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

Coherent electron cooling

Vladimir N. LitvinenkoC-AD, Brookhaven National Laboratory, Upton, NY, USA

Department of Physics and Astronomy, Stony Brook University

Center for Accelerator Science and Education

Thanks toIlan Ben-Zvi, Yue Hao, Vadim Ptitsyn, Gang Wang, Stephen Webb

Brookhaven National Laboratory, Upton, NY 11973, USA

Oleg A. Shevchenko, Nikolay A. VinokurovBudker Institute of Nuclear Physics, Novosibirsk, Russia

George I. Bell, David L. Bruhwiler, Andrey SobolTech-X Corp., Boulder, CO 80303, USA

Yaroslav S. Derbenev, Andrew Hutton, Geoff Kraft, Matt PoelkerTJNAF, Newport News, VA, USA

V.N. Litvinenko, EICC meeting, CUA, Washington DC, July 29, 2010

Content• Why it is needed?

• Classical Coherent Electron Cooling (CeC)

• How to cool transversely

• Theory & Simulations

• Recent advances in CeC

– Noise reduction in FEL

– Spin cooling

• Proof of Principle test using R&D ERL

• Q&A


Measure of ColliderPerformance is the Luminosity

Ý N events A B L

L fcoll N1 N2

4 *g( *,h, , z)

Main sources of luminosity limitation

Large or growing emittanceHour-glass effect

Crossing angleBeam Intensity & Instabilities

Beam-Beam effects

Why to cool hadron beams?


Why to coherent electron cooling?

• Traditional stochastic cooling does not have enough bandwidth to cool modern-day proton beams

• Efficiency of traditional electron cooling falls as a high power of hadron’s energy

• Synchrotron radiation is too fable – event at LHC energy cooling time is more than 10 hours

• Optical stochastic cooling is not suitable for cooling hadrons with large range of energies and has a couple of weak points:

• Hadron do not like to radiate or absorb photons, the process which OSC uses twice

• Tunabity and power of laser amplifiers are limited


Examples of hadron beams cooling

Machine SpeciesEnergy GeV/n

Trad.

Stochastic

Cooling, hrs

Synchrotron radiation, hrs

Trad.

Electron cooling

hrs

Coherent

Electron

Cooling, hrs

1D/3D

RHIC PoP

Au 40 - - ~ 1 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

Potential increases in luminosities:

RHIC pp ~ 6 fold, eRHIC ~ 50 fold, LHC ~ 2 fold; LHeC ~ 10 fold


X x

xo

; S s

so

2

E

sE

2

;

dX

dt

1

IBS

1

X 3 / 2S1/ 2

CeC

1

S;

dS

dt

1

IBS //

1

X 3 / 2Y

1 2

CeC

1

X; xn 0 2 m; s0 13 cm; 0 4 10 4

IBS 4.6 hrs; IBS // 1.6 hrs

IBS in RHIC foreRHIC, 250 GeV, Np=2.1011

Beta-cool, A.Fedotov

x n 0.2 m; s 4.9 cm

This allowsa) keep the luminosity as it is b) reduce polarized beam current down to 50

mA (10 mA for e-I)c) increase electron beam energy to 20 GeV

(30 GeV for e-I)d) increase luminosity by reducing * from 25

cm down to 5 cm

Dynamics:Takes 12 minsto reach stationarypoint

X CeC

IBS // IBS

1

1 2; S CeC

IBS //

IBS

IBS // 1 23

Gains from coherent e-cooling: Coherent Electron Cooling vs. IBS


eRHIC: ERL or ring for electrons?CeC is the key ingredient

– Ring-ring:

– Linac-ring:

RHIC

Electron storage ring

RHIC

Electron linear accelerator

Takes full advantage of CeCNatural staging strategy

�

L x 50

L4 h e

rhre

h e h

'

e

' f

L h f NhhZh

h

*rh

e 1

e ~ 0.1


eRHIC IR2

p /A e

Energy (max), GeV 325/130 20

Number of bunches 166 74 nsec

Bunch intensity (u) , 1011 2.0 0.24

Bunch charge, nC 32 4

Beam current, mA 420 50

Normalized emittance, 1e-6 m, 95% for p / rms for e 1.2 25

Polarization, % 70 80

rms bunch length, cm 4.9 0.2

β*, cm 5 5

Luminosity, cm-2s-11.4 x 1034

X x

xo

; S s

so

2

E

sE

2

;

dX

dt

1

IBS

1

X 3 / 2S1/ 2

CeC

1

S;

dS

dt

1

IBS //

1

X 3 / 2S1/ 2

1 2

CeC

1

X;

