Overview of a Synchrotron Design: LHC

Overview of a Synchrotron design: LHC

Winter Session 2018 MJS USPAS Fundamentals 1 Overview of LHC Accelerator Mike Syphers

Large Hadron Collider ( LHC ) Outline of Presentation

• Brief history... • Luminosity • Magnets • Accelerator Layout • Major Accelerator Issues • U.S. Participation A Brief History... • CERN built LEP Collider (27 km) in 1980’s to study Z, etc.; ran very successful program from 1989-2000. • In 1989 U.S. authorized building of SSC -- 20 TeV x 20 TeV, p-p, 87 km, 6.6 T magnets -- 1033cm-2sec-1; scheduled completion date of 1997. • ~1990, CERN speciﬁed the Large Hadron Collider (LHC), using LEP tunnel, to compete with SSC -- 8 TeV (lowered to 7 TeV; 8 T), 1034cm-2sec-1. • After $2B spent on site in Texas, SSC cancelled by U.S. government in 1993; LHC spec’s remained the same, and was commissioned about 15 years later... Luminosity • Want to achieve 1034cm-2sec-1 luminosity at 7 TeV... • For counter-rotating bunches of particles: fN2 L = ·F(θ) , where... 4πσ2 f = frequency of bunch collisions N = number of particles per bunch σ = rms transverse beam size at interaction point F = luminosity reduction factor due to crossing angle, θ f = c / bunch spacing = 3 × 108/7.5 = 40 MHz = 1/(25 nsec) F(θ) depends on beam crossing angle, but also on beam size, bunch length -- ~85% for LHC Luminosity

• Goal: compete with SSC (20 TeV, 1033), but with 7 TeV ===> 1034 cm-2 s-1

2 1 f0BN γ if ∗ L = ∗ · σz ≪ β 4πβ ϵN 2 1+ ασz 2σ0 ! " # c 3 × 108 Some Givens: f0 = = Hz = 11.2kHz C 2.67 × 104

γ =7000/0.938 = 7500

ϵN =3.75 µm(=22(rms,.5π mmnormalized)· mrad, FNAL) (from SPS) Luminosity (cont’d) ∗ 1 ∗ Take β ≈ 2 m; choose σz = 7 cm ≪ β (see next slide)

Choose frf = 400 MHz (200 MHz at injection)... h = 35640; then, ﬁll every 10 buckets −→ B = 3564 (25 nsec) gaps, for abort, ﬁlling scenarios, etc. −→ B =2808 α: use 285 µrad (givesx ˆ = 6 mm in triplet quads)

∗ ∗ note: σ0 = !ϵN β /γ = !(3.75)(0.5)/7500 = 16 µm then, ασz (285)(0.07) d β∗ = =0.623 ≈ α γ 2σ0 2(16) σ !ϵN · −6 1/2 · 3 and =28510 −6 (7.5 10 ) 1 !3.75 · 10 =0.85 =9 !1+(0.623)2 for N ≈ 1011,

3 11 2 (11.2 × 10 )(2808)(10 ) (7500) − − L = · 0.85 = 8 × 1033 cm 2sec 1 4π(50)(3.75 · 10−4)cm2sec

So, tweak... N =1.15 × 1011 −→ 1 × 1034 cm−2sec−1 34 −24 LΣint 10 · (0.060 · 10 ) ⟨n⟩ = = = 19 !! Note: Bf0 2808 · 11, 200 (Interactions per bunch crossing) (was = 1 in the SSC!!)

To get σz ≈ 7 cm ...

2 S 3π 3π 2πf σ = σ2 = rf z =0.4 A 8 φ 8 ! c "

Choose bucket area A = 8 eV-sec, 2 πAfrf and longitudinal emittance S =2.8 eV-sec: eV =2πhηEs → V = 16 MV ! 8Es "

A bucket height, k = πfrf =3.6 × 10−4 4Es

νs = hη · k/2=1/472 synchrotron frequency: fs = f0νs =23Hz Bunch Spacing • Quoted as 25 nsec, but structure is more complicated due to ﬁlling scheme from the SPS. • So, there will be various gaps created, with minimum spacing 25 nsec...

Hence, fewer bunches than simply 27km/7.5m ... Why a Crossing Angle?

