom NIM modules Few people can understand & maintain system Many cables, connections to fail Spares/testing problem with custom analog modules –Unique hardware needed for various machines, various RF bunch structures, etc. Difficult to modify for new RF freq. –Diagnostic signals unavailable in control room.

7. 14-Oct-02MI/RR Dampers - G. W. Foster Damper Design Choices for MI / RR Digital Signal Processing Commercial electronics, with custom firmware –might change for final implementation Common Hardware for MI, RR, (& Booster?) Standard commercial wideband FET power amps (same type used for Recycler RF, Booster (& TeV?) dampers,etc.)

8. 14-Oct-02MI/RR Dampers - G. W. Foster Advantages of Digital Filters Digital filter can also operate at multiple lower frequencies...simultaneously if desired.  MI will not be blind for 2.5 and 7.5 MHz Beam Digital filters more reproducible (=>spares!) Re-use Standard hardware with new FPGA code –or same code with different filter coefficients Inputs and Outputs clearly defined –filters can be developed & debugged offline

9. 14-Oct-02MI/RR Dampers - G. W. Foster Generic Damper tolerating frequency sweep FIFO needed due to phase shifts between DAC and ADC clocks as beam accelerates All Logic Inside FPGA

10. 14-Oct-02MI/RR Dampers - G. W. Foster Echotek Card Used for Dampers 105 MSPS AD6645 Prieto, Meyer et. al. evaluating 65MHz DDC for RR BPM upgrade Asmanskas, Foster, Schappert testing 105 MHz version for RR Dampers

11. 14-Oct-02MI/RR Dampers - G. W. Foster Digital Signal Processing with FPGA’s Commercial card from Echotek –8 channels of 14-bit, 106 MHz Digitization One card does all dampers for one machine Customized FPGA firmware –Bill Ashmanskas, GW Foster, et. al. Handles Wide Variety of Bunch Structure

12. 14-Oct-02MI/RR Dampers - G. W. Foster 53 MHz, TCLK, MDAT,... All-Coordinate Damper w/ Echotek Card Monster FPGA(s) Minimal Analog Filter FAST ADC Stripline Pickup Minimal Analog Filter FAST ADC 14 VME 106 / 212 MHz Stripline Kicker Power Amp Minimal Analog Filter FAST ADC Resistive Wall Monitor Broadband Cavity FAST DACs > 27 MHz FAST DACs Power Amp Transverse Dampers Identical X & Y Longi- tudinal (Z) Damper 2-10

13. 14-Oct-02MI/RR Dampers - G. W. Foster MI Longitudinal Damper (Ashmanskas, Foster) Single Bunch Digital Kick  using Digital Velocity Filter implemented in FPGA firmware  80 Bunch-by-Bunch synchrotron oscillations (on Pbar Stacking Cycle) measured with Echotek board & custom firmware TURN NUMBER AFTER INJECTION  BUNCH –BY-BUNCH PHASE (w/offset)

14. 14-Oct-02MI/RR Dampers - G. W. Foster MI/RR Transverse Dampers (Ashmanskas, Foster)  Bunch-by-Bunch betatron oscillations (Pbar Stacking Cycle) measured with Echotek board & custom FPGA firmware. Single board needed for: Bunch-by-bunch longitudinal & two transverse dampers. 53MHz, 7.5MHz & 2.5MHz. Debunched beam, single bunches and bunch trains. BUNCH–BY–BUNCH BEAM POSITION TURN NUMBER AFTER INJECTION 

15. 14-Oct-02MI/RR Dampers - G. W. Foster “Universal-Damper” Application: Signal Processing Steps (transverse) 1) Bandwidth-Limit input signal to ~53 MHz 2) 14 Bit Digitization at 106 MHz or 212 MHz 3) FIR filter to get single-bunch signal 4) Sum & Difference of plate signals 5) Multi turn difference filter (FIR) w/delay 6) Pickup Mixing for correct Betatron Phase 7) Bunch-by-bunch gain, dead band etc. 8) Timing Corrections for Frequency Sweep 9) Pre-Distortion for Kicker Power Amp 10) Power Amp for Kicker Inside FPGA Echotek Board Buy

16. 14-Oct-02MI/RR Dampers - G. W. Foster Damper Priorities in Main Injector & Recycler 1.Main Injector Longitudinal Dampers 2.Main Injector Transverse Dampers 3.Recycler Transverse Injection Dampers 4.Recycler Longitudinal Dampers 5.Recycler Broadband (DC Beam) Dampers

17. 14-Oct-02MI/RR Dampers - G. W. Foster 1. Longitudinal Damper in Main Injector 1.Benefits to Bunch Coalescing for Collider –“Dancing Bunches” degrade Proton coalescing and  L –Affects Lum directly (hourglass) and indirectly (lifetime) –We are deliberately blowing  L in Booster 2.Benefits for Pbar Stacking Cycles –Bunch Rotation is generally turned off ! (x1.5 stack rate?) –Slip-Stacking etc. (Run IIb) will require stable bunches 3.Needed for eventual NUMI operation

