Elementary ParticlesInstrumentation

Accelerators

Dec 15, 2014

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First accelerator: cathode ray tube

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distance D

Potential diffence V

heatedfilament

Efield = V / D

With electron charge q:

F = q . Efield

electron kinetic energy:Ee- = F dD = q.V

Ee- independent of:

- distance D- particle mass

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Energy unit: ElectronVolt: eV

1000 eV = 1 keV = 103 eV

1 MeV = 106 eV1 GeV = 109 eV1 TeV = 1012 eV

1 eV = |q| Joules = 1.6 x 10-19 Joules

ElectronVolt: eV

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Wimshurst’s electricity generator, Leidsche Flesschen5

From: Principles of ChargedParticle AccelerationStanley Humphries, Jr.,on-line edition, p. 222.http://www.fieldp.com/cpa/cpa.html

Van de Graaff accelerator

Vertical constructionis easier as support of belt is easierCorona discharge

deposits chargeon belt

Left: Robert van de Graaff

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gndHV = 10 kV

Faraday Cage!

belt

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From: Principles of ChargedParticle AccelerationStanley Humphries, Jr.,on-line edition, p. 223.http://www.fieldp.com/cpa/cpa.html

Beam pipe

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Hoogspanning (hoge potentiaal) met: Rumkorffse Klostransformatorbobine

bobine:ontsteking voorexplosie motoren

vonkenzender

Marconi

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From: Principles of ChargedParticle AccelerationStanley Humphries, Jr.,on-line edition, p. 210http://www.fieldp.com/cpa/cpa.html

Cockcroft-Waltonhigh-voltage generator

Sir John Douglas Cockroft Nobel Prize 1951

Ernest Walton

Practical limit to transformers

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Cockroft Walton generatorat Fermilab, Chicago, USA

High voltage = 750 kV

Structure in the foreground:ion (H-) source

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dpdt

q v B

Motion of charged particle in magnetic field

Lorentz force:

The speed of a charged particle, and therefore its does not change by a static magnetic field

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mv2

q v B

If magnetic field direction perpendicular to the velocity:

which can be written as : p = q B → p = 0.2998 B

radius of curvature (p in GeV/c, B in T, in m, for 1 elementary charge unit = 1.602177x10-19 C, and obtained using1 eV/c2 = 1.782663x10-36 kgand c = 299792458 m/s )

Motion of charged particle in magnetic field

D

ρ

Sh

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Force on charged particle due to electric and magnetic fields:

In direction ofmotion -> accelerationor deceleration

perpendicular tomotion: deflection

-> For acceleration an electric field needs to be produced: • static: need a high voltage: e.g. Cockroft Walton generator, van de Graaff accelerator• with a changing magnetic field: e.g. betatron• with a high-frequent voltage which creates an accelerating field across one or more regions at times that particles pass these regions: e.g. cyclotron• with high-frequency electro-magnetic waves in cavities

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"Dee": conducting, non-magnetic box

~

Constant magnetic field

r.f. voltage

Side view

Top view

The cyclotron

Speed increase smaller if particles become relativistic:special field configuration or synchro-cyclotron (uses particlebunches, frequency reduced at end of acceleration cycle)

Ernest O.Lawrence at the controlsof the 37" cyclotron in 1938,University of California at Berkeley.1939 Nobel prize for "the inventionand development of the cyclotron, and for the results thereby attained, especially with regard to artificial radioelements."(the 37" cyclotron could acceleratedeuterons to 8 MeV)

http://www.lbl.gov/Science-Articles/Archive/early-years.htmlhttp://www.aip.org/history/lawrence/ 15

From: S.Y. Lee and K.Y. Ng, PS70_intro.pdf in: http://physics.indiana.edu/~shylee/p570/AP_labs.tar.gz

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From: S.Y. Lee and K.Y. Ng, PS70_intro.pdf in: http://physics.indiana.edu/~shylee/p570/AP_labs.tar.gz

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Superconducting cyclotron (AGOR), KVI, GroningenProtons up to ~ 190 MeV, heavy ions (C, N, Ar, ...) ~ 50-60 MeV per nucleon

http://www.kvi.nl

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Eindhoven: new cyclotron for isotope production (2002)IBA Cyclone 30, 18 - 30 MeV protons, 350 A

http://www.accel.tue.nl/tib/accelerators/Cyclone30/cyclone30.html

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Linear Drift Tube accelerator, invented by R. Wideröe

