# Presentation: 682585

## Design Considerations for Antiproton Stacking and Cooling

- Dave McGinnis
- February 4, 2003
- Accelerator Advisory Committee Meeting

## Outline

- Parameter Goals
- Antiproton Stacking Process
- Issues
- Key Parameters
- Study Plan
- Summary

## Parameter Goals

- Goals
- Average Stacking Rate 40x1010 pbars/hour
- Stack at this rate for at least 12 hours
- Final Stack Parameters
- Size = 625x1010 pbars
- Transverse emittance < 15-mm-mrad (95% normalized)
- Longitudinal emittance < 50 eV-Sec
- Inputs
- Recycle 200x1010 pbars/store
- Transverse emittance = 30-mm-mrad (95% normalized)
- Longitudinal emittance = 160 eV-Sec
- Collect 280x106 antiprotons from the target every 2 seconds
- Transverse emittance = 35-mm-mrad (95% **un-normalized**)
- Momentum Spread = 4%
- Bunch lengths < 1.5 nS

## Antiproton Stacking Process

- Debuncher Bunch Rotation
- Exchange
- Large Momentum spread of 4% (360 MeV)
- Short bunches < 1.5 nS (95%)
- For
- Small momentum spread of 0.4%  (36 MeV)
- Coasting beam
- Debuncher Cooling
- System Configuration
- Liquid Helium front end (Teff=30K)
- Bandwidth = 4-8 GHz Subdivided into 4 bands
- Available kicker power
- 2400 Watts/ plane (transverse)
- 4800 Watts (momentum)
- Cooling Rate Specs.
- Momentum: 36 MeV to 6 MeV in 1.9 Seconds
- Transverse: 35-mm-mrad to 5 -mm-mrad (95% un-normalized) in 1.9 seconds

## Antiproton Stacking Process

- Accumulator Stacktail Cooling
- Process
- Beam is injected onto the Injection Orbit
- Beam is
- Bunched with RF
- Moved with RF to the Stacking Orbit
- Debunched on Stacking orbit
- Stacktail pushes  and compresses beam to the Core orbit
- Core Momentum system gathers beam from the Stacktail
- Accumulator Transverse Core Cooling system cools the beam transversely in the Stacktail and Core

## Antiproton Stacking Process

- Accumulator Stacktail Cooling
- Specifications
- Injection pulse width: 6 MeV
- Stacktail:
- Bandwidth  = 2-6 GHz
- Width  = 42 MeV
- Gain slope = 8 MeV (can handle 90x1010pbars/hr)
- Power = 550W into 6400
- Core momentum
- Bandwidth =  4-8 GHz
- Aperture  = 9.6 MeV
- Gain slope = 5 MeV (can handle 90x1010pbars/hr)
- Stacksize = 34x1010pbars
- Extraction
- Longitudinal emittance: 10eV-sec
- Transverse emittance 1.0-mm-mrad
- Stacking interval: 30 minutes
- Transfer size: 22.5x1010pbars

## Antiproton Stacking Process

- Recycler Electron Cooling
- Prior to end of store 570x1010pbars at 50 eV-Sec and 1-mm-mrad stored in Recycler
- 200x1010 pbars recycled from TEV in 160 eV-Sec (1.5 x 36 x 3eV-Sec) and 3-mm-mrad
- Transfer 570x1010pbars in 50 eV-Sec and 1-mm-mrad to the TEV
- Transverse stochastic cool for 2 hours to bring transverse emittances below 1.5-mm-mrad
- Turn on electron cooling and cool at a rate of 55eV-Sec/hour and 0.24-mm-mrad/hour
- Every 1⁄2 hour accept 22x1010pbars in  1.5 x 10 eV-Sec and 1.5 x 1-mm-mrad phase space

## Issues

- Debuncher Bunch Rotation
- Momentum cooling aperture
- Momentum Cooling rate is supposed to be very fast (0.2 Sec)
- Momentum spread after bunch rotation must be less than the momentum aperture of the Debuncher Momentum Cooling system

- X=precentage spread of Schottky band
- Fmax = 8.2 GHz, x =1/3 requires p/p<0.4%
- Bunch length < 1.5 nS
- Main Injector Coupled Bunch modes

