# Presentation: 335850

## PROGRESS WITH FEL-BASED COHERENT ELECTRON COOLING 

_**PROGRESS WITH FEL-BASED COHERENT ELECTRON COOLING**_** **

**Vladimir N. Litvinenko, Ilan Ben Zvi,  Michael Blaskiewicz, Yue Hao, Dmitry Kayran, Eduard Pozdeyev, Gang Wang*****Brookhaven National Laboratory, Upton, NY 11973, USA*****Oleg A. Shevchenko, Nikolay A. Vinokurov*****Budker Institute of Nuclear Physics, Novosibirsk, Russia*****George I. Bell, David L. Bruhwiler, Andrey Sobol*****Tech-X Corp., Boulder, CO 80303, USA******  *****Yaroslav S. Derbenev, ****TJNAF, Newport News, VA, USA****Sven Reiche****, *****UCLA, Los Angelis, CA, USA***

## 			Content*  What is Coherent electron Cooling? *  Why it is needed?*  Our plan of  the comprehensive studies*  Progress with Modulator, FEL, Kicker, PoP*  Conclusions

_**	**__**	**__**	**__**Content**_*  What is Coherent electron Cooling? *  Why it is needed?*  Our plan of  the comprehensive studies*  Progress with Modulator, FEL, Kicker, PoP*  Conclusions

**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 based on high-gain FEL and ERL was presented at last FEL conference [1]. This scheme promises significant increases in luminosities of modern high-energy hadron and electron-hadron colliders, such as LHC and eRHIC. In this talk we present progress in development of this concept, results of analytical and numerical evaluation of the concept as well our prediction for LHC and RHIC. We also present layout for proof-of-principle experiment at RHIC using existing R&D ERL. **
**In this paper we report on the progress in the development of the scheme of coherent electron cooling (CeC) since a specific scheme and its theoretical evaluation were proposed about an year ago [1].**
- 	[1] V.N. Litvinenko, Y.S. Derbenev, Proc. of FEL’07 Conference, Novosibirsk, Russia, August 27-31, 2007, p.268
-     	 _[http://accelconf.web.cern.ch/accelconf/f07](http://accelconf.web.cern.ch/accelconf/f07)_

## Coherent Electron Cooling

## Decrements for hadron beamswith coherent electron cooling

- Decrements for hadron beamswith coherent electron cooling

| Machine | Species | Energy GeV/n | Trad.
Stochastic
Cooling, hrs | Synchrotron radiation, hrs | Trad.
Electron cooling
 hrs | Coherent
Electron
Cooling, hrs 
1D/3D |
| --- | --- | --- | --- | --- | --- | --- |
| RHIC PoP | Au | 40 | - | - | - | 0.02/0.06 |
| eRHIC | Au | 130 | ~1 | 20,961  | ~ 1  | 0.015/0.05 |
| eRHIC | p | 325 | ~100 | 40,246  | > 30 | 0.1/0.3 |
| LHC | p | 7,000 | ~ 1,000 | 13/26 |   | 0.3/<1 |

## 			Comprehensive studies Analytical, Numerical and Computer Tools to:1. find reaction (distortion of the distribution function of electrons)    on a presence of moving hadron inside an electron beam2a. Find how an arbitrary f is amplified in high-gain FEL2b. Design cost effective lattice for hadrons + coupling3.  Find how the amplified reaction of the e-beam acts on the        hadron (including coupling to transverse motion)

_**	**__**	**__**	**_**Comprehensive studies**_** **_Analytical, Numerical and Computer Tools to:1. find reaction *(distortion of the distribution function of electrons)*    on a presence of moving hadron inside an electron beam2a. Find how an arbitrary f is amplified in high-gain FEL2b. Design cost effective lattice for hadrons + coupling3.  Find how the amplified reaction of the e-beam acts on the        hadron (including coupling to transverse motion)

## 			Modulator        Dimensionless equations of motion

_**	**__**	**__**	**_**Modulator**_** **_**       **Dimensionless equations of motion

**Parameters of the problem**

- +Ze

## Numerical (VORPAL @ TechX) 

- Perturbation caused by a hadron (co-moving frame)

- Analytical: for Lorentzian electron plasma, *G. Wang and M. Blaskiewicz, Phys Rev E 78, 026413 (2008)*

- Numerical (VORPAL @ TechX)

- Ion at rest

## VORPAL @ TechX

## CeC: FEL response

- 1D FEL response

## 			FEL’s Green Function 1D  - analytical approach3D - 3D FEL codes RON and Genesis 1.3

_**	**__**	**__**	**_**FEL’s Green Function**_** **_**1D  - analytical approach****3D - 3D FEL codes RON and Genesis 1.3**

- FEL parameters for Genesis 1.3 and RON simulationsFEL gain length: 1 m (power), 2m (amplitude)

## Response - 1D FEL 

- Response - 1D FEL

- E.L.Saldin, E.A.Schneidmiller, M.V.Yurkov, The Physics of Free Electron Lasers, Springer, 1999

## Response - 1D FEL after 10 gain lengths

- Green-functionenvelope (Abs, Re and Im)

- Maximum located at 3.744 slippage units,(i.e. just a bit further that expected 3 and 1/3)The Green function (with oscillations) had effective RMS length of 1.48 slippage units.

## Genesis: 3D FEL

- Genesis: 3D FEL

- Evolution of the maximum bunching in the e-beam
- and the FEL power simulated by Genesis.
- The location of the maxima, both for the optical power
-  and the bunching progresses with a lower speed compared
- with prediction by 1D theory,
-  i.e. electrons carry ~75% for the “information”

- Evolution of the maxima locations in the e-beam
- bunching and the FEL power simulated by Genesis.
- Gain length for the optical power is 1 m (20 periods)
- and for the amplitude/modulation is 2m (40 periods)

- ©Y.Hao, V.Litvinenko

## 3D FEL, RON codeRHIC 250 GeV, FEL @ 0.7 m, gain length - 40 periods  (amplitude). 20 (power)

- 3D FEL, RON codeRHIC 250 GeV, FEL @ 0.7 m, gain length - 40 periods  (amplitude). 20 (power)

- ©O.Shevchenko

- 20 GL

- 18 GL

- 16 GL

## Genesis: 3D FEL

- Genesis: 3D FEL

- Evolution of the normalized bunching envelope

- The Green function (with oscillations) after 10 gain-lengths
-  had also smaller effective RMS length [1] of 0.96 slippage units
- (i.e. about 38 optical wavelengths, or 27 microns

- ©Y.Hao, V.Litvinenko, S.Reiche

- Evolution of the bunching and optical power envelopes
- (vertical scale is logarithmic)

## Kicker: output from Genesis propagated for 25 m

**Kicker**: output from Genesis propagated for 25 m

- 0m

- 5m

- 10m

- 25m

- ©I.Ben Zvi

- 15m

- Preliminary

- 20m

## IR-2 layout for Coherent Electron Cooling

-  proof-of-principle experiment

## Conclusions

-  These initial studies did not find any phenomena, which challenges the concept of CeC
- Our initial CeC estimations passed the test
- At the same time, we found a number of new and interesting details to pursue further
- Future studies will refine the model and improve the quality of predictions
- We plan to test validity of the concept experimentally in Proof-of-Principle experiment using BNL’s R&D ERL installed in one of available IPs at RHIC
*Supported by office on Nuclear Physics, US DoE *

## V.N. Litvinenko, 30th FEL Conference, Gyeongju, Korea, August 28, 2008 

## Response - 1D FEL; z=13m

- Effect of energy spread and space charge
- Red - amplitude, Blue - phase

- @

- ©G.Wang