# Presentation: 352591

## Vladimir N. Litvinenko
 C-AD, Brookhaven National Laboratory, Upton, NY, USA

* **C-AD, Brookhaven National Laboratory, Upton, NY, USA*

**Coherent electron cooling for LHC**

- Cooling intense high-energy hadron beams remains a major challenge for accelerator physics. Synchrotron radiation is too feeble, while efficiency of two other cooling methods falls rapidly either at high bunch intensities (i.e. stochastic cooling of protons) or at high energies (i.e. e-cooling). Possibility of coherent electron cooling using instabilities in electron beam was discussed by Derbenev since early 1980's .
- The scheme presented in this talk -with cooling times under an hour for 7 TeV protons in LHC - is a first specific scheme with complete theoretical evaluation of  its performance. The scheme is based present-day accelerator technology - a high-gain free-electron laser driven by an energy recovery linac. I will present some numerical examples for LHC (LHeC) and  discuss a proof-of-principle experiment using R&D ERL at RHIC.

## Conclusions

**Coherent electron cooling is very promising method for significant luminosity increase in LHC (and LHeC)**
**Proof of principle experiment of cooling Au ions in RHIC at ~ 40 GeV/n is feasible with existing R&D ERL**
- Can test conjecture that strong cooling allows for higher beam-beam tune shifts
**Modest LARP efforts** **would be critical for CeC PoP experiment and for testing the LHC-specific aspects of coherent electron cooling**

## In collaboration with Yaroslav S. Derbenev
Thomas Jefferson National Accelerator Facility, Newport News, VA, USA

- In collaboration with Yaroslav S. Derbenev
*Thomas Jefferson National Accelerator Facility, Newport News, VA, USA*

- Inputs from George Bell, Ilan Ben-Zvi, David Bruhwiler, Dmitry Kayran, Eduard Pozdeyev, Frank Zimmerman, John Jowett

- _Collaboration on Coherent Electron Cooling_ includes scientists from BNL, Jlab, BINP (Novosibirsk), FNAL, Dubna, UCLA, TechX, LBNL... open for others: _[http://www.bnl.gov/cad/ecooling/cec.asp](http://www.bnl.gov/cad/ecooling/cec.asp)__Proposed LARP activity will involve BNL, FNAL, Jlab and LBNL __	__	__	__	__	__in collaboration with LHC AP group_

- First paper: Vladimir N. Litvinenko, Yaroslav S. Derbenev, Free-Electron Lasers and High-Energy Electron Cooling, Proc. of 29th International Free Electron Laser Conference, Novosibirsk, Russia, August 2008, _[http://accelconf.web.cern.ch/AccelConf/f07/HTML/AUTHOR.HTM](http://accelconf.web.cern.ch/AccelConf/f07/HTML/AUTHOR.HTM)_**  ***pp. 268-275*_*[http://ssrc.inp.nsk.su/FEL07/proceedings.html](http://ssrc.inp.nsk.su/FEL07/proceedings.html)*_** **

## IntroA bit of historyPrinciples of Coherent Electron Cooling (CeC) Analytical estimationsSimulationsCeC at LHCProof of Principle test using R&D ERL

## from the talk at International FEL  conference, Novosibirsk, Russia, August, 2007And so, my fellow FELers, ask not what storage rings can do for FELs; Ask what FELs can do for your storage rings!

- And so, my fellow Americans, ask not what your country can do for you; ask what you can do for your country.

