# Presentation: 512845

## Intensity Increase in the LER Tanaji SenFNAL

*** ***
*** ******Motivation***
*** ******Slip stacking in the Main Injector***
*** ******Constraints on LER slip stacking***
*** ******Preliminary slip stacking simulations (ESME)***
*** ******Preliminary conclusions***

- _Intensity Increase in the LER_ Tanaji SenFNAL

- Special thanks to Jim MacLachlan (FNAL)

## Motivation

-  SPS upgrade - allows an increase in injection energy and intensity.
-  LER -  increases the injection energy. Intensity?
*Intensity Increase*
-  SPS is intensity limited to the present value due to impedances, electron cloud, space charge, ...
-  LHC is very sensitive to beam losses, rules out the possibility of intensity increase in the LHC.
-  Is it possible to increase the bunch intensity in the LER ?
*Benefit*
-                            Luminosity ~ M Nb2

## Methods to increase bunch intensity

*Bunch coalescing*
-    Used to coalesce 2 or more bunches in adjacent buckets. The LHC bunch structure has a 10 bucket gap between bunches – lots of “white space” to be filled in
-  *Momentum stacking*
-     Used in the Accumulator to increase pbar intensity. Requires a large momentum aperture – beam is injected away from the reference orbit and then accelerated to the reference orbit.
-  *Slip stacking*
-    Used in the FNAL Main Injector. 2 batches at slightly different energies are brought together into 1 batch.

## Slip stacking schematic

- Stage 2 - slipping

- Stage 3 – reduce
- energy difference

- Stage 4 – recapture
-  in larger bucket

- Energy E1

- Energy E2 < E1

- Stage 1
- Raise batch 1: E0     E1
- Lower batch 2: E0     E2

- Batch 2

- Batch 1

## Frequency Curves - FNAL Main Injector

- K. Seiya, I. Kourbanis

- Frequency
- Separation
-  ~ 5 fs

## Losses during slip stacking (FMI)

- K. Seiya, I. Kourbanis

## Beam capture in the FMI

- K. Seiya, I. Kourbanis

- Tomographic reconstruction

## Constraints on slip stacking in the LER

-  Beam can be injected only once from the LER into the LHC – rings are Siamese Twins
-  Slip stacking can be done only at injection energy – batches have to be at different energies
-  The two beams must have different rf systems in the LER
-  Second beam has to be slip stacked while the first beam is circulating – constraints on aperture in the common areas
-  Losses in the LER must be absorbed in the LER

## Slip stacking in the LER

-  2 adjacent batches will be slip stacked.
- Assume: same bunch structure as at present. 234 bunches per batch, 10 bucket spacing between adjacent bunches and 38 bucket spacing between batches.
-  1st batch: accelerate to slightly higher energy.
-  2nd batch: decelerate to slightly lower energy.
-  Time for the 2nd batch to catch up with the 1st batch
-                                tslip = Δt/(η ΔE/E)
-  Δt = time interval from 1st to 2nd batch, ΔE/E= relative energy difference between batches.
-  During the slipping both rf systems act on both batches – energy separation should be large to minimize impact but needs to be chosen carefully.

## Energy difference between batches

-   Larger ΔE reduces
-     - the slipping time
-     - the interference of other rf system
-     - beam-beam forces between beams. But these are small at high energy ~ 1/γ3
-   But larger ΔE increases
-     - the required aperture of machine
-     - the emittance growth after recapture.
- Recapture process
-    Emittance growth and possibly beam loss can occur if voltages, energy difference and time for recapture are not properly chosen.

## Parameters for ESME simulations

| PARAMETER |  |
| --- | --- |
| Injection Energy in the LER
Longitudinal emittance (95%)
Initial rf voltage
Rf frequency
Bucket Area
Bunch spacing
Batch length
Batch spacing
Synchrotron frequency
Slip factor
Energy difference during slipping
Slipping time  |  450 GeV
 0.7 eV-sec
 2.7 MV
 400 MHz 
0.83 eV-sec
25 nano-sec
234 bunches or 6.4 μsec
38 buckets or 95 nano-sec
37 Hz
3.18 x 10-4
1.8 x 10-3 (rel)/ 0.81 GeV (abs) 
11.3 sec (between consecutive batches) |

## LER RF frequency curve

- Estimate required momentum aperture ΔE/E~1.8x10-3 if n=6
- RF voltage could be decreased while bunches are slipping to reduce interference
- Final capture voltage depends on energy difference.

