john adams institute for accelerator science lecture seriesjaiweb/slides/2013_abelleira.pdf ·...
TRANSCRIPT
Crab-waist collisions. From lepton to hadron colliders
José L. Abelleira, PhD candidate. École Polytechnique Fédérale de Lausanne (EPFL)
Oxford, 21st March 2013
John Adams Institute for Accelerator Science Lecture Series
Thanks to: R. de Maria, S.Russenschuck, F. Zimmermann (CERN), D.Shatilov (BINP SB RAS,Novosibirsk),
C. Milardi, M. Zobov (INFN/LNF, Frascati (Roma))
Contents
• The LHC • Flat beams • Crab-waists collisions concept • Crab-waist in DAΦNE • A new IR for LHC
2 José L. Abelleira
The Large Hadron Collider
José L. Abelleira 3
experiments
collimators
LHC final focus system
José L. Abelleira 4
Beam 1 Beam2
Antisymmetric optics due to the opposite direction of the beams
Luminosity
𝑑𝑑𝑑𝑑 = 𝐿σ𝑝
José L. Abelleira 5
The event rate for a process (number of collisions) is given by the cross section of the process times the luminosity.
Luminosity depends on by the beam parameters as follows.
𝐿 =𝑁2𝑛𝑏𝑓
4πσ∗𝑥σ∗𝑦1
1 + Φ2 Piwinski angle
𝑁 Particles per bunch. 1.15x1011 𝑛𝑏 Number of bunches. 2808 𝑓 Revolution frequency 11.245 kHz
σ𝑥,𝑦∗ Hor/vert beam size at IP* 16.7 μm
σ𝑧∗ bunch length 7.55 cm 𝜃 Crossing angle* 285 μm Φ Piwinski angle* 0.64 𝐿 Luminosity* 1034 cm-2 s-1
*For the experiments at IP1 and IP5.
Φ =θσ𝑧
2σ𝑥∗
The values for nominal LHC are given
Normalized separation
José L. Abelleira 6
A crossing angle is introduced to avoid parasitic collisions
Even thought there are collisions only in the IP, there are long range interactions between the two beams. A measure of the interaction between the beams is the normalized separation.
Δ𝑠𝑠𝑝 =𝑑𝑠𝑠𝑝σ𝑥
≈θσ𝑥′
Flat beams
José L. Abelleira 7
0 5 10 15 20 25 30 350
0.5
1
1.5
2
2.5
3
3.5
(σx σy )1/2 (µm)
L (1
034 c
m-2
s-1
)
f=1f=1.2f=1.4f=1.6f=1.8
Δ𝑠𝑠𝑝 ≈θσ𝑥′
= θε/β∗𝑥
For the same section area σ𝑥σ𝑦 Flat beams increase Δ𝑠𝑠𝑝, for a given θ Less θ for the same Δ𝑠𝑠𝑝
β𝑥 = 1.20 m β𝑦 = 1.20 m
β𝑥 = 0.60 m β𝑦 = 1.20 m
β𝑥 = 1.20 m β𝑦 = 0.60 m
R. De Maria
Hourglass effect
José L. Abelleira 8
Especially important when the β function at the IP approaches the bunch length.
Beam size is given as σ = εβ.
β(𝑠)=β∗ + 𝑠2
β∗
Length of the Collision section
θ
With Head-on collisions or small φ
But in Large Piwikinsi Angle (LPA) regime
𝑙𝑂𝑂 ≈ σ𝑧
𝑙𝑂𝑂 ≈2σ𝑥θ
What is important is the length of the collision section.
Crab-waist collisions
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An important limitation in hadron machines is beam-beam tune shift
;y
yNL
βξ
∝ ;1 2φσσ
βξ
+∝
yx
yy
N;
)1( 2φεξ
+∝
xx
N
x
z
σθσφ2
=
A Large Piwinski Angle Φ (LPA) reduces tune shift, allowing N↑ reduces the length of the collision section, allowing β𝑦↓
More luminosity
Suppressed by crab-waist scheme
On the other hand, a LPA induces strong X-Y resonances
2σz
2σx
θ z
x
4σx/θ
σz*θ
βY
José L. Abelleira 10
CP
With LPA. The Collision Point (CP) for each particle ≠ Interaction Point (IP), (minimum of β𝑦).
M. Zobov
2σz
2σx
θ z
x
4σx/θ
σz*θ
βY
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CP
M. Zobov
C-W scheme corrects this effect and brings for each particle the IP to the CP.