## Issues

- Debuncher Transverse Cooling
- Power Limited
- Cooling Rate
- Calculations done for 400x106 pbars in 25-mm-mrad give 1 sec cooling rate
- Scaling (good signal/noise) give 1 sec cooling rate for 280x106 pbars in 35-mm-mrad
- Final emittance is 6 which gives 85% into 5 aperture.
- Need 25% more power to get to 5 emittance

- Power Leveling
- Beam cools – power will drop – increase gain
- Increase gain linearly by 25% in 2 seconds
- Achieve 5-mm-mrad
- Final power level rises from 225W to 270W
- Common mode rejection
- Pbeta>10xPlong
- Alignment: d< 1.5 mm
- Phase Imbalance <1.5 degrees

## Issues

- Debuncher Momentum Cooling
- Uses filter cooling
- Large asymptotic momentum spread
- Good Signal/Noise
- Band to Band alignment
- Tnotch< 1ps
- Notch filter dispersion
- rms < 2 degrees
- fnotch < 0.4 Hz
- Slow Cooling Rate
- Calculated Cooling rate = 0.2 Sec
- Necessary cooling rate = 0.85 sec
- Measured cooling rate = 2 sec
- Caused by notch filter Dispersion?
- Need to develop model that includes dispersion.

- Time (secs)

## Issues

- Stacktail Momentum Cooling
- Design margin for flux = 90x1010pbars/hour
- Optimum profile that maximizes d/dE is exponential

- Large Ed needs a large momentum aperture or results in a low final core density
- The best way to increase flux is to increase the bandwidth

## Issues

- Stacktail Momentum Cooling
- Energy Aperture and Stability
- Would like energy aperture as big as possible to get a large core density
- Stacktail uses Notch Filters to shape gain near core
- For system stability, operate at frequencies where Schottky bands do not overlap
- Strategies
- Reduce 
- Increases  functions – decreases aperture
- Increases intra-beam scattering heating
- Reduce momentum aperture of cooling system
- Core Momentum system with higher bandwidth
- Energy aperture of core is limited by “bad” mixing between pickup and kicker at high frequencies

## Issues

- Stacktail Momentum Cooling
- Core Density and Stacking Interval
- Particles to be transferred must be inside desired Recycler longitudinal emittance
- Desire long stacking interval
- Small Debuncher energy spread Ebd
- Large energy aperture Es+Ec
- Small characteristic energy slope (Ed)
- Stacktail Power

## Issues

- Stacktail Momentum Cooling
- Design examples

## Issues

- Stacktail Momentum Cooling
- Design examples
- 2-4 GHz
- extremely short stacking intervals
- Requires large amount of power
- Proven design
- 4-8 GHz
- longest stacking intervals for small Debuncher momentum spreads
- Small energy aperture
- Difficult pickup design in high dispersion
- 2-6 GHz system
- Moderate stacking intervals for small Debuncher momentum spreads
- 4-8 Core system makes substantially higher intervals and core densities
- Moderate energy aperture
- Proven pickup design in high dispersion
- Large fractional bandwidth
- Multi-band system

## Issues

- Accumulator Transverse Cooling
- Cool 5-mm-mrad beam at injection to 1.5-mm-mrad beam at core
- Use present 3 band 4-8 GHz core system with bandwidth of 3.5 GHz
- Particles see wide range of densities on the way to the the Core

- Cooling

- Heating from other particles

- Noise

## Issues

- Accumulator Transverse Cooling
- Gain > gopt at core results in lower emittance because heating term is not important until particles arrive at the core.
- Emittance < 1.0-mm-mrad at core
- No heating in Stacktail assumed
- No margin assumed on bandwidth

## Issues

- Recycler Electron Cooling
- Design process
- Decide on whether to do longitudinal cooling and/or betatron cooling
- Longitudinal cooling rate independent of  function
- Important for the Recycler
- Transverse cooling rate proportional to 1/2
- Not as important for the Recycler
- Design for minimum angular spread in electron beam
- Cooling section solenoid field quality
- Aberrations in the beamline
- Stability of the antiproton orbit
- Stability of the electron optics
- Emittance and space charge
- Stray magnetic fields
- Decide on reasonable emittance range  for optimum cooling
- Design electron beam size

