a. castilla / january 2015 uspas accelerator physics 1 uspas accelerator physics 2015 old dominion...
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A. Castilla / January 2015 USPAS Accelerator Physics 1
USPAS Accelerator Physics 2015 Old Dominion University
Colliders, Luminosity, & Crabbing
Todd Satogata (Jefferson Lab) / [email protected]
Vasiliy Morozov (Jefferson Lab) / [email protected] Alex Castilla (ODU) / [email protected]
http://www.toddsatogata.net/2015-USPAS
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A. Castilla / January 2015 USPAS Accelerator Physics 2
Outline
Colliders Why and where? Issues
Accelerator Physics of Colliders Event rate Luminosity
Looking at the luminosity Fixed target Colliders: Gaussian bunches, head-on Optimization knobs and complications
Hourglass effect Crossing angle Crabbing
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A. Castilla / January 2015 USPAS Accelerator Physics 3
Colliders
Where?
Butchered slide from Steve Myers IPAC2012 New Orleans.
STAR detector at RHIC,J.G. Cramer UW Colloquium 2002.
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A. Castilla / January 2015 USPAS Accelerator Physics 4
Colliders (2)
Why?
www.businessinsider.com Laurent Egli.
Because they are super
cool!
True! But also:
Colliding beams
Fixed target
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A. Castilla / January 2015 USPAS Accelerator Physics 5
Probing “small things”
SUSY??
Weak nuclear force
Proton and neutron
Quarks, muon
Nuclear states transitions
Electron
Transitions in the inner-shell atomic states
Atomic states transitions
Lattice vibration in solids (phonons)1
1
1
1
1
1 ≈125
?? Higher energy →
higher resolution
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A. Castilla / January 2015 USPAS Accelerator Physics 6
Accelerator Basics of Colliders
More events in time → better statistic/resolution of the
processes.
- interactions per second,
- interaction cross section (machine independent),
- luminosity, relativistic invariant, independent of
the interaction and –very important- measurable.
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Accelerator Basics of Colliders (2)
*F. Zimmermann, SLAC Summer Institute (2012).
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Shining Beam on a Fixed Target
The interaction rate will be a function of:
- interaction cross section.
- beam particles flux.
- target density.
- target size. 𝒍=𝑐𝑜𝑛𝑠𝑡
𝝆𝑻=𝑐𝑜𝑛𝑠𝑡
𝝓
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The interaction rate will be a function of:
- Then:
- bunch frequency.
- number of particles per bunch.
- beam transverse profile.
Shining Beam on a Beam (Collider)
𝒍
𝝆𝑻=𝑐𝑜𝑛𝑠𝑡
target =
moving beam!
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Collider Luminosity
Per bunch crossing:
]
Where .
And is the kinematic factor .
Head-on collisions (), then .
For uncorrelated distributions:
𝑛1 𝑛2
𝑠0
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A. Castilla / January 2015 USPAS Accelerator Physics 11
Luminosity of Gaussian Bunches
https://en.wikipedia.org/wiki/Multivariate_normal_distribution
For two bunches with and particles respectively:
Where are the rms
horizontal/vertical beam sizes.
No offset and head-on collision.
𝑡=1𝑓
𝑛1 𝑛2
𝑠0
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For two beams:
]
The Gaussian distributions can be written:
, ;
where and indicates the bunch number.
Luminosity of Gaussian Bunches (2)
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Normal distributions are 0K for bunches in equilibrium.
Not Gaussian? → (most likely) numerical integration.
Simplest case: Identical bunches:
, , and
Even and can be easily calculated (we will keep ).
We will also consider no dispersion at the collision point.
Let’s try a bit of real-time math!
Luminosity of Gaussian Bunches (3)
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A. Castilla / January 2015 USPAS Accelerator Physics 14
Luminosity of Gaussian Bunches (4)
𝑡=1𝑓
𝑛1 𝑛2
Then
Again, for identical
beams, no crossing angle,
no dispersion, no off-set.
Where at the IP:
and
Is this “optimizable”?
What happens to the bunch’s shape here?
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A. Castilla / January 2015 USPAS Accelerator Physics 15
Turning Knobs for Luminosity
Not head-on collisions (crossing angle ).
Beam deformations at IP (hour-glass effects).
Desired or non-desired offsets.
Dispersion at IP.
Strong coupling, etc.
energy and
injector and beam-beam
total beam current
Reduction factor:hourglass effect,crossing angle…
More a complication rather than a knob?
