Proton Synchrotron

Example: LHC Accelerator Complex

Why Synchrotron?

! =qB

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Angular frequency:

Magnetic Field Frequency Orbit

Cyclotron FixedChange for relativistic particle.

Increase with ascending

energy

Synchrotron Vary Keep Constant Keep Constant

First synchrotron

Achieve high energy in circular ring

Outlines

• Earlier synchrotrons• Principle of operation• Synchrotron motions• Injection• Extraction

Earlier stage

Cosmotron at Brookhaven National Laboratory, 1948-1968, reach 3.3 GeV proton, Weak focusing accelerator.

Earlier Stage

ADA collider at LNF in Frascati (1961-1964), reaches 250 MeV and achieve electron-position collision.

Operation principle

• As the energy/momentum of the particle increases, the magnetic field is also ramped so that the following relation holds:

• The angular frequency gives

• Only in ultra-relativistic case, the orbit and frequency can be ‘synchronized’ together.

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!(t) =qB(t)

m�(t)=

�(t)c

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Energy Dynamic Range

• There is no one accelerator to accelerate the particle from source all the way to the top energy (>GeV level)

• Frequency changes a lot.

• Space charge at low energy.

• Linac handles up to ~MeV

• One synchrotron can boost the energy up 10x-100x, from its injection energy to the top energy

• Need accelerator complex to achieve high energy

• Injection and Extraction are important.

Accelerator complex

Injection, extraction and transfer!"#$%!&'()*+

LHC: Large Hadron ColliderSPS: Super Proton SynchrotronAD: Antiproton DeceleratorISOLDE: Isotope Separator Online DevicePSB: Proton Synchrotron BoosterPS: Proton SynchrotronLINAC: LINear AcceleratorLEIR: Low Energy RingCNGS: CERN Neutrino to Gran Sasso

Transfer (in, out, and between machines) is important!

• An accelerator has limited dynamic range.

• Chain of stages needed to reach high energy

• Periodic re-filling of storage rings, like LHC

• External experiments, like CNGS

Relativistic Heavy Ion Collider complex:1. EBIS (Electron Beam Ion Source); 2. Linac Accelerator3. Booster 4. AGS (Alternating Gradient Synchrotron)5. AGS to RHIC Line 6. RHIC

Synchronization

Synchrotrons in RHIC complex

Booster, from 200 MeV proton/ 2MeV ion to 100MeV/nucleon

Alternative Gradient Synchrotron, accelerate to ~9 GeV/ nucleon.

Synchrotrons in LHC complex

Proton Synchrotron Booster (50MeV to 1.4 GeV)

Proton Synchrotron (1.4 GeV to 25 GeV), 628m

Low Energy Ion Ring

Super Proton Synchrotron (25 GeV to 450 GeV), 7 km

Injection

Simple goals

• Simple Goal: “Put beam in to synchrotron at its lowest energy (injection energy).”• To the zero’s order, it looks like the right figure.

• More requirements:• Need to inject h particles, h>>1• The ith injected bunch not affect 1…i-1 bunches• Need time-depend kicks

Bunch Filling

One-turn injection

• The simplest scheme:Single-turn injection

Septum magnet

Kicker magnet

Transfer line

• Septum deflects the beam onto the closed orbit at the centre of the kicker• Kicker compensates for the remaining angle

Closed orbit bumpers

t

kicker field

intensity injected beam

‘boxcar’ stacking

Real layouts

RHIC

LHC

Transfer MatrixIf we know the twiss parameter of both end and phase advance in between

S1 represents the kicker.

S0 represents the septum.

Single-turn injection

Septum magnet

Kicker magnet

Transfer line

• Septum deflects the beam onto the closed orbit at the centre of the kicker• Kicker compensates for the remaining angle

Closed orbit bumpers

t

kicker field

intensity injected beam

‘boxcar’ stacking

What happened in phase spaceSingle-turn injection –normalised phase space

!

Large deflection by septum

θ septum

"!

Single-turn injectionπ/2 phase advance to kicker location

!

"!

Single-turn injectionKicker deflection places beam on central orbit

θ kicker

!

"!

The injected bunch experience three necessary steps in phase space, which put the bunch exactly same location in phase space, as other circulating bunches.

The circulating bunch does not experience this due to • Spatial separation at septum magnet• Time separation at injection kicker.

Septum

Magnetic septum

Soft iron Laminated yoke

Return coilSeptum coil

B0B=0

Yoke

Septum coil

I

Typically Ι 5-25kA

Pulsed or DC magnet with thin (2-20mm)septum between zero field and high field region

Septum Coil

Yoke

Magnetic septum

Soft iron Laminated yoke

Return coilSeptum coil

B0B=0

Yoke

Septum coil

I

Typically Ι 5-25kA

Pulsed or DC magnet with thin (2-20mm)septum between zero field and high field region

Lambertson septum

• Magnetic field in gap orthogonal to previous example of septa:– Lambertson deflects beam orthogonal to kicker: dual plane injection/extraction

• Rugged design: conductors safely hidden away from the beam

• Thin steel yoke between aperture and circulating beam – however extra steel required to avoid saturation, magnetic shielding often added

x I

I•

Circulating Beam

Steel yokeCoil

Steel to avoid saturation

Thin Septum

M. Paraliev’s Lecture

10

Lambertson

Injection Kicker

RHIC Injection Kicker

Time for injecting the bunch

Injection Errors, OscillationsInjection oscillationsFor imperfect injection the beam oscillates around the central orbit. 1kicker θ error

!

"!

Injection oscillationsFor imperfect injection the beam oscillates around the central orbit. 2

!

"!

Injection oscillationsFor imperfect injection the beam oscillates around the central orbit. 3

!

