one more look into erl-ring lhec vladimir n. litvinenko, frank zimmermann , rogelio tomas
DESCRIPTION
One more look into ERL-ring LHeC Vladimir N. Litvinenko, Frank Zimmermann , Rogelio Tomas. Key ingredients: CW ERL low β * ~ 10 cm c rossing angle to avoid synchrotron radiation in the detector using low electron beam current and coherent electron cooling - PowerPoint PPT PresentationTRANSCRIPT
One more look into ERL-ring LHeC
Vladimir N. Litvinenko, Frank Zimmermann, Rogelio Tomas
Key ingredients: CW ERL low β* ~ 10 cm crossing angle to avoid synchrotron radiation in the detector using low electron beam current and coherent electron cooling power consumption < 100 MW Luminosity > 1E34 cm-2 sec-1
Selecting key parameters
LHC protons Energy 7 TeVg_p 7.46E+03 N_p 1.70E+11 No Cooling Emittance, norm 3.75 mm mradEmittance 5.03E-01 nm radAllowable tune shift 0.01 Maximum # of e 3.07E+11 Rep-rate 2.00E+07 HzI max 9.84E-01 ARealistic 0.008 AN real 2.50E+09 Room for improvement 1.23E+02 b* 0.1 m4pbe 6.32E-10 m^2L/h 1.34E+33
With cooling Emittance, norm 0.2 mm mradEmittance 2.68E-02 nm radAllowable tune shift 0.01 Maximum # of e 1.64E+10 Rep-rate 2.00E+07 HzI max 5.25E-02 ABeam current 0.008 AN real 2.50E+09 Room for improvement 6.56E+00 b* 0.1 m4pbe 3.37E-11 m^2L/h 2.52E+34
Selecting key parametersfor 60 GeV ERL
Length acc 1 1 mGradient 15 18 MeV/m
Energy per cavity 15 18 MeVR/Q 403 403 WQ 4.00E+10 2.50E+10
Power loss, stat 5.00E+00 5.00E+00 WPower loss, RF 1.40E+01 3.22E+01 W
Power loss, total 1.90E+01 3.72E+01 WFilling factr 0.57 0.57
Real-estate gradient 8.55 10.26 MeV/mLength per 1 GeV 116.96 97.47 m
#of cavities per 1 GeV 66.67 55.56Power loss per GeV 1.26E+03 2.06E+03 W @ 2K
1.8K -> 320 K 177.78 177.78inefficiency 3.37 3.37Power boost 599.47 599.47
Power per 1 GeV 100% 7.58E+05 1.24E+06 W room T
Efficiency nominal 0.22
Doable 0.30
He 2K refrigerator: ~700 W at RT per 1 Watt at 2K
BNL type 700 MHz cavity
Selecting key parametersfor 60 GeV ERL
Radius, r Cryo RF main RF SR Magnets Total Passes
500.00 MW
2 x 7.5 GeV linacs 18.56 16.67 60.25 4 99.48 4
2 x10 GeV linacs 24.75 22.22 46.08 3 96.05 3
2 x 15 GeV linacs 37.13 33.33 32.40 2 104.86 2
30 GeV linac, dogbone 37.13 33.33 48.17 3 121.63 DGBN
CW linac for ERL 10 10 GeVat 2 K 13 21 kWCryo-plant power 7.58 12.38 MW
60 GeV ERL
Coherent-electron-Cooling would provide following for linac-ring
LHeC• Smaller proton beam emittance down to 0.2 mm
mrad
• Can provide shorted bunches down to 1 cm (if needed)
• Allows to reduce electron beam current 20-fold to achieve of e-p luminosity above 1034 level with 60 GeV electrons and 7 TeV protons
Layout for ERL based LHC
• Energy of the ERL - 60 GeV• Polarized electron beam current - 8 mA• Number of passes – 3• AC power consumption – 100 MW
R=700mR=700m
10 GeV linac
10 GeV linac
0.5 GeVERL-injector
DumpGun
Sample of CeC for LHeC
LHC Cooling time
Circumference 26658.883 m Full bunch 0.346 hrs
Main Parameters CeC Local 176.27 sec
Modulator Length 70 m Length of the system 153.70 m
Kicker length 35 m FEL length 48.70 m
Peak current, e 100.0 A FEL gain length 3.08 m
Amplification 1000.00
Wavelength 10 nm FEL formula TRUElw 5 cm Checks TRUE
FEL bandwidth 0.02
We are using here conservative 0.8 hrs cooling time
V.N. Litvinenko, ABP Forum, CERN, April 9, 2010
€
X =εxεxo
; 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 / 2S1/ 2−
1− 2ξ⊥
τ CeC
1
X;
Evolution of beam in LHC at 7 TeV with IBS and CeC(assuming nominal LHC bunch intensity 1.15e11 p/bunch and 40% of CeC cooling capability)
