Slava and Coherent Electron Cooling or Cool side of Slava Vladimir N. Litvinenko C-AD, Brookhaven...

Slava andCoherent Electron

Cooling

or Cool side of Slava

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

Department of Physics and Astronomy, Stony Brook UniversityCenter for Accelerator Science and Education

V.N. Litvinenko, Yaroslav Derbenev's 70th Birthday Symposium, JLab, August 2, 2010

Content

• Bits of memory from 36 years ago forward

– Cool side of Slava

• Few serious slides

• Instead of conclusion

V.N. Litvinenko, Y.Derbenev's 70th Birthday Symposium, JLab, August 2, 2010

From Slava’s resume….• M.S., Moscow State University, 1963• Soviet Candidate Degree, Institute of Nuclear Physics, Novosibirsk, 1968• Soviet Doctoral Degree, Institute of Nuclear Physics, Novosibirsk, 1978

Doctoral Thesis "Theory of Electron Cooling”Career:• Staff Scientist, JLab, 2001-present xxxxxxxx 2003-2010• Visiting Research Scientist and Adjunct Professor, Physics Dept., University of

Michigan, 1990 - 2001• Chief Scientist, Accelerator Physics and Laser Technology Group, Institute of

Complete Electric Drive, Novosibirsk, Russia, 1986-1990• Chief Scientist, Institute of Physics, Atomic Energy Committee, Yerevan, USSR,

1985-1986• Chief Scientist, Accelerator Theory Group, Institute of Nuclear

Physics, Novosibirsk, Russia, 1969-1985 1977-1985• Junior Scientist, Theoretical laboratory of the Institute of Nuclear Physics,

Novosibirsk ,Russia, 1963-1968Teaching • 1990-1993: Advanced Accelerator Physics Graduate Course (level 600), University

of Michigan, • 1965-1983 Graduate level seminars in general and quantum physics,

Novosibirsk State University 1974

From Moscow to Siberia

NovosibirskBudker Institute of Nuclear Physics

Siberian snakes

Magnetized cooling B

eam-beam effects

Slava as my teacherAnalytical Mechanics 1974

€

H(r x ,

r P ,t ) =

r P −

er A

c

⎛

⎝ ⎜

⎞

⎠ ⎟

2

c2 + m2 c 4 +

e ⋅ j

Electron Cooling

Kinetic equation (plasma relaxation) was derived by Landau in 1937. But… can it work for beams? It does! Yet very interesting and important phenomena have been discovered (magnetized cooling, super-deep cooling, christaline beams…) © Ya. Derbenev

V.N. Litvinenko, Laser and Plasma Accelerators Workshop 2009, Καρδαμύλη, Greece

Budker’s idea – if we put hot hadron gas in contact with cold electron gas after a period of thermal relaxation they will have the same temperature in the c.m. frame

€

Mh

r v h

2

2= me

r v e

2

2

€

Mh

r v h

2

2= me

r v e

2

2⇒

r v h

2 =me

Mh

r v e

2

Was is too simple for Slava to get involved?

1975 – NAP Surprise!

Just complex enough to get

Slava interested !

The cooling time is much shorter thanBudker’s estimate!

Rise to the cool side of Slava

Be

-

Interaction of an ion with “a Larmor circle”

Explained!

Magnetized Cooling

Not cool enough for Slava?• Slava is on of the first who

recognized direct connection between stochastic and electron cooling

• Since 1980 he works on the ways to electron cooling by all means possible, including amplifying the media response on presence of a charged hadron.

• Many e-Beam instabilities (including FEL) were tried to fit the task• 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

• And many more…

Coherent Electron Cooling

CeC - Equations

Coherent Electron Cooler

Amplifier of the e-beam modulation in an FEL with gain GFEL~102-103

€

RD //,lab =cσ γ

γ 2ωp

<< λ FEL

€

RD⊥ =cγσ θe

ωp

vh

2 RD//

FEL

2 RD

€

q = −Ze ⋅(1− cosϕ1)

ϕ1 = ωp l1 /cγ

qpeak = −2Ze

FEL

€

LGo =λ w

4πρ 3

€

LG = LGo(1+ Λ)

GFEL = eLFEL / LG

€

Δϕ =LFEL

3LG

€

cΔt = −D ⋅γ − γ o

γ o

; D free =L

γ 2; Dchicane = lchicane ⋅θ

2.......