18. 14-Oct-02MI/RR Dampers - G. W. Foster Longitudinal Beam Instability in MI Driven by cavity wake fields within bunch train Seeded by Booster & amplified near MI flat top. First Bunch ~ OK 7th Bunch Trashed Occurs with as few as 7 bunches (out of 588) Prevents low emittance bunch coalescing and efficient Pbar bunch rotation see Dave Wildman’s Talk

19. 14-Oct-02MI/RR Dampers - G. W. Foster Longitudinal Damper Works by Modulating Phase of RF Zero Crossing

20. 14-Oct-02MI/RR Dampers - G. W. Foster Damping of Bunch Motion by Modulation of Center of Rotation (RF zero-crossing) on Alternate Half-cycles of Synchrotron Motion

21. 14-Oct-02MI/RR Dampers - G. W. Foster Numerical Examples for Longitudinal Dampers Damping can be made faster by raising V DAMPER and/or lowering V RF

22. 14-Oct-02MI/RR Dampers - G. W. Foster MI Longitudinal Damper- Inputs (Ashmanskas, Foster)  80 Bunch-by-Bunch synchrotron oscillations (Pbar Stacking Cycle) measured with Echotek board & custom firmware TURN NUMBER AFTER INJECTION  BUNCH –BY-BUNCH PHASE (w/offset)

23. 14-Oct-02MI/RR Dampers - G. W. Foster Longitudinal Damper FPGA Logic ADC Resistive Wall Pickup 14 Synchrotron Motion Velocity Filter Bunch-by- Bunch Digital Phase Detector +THRESH -THRESH Multi-Turn Memory Bunch Intensity FIR Filter +THRESH +/- KICK to DAMPER Individual Bunches are kicked + or – depending on whether they are moving right or left in phase

24. 14-Oct-02MI/RR Dampers - G. W. Foster MI Longitudinal Damper Kick Calculated in FPGA Firmware (Ashmanskas, Foster) Single-Bunch Phase Signal Single-Bunch Digital Kick (velocity filter)

25. 14-Oct-02MI/RR Dampers - G. W. Foster What ADC Clock Speed is needed? ~53 MHz Bandwidth limited signal, sampled by 106 MHz ADC, measures either in-phase (cosine) or quadrature (sine) component –but not both ==> ADC clock phasing matters! 212 MHz sampling measures both in-phase and quadrature components. Phasing is not critical to determine vector magnitude. 212 MHz  built in phase measurement

26. 14-Oct-02MI/RR Dampers - G. W. Foster Bandwidth Limit Signal Raw signal has high-frequency components which can cause signal to be missed by ADC – “Aliasing” Bandwidth limited signal (to ~50 MHz) cannot be missed by 106 MHz ADC Eliminate low-frequency ripple, baseline shifts, etc. with Transformer or AC coupling –Digital Filtering can provide additional rejection

27. 14-Oct-02MI/RR Dampers - G. W. Foster Gaussian Filter - Impulse Response Many implementations, e.g. traversal filter Spreads signal +/-5ns in time so it will not be missed by ADC Reduces ADC Dynamic Range requirement, since spike does not have to be digitized

28. 14-Oct-02MI/RR Dampers - G. W. Foster Gaussian Filter - Doublet Response Filtered Signal can be sampled by 100 MHz ADC Filtered Output Pulse Shape is insensitive to Bunch Length (for Tb < 10ns) Digitized Pulsehight is “A - B”

29. 14-Oct-02MI/RR Dampers - G. W. Foster Gaussian Filter - Pulse Train Response Filter Output is good sine wave independent of bunch length “A - B” still gives good bunch-by-bunch measurement Can digitally average over many bunches in a batch to get lower noise

30. 14-Oct-02MI/RR Dampers - G. W. Foster In-Phase and Quadrature Sampling “A - B” gives bunch-by-bunch “in-phase” signal Vector Sum sqrt(I**2 +Q**2) is insensitive to clock jitter “D - (C+E)/2” gives bunch-by-bunch “out-of-phase” or “quadrature” signal This is the argument for sampling at 2x Nyquist

31. 14-Oct-02MI/RR Dampers - G. W. Foster 2. Transverse Damper in Main Injector 1.Bunch-by-Bunch 53 MHz Injection Damper –Forgive Pbar injection errors caused by AP3… line drift –Simplify & speed up Shot Setup –Eliminate emittance growth due to waveform defect in Accumulator extraction kicker 2.Bunch-by-Bunch 2.5 MHz Injection Damper –Eliminate emittance growth in RR  MI transfers 3.Suppress RW instability for NUMI & FT operation –May also be needed for slip-stacking intensities (Run IIb)