• Across each interaction region, for about 120 m, the two beams are contained in the same beam pipe • Thus, there would be ~(120/(7.5/2)) ~ 30 bunch interactions through the region • Want a single Head-on collision at the IP, but will still have long-range interactions on either side • Beam size grows from IP, and so does separation; can tolerate beams separated by ~10 sigma • d/ σ = θ · (β∗/σ∗) ≈ 10 −→ θ =10· (0.017)/(550) ≈ 300 µrad Other parameters... N # standard bends = b (#dip, 1/2 cells, cells, sides) · · · N · · · =8 [3 2 cells/arc +2 2 2 2] =8· (6 · 23 + 16) =1232

· 2π so, θ0 =3 1232 =15.3 mrad (per half cell)

√ ˆ Lθ0 1 2 D = 2 1+ =2.2m (√2/2) ! 2 2 "

1 1 bends 1 ν ≈ 8 · (23 + 4 + 4) · +4· ≈ 60 γt ≈ νx ≈ (23 + 4) · · 8=54 (55.7) 4 2 4

To deal with coupling, split tunes: νx − νy =5

◦ µx − µy ≈ 5/(8 · 23) = 0.027 = 1.5 General Map

Underground Facilities red = LHC project rest = from LEP General Layout Straight Sections

• 1,5: Low-beta • 2,8: not-so-low beta • 3,7: cleaning • 3: momentum; 7: x-verse • 4: RF • 6: abort/dump All different designs, with different requirements Optics • Use of LEP tunnel ... −→ ρ ∼ 2.8km Bρ 7000 · 10/3Tm = =8.33 T ρ 2.8 × 103m

≈ ≈ Ncells !2Cfeet √87464 300 each IR 9 cells + 4 DS 13 cells ∼ ≈ ≈ thus, 300 − 8×13 = 196 196 8 = 24.5 cells/arc

30 km 1 (optimization −→ 23 cells/arc) L ≈ · ≈ 50 m 300 2 53.45 1+√2/2 Chosen value : L =53.45 m βˆ = =182m √2/2!1 √2/2 − Also chose: µ =90◦/cell 53.45 1 √2/2 βˇ = − =30m √2/2!1+√2/2 Standard Cell F Bending D Bending F

LHC V6.5 Beam1 Arc CellCELL.12.B1 450GeV Injection (pp) %Crossing Bumps(IP1=100% IP5=100% 200. 2.1 ) ) x y x (m ! ! D (m y 2.0 x ! 182. D ), 1.9 (m

x 164. ! 1.8

146. 1.7

128. 1.6

110. 1.5

1.4 92.

1.3 74.

1.2

56. 1.1

38. 1.0

20. 0.9 0.0 10. 20. 30. 40. 50. 60. 70. 80. 90. 100. 110. 120. Momentum spread = 0.00 % s (m) Interaction Regions • Beams collide in region much like at Tevatron... • asymmetric triplet magnets focus to small spot • zero momentum dispersion

LHC V6.500 Collision LHCB1 IR1 Crossing Bumps(IP1=100% IP5=100% IP2=100% IP8=100%) MAD-X 3.03.02 23/0

) 5000. 2.5 ) m m ( (

optics adjusted y β x β y Dx Dy y β D , , ) 4500. ) • m m ( ( x x β (“squeeze”) once at 2.0 D 4000.

1.5 ﬁnal energy 3500.

3000. ∼ σ2 1.0 2500.

0.5 2000.

1500. 0.0

1000.

-0.5 500.

0.0 -1.0 12.78 13.00 13.22 13.44 13.66 13.88 Momentum offset = 0.00 % Distance (km) s (m) [*10**( 3)] RF straight section

LHC V6.5 Beam1 IR4 450GeV Injection (pp) %Crossing Bumps(IP1=100%. IP5=100% IP2=100% MAD-X 2. IP8= 500. 2.2 ) ) x y x y (m ! ! D D (m y y ! 450. 2.0 D , ), ) (m (m x 400. 1.8 x ! D

350. 1.5

300. 1.2

250. 1.0

200. 0.8

150. 0.5

100. 0.2

50. 0.0

0.0 -0.2 9.4 9.6 9.8 10.0 10.2 10.4 10.6 Momentum offset = 0.00 % s (m) [*10**( 3)] Beam Dump SS

LHC V6.5 Beam1 IR6 7000GeV Low beta in all IPs %Crossing Bumps(IP1=100%MA IP5=100% IP2=100 650. 2.2 ) ) x y x y (m ! ! D D (m y 2.0 y ! 585. D , ), ) 1.8 (m (m x 520. x ! D 1.5 455. 1.2

390. 1.0

325. 0.8

0.5 260.

0.2 195.

0.0 130. -0.2

65. -0.5

0.0 -0.8 16.1 16.3 16.5 16.7 16.9 17.1 17.3 Momentum offset = 0.00 % s (m) [*10**( 3)] Momentum Cleaning SS

LHC V6.5 Beam1 IR3 450GeV Injection (pp) %Crossing Bumps(IP1=100% IP5=100%. IP2=100% MAD-X 2. IP8= 450. 3.0 ) ) x y x y (m ! ! D D (m

y 2.5 y ! 405. D , ), ) 2.0 (m (m x 360. x ! D 1.5 315. 1.0

270. 0.5

225. 0.0

-0.5 180.