Evolution of beam in LHC at 7 TeV(assuming nominal LHC bunch intensity 1.15e11 p/bunch and 40% of CeC cooling capability)

xn 0 3.75 m; s0 7.55cm

IBS 80 hrs; IBS // 61 hrs

2

IBS //

Nrc

2c

25 3

x

3 / 2

s

f m

yv; x

IBS

Nrc

2c

25 3

x

3 / 2

s

H

y

1/ 2f m ; 1

f m

d

m

lnm

e ; m

rcm2c 4

bmax E

2;bmax n 1/ 3; rc

e2

mc 2; (e Ze;m Am)

IBS rates in LHC from

Table 2.2

X CeC

IBS // IBS

1

1 2; S CeC

IBS //

IBS

IBS // 1 23

Stationary solution for τCeC = 0.8 hrs

x n 0.19 m; s 0.87 cm

J.LeDuff, "Single and Multiple Touschek effects", Proceedings of CERN Accelerator School, Rhodes, Greece, 20 September - 1 October, 1993, Editor: S.Turner, CERN 95-06, 22 November 1995,Vol. II, p. 573


Layout for ERL based LHC

• Hadrons – 1.15e11 per bunch

– Cooled by CeC

• Electron– Accelerated in the ERL - 60 GeV

– Polarized electron beam current - 8 mA

• Number of passes – 3

• AC power consumption – 100 MW

• Crab-crossing

• β*=12 cm

• L = 2.1034 cm-2 sec-1

R=700mR=700m

10 GeV linac

10 GeV linac

0.5 GeVERL-injector

DumpGun


Coherent Electron Cooler

Amplifier of the e-beam modulationin an FEL with gain GFEL~10

2-103

RD //,lab

c2

p

FEL

RD

c e

p

vh

2 RD//

FEL

2 R

D

q Ze (1 cos 1)

1 pl1 /c

qpeak 2Ze

FEL

LGow

4 3

LG LGo(1 )

GFEL eLFEL / LG

LFEL

3LG

c t D o

o

; Dfree

L2; Dchicane lchicane

2.......

kFEL 2 / FEL; kcm kFEL /2 o

4 en 0 cos kcmzr E

r ˆ z Eo X sin kcmz

namp Go nk cos kcmz

A

2 n / o

qFEL

(z)0

FEL

cos kFELz dz

k kq( 1); nkk

2

Ez

Eh e Eo l2 sin kFELDE Eo

Eo

sin 2

2

sin 1

2

2

Z X; Eo 2Goe o / n

pt

q /Ze

FEL

E0

E < E0

E > E0

Modulator KickerDispersion section ( for hadrons)

Electrons

Hadrons

l2l1 High gain FEL (for electrons)

Eh

E < Eh

E > Eh

DispersionAt a half of plasma oscillation

Debay radii

RD RD //

p 4 nee2 / ome

Density

pt

fel w 1r a w

2 /2 o

2

r a w e

r A w / mc2

Eo 2Go o

e

n

X q/e Z(1 cos 1) ~ Z


Note that damping decrement

a) Does not depend on the energy of particles ! b) Improves as cooling goes on

It makes it realistic to think about cooling intense proton beam in RHIC & LHC at 100s of GeV and 7 TeV energies

Even though LHC needs one more trick (back up slides)

CeC ~1

long,h trans,h

CeC,e

,h

2Go

Z 2

A

rp ,e

n ,h

; ~ 1

Analytical formula for damping decrement


Effects of the surrounding particles

Each charged particle CUAses 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/Neff, Neff is effective

number of hadrons in coherent sample (Λk=Nc )

