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