-1.0 135. -1.5 90. -2.0

45. -2.5

0.0 -3.0 6100. 6300. 6500. 6700. 6900. 7100. 7300. Momentum offset = 0.00 % s (m) X-verse Cleaning SS

LHC V6.5 Beam1 IR7 7000GeV Low beta in all IPs %Crossing Bumps(IP1=100%MA IP5=100% IP2=100 400. 3.0 ) ) x y x y (m ! ! D D (m y y ! D

350. 2.5 , ), ) (m (m x x ! D 300. 2.0

250. 1.5

200. 1.0

150. 0.5

100. 0.0

50. -0.5

0.0 -1.0 19.4 19.6 19.8 20.0 20.2 20.4 20.6 Momentum offset = 0.00 % s (m) [*10**( 3)] All Together (inj optics)...

LHC V6.5 Beam1 Quads 450GeV Injection (pp) %Crossing Bumps(IP1=100%. IP5=100 MAD-X % 600. ) x (m !

x 550. !

500.

Horiz 450. only 400.

350.

300.

250.

200.

150.

100.

50.

0.0 0.0 5.0 10.0 15.0 20.0 25.0 30.0 Momentum spread = 0.00 % s (m) [*10**( 3)] Dispersion

LHC V6.5 Beam1 Quads 450GeV Injection (pp) %Crossing Bumps(IP1=100%. IP5=100% MAD-X IP 3.0 ) x

(m D x 2.5 D

2.0

1.5

1.0

0.5

0.0

-0.5

-1.0

-1.5

-2.0

-2.5

-3.0 0.0 5.0 10.0 15.0 20.0 25.0 30.0 Momentum spread = 0.00 % s (m) [*10**( 3)] Magnets

• Required Bend Radius: • circumference ~27 km; ~65% packing fraction • pckg. frac. small, due to prior use as e-collider • thus, bend radius ~ 2.8 km 10 · B =(Bρ)/ρ =(p/e)/ρ = 3 7000 T-m/2800 m = 8.3 T

• Use superconducting magnets, at superﬂuid He temperatures (1.8 K) to get maximum ﬁeld Magnets (cont’d) • “Cosine theta” design... • Tevatron, for instance: B • LHC -- dual-bore: Tevatron Dipole Coil coil thickness ⃗ = µ0 Jd ˆ B 2 j

4πT m/A (500 A/mm2)(25 mm) B ≈ ! 107 " 2 ≈ 8T

(crude approx.) Magnets (cont’d)’

• Very complicated objects! • Two magnet systems in one • All power cables run through at 1.8K • Final magnet current at 8.3 T -- 11,850 A Magnet Interconnects

• Not a simple operation ... Magnets (cont’d)’’ Magnets (cont’d)’’’

• Parts produced by outside vendors, ﬁnal assembly was at CERN (Prevessin)

• 1232, 15 m-long dipole magnets + quadrupoles! Major Accelerator Issues • Stored Energy • Tevatron = 1-2 MJ per beam; LHC = 360 MJ ! • extensive collimation and protection system

Dec 5, 2003 accident in Tevatron -- ~1 MJ D49 target E03 1.5m collimator Major Accelerator Issues

• IR Protection • not only stored energy of beam, but also the product power at the IP: (60 mb)(1034 cm−2sec−1)(2×7 · 1012 eV) = 1.3 kW signiﬁcant fraction of this power will be deposited into SC magnets at each IR!

Certainly an issue for future increases in luminosity Accel. Issues (cont’d) • Electron Cloud • Protons in the LHC will emit synchrotron radiation -- 6.7 keV/turn -- 3.6 kW/ring! • photo-electrons emitted from beam pipe wall, can further interact with wall molecules and cause a build-up of vacuum pressure -- beam screen required

• photo-electrons can also interact with beam, causing beam instabilities Accel. Issues (cont’d)

• ... and many others... • Persistent Currents and Field Control of magnets • Beam-beam interactions -- head-on and long-range • Impedance effects and beam instabilities • Future luminosity upgrade path.... • Has been an exciting accelerator project!! U.S. LHC Accelerator Research Program (LARP) • DoE-funded program (~$11M/year) which provided... • help with commissioning of hardware and beam • accelerator physics calculations • instrumentation development • luminosity monitors, beam diagnostics, etc. • studies of collimator improvements for future luminosity upgrades • help for development of future IR and IR magnet upgrades https://home.cern/topics/large-hadron-collider