**Measure of Performance**_**Luminosity**_

**    ****Main sources of luminosity limitation**
**Large emittance**
**Hour-glass effect**
**Crossing angle**
**Beam Intensity & Instabilities**
**Beam-Beam effects**

## CERN – Large Hadron Collider (LHC)

| Time | 2008- |
| --- | --- |
| Circumference, [km] | 26.7 |
| Energy, [TeV] | 7 p2.75/u Pb |
| Particles | p-pPb-Pb |
| Peak luminosity[1034cm-2s-1] | 1(design) |

**e-Cooling at LHC - is it possible to even dream about?**
**It is just 10****10**** times harder that cooling antiprotons in**
**Fermilab recycler; 10****8**** times harder than cooling Au ions in RHIC **

## Cooling of hadron beamswith coherent electron cooling

| Machine | Species | Energy GeV/n | Trad.
Stochastic
Cooling, hrs | Synchrotron radiation, hrs | Trad.
Electron cooling
 hrs | Coherent
Electron
Cooling
hrs |
| --- | --- | --- | --- | --- | --- | --- |
| RHIC PoP | Au | 40 | - | - | - | 0.04 |
| RHIC | Au | 100 | ~1 | 20,961  | ~ 1  | 0.03 |
| RHIC | p | 250 | ~100 | 40,246  | > 30 | 0.8 |
| LHC | p | 7,000 | ~ 1,000 | 13/26 |   | <1 |

| LHC | Pb | 2.75 | ? | ~10 |  | 0.15 |
| --- | --- | --- | --- | --- | --- | --- |

## History possibility of coherent electron cooling was suggested by Yaroslav Derbenev about 26 years ago

- History **possibility of coherent electron cooling** was suggested by Yaroslav Derbenev about 26 years ago

- Y.S. Derbenev, Proceedings of the 7th National Accelerator Conference, V. 1, p. 269, (Dubna, Oct. 1980)
- Coherent electron cooling, Ya. S. Derbenev, Randall Laboratory of Physics, University of Michigan, MI, USA, UM HE 91-28, August 7, 1991
- Ya.S.Derbenev, Electron-stochastic cooling, DESY , Hamburg, Germany, 1995 ..........

## Q: What changed in last 25 years?

**A1. Accelerator technology progressed and ****	**
**energy recovery linacs with high quality e-beam**
**high gain amplification in FELs at ********m and nm wavelengths **
**became reality in last decade**
**A2. A specific scheme and a complete theoretical evaluation (from first principles) had been developed (**vl**) in 2007/2008**
**A3. Most important tolerances on e-beam, hadron beam and lattice had been performed**
**A4. The scheme had been presented at major international forums (FEL’07 and COOL’07), at major accelerator labs (BNL, CERN, BINP, Jlab...) and passed fist test of scrutiny    **

## Coherent electron cooling:ultra-relativistic case (>>1), Start from longitudinal cooling 

**Amplifier of the e-beam modulation via High Gain FEL**

**Modulator:region 1**** about a quarter of plasma oscillation**

**Kicker:  region 2**

**Longitudinal dispersion for hadrons**

**Electrons**

**Hadrons**

**<-       L****1        ****->**

**<-     L****2     ****->**

**Electrons**

**Hadrons**

**<-                L****1                     ****->**

**<-            L****2              ****->**

- Most versatile option

- Most economical option

## Modulator: Interaction region 1Length: about a quarter of plasma oscillation

**Electrons**

**Hadrons**

**Each hadron generates modulation in the electron **
**density with total charge of about minus charge of the hadron, ****Z**

**L****1 ****~ 5 -10 m**

**Modulator: Interaction region 1****Length: about a quarter of plasma oscillation**

- vh

## Longitudinal dispersion for hadrons, time of flight depends on its energy:  (T-To) vo= -D (E-Eo)/Eo

**Longitudinal dispersion for hadrons, time of flight depends on its energy:  (T-T****o****) v****o****= -D (E-E****o****)/E****o**

**Amplifier of the e-beam modulation- a high gain FEL**

**Electrons**

**Hadrons**

**Electron density modulation is amplified in the FEL and made into a train with duration of N****c**** ~ L****gain****/********w ****alternating hills (high density) and valleys (low density) with period of FEL wavelength ********. Maximum gain for the electron density of HG FEL is ~ 10****3.**

