Beam Dampers for Main Injector and Recycler Bill

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

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

Damper Operating Modes Booster Main Inj. Recycler Tevatron Pbar 53 MHz Full Batches P Pbar P X X 53 MHz Short Batches X X 53 MHz Coalesced Bunch X X 2. 5 MHz Batch (4) X C 7. 5 MHz Batch (12) X C DC Beam X = Operation 14 -Oct-02 Pbar P X X C X C c = Commissioning & Tuneup MI/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. 14 -Oct-02 MI/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. 14 -Oct-02 MI/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 (& Te. V? ) dampers, etc. ) 14 -Oct-02 MI/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 14 -Oct-02 MI/RR Dampers - G. W. Foster

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

Echotek Card Used for Dampers 105 MSPS AD 6645 • Prieto, Meyer et. al. evaluating 65 MHz DDC for RR BPM upgrade • Asmanskas, Foster, Schappert testing 105 MHz version for RR Dampers 14 -Oct-02 MI/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 14 -Oct-02 MI/RR Dampers - G. W. Foster

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

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

MI/RR Transverse Dampers (Ashmanskas, Foster) BUNCH–BY–BUNCH BEAM POSITION ¬Bunch-by-Bunch betatron oscillations (Pbar Stacking Cycle) measured with Echotek board & custom FPGA firmware. • Single board needed for: TURN NUMBER AFTER INJECTION 14 -Oct-02 • Bunch-by-bunch longitudinal & two transverse dampers. • 53 MHz, 7. 5 MHz & 2. 5 MHz. • Debunched beam, single bunches and bunch trains. MI/RR Dampers - G. W. Foster

“Universal-Damper” Application: Signal Processing Steps (transverse) Echotek Board Inside FPGA Buy 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 14 -Oct-02 MI/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 14 -Oct-02 MI/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 ! (x 1. 5 stack rate? ) – Slip-Stacking etc. (Run IIb) will require stable bunches 3. Needed for eventual NUMI operation 14 -Oct-02 MI/RR Dampers - G. W. Foster

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

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

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

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

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

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

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

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

In-Phase and Quadrature Sampling “A - B” gives bunch-by-bunch “in-phase” signal “D - (C+E)/2” gives bunch-by-bunch “out-of-phase” or “quadrature” signal Vector Sum sqrt(I**2 +Q**2) is insensitive to clock jitter • This is the argument for sampling at 2 x Nyquist 14 -Oct-02 MI/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 AP 3… 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 – 14 -Oct-02 May also be needed for slip-stacking intensities (Run IIb) MI/RR Dampers - G. W. Foster

MI/RR Transverse Dampers - Inputs (Ashmanskas, Foster) BUNCH–BY–BUNCH BEAM POSITION ¬Bunch-by-Bunch betatron oscillations (Pbar Stacking Cycle) measured with Echotek board & custom FPGA firmware. • FPGA Filter can be reprogrammed for: • 53 MHz, 7. 5 MHz & 2. 5 MHz. • Debunched beam, single bunches and bunch trains. TURN NUMBER AFTER INJECTION 14 -Oct-02 MI/RR Dampers - G. W. Foster

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

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

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

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

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

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. 14 -Oct-02 MI/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 AP 3 line drift • Eliminate emittance growth due to waveform defect in Accumulator extraction kicker • Simplify & Speed up Accumulator RR Transfers – 14 -Oct-02 Will take place every ~30 mins in Run IIb MI/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. 14 -Oct-02 MI/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 14 -Oct-02 MI/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 14 -Oct-02 MI/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 <~20 W 14 -Oct-02 MI/RR Dampers - G. W. Foster