Tools of Particle Physics I Acceleratorsweb.mit.edu/panic11/talks/sunday/Graves_Accelerators.pdf ·...

Courtesy of C. Prior, RAL

Motion in Electric and Magnetic Fields Governed by Lorentz force

Acceleration along a uniform electric field (B=0)

BvEqdtpd

EpE

qcBvEpE

qcdtdE

dtpdpc

dtdEE

cmcpE

22

2

420

222

cvtmeEx

vtz

for path parabolic

22

0

A magnetic field does not alter a particle’s energy. Only an electric field can do this.


0

0

20

)(

)(

mqBvb

qBvma

Bvqvm

Behaviour under constant B-field, E=0 Motion in a uniform, constant magnetic field Constant energy with spiralling along a uniform magnetic

field

qBp

vE

qBc

2


Methods of Acceleration: Linear Simplest example is a vacuum chamber

with one or more DC accelerating structures with the E-field aligned in the direction of motion. Limited to a few MeV

To achieve energies higher than the highest voltage in the system, the E-fields are alternating at RF cavities. Avoids expensive magnets

No loss of energy from synchrotron radiation

But requires many structures

Large energy increase requires a long accelerator

SLAC linear accelerator

SNS Linac, Oak Ridge


Methods of Acceleration: Circular Synchrotron Principle of frequency modulation but in addition variation in

time of B-field to match increase in energy and keep revolution radius constant.

Magnetic field produced by several bending magnets

(dipoles), increases linearly with momentum. For q=e and

high energies:

.

Practical limitations for magnetic fields => high energies only

at large radius

e.g. LHC E = 8 TeV, B = 10 T, = 2.7 km

nf

v

EqBc

2

qBp

chargeunit per [m] [T] 0.3[GeV]so BEceE

epBρ


Ring Concepts Important concepts in rings:

Revolution period

Revolution (angular) frequency

If several bunches in a machine, introduce RF cavities in

straight sections with fields oscillating at a multiple h of the

revolution frequency. h is the harmonic number.

For synchrotrons, energy increase E when particles pass RF cavities can increase energy only so far as can increase B-field in dipoles to keep constant .

cL

vR

2

Lc

12

Lhchrf

2

qBp

qpB


Effect on Particles of an RF Cavity Cavity set up so that particle at the centre of bunch,

called the synchronous particle, acquires just the right amount of energy.

Particles see voltage

In case of no acceleration, synchronous particle hass = 0 Particles arriving early see < s

Particles arriving late see > s

energy of those in advance is decreased relative to the synchronous particle and vice versa.

To accelerate, make 0 < s< so that synchronous particle gains energy

)(sin2sin 00 tVtV rf

Bunching EffectsqVE sin0


Strong Focusing: Alternating Gradient Principle

A sequence of focusing-defocusing fields provides a stronger net focusing force.

Quadrupoles focus horizontally, defocus vertically or vice versa. Forces are linearly proportional to displacement from axis.

A succession of opposed elements enable particles to follow stable trajectories, making small (betatron) oscillations about the design orbit.

Technological limits on magnets are high.


Sextupoles are used to correct longitudinal momentum errors.

Focusing Elements

SLAC quadrupole


General equation of ellipse is

, , are functions of distance (Twiss parameters), and is a constant. Area = .

RMS emittance

(statistical definition)

Transverse Phase Space Under linear forces, any particle

moves on an ellipse in phase space (x,x´).

Ellipse rotates in magnets and shears between magnets, but its area is preserved: Emittance

x

x´

x

x´

22 2 xxxx

222 xxxxrms


Electrons and Synchrotron Radiation Particles radiate when they are accelerated, so charged

particles moving in dipole magnetic fields emit radiation (due to centrifugal acceleration) in the forward direction.

After one turn of a circular accelerator, total energy lost by synchrotron radiation is

mp/me = 1836 and m/me = 207. For the same energy and radius,

4

20

18

/GeVm10034.6GeV

cmGeVEE

13 9/ 10 / 10e p eE E E E


Luminosity Measures interaction rate per unit cross section -

an important concept for colliders. Simple model: Two cylindrical bunches of area A.

Any particle in one bunch sees a fraction N /A of the other bunch. (=interaction cross section). Number of interactions between the two bunches is N2 /A. Interaction rate is R = f N2 /A, and

Luminosity

CERN and Fermilab p-pbar colliders have L ~ 1030

cm-2s-1. SSC was aiming for L ~ 1033 cm-2s-1

Area, A

ANfL

2


Pierre Oddone

0.5 TeV e+e-

3 TeV e+e-

3-4 TeV +-

Decision Tree for Future HEP Facilities


HEP Facility Sizes

14.0

6.20

11LH

C p

erfo

rman

ce in

201

1 -L

AL/

Ors

ay

LHC accelerator complex

16

Beam 1

TI2

Beam 2TI8

LHC proton path

The LHC needs most of the CERN accelerators...