"!

Injection oscillationsFor imperfect injection the beam oscillates around the central orbit. 4

!

"!

Injection Error, Filamentation

!

"!

Filamentation

!

"!

Filamentation

!

"!

Filamentation

!

"!

Filamentation Filamentation

!

"!

!

"!

Filamentation

Injection Error, Filamentation

!

"!

Filamentation

!

"!

Filamentation

!

"!

Filamentation

!

"!

Filamentation

!

"!

Filamentation

!

"!

Filamentation

Injection Error, FilamentationFilamentation

!

"!

Eventually phase space is effectively filled ⇒ emittance increase

!

"!

Filamentation

Injection Error, MismatchOptical Mismatch at InjectionFilamentation fills larger ellipse with same shape as matched ellipse

x

x’

Treatment of this effect in lecture tomorrow

Emittance Blowup

• Both Injection angle/position error and mismatch cause emittance blowup• The Blowup is due to filamentation• Filamentation is due to the frequency spread of the particles• Nonlinearity • Chromatic effect

• Have to correct both the injection orbit and optical mismatch to avoid emittance growth.

Multi-turn injection

• Some times it is impossible to have high intensity one-turn injection• Limited by the intensity of previous accelerator or source• Limited from space charge effect

• Solution: Multi-turn injection• Instead of one kicker, we need several fast dipole to create ‘bump’• These fast dipole create varying bump strength throughout the

injection process• Well controlled transverse tune.• This is the process of ‘Painting in transverse phase space’

Multi-Turn Idea Multi-turn injection for hadrons

Septum magnet

Transfer line

• Bump amplitude varies with time• Inject a new bunch at each turn• Phase-space painting

Closed orbit bumpers

Varying amplitude bump

Multi-turn InjectionMulti-turn injection for hadrons

1

Turn 1

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Septum

Multi-turn injection for hadrons

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Turn 2

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Multi-turn injection for hadrons

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Turn 3

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xMulti-turn injection for hadrons

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12

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Turn 4

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Multi-turn injection for hadrons

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51

Turn 5

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Multi-turn injection for hadrons

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21

Turn 6

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Multi-turn InjectionMulti-turn injection for hadrons

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Turn 7

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Multi-turn injection for hadrons

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Turn 8

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Multi-turn injection for hadrons

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Turn 9

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xMulti-turn injection for hadrons

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Turn 10

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Multi-turn injection for hadrons

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Turn 11

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Multi-turn injection for hadrons

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Turn 12

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Charge exchange H- InjectionCharge exchange H- injection

H- beam

Closed orbit bumpers

Circulating p+p+

Stripping foil

H0

H-

Bump amplitude

Essential for low loss injection for high intensity beam. May achieve ~0.02%

Without CEI, the best loss is 10%.

Extraction

Schemes

• Treat extraction as reverse procedure of Injection (fast)• Single turn extraction• Multi-turn extraction (No resonance)

• We can play more tricks with using nonlinear resonance• Nonlinear resonance slow extraction• Nonlinear low-loss extraction

Single Turn ExtractionFast extraction: spatial considerations

Septum magnet

•  Bumpers move circulating beam close to septum

•  Kicker deflects the beam into the septum

Extracted beam

F-quad Defocusing-quad

“kick enhancing quad”

Circulating beam

Focusing-quad

Phase advance through lattice: e.g. FODO lattice

µkicker→septum

•  Important considerations: -  optimum phase advance between kicker and septum, e.g. ≈ QD in between: βx large at F-quads (near kicker and septum in this case)

-  aperture, e.g. inside quads, position of septum etc. -  integration constraints, e.g. extracted beam trajectory

Kicker

Fast Extraction – CERN Accelerator School – Beam Injection, Extraction & Transfer, Erice, Italy, 2017

Closed orbit bumpers

(slow ~ ms)

4/48

@ Matthew Fraser, CERN ACC. School, 2017

Multi-Turn extraction (Non-resonance)

Extracted beam

Bumped circulating beamparticles moved across Septum by resonance

Septum

• Slow bumpers move the beam near the septum• Horizontal tune adjusted closed to nth order betatron resonance• Multipole magnets excited to define stable area in phase

space, size depends on ∆Q = Q - Qr

Resonant multi-turn extraction

Closed orbit bumpers

Multi-Turn extraction (Non-resonance)Non-resonant multi-turn extraction

!

"!

CERN PS to SPS: 5-turn continuous transfer

Qh = 0.25

1 2 3 4 5

Bump vs. turn

1

2

3

4

5

septum

Multi-turn extraction (Non-resonance)

• This scheme will extract the beam within few turns.• Beam loss is an issue.• Septum need to be very thin.• It is hard to have same intensity, emittance, centroid for every part of

the beam.

• We can use nonlinear resonance to do a better job.

Resonance (slow) extractionThird-order resonant extraction

• ∆Q now small enough that largest amplitude particles are unstable• Unstable particles follow separatrix branches as they increase in amplitude

!

"!

Septum wire

Very slow extraction~1000 turns, perfect for low dose applications like medical applications

This example is third order resonance, when the tune is about 1/3 or 2/3

Still have loss at septum

Resonance Low Loss Extraction

• Use sextrupole and Octupole to control the nonlinear island. • The beam is split into many,

usually 4 equally populated island and then use septum wire to extract them.

Resonant low-loss multi-turn extraction

Septum wire

a. Unperturbed beam

b. Increasing non-linear fields

c. Beam captured in stable islands

d. Islands separated and beam bumped across septum – extracted in 5 turns

1 2 3 4 5

Bump vs. turn

Qh = 0.25

More readings

• Injection and extraction material are largely borrowed from:• http://cas.web.cern.ch/schools/erice-2017