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### ILC Beam Dynamic

ILC= International Linear Collider

It is a project designed to smash together electrons and positrons at the center of mass energy of 0.5 TeV initially and 1 TeV later.

The ILC Global Design Effort team, established in 2005, has been making its accelerator design. Recently, it worked out the baseline configuration for the 30-km-long 500 GeV collider.

Freddy Poirier

FLC / EUROTEV group

R

At high energy,

linear collider is

more cost effective

Circular

Collider

cost

Linear Collider

Energy

Why a straight machine?- Synchrotron Radiation
Bending a particle = loosing some energy

DE ~ (E4 /m4 R)

- From a cost point of view:

Physics at the ILC (1)

Exemple with e+/e- LEP experiment: Indirect determination of

the top quark mass.

Proves high energy reach

through virtual processes

- Explore new Physics through high precision at high energy
- Study the properties of new particles (Cross-sections, BR’s, Quantum numbers) ILC=microscope
- Study known SM processes to look for tiny deviations through virtual effects (needs precision of measurements and theoretical predictions)

- Precision measurements will allow:
- Distinction of different physics scenarios
- Extrapolation to higher energies
ILC=telescope

ILC will provide a detailed map of new physics

Physics at ILC (2)

- Comprehensive and high precision coverage of energy range from Mz to ~ 1TeV
- Physics Topics:
- Higgs Mechanism
- Supersymmetry
- Strong Electroweak Symmetry Breaking
- Precision Measurements at lower energies

- Physics Topics:

cross sections few fb to few pb

e.g. O(10,000) HZ/yr

Luminosity

- Parameters for the ILC from physics point of view:
- Ecms adjustable (90500GeV)
- Luminosity int Ldt=500 fb-1 in 4 years
- Ability to scan
- Energy stability and precision below 0.1%
- Polarisation of electrons (at least 80%)

To achieve high luminosity small sizes at the interaction point have to be achieved

What is needed to reach high luminosity?

Before going to the world of beam dynamic, let’s have a look at the ILC

Layout of the ILC

Long straight sections (e-/e+)

500 GeV

10 km

~31 km

Upgraded energy (~1TeV)

Nominal:

Scheme of the ILC

Electron source

To produce electrons, light from a titanium-sapphire laser hit a target and knock out electrons. The laser emits 2-ns "flashes," each creating billions of electrons. An electric field "sucks" each bunch of particles into a 250-meter-long linear accelerator that speeds up the particles to 5 GeV.

Damping Ring for electron beam

In the 6-kilometer-long damping ring, the electron bunches traverse a wiggler leading to a more uniform, compact spatial distribution of particles.

Each bunch spends roughly 0.2 sec in the ring, making about 10,000 turns before being kicked out. Exiting the damping ring, the bunches are about 6 mm long and thinner than a human hair.

Main Linac

2 main linear accelerators, one for electrons and one for positrons, accelerate bunches of particles up to 250 GeV with 8000 superconducting cavities nestled within cryomodules. The modules use liquid helium to cool the cavities to - 2°K. Two ~10-km-long tunnel segments, house the two accelerators. An adjacent tunnel provides space for support instrumentation, allowing for the maintenance of equipment while the accelerator is running.

5 nano m

Squeeze the beam as small as possible

for High luminosity

Beam Dynamic

- Beam dynamic is the study of the evolution of the beam through the various sections:
- Here we’ll look at the beam dynamic in the linear accelerator section.
- i.e. after the Bunch compressor and before the Beam Delivery System (BDS)

- The accelerator section is part of the LET (Low Emittance Transport):
- The goal of game here is to accelerate the beam from 15 GeV up to 250 GeV (for center of mass energy of 500 GeV)
- Keep the emittance growth as low as possible

- Here we’ll look at the beam dynamic in the linear accelerator section.

Lattice

- The lattice is a series of components (periodic arrangement) in the beam line
- It is constituted mainly of
- Magnets (quadrupoles, dipoles,…)
- Accelerating cavities - SuperConducting Radio Frequency (SCRF)
- Diagnostic Systems

- The most basic repetitive sequence of components is called a FODO cell (focusing and defocusing quadrupole interspaced with drift space)

- It is constituted mainly of

x

- Trajectory of an individual electron in the FODO lattice.
- The magnetic lattice is periodic (2d)
- The pseudo-sinusoidal motion is referred to as the Betatron oscillation.
- The phase advance per FODO cell period is here µ=π.