€

kFEL = 2π /λ FEL; kcm = kFEL /2γ o

€

Δϕ =4πen ⇒ ϕ = −ϕ 0 ⋅cos kcmz( )r E = −

r ∇ϕ = −ˆ z Eo ⋅X sin kcmz( )€

namp = Go ⋅nk cos kcmz( )

€

A⊥ =

2πβ⊥εn /γ o

€

qλFEL≈ ρ(z)

0

λFEL

∫ cos kFELz( )dz

ρ k = kq(ϕ1); nk =ρ k

2πβε⊥

Ez

€

ΔEh = −e ⋅Eo ⋅ l2 ⋅sin kFELDE − Eo

Eo

⎛

⎝ ⎜

⎞

⎠ ⎟⋅

sinϕ 2

ϕ 2

⎛

⎝ ⎜

⎞

⎠ ⎟⋅ sin

ϕ1

2

⎛

⎝ ⎜

⎞

⎠ ⎟2

⋅Z ⋅X; Eo = 2Goeγ o /βε⊥n

€

ω p t

€

−q /Ze

FEL

E0

E < E0

E > E0

Modulator

Kicker

Dispersion 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 //

€

ωp = 4πnee2 /γ ome

Density

€

ω p t

€

λ fel = λ w 1+r a w

2( ) /2γ o

2

€

ra w = e

r A w / mc2

€

Eo = 2Goγ o

e

βε⊥n

€

X = q / e ≅ Z(1− cosϕ1) ~ Z


€

ζCeC ~1

ε long,hε trans,h

€

ζCeC = ζσ τ ,e

σ τ ,h

= κ ⋅2Go ⋅Z 2

A⋅

rp ⋅σ τ ,e

ε⊥n σ δ ⋅σ τ ,h( ); κ ~ 1

Analytical formula for damping decrementwhich most of us can understand…


e-Density modulation caused 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 =10σ vze

€

q = −Ze ⋅(1− cosωp t)

€

˜ n r r ,t( ) =

Znoωp3

π 2σ vxσ vyσ vz

τ sinτ τ 2 +x - vhxτ /ωp

rDx

⎛

⎝ ⎜

⎞

⎠ ⎟

2

+y - vhyτ /ωp

rDy

⎛

⎝ ⎜

⎞

⎠ ⎟

2

+z - vhzτ /ωp

rDz

⎛

⎝ ⎜

⎞

⎠ ⎟

2 ⎛

⎝

⎜ ⎜

⎞

⎠

⎟ ⎟

−2

0

ωpt

∫ dτ

Numerical: VORPAL @ TechX)

€

R =σ v⊥

σ vz

; T =vhx

σ vz

; L =vhz

σ vz

; ξ =Z

4πneR2s3

;

A =a

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 = τ /ωp; r v =

r ν σ v z

; r r =

r ρ σ v z

/ωp ; ωp =4πe2ne

m

€

s = rDz=

σ v z

ωp

+Ze

€

RDα∝ vα +σ vα( ) /ωp; α = x,y,z


3D FEL responsecalculated Genesis 1.3, confirmed by RON

Main FEL parameters for eRHIC with 250 GeV protons

Energy, MeV 136.2 γ 266.45

Pea k current, A 100 λo, nm 700

Bunchlengt , h psec 50 λw, cm 5

Emittanc , e norm 5 m mmrad aw 0 .99 4

Ener gy spread 0 .03 % Wiggler Helical

The amplitude (blue line) and the phase (red line, 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 ζ( ) = Go Re K ζ( ) ⋅e ikζ( ); ζ = z − vt; k =

2π

λ

€

Λk = K z - ζ( )2dζ∫∫


Examples of hadron beams cooling

Machine SpeciesEnergy GeV/n

Trad.StochasticCooling,

hrs

Synchrotron radiation, hrs

Trad.Electron cooling

hrs

CoherentElectron

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


How to understand your ideas and concepts?


How get them into the limelight?

Instead of conclusion• Landau loved generating

ideas and cracking problems - but he did not liked writing words between equations

• He found Liftshitz to do the later and result was fantastic – many generation of physicists admire classics books by Landau and Liftshitz

• Slava – where is your Lifshitz?

Virginia beach

Question to the birthday boy to

think while relaxing on a summer day..


Main message to take home:

Happy Birthday!30 more productive

years!


