# Presentation: 820616

## Stochastic Stacking for Run IIb

- 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)
- Last Presentation (17 Sept 01):  ~50 mA/hour design
- AAC Meeting (12 Dec 01):  ~70 mA/hour design

## 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

## Schematic diagram of stacktail electronics

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

## Design Specs

- Design 1:  vary transverse aperture
- Gain ~ e-(π∂x/d) where d is transverse aperture
- Ed ~ d for our model
- 1.6x wider, needed lots of power to account for loss of sensitivity
- ~50 mA/hour

- Design 2:  vary pickup position
- Keep same transverse aperture, vary sum to vary Ed
- Move pickup locations a few mm, change relative gains and phases
- ~75 mA/hour for 30 minutes
- ~70 mA/hour with transfers every 15 minutes

- Both designs limited by how well move beam off deposition orbit!

## 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

## Simulation Performance6 MeV bucket

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

## Single Pulse Evolution Analysis

- Study how beam moves off the deposition orbit:
- Single pulses into the Accumulator
- Use 79 MHz longitudinal Schottky & VSA
- Start when beam is dropped off, follow for ~9 seconds
- Traces at 5 Hz, 3x average
- For 5 gain settings:
- Nominal Stacktail settings
- ±3 dB
- ±6 dB

## Nominal Settings

- Calculate noise floor, then mean, RMS, & power in pulse
- Mean with respect to Accumulator Central Frequency (628840 Hz)
- RMS at the fundamental
- Actually got 2 pulses on this one

## 5 data sets

- -6 dB
- -3 dB
- Nominal
- +3 dB
- +6 dB

## Simulation data sets

- -6 dB
- -3 dB
- Nominal
- +3 dB
- +6 dB

## Data and Simulation

## RMS Behavior

- Expect profile to become exponential in form
- RMS grows initially asymmetric
- As density increases, asymmetry decreases
- Simulation at times
- T=1 second
- T=2 seconds
- T=9.5 seconds

## Losing beam?

- -6 dB
- -3 dB
- Nominal
- +3 dB
- +6 dB
- Lose about 2 dB
- From start to end?

## Losing Beam?

- ~20% lower integrated power after 9 seconds
- In 4 of the 5 traces (-6 dB trace is ~constant)

## RF Phase Displacement

- Put 0.5 mA at 628830 (nominal deposition orbit)
- Triggered 1 ARF1 stacking cycle

- Initial and Final distribution in data

## Data and Simple Model

- Simple model:
- F<628830, displace by bucket height
- F>628830, displace fraction by bucket height (from 1 to 0 at edge of bucket)

- Data and Model distribution

## Two ARF1 cycles!

- ???

- Data and Model distribution

## What I am working on

- Pulse evolution & RF Phase displacement measurements:  list of things to measure when opportunity arises
- New system designs to gain margin:
- Increase bandwidth (4-8 GHz)
- New pickup design:  estimate ~1 year development time or more?
- increase bandwidth (2-4 GHz + 4-6 GHz)
- Use current 2-4 GHz and 4-8 GHz (which are really more like 4-6 GHz)