QF

QD

1 FODO cell

Betatron Oscillation

- Property of the focusing arrangement
phase advance variation

- The betatron oscillation are e.g. dependent on the strength of the quadrupole, (independently) for x and y:

Nominal focus. Quad. strength |k0|= 0.0524 m-2

Changed to |k1|= 0.0624 m-2

k0

k1

QD

QF

Phase advance (dependant on focusing strength)

Emittance: e

(initial condition)

Beta amplitude: b, periodic

(dependant on focusing strength)

Motion- From the equation of motion (Hill’s equa.):
Where K(S) is the quadrupole strength and is periodic i.e. K(S)=K(S+2d)

One can get the solution in the form (Floquet’s theorem):

Initial phase

And get the differentiate along the beam axis:

Emittance

- To talk to an accelerator physicist, talk in phase-space diagram (x’ vs x):
- 1 particle travelling along the linac will describe in x’,x plane an ellipse (approx.)
- Now we are not dealing with 1 particle but with a bunch of them.
- At 1 location, x’,x plane:
- All particles travelling will form an elliptical surface on the plane.
- The ellipse envelope is a characteristic of the quality of the beam (it encompasses 95% particles). It is called the emittance e.

Beam Size

- The Beam size is computed with
Luminosity is then defined (gaussian beam) by:

Dispersion not included

Quality of the beam at IP and dependent of emittance prior to IP

Defined by focussing arrangement at IP

The challenge with the (normalised) emittance is that along a transport line it can only get worse.

Degradation of emittance

- In a linac the emittance will inevitably degrade due to:
- Synchrotron Radiation
- Collective effects
- Wakefields

- Residual gas scattering
- Accelerator errors:
- Beam mismatch (field errors)
- Dispersion, x-y coupling
- Magnet alignment errors

Wakefields

- Passage of charged particle beams induce electromagnetic field in RF cavities and other structures in accelerator.
- These wakefields act back on the beams and may cause instabilities
- Long range Wakes: acts on following beam
- Short range W: head of bunch acts on its tail

Wakefields

- Bunch ‘current’ generates wake that decelerates trailing bunches.
- Bunch current generates transverse deflecting modes when bunches are not on cavity axis
- Fields build up resonantly: latter bunches are kicked transversely

Long range:

Short range:

When bunch is offset wrt cavity axis, transverse (dipole) wake is excited.

Wtαa-3.5

Effect of misalignment

Multibunch emittance growth for cavities with 500mm RMS misalignment

The misalignements contribute largerly into the emittance growth along the linac.

A challenge

RMS random misalignments to produce 5% vertical emittance growth

BPM offsets 11 mm

RF cavity offsets 300 mm

RF cavity tilts 240 mrad

- Impossible to achieve with conventional mechanical alignment and survey techniques
- Typical ‘installation’ tolerance: 300 mm RMS
- On BPM this would imply an emittance growth of 3800%

- At Beginning of linac gey=20 nm.rad
- At IP gey=~40 nm.rad

Beam Based Alignment is crucial

gij

Yi

Yj

Ki

Beam Based Alignment- Alignment performed on the beam using the beam itself.
- It involves steerers and BPM (measure beam centroid position)
- BACK to BASIC:

- A particle arriving non centered on a quad will get a kick.
- Betatron oscillation surimposed
- Emittance grows

yj

Standard notation used: i.e. focusing for x, but defocusing of y

dipole corrector

steerer

A BBA solution? 1-to-1 steering- To limitate the kick one could think of a solution:

- Assuming:
- A BPM adjacent to each quad,
- A ‘steerer at each quad

simply apply one to one steering to orbit: i.e. at each BPM zeroing the orbit with a steerer such that the bunch centroid is in the central axis of the quad.

But BPM are offset wrt quad.