≥ 7 seconds from source to LHC

14.0

6.20

11LH

C p

erfo

rman

ce in

201

1 -L

AL/

Ors

ay

14.0

6.20

11LH

C p

erfo

rman

ce in

201

1 -L

AL/

Ors

ayLH

C p

erfo

rman

ce in

201

1 -L

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ay

LHC layout and parameters

17

8 arcs (sectors), ~3 km each 8 long straight sections (700 m each) beams cross in 4 points 2-in-1 magnet design with separate

vacuum chambers → p-p collisions

-- β* = 0.55 m (beam size =17 μm)- Crossing angle = 285 μrad- L = 1034 cm-2 s-1

RF

14.0

6.20

11

Nominal LHC parametersBeam energy (TeV) 7.0No. of particles per bunch 1.15x1011

No. of bunches per beam 2808Stored beam energy (MJ) 362Transverse emittance (μm) 3.75Bunch length (cm) 7.6

The LHC ArcsThe LHC Arcs

8.33 Tnominal field

11850 A nominalcurrent

14.0

6.20

11LH

C p

erfo

rman

ce in

201

1 -L

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Ors

ay

Incident of Sept. 19th 200814

.06.

2011

LHC

per

form

ance

in 2

011

-LA

L/O

rsay

21

The final circuit commissioning was performed in the week following the startup with beam.

During the last commissioning step of the last main dipole circuit an electrical fault developed at ~5.2 TeV (8.7 kA) in the dipole bus bar (cable) at the interconnection between a quadrupole and a dipole magnet.

Later correlated to quench due to a local R ~220 n – nominal 0.35 n

An electrical arc developed and punctured the helium enclosure.Around 400 MJ from a total of 600 MJ stored in the circuit were dissipated in the cold-mass and in electrical arcs.

Large amounts of Helium were released into the insulating vacuum.The pressure wave due to Helium flow was the cause of most of the damage (collateral damage).

14.0

6.20

11LH

C p

erfo

rman

ce in

201

1 -L

AL/

Ors

ay

Magnet Interconnection14

.06.

2011

LHC

per

form

ance

in 2

011

-LA

L/O

rsay

22

Dipole busbar

Melted by arcMelted by arc

14.0

6.20

11LH

C p

erfo

rman

ce in

201

1 -L

AL/

Ors

ay

Collateral damage14

.06.

2011

LHC

per

form

ance

in 2

011

-LA

L/O

rsay

23

Quadrupole-dipole interconnection

Quadrupole support

Main damage area covers ~ 700 metres. 39 out of 154 main dipoles, 14 out of 47 main quadrupoles

from the sector had to be moved to the surface for repair (16) or replacement (37).

Sooth clad beam vacuum chamber


International Linear ColliderInternational Linear Collider

e- main linac

IP and 2 moveable detectors

e+ main linac

e+ beam dump e- beam dump

e- e+ damping rings

e- source + pre-acceleration

e+ pre-acceleration

e+ production

undulator

target

e+ transport line

e- transport line

2-stage bunch compression


e- main linac

IP and 2 moveable detectors

e+ main linac

e+ beam dump e- beam dump

e- e+ damping rings

e- source + pre-acceleration

e+ pre-acceleration

e+ production

undulator

target

e+ transport line

e- transport line




Why Superconducting RF Cavities?SC cavities offer

– a surface resistance six orders of magnitude lower than normal conductors

– high efficiency even when cooling is included– low frequency, large aperture for smaller wake-field effects

Relations for the surface fields to acclerating gradient:

Epeak/Eacc = 2 -minimize this to reduce field emission

Bpeak/Eacc = 4 mT/(MV/m) -minimize to avoid quenches

Cavity FabricationCavity Fabrication


ILC RF unit at Fermilab


MuonMuon ColliderCollider


Muon Collider Schematic

Proton source: Upgraded PROJECT X (4 MW, 2±1 ns long bunches)

1021 muons per year that fit within the acceptance of an accelerator

√s = 3 TeVCircumference = 4.5kmL = 3×1034 cm-2s-1

/bunch = 2x1012

(p)/p = 0.1%* = 5mmRep Rate = 12Hz

Courtesy of S. Geer, FNAL


Challenges

● Muons are born within a large phase space ( → )

- To obtain luminosities O(1034) cm-2s-1, need to reduce initial phase space by O(106)

● Muons Decay (0 = 2s) - Everything must be done fast

→ need ionization cooling- Must deal with decay electrons- Above ~3 TeV, must be careful about decay

neutrinos !



6D Cooling

liqHs

MC designs require the muon beam to be cooled by ~ O(106) in 6D

Ionization cooling reduces transverse (4D) phase space.

To also cool longitudinal phase space (6D) must mix degrees of freedom as the cooling proceeds

This can be accomplished with solenoid coils arranged in a helix, or with solenoid coils tilted.

Palmer

Alexhin & Fernow


W.S. Graves July, 2011Courtesy of W. Leemans, LBL

Laser/Plasma AcceleratorsLaser/Plasma Accelerators

W.S. Graves July, 2011Courtesy of W. Leemans, LBL


Thank you!Thank you!

Questions?Questions?

Tools of Particle Physics I Acceleratorsweb.mit.edu/panic11/talks/sunday/Graves_Accelerators.pdf ·...

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