**Economic option requires: 2a****w****2 ****< 1 !!!**

## Kicker: Interaction region 2

**Kicker: Interaction region 2**

**Electrons**

**Hadrons**

**A hadron with central energy (****E****o****) phased with the hill where longitudinal electric field is zero, a hadron with higher energy (****E>E****o****) arrives earlier and is decelerated, while hadron with lower energy (****E<E****o****) arrives later and is accelerated by the collective field of electrons **

**<-         L****1         ****->**

**<-      L****2     ****->**

## Analytical formula for damping decrement

- 1/4 of plasma oscillation in the modulator with a clamp of electrons with the charge -Ze is formed at the end
- longitudinal extend of the electron clamp is well within o /2
- gain in SASE FEL* is G ~ 102-103
- electron beam is wider than             - it  is 1D field
- Length of the region 2 is ~ beta-function

- After the FEL charge modulation is  -G*Ze

- i.e. the charge density in CM frame can be written as

**Note that damping decrement:**
**does not depend on the energy of particles ! **
**Improves as cooling goes on**
**Protons in RHIC !!! **
**Tevatron ? LHC ? **

- Longitudinal electric field is the same in the lab and CM frames. Locally:

- CM frame

- Electron bunches are usually much shorter that the hadron bunches and cooling time for the entire bunch is proportional to the bunch-lengths  ratios

## Transverse cooling

- Transverse cooling can be obtained by using coupling with longitudinal motion via transverse dispersion
- Sharing of cooling decrements is similar to sum of decrements theorem for synchrotron radiation damping, i.e. decrement of longitudinal cooling can be split into appropriate portions to cool both transversely and longitudinally: Js+Jh+Jv=JCEC
- Vertical (better to say the second eigen mode) cooling is coming from transverse coupling

- Non-achromatic chicane installed at the
- exit of the FEL before the kicker section
- turns the wave-fronts of the charged planes
- in electron beam

- R260

- Example:

## Effects of the surrounding particles

- Each charged particle causes generation of an electric field wave-packet proportional to its charge and synchronized with its initial position in the bunch

- Evolution of the RMS value resembles stochastic cooling!Best cooling rate achievable is ~ 1/Ñ, Ñ is effective number of hadrons in  coherent sample (**N****c******)

## Four independent parameters to vary:

Initially, we consider the following values:
R=3;  Z=0., 0.2, 0.6;  T=0., 1.8, 5.4

- Initially, we consider the following values:
- R=3;  Z=0., 0.2, 0.6;  T=0., 1.8, 5.4

- Dimensionless variables are used to clarify the physics

## We consider a single ion in a uniform e- distribution
electron velocities are Gaussian, separable,asymmetric
initial electron density is uniform
boundary conditions are periodic (at present)
in future, will try to better emulate semi-infinite plasma

- electron velocities are Gaussian, separable,asymmetric
- initial electron density is uniform
- boundary conditions are periodic (at present)
- in future, will try to better emulate semi-infinite plasma

- ©Tech-X: Courtesy of D.Bruhwiler & G. Bell

**Simulations****Modulator - VORPAL, Kicker - VORPAL ****FEL amplifier - Genesis3 **

## R=3; Z=0; T=0  –  Asymmetry of electron velocity distribution  pancake-shaped wake

- ©Tech-X: Courtesy of D.Bruhwiler & G. Bell

- ©Tech-X

## Observables: example is for F(z) 

**Observables: ****example is for F(z) **

- ©Tech-X

## LHC specific issues

- Energy too high and plasma oscillations are **toooooooooooo slow** - plasma period is 6.9 km!!!!
- Charge ~ (1-cos(pt))~Lmod2
- For 100 m modulator (1-cos(pt))~4 10-3  or loss of factor 250 n cooling!
- Is there a way to make ~100 m inot a useful modualator

## Velocity map & buncher

- z/a

- z/a

- Vz

- ñ

- Buncher

## Exact calculations: solving Vlasov equation

- y

- u

- fel

- For 7 TeV p in LHC CeC case: My simple “gut-feeling” estimate gave 22.9 boost in the induced charge by a buncher, while exact calculations gave 21.7.

