slava and coherent electron cooling or cool side of slava vladimir n. litvinenko c-ad, brookhaven...
TRANSCRIPT
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
CeC - Equations
CeC - Equations
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
V.N. Litvinenko, Y.Derbenev's 70th Birthday Symposium, JLab, August 2, 2010
€
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…
V.N. Litvinenko, Y.Derbenev's 70th Birthday Symposium, JLab, August 2, 2010
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
V.N. Litvinenko, Y.Derbenev's 70th Birthday Symposium, JLab, August 2, 2010
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∫∫
V.N. Litvinenko, Y.Derbenev's 70th Birthday Symposium, JLab, August 2, 2010
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
V.N. Litvinenko, Y.Derbenev's 70th Birthday Symposium, JLab, August 2, 2010
How to understand your ideas and concepts?
V.N. Litvinenko, Y.Derbenev's 70th Birthday Symposium, JLab, August 2, 2010
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..
V.N. Litvinenko, Y.Derbenev's 70th Birthday Symposium, JLab, August 2, 2010
Main message to take home:
Happy Birthday!30 more productive
years!
V.N. Litvinenko, Y.Derbenev's 70th Birthday Symposium, JLab, August 2, 2010
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
V.N. Litvinenko, Y.Derbenev's 70th Birthday Symposium, JLab, August 2, 2010
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
V.N. Litvinenko, Y.Derbenev's 70th Birthday Symposium, JLab, August 2, 2010
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
;
V.N. Litvinenko, Y.Derbenev's 70th Birthday Symposium, JLab, August 2, 2010
€
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
V.N. Litvinenko, Y.Derbenev's 70th Birthday Symposium, JLab, August 2, 2010
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
V.N. Litvinenko, Y.Derbenev's 70th Birthday Symposium, JLab, August 2, 2010
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
V.N. Litvinenko, Y.Derbenev's 70th Birthday Symposium, JLab, August 2, 2010
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