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)

€

ξCeC (max) =Δ

2σ γ

=2

Neff

kDσ ε( )∝1

Neff

€

Etotal (ζ ) = E o ⋅Im X ⋅ K ζ - ζ i( )e ik ζ -ζ i( ) − K ζ - ζ j( )eik ζ -ζ j( )

j ,electrons

∑i,hadrons

∑ ⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

€

X = q / e ≅ Z(1− cosϕ1) ~ Z

€

Λk = K z - ζ( )2dζ∫∫

€

Neff ≅ Nh

Λk

4πσ z,h

+Ne

X 2

Λk

4π σ z,e

€

δ 2 ′ = −2ξ δ 2 + D

€

ξ =−g δ i Im K Δζ i( )e ikΔζ i( ) / δ 2 ; D = g2Neff /2;

g = Go

Z 2

A

rp

ε⊥n

2 f ϕ 2( )(1− cosϕ1)l2

β⋅

⎧ ⎨ ⎩

⎫ ⎬ ⎭

,

€

Eo = 2Go ⋅γ o ⋅e

βε⊥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


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

distributions andfinite electron beam size

VORPAL Simulations Relevant to Coherent Electron Cooling, G.I. Bell et al., EPAC'08, (2008)

€

R =σ v⊥

σ vz

; T =vhx

σ vz

; L =vhz

σ vz

€

q = −Ze ⋅(1− cosωp t)

© TechX


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

R260

€

δ ct( ) = −R26 ⋅ x

€

ΔE = −eZ 2 ⋅Eo ⋅ l2 ⋅sin k DE − Eo

Eo

+ R16 ′ x − R26x + R36 ′ y + R46y ⎛

⎝ ⎜

⎞

⎠ ⎟

⎧ ⎨ ⎩

⎫ ⎬ ⎭

;

€

Δx = −Dx ⋅eZ 2 ⋅Eo ⋅L2 ⋅kR26x + ....

€

ζ⊥ =J⊥ζ CeC ; ζ // = (1− 2J⊥)ζ CeC ;

dεx

dt= −

εx

τ CeC⊥

;dσ ε

2

dt= −

σ ε2

τ CeC //

τ CeC⊥ =1

2J⊥ζ CeC

; τ CeC⊥ =1

2(1− 2J⊥)ζ CeC

;


€

X =εx

εxo

; S =σ s

σ so

⎛

⎝ ⎜

⎞

⎠ ⎟

2

=σ E

σ sE

⎛

⎝ ⎜

⎞

⎠ ⎟

2

;

dX

dt=

1

τ IBS⊥

1

X 3 / 2S1/ 2−

ξ⊥

τ CeC

1

S;

dS

dt=

1

τ IBS //

1

X 3 / 2Y−

1− 2ξ⊥

τ CeC

1

X;

€

εxn 0 = 2μm; σ s0 =13 cm; σ δ 0 = 4 ⋅10−4

τ IBS⊥ =4.6 hrs; τ IBS // =1.6 hrs

IBS in RHIC foreRHIC, 250 GeV, Np=2.1011

Beta-cool, A.Fedotov

€

εx n = 0.2μm; σ s = 4.9 cm

This allows a) 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 =τ CeC

τ IBS //τ IBS⊥

1

ξ⊥ 1− 2ξ⊥( ); S =

τ CeC

τ IBS //

⋅τ IBS⊥

τ IBS //

⋅ξ⊥

1− 2ξ⊥( )3

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


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

€

kDσ δ ~ 1

σ δ =σ E

Eo

€

ζCEC = −ΔE

E − Eo

≈e ⋅Eo ⋅ l2

γ ompc2 ⋅σ ε

⋅Z 2

A€

dE

dz= −eE peak ⋅sin kD

E − Eo

Eo

⎧ ⎨ ⎩

⎫ ⎬ ⎭

;

€

Δϕ =4πρ ⇒ ϕ = −8G ⋅Ze

πβεnkcm

⋅cos kcmz( ); r E = −

r ∇ϕ = −ˆ z

8G ⋅Ze

πβεn

⋅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


Polarizing Hadron Beams with Coherent Electron Cooling

New LDRD proposal at BNL: VL & V.Ptitsyn

Modulator

Kicker

Delay for hadrons

Electrons

Hadrons

l2High gain FEL (for electrons)

HW1left

helicity

HW2right

helicity

Modulation of the electron beam density around a hadron is CUAsed by value of spin component along the longitudinal axis, z. Hardons with spin projection onto z-axis will attract electrons while traveling through helical wiggler with left helicity and repel them in the helical wiggler with right 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 / dγ

This process will polarize the hadron beam V.N. Litvinenko, Y.Derbenev's 70th Birthday Symposium, JLab, August 2, 2010

Proposal to NP DoE, 5 years, $5.9M


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

Collaboration between BNL & JLab

DX DX19.6 m

Modulator, 4 mWiggler 7mKicker, 3 m

20 MeV SRF linacBea

m

dum

p

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

NovosibirskBudker Institute of Nuclear Physics

Siberian snakes

Magnetized cooling B

eam-beam effects

Slava and Coherent Electron Cooling or Cool side of Slava Vladimir N. Litvinenko C-AD, Brookhaven...

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