## Slipping at constant energy difference

- Start of slipping

- Time

- End of slipping

- ESME simulation

- Frequency separation = 6fs

## Capture of both bunches

- ESME simulation

## Movie of Slipping and Capture

## Capture Voltage and Initial Emittance

-  Present emittance is sufficient if the final separation can be 4 fs
- Losses increase with smaller separation
- Emittance of captured bunch increases with larger separation
-  Larger capture voltage increases final emittance.

##  Losses, Emittance vs Capture Voltage

-  Loss results are **very** preliminary – intended only to show variation with Vrf. This level of losses is **not** acceptable.
-  Largest fraction of losses occur as beams are brought closer just before recapture
-  Better control of the rf phases will reduce losses - losses in FMI < 7%

## Filling the LER and Slip stacking

-  Inject 12 batches from the SPS into the LER at reference energy
-  Accelerate these batches to ΔE. These batches will slip before next SPS injection
-  Inject the next 12 SPS batches at reference energy
- Decelerate both sets of 12 batches by 0.5 ΔE. Batches will be slip at constant energy difference.
- Capture when batches are aligned.

- 1

- 2

- 12

- 12 batches, gaps not shown

- Abort

*Adapted from proposed slip stacking in Recycler (I. Kourbanis)*

## Slip stacking Issues

-  Beam loading compensation
-  Instabilities during recapture. Intensity limits in LER.
-  Final emittance after recapture – resulting requirement of capture voltage in the LHC
- Time taken to inject and slip stack both beams in the LER
-  Robustness of the LER to losses – what fraction of the beam can be lost without quenching?
-  Shorter batches from the SPS would reduce the slipping time. This needs to be balanced against the total number of bunches – gaps are limited by the injection kicker rise and fall time.

## Preliminary Conclusions

-  The likely robustness of the LER to beam loss makes it a candidate to consider increasing the intensity in this machine.
- Slip stacking will have to be done at injection energy.
- Preliminary simulations show that there is little emittance increase during slipping and the beam loss during slipping is not excessive if frequency separation is kept at 6 fs.
- The capture process requires detailed simulations and reducing losses.
- Capture voltage of 16MV is sufficient if the frequency separation between batches just before capture is reduced to 4 fs.
- A possible (plausible?) LER filling scenario with slip stacking will increase the bunch intensity (~2 fold). Luminosity increase Nb2 or ~ 4 fold. Other filling scenarios may be possible.
- Detailed analysis of other slip stacking issues (beam loading compensation, final emittance,...) is necessary.

## Backups

## Horizontal Aperture

-  Relative energy separation = 1.8x10-3
-  Hor. Space between slipping batches = 3.6mm at Dx = 2m
-   Average transverse displacement between beams ~ 15σ.
-  Clearance of ~ 9σ for each beam to limiting aperture
-  Total space required = 33 σ + 3.6mm
-  At βmax = 185m in arc cell,
-      σ = 0.35mm
-  Required space = 15.1mm

- 9σ

- 9σ

- 15σ

## Mechanics of momentum stacking

- Circulating beam on central orbit
- Inject beam onto off-momentum closed orbit. Requires a special kicker
-  Decelerate off-momentum beam to central orbit
- Capture both beams in a larger RF voltage. Dynamics of the final capture process is the same as in slip stacking.

## Filling the LER and Slip stacking

- Alternate scenario
- Inject odd numbered batches 1, 3, .... 11 for the 1st beam from the SPS. Raise energy of these odd batches
- Inject even numbered batches 2, 4, ... 12 from the SPS. Lower energy of these even batches
- Let batches slip until (1,2), (3,4), ... (11,12) align. This assumes spacing between batches is uniform.
- Turn on main RF capture voltage at this time.
- Bunch intensity is doubled, number of bunches is halved, spacing between batches is doubled.
- Repeat process with 2nd beam using its rf system. 1st beam is circulating
- Accelerate both beams to top energy. DC beam from losses at lower energy is dumped in absorbers.
- Extract both beams to the LHC