## 7 TeV protons in LHC: CeC ~200mPotential of 4x increase in luminosity 

| N per bunch | 1.4 1011 | Z, A | 1,  1 |
| --- | --- | --- | --- |
| Energy Au, GeV/n | 7000 |  | 7460 |
| RMS bunch length, nsec | 0.25 | Relative energy spread | 0.0113% |
| Emittance norm,  m | 3.8 | , m | 47 |
| Energy e-, MeV | 3,812 | Peak current, A | 100 |
| Charge per bunch, nC | 5 | Bunch length, nsec | 0.05 |
| Emittance norm,  m | 3 | Relative energy spread | 0.01% |
| , m | 59 | L1 (lab frame) ,m  | 70 |
| pe, CM, Hz | 2.44 109 | Number of plasma oscillations | 0.0121 |
| D, mm | 3.7 | D, m | 0.17 |
| FEL, m | 0.01 | w, cm | 5 |
| aw | 4.61 | LGo, m | 2.7 |
| Amplitude gain =1000, Lw , m | 61.8 | LG3D, m | 3.9 |
| L2 (lab frame) ,m  | 35 | Cooling time, local, min | 3 minutes |
| Nmin turns  or Ñ in 10% BW | 2 106 >> 2.8 105 | Cooling time, beam | 23 minutes |

## R&D ERL at BNL

- Einj =2.5-.3.5 MeV
- Etotal = 25 MeV, Imax = 0.5 A
- n ~ 2 mm mrad @ 1.4 nC
- Single Loop, SRF Gun
- 5 cell SRF linac, 703.75 MHz

## IR-2 layout for Coherent Electron Cooling

- DX

- DX

-  proof-of-principle experiment

- 19.6 m

- Modulator
- 4 m

- Wiggler 7m

- Kicker
- 3 m

## PoP test using BNL R&D ERL:Au ions in RHIC with 40 GeV/n, Lcooler = 14 m 

| N per bunch | 1 109 | Z, A | 79,  197 |
| --- | --- | --- | --- |
| Energy Au, GeV/n | 40 |  | 42.63 |
| RMS bunch length, nsec | 3.2 | Relative energy spread | 0.037% |
| Emittance norm,  m | 2.5 | , m* | 8 |
| Energy e-, MeV | 21.79 | Peak current, A | 60 |
| Charge per bunch, nC | 5 (or 4 x 1.4) | Bunch length, RMS, psec | 83 |
| Emittance norm,  m | 5 (4) | Relative energy spread | 0.15% |
| , m | 5 | L1 (lab frame) ,m  | 4 |
| pe, CM, Hz | 5.03 109 | Number of plasma oscillations | 0.256 |
| D, m | 611 | D, m | 3.3 |
| FEL, m | 18 | w, cm | 5 |
| aw | 0.555 | LGo, m | 0.67 |
| Amplitude gain =150, Lw , m | 6.75 (7) | LG3D, m | 1.35 |
| L2 (lab frame) ,m  | 3 | Cooling time, local, minimum | 0.05 minutes |
| Nturns, Ñ, 5% BW | 8 106> 6 104 | Cooling time, beam, min | 2.6 minutes |

- PoP test using BNL R&D ERL:Au ions in RHIC with 40 GeV/n, Lcooler = 14 m

## Timeline Both eRHIC R&D and LARP

- Complete CeC theory - 2009
- Start R&D ERL operation in Bldg. 912  - 2009
- Complete fist round of CeC simulations - 2009
**Design CeC PoP system - 2010**
**Modify and build necessary hardware - 2012 **
- LHC CeC simulations - 2012
**Install R&D ERL at IP2 in RHIC - 2012-2013**
**CeC PoP experiments - 2013-2014**