CeC (max)2

2

Neff

kD1

Neff

Etotal( ) E o Im X K - i eik - i K - j e

ik - j

j ,electronsi,hadronsX q/e Z(1 cos 1) ~ Z

k K z -2

d

Neff Nhk

4 z,h

Ne

X 2

k

4 z,e

2 2 2 D

g i Im K i e ik i / 2 ; D g2Neff /2;

g Go

Z 2

A

rp

n

2 f 2 (1 cos 1)l2 ,

Eo 2Go o

e

n

Fortunately, the bandwidth of FELs f ~ 1013-1015 Hz is so large that this limitation does not play any practical role in most HE cases

Λk ~ 38 λfel


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=1

• Vertical (better to say the second eigen mode) cooling is coming from transverse coupling

Non-achromatic chicane installed at theexit of the FEL before the kicker sectionturns the wave-fronts of the charged planesin electron beam

R26 0

ct R26 x

E eZ2 Eo l2 sin k DE Eo

Eo

R16x R26x R36y R46y ;

x Dx eZ2 Eo L2 kR26x ....

J CeC ; // (1 2J ) CeC ;

d x

dt

x

CeC

;d

2

dt

2

CeC //

CeC

1

2J CeC

; CeC

1

2(1 2J ) CeC

;


e-Density modulation CUAsed by a hadron (co-moving frame)

Analytical: for kappa-2 anisotropic electron plasma,

G. Wang and M. Blaskiewicz, Phys Rev E 78, 026413 (2008)

vhz 10 vze

q Ze (1 cos pt)

˜ n r ,tZno p

3

2

vx vy vz

sin 2 x - vhx / p

rDx

2

y - vhy / p

rDy

2

z - vhz / p

rDz

22

0

pt

d

Numerical: VORPAL @ TechX)

Rv

vz

; Tvhx

vz

; Lvhz

vz

; Z

4 neR2s3

;

Aa

s; X

xho

a;Y

yho

a.

Parameters of the problem

Induces charge:

z/RD// z/RD//

r/RD//r/RD//

Density plots for a quarter of plasma oscillation

Ion rests in c.m.(0,0) is the location of the ion

Ion moves in c.m. with

(0,0) is the location of the ion

t / p; r v =

r v z

; r r

r v z

/ p; p

4 e2ne

ms rDz

v z

p

+Ze

RD v v / p; x,y,z


Numerical simulations (VORPAL @ TechX)Provides for simulation with arbitrary distributions and

finite electron beam sizeVORPAL Simulations Relevant to Coherent Electron Cooling, G.I. Bell et al., EPAC'08, (2008)

Rv

vz

; Tvhx

vz

; Lvhz

vz

q Ze (1 cos pt)

© TechX


3D FEL responsecalculated Genesis 1.3, confirmed by RON

Main FEL parameters for eRHIC with 250 GeV protons

Energy, MeV 136.2 266.45

Peak current, A 100 o, nm 700

Bunchlength, psec 50 w, cm 5

Emittance, norm 5 mm mrad aw 0.994

Energy spread 0.03% Wiggler Helical

The amplitude ( ) and the phase ( , in the units of ) of the FEL gain envelope after 7.5 gain-lengths (300 period). Total slippage in the FEL is 300 , =0.5 m. A clip shows the

central part of the full gain function for the range of ={50 , 60 }.

G Go Re K eik ; z vt; k =2

k K z -2

d


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

kD ~ 1

E

Eo

CEC

E

E Eo

e Eo l2

ompc2

Z 2

A

dE

dzeEpeak sin kD

E Eo

Eo

;

48G Ze

nkcm

cos kcmz ; r E

r ˆ z

8G Ze

n

sin kcmz

FEL

E0

E < E0

E > E0

Periodical longitudinal electric field

Analytical estimationSimulations: only started

Step 1: use 3D FEL code out output + trackingFirst simulation indicate that equations on the left significantly underestimate the kick, i.e. the density modulation continues to grow after beam leaves the FEL

©I.Ben Zvi

Output from Genesis propagated for 25 m

0m 5m 10m

25m15m 20m

Step 2: use VORPAL with input from Genesis, in preparation


New theoretical developments beyond 1D

©V.Litvinenko, G.Wang, S.Webb – will be presented in details at FEL’2010


Polarizing Hadron Beams with Coherent Electron Cooling

New LDRD proposal at BNL: VL & V.Ptitsyn

Modulator KickerDelay for hadrons

Electrons

Hadrons

l2High gain FEL (for electrons)HW1

left helicityHW2

right helicity

Modulation of the electronbeam density around a hadron isCUAsed by value of spincomponent along thelongitudinal axis, z. Hardonswith spin projection onto z-axiswill attract electrons whiletraveling through helical wigglerwith left helicity and repelthem in the helical wiggler withright helicity.