32. 14-Oct-02MI/RR Dampers - G. W. Foster MI/RR Transverse Dampers - Inputs (Ashmanskas, Foster)  Bunch-by-Bunch betatron oscillations (Pbar Stacking Cycle) measured with Echotek board & custom FPGA firmware. FPGA Filter can be reprogrammed for: 53MHz, 7.5MHz & 2.5MHz. Debunched beam, single bunches and bunch trains. BUNCH–BY–BUNCH BEAM POSITION TURN NUMBER AFTER INJECTION 

33. 14-Oct-02MI/RR Dampers - G. W. Foster Transverse Bunch-By-Bunch Dampers - Results (Ashmanskas, Foster)  Damping active for Bunch #43 BUNCH–BY–BUNCH BEAM POSITION TURN NUMBER AFTER INJECTION  …CAN ALSO ANTI-DAMP TO BLOW ANY SELECTED BUNCHES OUT OF THE MACHINE  Anti-Satellite Device

34. 14-Oct-02MI/RR Dampers - G. W. Foster Transverse Bunch-By-Bunch Dampers - Results (Ashmanskas, Foster)  Pickup Signal from Bunch #43 BUNCH–BY–BUNCH BEAM POSITION TURN NUMBER AFTER INJECTION  Damping kick shared for Bunches #41 - #51

35. 14-Oct-02MI/RR Dampers - G. W. Foster Three-Turn Filter for Transverse Damper Damper kick is calculated from single BPM position reading on 3 successive turns. Arbitrary Betatron Phase of Kicker can be accommodated

36. 14-Oct-02MI/RR Dampers - G. W. Foster HERA-P Damper uses a 3-turn Digital FIR Filter Klute, Kohaupt et. al. EPAC ‘96

37. 14-Oct-02MI/RR Dampers - G. W. Foster 3 Turn Filter Coefficients Damper kick is weighted sum of beam positions on the 3 previous turns. 3 Filter Coefficients Uniquely Determined by: –System Gain –Betatron Phase Desired at Kicker –Constraint that sum of filter coefficients = 0 (so that filter does not respond to DC offsets.)

38. 14-Oct-02MI/RR Dampers - G. W. Foster Transverse/ Injection Damper FPGA Logic (single pickup with 3-turn filter) ADC Pickup 14 Stripline Kicker Power Amp. 106 MHz > 27 MHz ADC Gain Balance FIR Filter 1-turn Delay 1-turn Delay 1-turn Delay Weighted Sum for Arbitrary Betatron Phase Standard BPM Processing3 - Turn Filter Optional Pre-compensation Filter for Cable DAC

39. 14-Oct-02MI/RR Dampers - G. W. Foster Narrow band vs. Wide band Dampers In some cases instabilities only occur with specific frequency and mode patterns in ring Dealing specifically with those modes lowers the required kicker power and reduces noise. A wide band (bunch-by-bunch) damper can use digital filtering to provide higher gain for specific mode patterns (  lower power amp.) Many digital filters can operate simultaneously inside some device -- ADC and DAC are shared The flexibility of Digital Filtering inside the FPGA is a major advantage of this approach.

40. 14-Oct-02MI/RR Dampers - G. W. Foster 3. Recycler Transverse Injection Dampers 2.5 MHz Bunch-by-Bunch Injection Damper  Reduces load on Recycler Stochastic Cooling system Eliminate Emittance Growth from Pbar injection errors caused by AP3 line drift Eliminate emittance growth due to waveform defect in Accumulator extraction kicker Simplify & Speed up Accumulator  RR Transfers –Will take place every ~30 mins in Run IIb

41. 14-Oct-02MI/RR Dampers - G. W. Foster Differences between Recycler and MI Dampers RR dampers will track 4 bunches (vs. 588 in MI) RR signals will have 21 samples/bunch (vs.5) RR firmware will provide ACNET registers representing the Amplitude, Phase and Bunch length of each of the 4 bunches. RR firmware will also provide registers for phase and amplitude of stacked DC beam.

42. 14-Oct-02MI/RR Dampers - G. W. Foster 106 MHz Digitization of the Recycler signals is overkill, but allows the same hardware to be used in MI & Recycler

43. 14-Oct-02MI/RR Dampers - G. W. Foster 4. Recycler Longitudinal Damper Bunch-by-Bunch 2.5 MHz Injection Damper Eliminate Emittance Growth from Pbar injection mismatches caused by Phase and Energy errors –Reduces load on Recycler Stochastic Cooling system Simplify & Speed up Accumulator  RR Transfers –Will take place every ~30 mins in Run IIb THE IMPORTANCE OF THIS DAMPER DEPENDS ON THE PERFORMANCE OF THE RECYCLER STOCHASTIC COOLING

44. 14-Oct-02MI/RR Dampers - G. W. Foster 5. Recycler Transverse Dampers Instability Control Damper to Suppress Possible Transverse Instabilities of Debunched (DC) Beam in Recycler These instabilities have been seen in Accumulator but not yet in Recycler. Low-noise pickup w/hybrid & preamp in tunnel 1-3 Turn Digital delay filter using Echotek board Kicker amplifier has low power requirement <~20W