# Presentation: 338865

**                                    **
**             ****Electron Cooling in RHIC at Low Energies**
**                                           ****Alexei Fedotov**
**                        ****Collider-Accelerator Department, BNL**
**                                          ****(March 10,  2006)**

**Electron cooling**
**was invented by**
**G.I. Budker **
**(INP, Novosibirsk, 1966)**

**First experimental**
**cooling. NAP-M storage**
**ring (Novosibirsk, 1974)**

**Principles of electron cooling:**
**Produce a beam of cold (low emittance) electrons.**
**Move these electrons with a velocity of the heavy particles  to be cooled.**
**Heavy particles scatter off the electrons and energy is transferred to electrons. This energy transfer appears as a friction force acting on the ions. The ions are “cooled”.**
**The electrons are renewed.**

## Low-energy (3-400 KeV electrons) cooling ( <  1 GeV/u ions):           10’s of coolers were constructed: 1975-2005

## Medium-energy (4 MeV electrons) cooling at FNAL – to cool  8 GeV pbars – successfully operating since July 2005 

## High-energy (54 MeV electrons) cooling - to cool Au ions at 100 GeV/u energies – RHIC-II upgrade

**54 MeV electrons**
**delivered by**
**Energy Recovery Linac (ERL)**

## Magnetized and Non-magnetized cooling

**1. All ****low-energy (3-400KeV electrons) coolers 1975-2005**** are based on ****“magnetized cooling”**** – electron beam transport and alignment of electron and ion beam is done with continuous magnetic field.  Strong magnetic field completely suppresses transverse temperature of electron beam, so that effectiveness of cooling is determined by a very low longitudinal temperature of electrons.**
**2. ****“Non-magnetized cooling”**** – relies on  the fact that rms velocity spread of electrons  is comparable or smaller than the one of ions which need to be cooled.**

## Practical  implementation of e-cooling for low energy  in RHIC

**Magnetized cooling:**** 2 MeV electrons  is considered as COSY upgrade.  4.3 (8) MeV electrons ****8 (15) GeV  pbars**** is planned for HESR GSI (FAIR project) – both are technically challenging projects.**
**Non-magnetized cooler**** at FNAL 4.3 MeV electron energy - can cover ion energies up to ****(E****k****=8 GeV)****.**
**RHIC-II cooler****  54 MeV electrons (****100 GeV/u ions****) is based on RF SC gun. **
**      ****Two guns are presently being designed:**
**3.1 Prototype ERL gun (1/2 cell): designed energy of electrons at gun exit 2.5 MeV – ****( E****k****= 4.6 GeV ions)**
**3.2 RHIC-II cooler gun (1.5 cell): designed energy of electrons at gun exit 4.5 MeV – ****( E****k****= 8.3 GeV ions)**

## Cooling at different energies

**     ****Cooling times for relativistic energies are much longer than for typical low-energy coolers (********=1).**
**     ****In approximation of cold electron beam one gets cooling time:**
**    **

**When rms velocity spread of electron beam is significant compared to the ion beam, dependence of cooling time on relativistic factor  ******** is less pronounced.**
** **

** ****Very fast for low energies**
** ****Very fast for heavy ions**

**     ****Present design of high-energy electron cooler for RHIC-II is based on the non-magnetized approach.**
**     ****For non-magnetized cooling – the challenging requirement is to get small electron emittance for high charge of electron beam. **
**    ****For 100 GeV/u, ********=108 cooling, we need  **
**    ****electron beam with Q=5nC and rms normalized emittance ********e,n**** < 4 ********m**
**    ****Present simulations (Chang, Kayran) for 1.5 cell gun give ********e,n****=3-5 ********m**
**   **
**    ****For 1⁄2 cell gun (ERL prototype under construction at BNL): **
**   ****expected rms normalized emittance for Q=5nC:  ********e,n**** ****< 10 ********m**