Crab-waist collisions
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José L. Abelleira 13
Conditions for the crab-waist sextupole
yy
xxskl
βθβββ
*
* /=Sextupole
strength
σx*/σy
*≥10 βx*/βy
*≥100 𝜀 𝑥 = 𝜀 𝑦
Suitable for lepton machines (ε𝑥≠ε𝑦) More challenging for hadron colliders
Crab-waist collisions
Δ𝜇 𝑥 = π𝑚 Δ𝜇 𝑦 = π
2(2𝑛 + 1)
Crab waist collisions in DAΦNE
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Start of switching off the CW sextupoles in both rings: 200 A 0 A
900 mA x 500 mA
C. Milardi M. Zobov
Crab waist collisions in DAΦNE
José L. Abelleira 15
OFF ON Minimum luminosity, highest background when the sextupoles are OFF
DAFNE luminosity monitor
KLOE luminosity monitor
KLOE background
C. Milardi M. Zobov
C-W collisions for hadron colliders
There are several facts that make difficult the implementation of crab-waist collisions in LHC: • Same charge of particles • Large L* • Large energy • Same emittance in the two planes
José L. Abelleira 16
A new IR for HL-LHC is presented with the following ingredients: • Large Piwinski Angle • Flat beams • Local chromatic correction ? • Crab-waists
A new IR for LHC
Local chromatic correction in both planes + crab-waist collisions
sext1
sext5
sext3
Chromatic correction
βx*=1.5 m
βy*=1.5 cm
17 José L. Abelleira
Δμx Δμy sext1 sext2 sext3
sext4
sext5
π/2 π/2 π/2
3π/2 3π/2 3π/2 3π/2 2π 5π/2 sext2 sext4
CRAB-WAIST SEXTUPOLE π/2
The extremely low 𝜷𝒚 asks for a symmetric optics in the IR
Phase advance from IP
Separation magnets
A new IR for LHC
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José L. Abelleira 18
A new IR for LHC
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45 mm 15σy
15σx
σ∗𝑥 / σ∗𝑦 =10 Minimum required according to beam-beam simulations.
Reference orbit
18 José L. Abelleira
θ = 4𝑚𝑚𝑚𝑑
A new IR for LHC
José L. Abelleira 19
Present IR LHC
Proposed IR What is this element?
Last quadrupole
José L. Abelleira 20
B0=-5.8 T
g=115 T/m
Double half quadrupole
By(x)
solution to have diff quadrupole sign for the 2 beams in the same aperture
S. Russenchuck
Dipolar component and sextupolar component
Kick due to the dipolar term
21 José L. Abelleira
Crab-waist simulations
CW = 0
CW = 0.5
Resonances
22 José L. Abelleira
Frequency Map Analysis (FMA) Effective for the beam-beam resonance suppression. Plot shown for θc = 1.5 mrad
Dmitry Shatilov Mikhail Zobov
Resonances suppressed
Work on progress
• Chromatic correction and sextupole compensation
José L. Abelleira 23
• Plan B
βx*=1.5 m
βy*=1.5 cm
θ = 4 mrad
βx*=3.5 m
βy*=3.5 cm
θ = 2.6 mrad
Conclusions
• An extremely-flat beam optics (βy*/βy
*=100) is conceptual possible for LHC and HELHC – Large Piwinski angle, to reduce the collision area and allow for a lower βy
* – Local chromatic correction – Possibility to have crab waist collisions that can increase luminosity and suppress
resonances – Can accept higher brightness.
24 José L. Abelleira
Bibliography
• W. Herr and B. Muratori. Concept of luminosity. • P. Raimondi1, D. Shatilov, M. Zobov, Beam-beam issues for colliding schemes with large Piwinski
angle and crabbed waist .
• J.L. Abelleira, et. al. ”Local Chromatic Correction Scheme and Crab-Waist Collisions for an Ultra-low beta* at the LHC”, Proc. of the 2012 International Particle Accelerator Conference, New Orleans, USA, p. 118 (2012).
• J.L. Abelleira,”Flat beam IR optics”, Joint Snowmass-EUCARD/AccNet-HiLumi LHC meeting Frontier capabilities for Hadron colliders. February 22-23; 2013, CERN, Switzerland
• J.L. Abelleira, ”Towards an extremely-flat beam optics with large crossing angle for the LHC”, EUCARD Annual Meeting, April 25-27, 2012, Warsaw, Poland.
José L. Abelleira 25
Thank you…
…For your attention
26 José L. Abelleira