Dispersion are increased

(Particle with different energy will undergo a different angle in electromagnetic field)

Emittance grows

BBA - DFS

- Dispersion Free Steering (DFS)
- Measure beam orbit (BPM) for a beam at E0
- Measure beam orbit for beam(s) at other energies
- Find a set of steerer settings which minimise the orbit difference. (for the case of curved linac: minimize wrt to the designed orbit difference)

BBA (2)

- An exemple of results for the BBA:

DFS lower emittance growth

DFS along linac

With 2 beams

With jitter

Normalized emittance (m.rad)

Good result for DFS technique.

- Benchmarking of the various DFS algorithm are being done

- Dynamic effect of ground motion not included

No position jitter

Energy (GeV)

BBA(3)

- BBA when?
- In general following a startup, or at regular intervals (DFS for SLC: monthly basis)
- this process takes time; during which the machine is not integrating luminosity (TT)
- typically takes ~ 100 pulses per focusing magnet; with ~5 different energies.
- 300 magnets: ~ 2 hours per linac

Measuring the Emittance

How to measure the emittance:

At Several (≥3) locations measure beam size emittance

- Conventional (wire scanners) diagnostic: damaged
- Need for a non-invasive system

It is foreseen to use laser-wires (finally focused laser) diagnotics system to perform emittance measurements.

Laser-Wire Principle

- Collision between electron and laser beam
- Detection of scattered photons
- Waist of laser < e- beam size

- Number of scattered photons depend on:
- Compton cross section
- Number of electrons / bunch
- Laser power and wavelength
- 1/ interaction area
- relative position of laser and el. beam

Bunch Length

Charge/bunch

Hor. beam size

Ver. beam size

E/GeV

z/ps

nC

x/m

y/m

4.5 to 12

~100

3 to 20

1000 to 100

100 to 10

Laser-Wire at PETRA- Positron Electron Tandem Ring Accelerator
- Long free straight section
- Easy installation of hardware due to existing access pipe and hut outside tunnel area
- 1 IP

Laser-Wire (2)

First vertical beam size measurements: 2003

2005: New vacuum chamber faster scan

- m = (68 ± 3 ± 14) m

A new high power laser is being installed at PETRA will be used in 2006

2nd vertical plane at IP is in place for horizontal measurements

InternationalLinear Collider Timeline

2005 2006 2007 2008 2009 2010

Global Design Effort

Project

Baseline configuration

Reference Design

Technical Design

ILC R&D Program

Expression of Interest to Host

1990

ILC DesignHere was presented a snapshot of studies related to the ILC Beam Dynamic.

More is done at DESY on:

Damping Ring, Bunch Compressor, Failure mode, Vibrations,…

Check Beam Dynamic activities website at DESY.

- Linear collider design is complex due to the interrelationships among the various parameters and the soft constraints on their values.

References

Picked up of lot of the plots, drawings, … from:

- recent ILC school:
- http://www.linearcollider.org/school/

- Accelerator school:
- USPAS 2003

- and other reference papers or conference:
- Baseline Configuration Design (BCD) website: http://www.linearcollider.org/wiki/doku.php?id=bcd:bcd_home
- Talks at Snowmass 2005

Ground motion spectra

Both frequency spectrum and spatial correlation important for LC performance

Test of Unification

MSSM:

105 parameters: some from LHC, some from ILC

Extrapolation of SUSY parameters from weak to GUT scale (e.g. within mSUGRA)

Gauge couplings unify at high energies,

Gaugino masses unify at same scale

Precision provided by ILC for sleptons, charginos and neutralinos will allow to test if masses unify at same scale as forces

Gluino (LHC)

SUSY partners of electroweak bosons and Higgs

Extra dimensions

cross section for anomalous single photon production

Emission of gravitons

into extra dimensions

Experimental signature:

single photons

d = # of extra dimensions

e+e- -> gG

measurement of cross sections at different energies allows to determine number and scale of extra dimensions

(500 fb-1 at 500 GeV,

1000 fb-1 at 800 GeV)

Energy

Precision Electroweak Tests

- high luminosity running at the Z-pole
- Giga Z (109 Z/year) ≈ 1000 x “LEP” in 3 months
- with e- and e+ polarisation

ΔsinΘW = 0.000013

together with

ΔMW = 7 MeV

(threshold scan)

and

ΔMtop = 100 MeV

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