**Cooling times at low energies in RHIC will slightly depend on:**
**Emittance of ion beam at such low energy**
**Emittance of electron beam**
**       ****Simulations results  (using BETACOOL) are shown for the followings emittances of electron beam (electron charge Q=5nC):**
**E****k****=1.5 GeV/u (c.m. 5  GeV) ****– electron rms normalized emittance 15 ********m.**
**E****k****=5.0 GeV/u (c.m. 12 GeV)**** – electron rms normalized emittance 10 ********m**
**E****k****=9.0 GeV/u (c.m. 20 GeV)**** – electron rms normalized emittance 10 ********m.**
**       ****Technical aspects such as electron beam transport at  low energy, emittance preservation for such a beam, alignment of electron and ion beams require careful consideration and are not discussed here.**

## Cooling Au ions at Ek=1.5 GeV/u (=2.61)Electron beam: q=5nC, rms e,n=15m, p=1e-3, L=80m(Figs: plotted emittance is rms  unnormalized)

**emittance growth**
**(95% normalized) due to IBS: **
******i,n,95%****: 15********  ********m -> 48 ******** ********m in 30 min**

**Cooling of transverse emittance**
**(95% normalized):**
** ********i,n,95%****: 15 ********m******** -> 4 ********m in 10 sec**

**rms bunch length due to cooling:**
** ****400 cm -> 84 cm in 10 sec**

- Cooling section length: L=80m

**rms momentum spread:**
**0.001 -> 0.0002**

## Cooling Au ions at Ek=1.5 GeV/u (=2.61)Electron beam: q=5nC, rms e,n=15m, p=1e-3, L=10m(Figs: plotted emittance is rms  unnormalized)

- Cooling section length: L=10m

**Cooling of transverse emittance**
**(95% normalized):**
******i,n,95%****: 15 ********  -> 8.6******** in 80 sec**

**rms bunch length due to cooling:**
** ****400 cm -> 130 cm in 80 sec**

## Cooling Au ions at Ek=5 GeV/u (=6.37)Electron beam: q=5nC, rms e,n=10m, p=1e-3, L=10m(Figs: plotted emittance is rms  unnormalized)

**Emittance growth ****(95% normalized) due to IBS:**
** ********i,n,95%****: 15 ********  -> 30 ******** in 60 min**

- Cooling section length: L=10m

**Cooling of transverse emittance**
**(95% normalized): **
******i,n,95%****: 15 ********  -> 5.6 ******** in 200 sec**

** ****rms bunch length due to cooling:**
** ****268 cm -> 105 cm in 200 sec**

## Cooling Au ions at Ek=5 GeV/u (=6.37)Electron beam: q=5nC, rms e,n=10m, p=1e-3, L=80m(Figs: plotted emittance is rms  unnormalized)

- Cooling section length: L=80m

**Cooling of transverse emittance**
**(95% normalized): **
******i,n,95%****: 15 ********  -> 3 ******** in 35 sec**

**Cooling of rms bunch length:**
** ****268 cm -> 70 cm in 35 sec**

## Cooling of Au ions at Ek=9 GeV/u (=10.66)Electron beam: q=5nC, rms e,n=10m, p=1e-3, L=10m(Figs: plotted emittance is rms  unnormalized)

**cooling at present RHIC injection**
**energy just with L=10 m cooling section**

**emittance growth due to IBS:**
** ********i,n,95%****: 15 ********  -> 20 ******** in 30 min**

**cooling: ********i,n,95%****: 15 ********  -> 5.5 ******** in 6 min**

**rms bunch length growth due to IBS:**
** ****144 cm -> 177 cm in 30 min**

**cooling of rms bunch length:**
** ****144 cm -> 90 cm in 6 min**

## Summary

**    ****Cooling times at low-energies in RHIC are very short.**
**    ****It seems feasible to employ RF gun which is developed for ERL project at BNL (presently under construction at Collider-Accelerator Department) to provide such a low-energy cooling.**
**    ****Actual technical aspects of electron beam transport will need to be addressed when the energy of interest or a range of energies will be defined.**