The high gain FEL amplify the imprinted modulation.

Hadrons with z-component of spin will have an energy kick proportional to the value and the sigh if the projection. Placing the kicker in spin dispersion will result in reduction of z-component of the spin and in the increase of the vertical one.

dr n /d

This process will polarize the hadron beamV.N. Litvinenko, EICC meeting, CUA, Washington DC, July 29, 2010

Shot-Noise Suppressor(in time)

Laser amplifier

Wiggler 1 Wiggler 2

Buncher

to HG FEL

ho ei n

n 1

N

; ho2

N

Such system will reduce the amplitude of shot-noise by the factor N 1/2 , and the power of short-noise (spontaneous radiation, SASE) by a factor of N.

V.N. Litvinenko, FLS 2010, SLAC, March 4, 2010

kl c

Proposal to NP DoE, 5 years, $5.9M


Layout for Coherent Electron Coolingproof-of-principle experiment in RHIC IR 2

Collaboration between BNL & JLab

DXDX

19.6 m

Modulator, 4 mWiggler 7mKicker, 3 m

Parameter

Species in RHIC Au ions, 40 GeV/u

Electron energy 21.8 MeV

Charge per bunch 1 nC

Rep-rate 78.3 kHz

e-beam current 0.078 mA

e-beam power 1.7 kW

V.N. Litvinenko, IPAC’11, Kyoto, May 26, 2010

©G.Mahler

Beam Parameters in CeCFEL gain set at a realistic value of about 100, local cooling time is estimated at 10.3 seconds,

and 20 minutes for cooling entire bunch.


Optics (preliminary)


Amplifier of the e-beam modulation via High Gain FEL andLongitudinal dispersion for hadrons

Modulator:region 1a quarter to a half of plasma oscillation

Kicker: region 2Electrons

Electron density modulation is amplified in the FEL and made into a train with duration of Nc ~ Lgain/ w alternating hills (high density) and valleys (low density) with period of FEL wavelength . Maximum gain for the electron density of HG FEL is ~ 103.

vgroup (c 2v//) /3 c 11 aw

2

3 2c 1

1

2 2

c

3 21 2aw

2 vhadrons

c

3 21 2aw

2

Economic option requires: 2aw2 < 1 !!!

Modulator Kicker

Electrons

Hadrons

l2l1

High gain FEL (for electrons) / Dispersion section ( for hadrons)

CeC: Economic option


Genesis 3D FEL for CeC PoP

Evolution of the maximum bunching in the e-beam and the FEL power simulated by Genesis.

Evolution of the maxima locations in the e-beambunching and the FEL power simulated by Genesis.

vg

c 3 vz

4c 1

3

8

1 aw

2

o

2

©Y.Hao, V. Litvinenko

V.N. Litvinenko, RHIC Retreat, July 2, 2010

Profile effect

• The phase velocity in the FEL depends on the peak current through its gain length

• Expected beam-current profile for the beer-can bunch, and corresponding FEL gain (in amplitude) and phase in the kicker. Right graph: The strength of cooling/anti-cooling along the e-bunch.


Conclusions• Coherent electron cooling has potential of cooling high intensity

TeV scale proton and ion beams with reasonable (under an hour) cooling time

• Electron accelerator of choice for such cooler is energy recovery linac (ERL)

• ERL seems to be capable of providing required beam quality for such coolers

• Majority of the technical limitation and requirements on the beam and magnets stability are well within limit of current technology, even though satisfying all of them in nontrivial fit

• We plan a proof of principle experiment of coherent electron cooling with Au ions in RHIC at ~ 40 GeV/n


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

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