A. Castilla / January 2015 USPAS Accelerator Physics 1 USPAS Accelerator Physics 2015 Old Dominion...

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

mailto:[email protected]







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


Colliders

Where?

Butchered slide from Steve Myers IPAC2012 New Orleans.

STAR detector at RHIC,J.G. Cramer UW Colloquium 2002.


Colliders (2)

Why?

www.businessinsider.com Laurent Egli.

Because they are super

cool!

True! But also:

Colliding beams

Fixed target

http://www.businessinsider.com/


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


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.


Accelerator Basics of Colliders (2)

*F. Zimmermann, SLAC Summer Institute (2012).


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


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!


Collider Luminosity

Per bunch crossing:

]

Where .

And is the kinematic factor .

Head-on collisions (), then .

For uncorrelated distributions:

𝑛1 𝑛2

𝑠0


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




For two beams:

]

The Gaussian distributions can be written:

, ;

where and indicates the bunch number.

Luminosity of Gaussian Bunches (2)


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!




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?


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?


Hourglass Effect

-functions dependent on , usually:

Then :

Results important if .

*Werner Herr, CAS-Lectures, Bulgaria (2010).


So the luminosity reduction factor:

Hourglass Effect (2)

“Enigmatic” dependency mentioned before!


A Bit More Interesting Case (Crossing Angle)

Reduce parasitic collisions.

Physical space for magnets.

Better detector resolution.

𝑛1𝑛2

s

x

𝜃𝑐

2

𝜃𝑐

2


Rotating Reference Frames (for each bunch)

s

x

, .

𝑠1

𝜃𝑐

2

𝑥1

𝑠2

𝜃𝑐

2

𝑥2

, .


For the Distributions in the New Systems

For two beams:

]

Now we will use:

With some approximations: fairly small (mrad ~deg),

then:


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)


Crossing Angle w/o Correction

IP

𝜽𝒄


*R. Palmer, SLAC-PUB-4707 (1988)..

electrons protons

The Crabbing Concept


RF Transverse Deflection

𝑉 𝑇=∫−∞

∞

[𝐸𝑥 (𝑧 ) cos𝜔𝑧𝑐

+𝑐𝐵𝑦 (𝑧 ) sin𝜔𝑧𝑐 ]𝑑𝑧

𝑉 𝑇

𝑡


RF Transverse Deflection (special case)

𝑉 𝑇=∫−∞

∞



𝑉 𝑇

𝑡


Local Crab Crossing Correction

IP

𝜽𝒄


Jefferson Lab’s Medium Energy Electron-Ion Collider


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.


The MEIC Layout

V. S. Morozov , MEIC study group (2013).

IP’s

IP

Ions

Ions

Electrons

Electrons


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.


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−


Transverse Kick (e.g. 750 MHz SRFD)

𝑉 𝑇=∫−∞

∞



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


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…

A. Castilla / January 2015 USPAS Accelerator Physics 1 USPAS Accelerator Physics 2015 Old Dominion...

Documents

Transcript of A. Castilla / January 2015 USPAS Accelerator Physics 1 USPAS Accelerator Physics 2015 Old Dominion...