## Issues

- Recycler Electron Cooling
- Design Specs.
- Emphasis on longitudinal cooling
- Angular spread of electron beam = 0.1 mrad
- Design cooling for transverse emittance of 1.5-mm-mrad with =30m
- Electron beam size = 6 mm
- Cooling rate
- 22 eV-s/hr per 100 mA of electron current
- 0.12  mm mrad/hr per 100 mA of electron current

## Issues

- Recycler Stochastic Cooling
- Needed to transversely cool “hot” recycled antiprotons from 3.0-mm-mrad to 1.5-mm-mrad in 2 hours.
- Bad mixing from pickup to kicker limit the maximum frequency of cooling system to 4 GHz
- Tbarrier > 6.6us for 4 GHz with L=160 eV-Sec
- Cooling rate proportional to bandwidth and center frequency
- Effective number of particles modified by the beam pulse length
- Cooling rate is 1.3 hours for 2-4 GHz, 200x1010 pbars in 160 eV-Sec

## Key Parameters

## Key Parameters

## Key Parameter Comparison

## Key Parameter Comparison

## FY03 Cooling Upgrades

- Debuncher Momentum Notch Filter Equalizer Upgrade
- Debuncher Transverse Notch filters for Bands 1 & 2
- Accumulator Transverse Core Cooling Equalizers
- Accumulator Stacktail Momentum Transverse  Compensation Upgrade
- Commission 4-8 GHz Accumulator Core Momentum system for stacking

## FY06 Cooling Upgrades

- 4-6 GHz Band in Stacktail
- Recycler Electron cooling
- Accumulator Stacktail betatron cooling (subject to  outcome of beam studies)

## Beam Studies

- Debuncher Bunch Rotation
- Experimentally verify the calculations of the final momentum spread as a function of proton bunch length
- Debuncher Transverse Stochastic Cooling
- Document the cooling rate for a given starting emittance, power level, and number of particles for each band and all bands together.
- Measure the signal to noise of each band for a given emittance and beam current and determine pickup impedance
- Measure the common more rejection tolerances of each band
- Debuncher Momentum Stochastic Cooling** **
- Develop Fokker-Plank Computer simulations to account for dispersion properties of notch filters** **
- Measure cooling rate and dispersion for each band and compare to simulations
- Measure the signal to noise of each band for a given momentum spread and beam current
- Measure the momentum aperture of the cooling system

## Beam Studies

- Accumulator Stacktail Momentum Stacking
-  Measure signal to noise and determine impedance of the Stacktail pickups, Core Momentum 2-4 GHz Pickups, and Core Momentum 4-8 GHz pickups
- Characterize the beam transfer function as a function of energy for the Stacktail system, the Core 2-4 GHz
- Develop detail Fokker-Plank model based on measurements
- Measure Stacktail pulse evolution as a function of initial distribution intensity, width, and position. Compare to model
- Measure zero stack Stacktail profile evolution as a function of initial distribution and pulse repetition rate. Compare to model

## Beam Studies

- Accumulator Transverse Cooling
- Measure signal to noise and determine impedance of core transverse pickups.
- Document beam transfer function measurements at the core.
- Measure cooling rate as a function of stack size and system gain. Measure and subtract natural emittance growth of the accelerator from cooling measurements.
- Recycler Stochastic Cooling
- Measure signal to noise and determine impedance of transverse and longitudinal pickups.
- Document beam transfer function measurements.
- Measure cooling rate as a function of stack size and system gain. Measure and subtract natural emittance growth of the accelerator from cooling measurements.

## Summary

- We have a design on paper in which all the parameters mesh
- In reality, we have a number of systems where we would like to improve the design margin
- Debuncher Cooling
- Momentum System
- dominated with dispersion in filters
- Momentum width is a key parameter for
- Stacktail
- Debuncher Bunch rotation
- Transverse Systems have tight constraints on common mode rejection
- Accumulator Transverse Cooling
- Just meets spec.
- No account of Stacktail heating
- Electron Cooling
- Design current dominated by recycling parameters
- Hinges on performance of Recycler
- Backup plan?
- Upgrades identified
- 4-6 GHz band for the Stacktail Momentum system
- Low dispersion notch filters for the Debuncher Momentum system
- Common mode rejection upgrade for the Debuncher transverse system
- Stacktail betatron cooling