## Participants in LARP efforts

**BNL Personnel and tasks: **Vladimir Litvinenko - CeC PoP, theory and experiments; Post-Doc (TBD) – CeC and FEL simulations, Ilan Ben Zvi -  SRF and ERL, Dmitry Kayran and Eduard Pozdeyev – R&D ERL and CeC lattice; Dejan Trbojevic and Steven Tepikian– RHIC lattice for CeC PoP; Wuzheng Meng  and George Mahler– magnet design; Animesh Jain – magnetic measurements; C-AD engineers and technicians (as needed for specific tasks).
**SBU Personnel and tasks: **Stephen Webb (graduate student), theory and simulations
**FNAL Personnel and tasks: **Alexey Burov - theoretical support; Sergei Nagaitsev, Vladimir Shiltsev – participation in the PoP experiment.
**JLab Personnel and tasks: **Yaroslav Derbenev - theoretical support.
**LBNL Personnel and tasks: **John Byrd and others – development of the wiggler and the buncher for CeC PoP.
**CERN liason**: Frank Zimmerman

## Proposed Budget & Goals

***MSTC Budget Breakdown:                 K$***
- Post doc, Graduate student			160
- Other Labor/Materials 			315
- Travel 						 25
_**Total**__**	**__**	**__**	**__**	**__**	**__**	**__**500**_
*Cost sharing: This work will be performed as part of eRHIC R&D with expected budget $2M/year (NP DoE) and about 4 FTE efforts from C-AD, BNL. It will take advantage of R&D ERL at BNL with estimated value of $25M. There is possible SBIR support for VORPAL simulations for CeC at Tech X*
**Ultimate goal of these efforts:**
**1.****	****Experimental demonstration of coherent electron cooling in CeC PoP at RHIC and test of the LHC specific modes of operation. **
**2. ****Conceptual design of the CeC for LHC.**

## Conclusions

**Coherent electron cooling is very promising method for significant luminosity increase in LHC (and LHeC)**
**Proof of principle experiment of cooling Au ions in RHIC at ~ 40 GeV/n is feasible with existing R&D ERL**
- Can test conjecture that strong cooling allows for higher beam-beam tune shifts
**Modest LARP efforts** **would be critical for CeC PoP experiment and for testing the LHC-specific aspects of coherent electron cooling**

## 2.75 TeV/u Pb ions in LHC 

| N per bunch | 2 1011 | Z, A | 82,  207 |
| --- | --- | --- | --- |
| Energy Au, GeV/n | 2750 |  | 2940 |
| RMS bunch length, nsec | 0.25 | Relative energy spread | 0.0113% |
| Emittance norm,  m | 3.8 | , m | 47 |
| Energy e-, MeV | 1.503 | Peak current, A | 100 |
| Charge per bunch, nC | 5 | Bunch length, nsec | 0.05 |
| Emittance norm,  m | 3 | Relative energy spread | 0.01% |
| , m | 59 | L1 (lab frame) ,m  | 70 |
| pe, CM, Hz | 2.44 109 | Number of plasma oscillations | 0.0308 |
| D, mm | 3.7 | D, m | 0.17 |
| FEL, m | 0.04 | w, cm | 5 |
| aw | 3.58 | LGo, m | 1.7 |
| Amplitude gain =250, Lw , m | 30.7 | LG3D, m | 2.35 |
| L2 (lab frame) ,m  | 35 | Cooling time, local, min | 0.5 minutes |
| Nmin turns  or Ñ in 10% BW | 2 106 >> 2.8 105 | Cooling time, beam | 3.2 minutes |

## ERL based LHeC with cooling: 30 x luminosity

|  | Electrons | Protons |
| --- | --- | --- |
| Energy | 70 GeV | 7 TeV |
| N per bunch | 0.14 1011 | 1.7 1011 |
| Rep rate, MHz | 40 |  |
| Beam current, mA | 90 | 1090 |
| Norm emittance, m | 3 | 0.3 |
| *, m | 0.5 | 1.3 |
| *
D | 12.7
4.56 | 0.0057
 |
| Luminosity | 3.77 x 1034 cm-2 sec-1 |  |
| Loss for SR, MW | 67 | Kink =0.93 |