# Presentation: 775855

## Stochastic Cooling for Run IIb

- Upgrade to handle increased flux
- Design Goals
- flux 80 mA/hour
- Recycler cooling requires  ≤ 10 eV-sec, 15  every 15 minutes
- Assumptions:
- Recycler final repository for anti-protons
- Stochastic cooling performance degrades with increasing density
- Electron cooling performance improves with increasing density
- Optimize for maximum flux
- Not maximum momentum density!
- Frequent transfers from Accumulator to Recycler (<30 minutes between transfers)
- Dependent upon incoming longitudinal phase space

## Stacking terminology

- Stacking cycle:
- Accelerate to 120 GeV in MI
- Extract to target
- Transport  8 GeV to Debuncher
- Debunch and stochastically cool
- Inject beam into Accumulator
- RF decelerate to deposition orbit
- ~2 sec cycle
- Stacktail cooling moves beam to core

## Longitudinal Phase Space

- From MI to Debuncher
- Slip stacking at 8 GeV:  0.3 eV-sec
- At 120 GeV:  0.35 eV-sec
- ESME simulation of MI Bunch rotation with 0.35 eV-sec:
- t = 809 psec (95%)
- E/E = 0.185% (95% 1/2 width)
- Beam transport after target:
- ±2% acceptance into Debuncher

- Debuncher to Accumulator
- Debuncher Bunch Rotation:
- E/E = 0.134% (95% 1/2 width)
- E = 12 MeV
- Debuncher Cooling Upgrades for Run IIa designed to meet IIb goals
- Momentum Cooling Models:
- Moment method calculations (which agree well with simulation model)
- Predict 6 MeV half width
- ESME simulations of RF deceleration preserve width

## Debuncher Bunch Rotation

- Momentum width in Debuncher after bunch rotation not too dependent upon MI longitudinal emittance -- dominated by non-linear rotation in Debuncher

## Stochastic Stacking

- Simon van Der Meer solution:
- Constant Flux:
- Solution:
- Exponential Density Distribution generated by Exponential Gain Distribution
- Max Flux = (W2||*E**d*)/(f0p ln(2))

- Using log scales on vertical axis

## Flux for current stacktail

- Fit in stacktail region
- Calculate maximum flux based on slope
- 2-4 GHz bandwidth
- = 0.012

- 37.5 ± 2.5 mA/hour
- Stack rate ~3 mA/hour
- Data of 1 Aug 01
- Achieved 10 mA/hour about 2 weeks later

## Creating Exponential Gain Distribution

- Current intercepted by pickup
- Locate pickups in region of high dispersion
- As particles at different energies have different flight times but electronics delays constant
- Location of pickups, relative gain, relative phase to give proper gain shape

## Schematic diagram of stacktail electronics

- All parameters (except loop
- positions) easily variable
- via control system

## Design Goals, Specifications and Challenges

- Goals:
- Input flux of 80 mA/hour
- 30 minutes
- >95% efficiency

- Specifications:
- 2 second cycle time (slip stacking and NUMI)
- 6 MeV bucket height at h=84

- Challenges:
- Finite momentum aperture:
- constant flux has to be ‘stopped’ and accumulated at some point
- Maximum density
- Transient input:
- Pulses every 2 seconds
- Move beam off deposition orbits

## Input Longitudinal Phase Space

- Moving beam off deposition orbit depends on:
- Gain:  more efficient at higher gain
- Cycle time:  more efficient with longer cycle time
- Beam width:  more efficient with smaller width (assuming completely full buckets)
- Constraints:
- Gain:  power and matching
- Cycle time:  longer cycle, less total flux
- Beam width:  Debuncher cooling performance

- 6 MeV
- width

- 8 MeV
- width

## Gain Constraints

- Match stacktail gain to core gain to preserve gain slope
-  is local beam density
- F is local kicker voltage
- Cooling term  F
- Diffusive beam heating F2 
- As density increases (core), necessary to decrease kicker voltage (system gain) so that cooling term > diffusive heating term
- Maximum gain for given stack size

## Design and Simulation Performance

- Design:
- Leg 1 pickup at 15 MeV
- (Run IIa:  16 MeV)
- Leg 2 pickup at -8 MeV
- (Run IIa:  0 MeV)
- Gain and phase adjustments
- Core centered at -52 MeV
- (Run IIa:  -50 MeV)
- p = 1 MeV  ̨x = 0.9 mm

- Simulation of 30 minutes:
- ~82 mA/hour input
- 6 and 8 MeV buckets
- 2 second cycle time
- Dropoff at 13.6 MeV (could be optimized)
- RF phase displace all beam from dropoff + height by 2*height

## Simulation Performance8 MeV bucket

- Mean Rate:	64.3 mA/hour
- Efficiency:	79%
- Mean Power:	1853 W

## Simulation Performance6 MeV bucket

- Mean Rate:	75.7 mA/hour
- Efficiency:	92.7%
- Mean Power:	1150 W

## Conclusions

- Bunch Rotation and Debuncher momentum cooling can achieve necessary momentum width
- Stack 75 mA/hour for 30 minutes with 2 sec rep rate and 6 MeV width
- Simulate 15 minutes to extraction, 30 seconds to perform extraction

| Time (minutes) | mA in 10 eV-sec | Transfer rate (mA/hour) | Total Transferred (mA) | Average rate (mA/hour) |
| --- | --- | --- | --- | --- |
| 15.5  | 10.24 | 39.6 | 10.24 | 39.6 |
| 31 | 14.99 | 58.2 | 25.23 | 48.8 |
| 46.5 | 15.98 | 61.9 | 41.21 | 53.2 |
| 62 | 16.78 | 64.9 | 57.99 | 56.1 |
| 77.5 | 19.1 | 73.9 | 77.09 | 59.7 |
| 93 | 14.8 | 57.3 | 91.9 | 59.3 |
| 108.5 | 19.1 | 73.9 | 111 | 60.8 |
| 124  | 17.8 | 68.8 | 128.8 | 62.3 |

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