€
εxn0 = 3.75μm; σ s0 = 7.55cm
τ IBS⊥ = 80 hrs; τ IBS // =61 hrs €
σε2
τ IBS //
=Nrc
2c
25πγ 3εx3 / 2σ s
f χ m( )β yv
; εx
τ IBS⊥
=Nrc
2c
25πγ 3εx3 / 2σ s
H
β y1/ 2 f χ m( ) ;κ =1
f χ m( ) =dχ
χχ m
∞
∫ lnχ
χ m
⎛
⎝ ⎜
⎞
⎠ ⎟e
−χ ; χ m =rcm
2c 4
bmaxσ E2 ;bmax ≅ n−1/ 3; rc =
e2
mc 2; (e− > Ze;m− > Am)
IBS rates in LHC from
Table 2.2
€
X =τ CeC
τ IBS //τ IBS⊥
1
ξ⊥ 1− 2ξ⊥( ); S =
τ CeC
τ IBS //
⋅τ IBS⊥
τ IBS //
⋅ξ⊥
1− 2ξ⊥( )3
Stationary solution for τCeC = 0.8 hrs
€
εx n = 0.19μm; σ 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
Details on power consumption
Details of Coherent Electron Cooler for LHC
Sample of CeC for LHeC
Hadrons Z 1 A 1
Energy per nucleon 7000 GeVEnergy per nucleon 7.000000E+12 eV
g 7460.52 N, part/bunch 1.70E+11
Charge 27.24 nCBunch length 0.250 nsec
Bunch lengt, RMS 0.075 mPeak current 43.46 A
Emmitance, norm 3.75 mm mradEmmitance, m rad 5.02646E-10
sE/E 1.00E-04 sE (for entire ion, if one) 7.00E+08 eVLong emittance, RMS 0.175 eV sec
f rev 1.12455E+04 HzF beam 4.00000E+07 HzBuckets 3557
c-v 2.69E+00 m/sec1-bo 8.98E-09
Electrons 1 Energy 3.812 GeVEnergy 3.812E+09 eVg 7460.52 N, part/bunch 3.12E+10 Charge 5.0 nCBunch length 0.050 nsecBunch lengt, full 0.015 mPeak current 100.0 AEmittance, norm, RMS 2 mm mradEmittance, RMS 2.681E-10 m radsE/E 5.25E-05 sE 2.00E+05 eVLong emittance 1.000E-05 eV sec
Sample of CeC for LHeCModulator Hadrons Electrons Length 70 m Time of flight, Lab 2.33495E-07 sec
Time, co-moving 3.12974E-11 sec*b 35 m *b 82.55 m
< >b 46.67 m < >b 87.50 ms 1.53E-04 m s 1.53E-04 m Density, Lab Frame 1.41E+19 m-3
ne, density CM 1.89E+15 m-3
le, lab frame 5726.7 m we, CM 2.45E+09 HzPhase advance, plasma 7.68E-02 rad
s v// 2.99792E+04 m/sec s v// 1.57274E+04 m/sec
rD_//, CM 9.38E-07 m rD_//, CM 4.92E-07 mrD_//, Lab frame 0.126 nm rD_//, Lab frame 0.066 nm
sq 3.78963E-06 rad sq 1.80203E-06 rad
s v_t/c2.827263E-
02 s v_t/c1.344408E-
02 s vt 8.47592E+06 m/sec s vt 4.03044E+06 m/secr_t 2.653E-04 m r_t 1.261E-04 m
Z, rms 1.91 T, rms 538.93 R 256.27
Buncher <= 1 1 Modulation 7.97E-02
Sample of CeC for LHeCFEL
Wavelength 10 nm lcritical 3.369 nmAmplification 1000.00 4 /pe l 0.337 FEL length 48.70 m Wavelength 1.00E-08 m b 5 m
k 6.28E+08 m^-1 s 3.66E-05 mWiggeler hd 1.127E+00 TRUE
lw 5 cm he 1.279E-01 TRUElw 0.05 m hg 2.502E-02 TRUE
lw/2g2 4.49E-10 m L 6.228E-01 TRUEaw 4.611 Helical 10 14.18 m
Field 0.000 100 28.36 mKo 6.521 Plane 1000 42.54 m
ku1.25664E+0
2 //g 1581.13883 Gain Sat L SAT GL 1- //b 2.00E-07
r 1.211E-03 41.3 21.8 1-bgroup 1.33E-07 L_Go 1.898E+00 m Power -bo bgroup -1.24E-07
2*L_Go 3.795E+00 m Ampl DS -6.06E-06 mGain length 3.079E+00 m Power Gain length 6.159E+00 m Ampl
Periods per gain length 62 Result TRUE
Sample of CeC for LHeC
Dispersion for hadrons
Long. dispersion 1.59E-05 mLength required 885.85 mWith chicane 38.96 m
Req angle 0.000639137 radMagnets, 4 x 14.91 T mDispacement 0.012 m
Kicker Length of the kicker 35 m
b* h 17.5 mb* e 32.8 m b eff 35.72 m
Area 6.016E-08 m2
Area 6.016E-04 cm2
ne, density CM 4.64E+15 m-3
we, CM 3.84E+09 Hzle, lab frame 3658.82 m
Plasma phase advance 0.060 radReduction 9.99E-01
Charge 3.83E-08 ESUDensity 6.36E-05 ESU/cm
Field, Amplitude 7.99E-04 GsField, Amplitude 2.40E-01 V/cmField, Amplitude 2.40E+01 V/mPhase advance 1.00E+00Field at hadron 2.02E+01 V/m
DE 7.06E+02 eVN_turns 1.98E+06
Local cool time 176.27 secFull bunch 1246.42 sec
Local cool time 2.94 minsFull bunch 20.77 mins
Local cool time 0.049 hoursFull bunch 0.346 hours