# Presentation: 177388

## Beam Dampers for        Main Injector and Recycler

- Bill Ashmanskas, Bill Foster, Dave Wildman
- Warren Schappert, Jim Crisp, Dennis Nicklaus
- Oct ‘02

## Wide Variety of Beam Dampers Required in MI & Recycler

- Transverse (X,Y) and Longitudinal
- 53 MHz, 2.5 MHz, 7.5 MHz, and DC Beam
- Single Bunches, Full Batches, Short Batches
- Injection, Ramping, and Stored Beam
- Pbar and Proton Directions (different timing)

## ... plus unbunched DC Beam in Recycler...

*... **plus unbunched DC Beam in Recycler...*

## Damper Operating Modes

**X** = Operation          **c**** **= Commissioning & Tuneup

|  | Booster |  | Main Inj. |  | Recycler |  | Tevatron |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
|  | Pbar | P | Pbar | P | Pbar | P | Pbar | P |
| 53 MHz Full Batches |  | X |  | X |  | C |  |  |
| 53 MHz Short Batches |  |  | X | X |  |  |  |  |
| 53 MHz Coalesced Bunch |  |  | X | X |  |  | X | X |
| 2.5 MHz Batch (4) |  |  | X | C | X | C |  |  |
| 7.5 MHz Batch (12) |  |  | X | C |  |  |  |  |
| DC Beam |  |  |  |  | X | C |  |  |

## 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.

## Difficulties in Maintaining Beam Dampers

- Specialized custom built power amps
- e.g. distributed tube amplifier for Superdampers
- 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.

## 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.)*

## 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

## Generic Dampertolerating frequency sweep 

*FIFO needed due to phase shifts between DAC and ADC clocks *
*as beam accelerates*

*All Logic*
*Inside*
*FPGA*

## Echotek Card Used for Dampers

## 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

## All-Coordinate Damper w/ Echotek Card

- 53 MHz, TCLK, MDAT,...

- 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

- 2-10

## 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)

## 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 

## “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

## Damper Priorities in Main Injector & Recycler

- Main Injector Longitudinal Dampers
- Main Injector Transverse Dampers
- Recycler Transverse Injection Dampers
- Recycler Longitudinal Dampers
- Recycler Broadband (DC Beam) Dampers

## 1.  Longitudinal Damper  in Main Injector

- 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
- Benefits for Pbar Stacking Cycles
- Bunch Rotation is generally turned off !  (x1.5 stack rate?)
- Slip-Stacking etc. (Run IIb) will require stable bunches
- Needed for eventual NUMI operation

## 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***

## Longitudinal Damper Works by Modulating Phase of RF Zero Crossing

## Damping of Bunch Motion by Modulation of Center of Rotation (RF zero-crossing) on Alternate Half-cycles of Synchrotron Motion 

## Numerical Examples for Longitudinal Dampers

*Damping can be made faster *
*by raising V**DAMPER **   and/or  lowering V**RF*

## 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)

## Longitudinal Damper FPGA Logic

- ADC

**ResistiveWall 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*

## MI Longitudinal Damper Kick Calculated in FPGA Firmware(Ashmanskas, 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

- ~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

## 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

## 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***

## 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”***

## 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***

## 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

## 2.  Transverse Damper  in Main Injector

- 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
- Bunch-by-Bunch 2.5 MHz Injection Damper
- Eliminate emittance growth in RRMI transfers
- Suppress RW instability for NUMI & FT operation
- May also be needed for slip-stacking intensities (Run IIb)

## 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.

## Transverse Bunch-By-Bunch Dampers - Results(Ashmanskas, Foster)

- Damping active
-      for Bunch #43

***...******CAN ALSO ANTI-DAMP TO ***
***BLOW ANY SELECTED BUNCHES ***
***OUT OF THE MACHINE***
********* ******Anti-Satellite Device***

## 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

## 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*

## HERA-P Damper uses a 3-turn Digital FIR Filter

*Klute, Kohaupt et. al.   EPAC ‘96*

## 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.)

## Transverse/ Injection Damper FPGA Logic(single pickup with 3-turn filter)

- 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 Processing

- 3 - Turn Filter

- Optional
- Pre-compensation
- Filter for Cable

- DAC

## 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.** *

## 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

## 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.

## 106 MHz Digitization of the Recycler signals is overkill, but allows the same hardware to be used in MI & Recycler

## 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***

## 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