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Hourglass Effect
-functions dependent on , usually:
Then :
Results important if .
*Werner Herr, CAS-Lectures, Bulgaria (2010).
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So the luminosity reduction factor:
Hourglass Effect (2)
“Enigmatic” dependency mentioned before!
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A Bit More Interesting Case (Crossing Angle)
Reduce parasitic collisions.
Physical space for magnets.
Better detector resolution.
𝑛1𝑛2
s
x
𝜃𝑐
2
𝜃𝑐
2
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Rotating Reference Frames (for each bunch)
s
x
, .
𝑠1
𝜃𝑐
2
𝑥1
𝑠2
𝜃𝑐
2
𝑥2
, .
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For the Distributions in the New Systems
For two beams:
]
Now we will use:
With some approximations: fairly small (mrad ~deg),
then:
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A. Castilla / January 2015 USPAS Accelerator Physics 21
For the Distributions in the New Systems (2)
Some more approximations since is small:
discarding
And so the result is slightly different:
• is ?• .
𝑹 (𝜽𝒄 ,𝝐 ,𝜷❑∗ ,𝝈𝒔)
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Crossing Angle w/o Correction
IP
𝜽𝒄
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*R. Palmer, SLAC-PUB-4707 (1988)..
electrons protons
The Crabbing Concept
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RF Transverse Deflection
𝑉 𝑇=∫−∞
∞
[𝐸𝑥 (𝑧 ) cos𝜔𝑧𝑐
+𝑐𝐵𝑦 (𝑧 ) sin𝜔𝑧𝑐 ]𝑑𝑧
𝑉 𝑇
𝑡
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RF Transverse Deflection (special case)
𝑉 𝑇=∫−∞
∞
[𝐸𝑥 (𝑧 ) cos𝜔𝑧𝑐
+𝑐𝐵𝑦 (𝑧 ) sin𝜔𝑧𝑐 ]𝑑𝑧
𝑉 𝑇
𝑡
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Local Crab Crossing Correction
IP
𝜽𝒄
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Jefferson Lab’s Medium Energy Electron-Ion Collider
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The MEIC at JLab
Y. Zhang, et al. arXiv:1209.0757v2 (2012).
A. Accardi, et al. arXiv:1110.1031v1 (2011).
• () and luminosity.
Deep inelastic scattering.
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A. Castilla / January 2015 USPAS Accelerator Physics 29
The MEIC Layout
V. S. Morozov , MEIC study group (2013).
IP’s
IP
Ions
Ions
Electrons
Electrons
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The MEIC Luminosity Approach
Short bunches for both species.
Small transverse emittance.
Ultrahigh collision frequency CW beams.
Staged electron cooling.
Small final focusing .
Large beam-beam tune shift.
Crab crossing.
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A. Castilla / January 2015 USPAS Accelerator Physics 31
MEIC Crabbing Requirements
𝑉 𝑇=𝑐𝐸𝑏 tan
𝜽𝒄
2
𝜔𝑟𝑓 √𝛽𝑥∗𝛽𝑥
𝑐
Parameter Units Electron Proton
Beam energy GeV 5 60Bunch frequency MHz 750.0Crossing angle mrad 50Betatron function at the IP cm 10Betatron fn. at the crab cavity m 300 1400Integrated kicking voltage MV 1.35 8
• High repetition.• Big crossing angle. 𝒑
𝒆−
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Transverse Kick (e.g. 750 MHz SRFD)
𝑉 𝑇=∫−∞
∞
[𝐸𝑥 (𝑧 ) cos𝜔𝑧𝑐
+𝑐𝐵𝑦 (𝑧 ) sin𝜔𝑧𝑐 ]𝑑𝑧
Electric Field Magnetic Field 𝐸𝑇=𝑉 𝑇
𝜆2
⇒𝑉 𝑇∗=0.2𝑀𝑉
𝐸𝑇∗=1
𝑀𝑉𝑚
𝑉 𝑇 ,𝐻∗ =−0.2𝑀𝑉
𝑉 𝑇 ,𝐸∗ =0.4𝑀𝑉
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Most of the Content Borrowed from
W. Herr “Concepts of luminosity for particle colliders” CAS-Lectures, Varna, Bulgaria 2010.
F. Zimmermann “LHC: The machine”, SLAC Summer Institute 2012.
J. G. Cramer “Surprises from RHIC” UW Phys. Dept. Colloquium 2002.
And many more…