~r.f. voltage: frequencymatched to velocity particles,so that these are acceleratedfor each gap crossed

Particles move throughhollow metal cylinders inevacuated tube

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Linear Drift Tube accelerator, Alvarez type

~ small antenna injects e.m. energyinto resonator, e.m. wave in tankaccelerates particles when they crossgaps, particles are screened from e.m.wave when electric field would decelerate

Metal tank

Particles move throughhollow metal cylinders inevacuated tube

Luis Walter AlvarezNobel prize 1968, but not for his work on accelerators:"for his decisive contributions to elementary particle physics, in particular the discovery of a large number of resonance states, made possible through his development of the technique of using hydrogen bubble chamber and data analysis"

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Inside the tank of theFermilab Alvarez type200 MeV proton linac

http://www-linac.fnal.gov/linac_tour.html

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R.f. cavity with drift tubes as used in theSPS (Super Proton Synchrotron) at CERNNB: traveling e.m. waves are used

Frequency = 200.2 MHzMax. 790 kW8MV accelerating voltage

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Standing waves in cavity:particles and anti-particlescan be accelerated at the same time

t1

t2

The direction of E is indicated

Superconducting cavity for the LEP-II

e+e- collider (2000: last year of operation)

Cavities in cryostat in LEP

"iris"

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Non-superconducting cavity as used in LEP-I.The copper sphere was used for low-loss temporary storage of thee.m. power in order to reduce the power load of the cavity

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Generation of r.f. e.m waves with a klystron

* The electron gun 1 produces a flow of electrons. * The bunching cavities 2 regulate the speed of the electrons so that they arrive in bunches at the output cavity. * The bunches of electrons excite microwaves in the output cavity 3 of the klystron. * The microwaves flow into the waveguide 4, which transports them to the accelerator. * The electrons are absorbed in the beam stop 5.

from http://www2.slac.stanford.edu/vvc/accelerators/klystron.html

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Synchrotron : circular accelerator with r.f. cavitiesfor accelerating the particles and with separate magnetsfor keeping the particles on track. All large circularaccelerators are of this type.

r.f. cavity

Injection

Extracted beam

Bending magnet

Vacuum beam line

Focussing magnetDuring acceleration the magnetic field needs to be "ramped up".

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CERN, Geneve

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During acceleration the magnetic field needs to be "ramped up".

Fast extractionof part of beam

Slow extraction

Fast extractionof remainder of beam

SPS used asinjector for LEP

For LHC relatedstudiesAt time of operation of LEP

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Collider: two beams are collided to obtain a high Centre of Mass (CM) energy.

Colliders are usually synchrotrons (exception: SLAC). In a synchrotron particles and anti-particles can be accelerated and stored in the same machine (e.g. LEP (e+e-), SppS and Tevatron (proton - anti-proton). This is not possible for e.g. a proton-proton collider or an electron-proton collider.

Important parameter for colliders : Luminosity L

N = L number of events /s

cross-section

Unit L: barn-1 s-1 or cm-2 s-1

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to Gran-Sasso (730 km)

CERN accelerator complex

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Charged particles inside accelerators and in external beamlinesneed to be steered by magnetic fields. A requirement is that small deviations from the design orbit should not grow withoutlimit. Proper choice of the steering and focusing fields makes thispossible.

Consider first a charged particle moving in a uniform field and in a plane perpendicular to the field:

design orbit

displaced orbitIn the plane a deviation from the design orbit does not grow beyond a certain limit: it exhibits oscillatory behavior. However, a deviation in the direction perpendicular to the plane grows in proportion to the number of revolutions made and leads to loss of the particle after some time.

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To prevent instabilities a restoring force in the vertical direction isrequired. Possible solution : "weak focusing" with a "combined function magnet"

poleshoe

poleshoe

design orbitplane (seenfrom the side)

Components of magnetic field parallel to the design orbit plane force particles not moving in theplane back to it, resulting inoscillatory motion1) perpendicularto plane. The field componentperpendicular to the plane now depends on the position in thedesign orbit plane: the periodof the oscillatory motion1) in thisplane around the design orbitbecomes larger than a singlerevolution.

fieldcomponentcauses downward force

fieldcomponentcausesupwardforce

1) "betatron oscillations"

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Dipoles and quadrupoles in LEP

Quadrupole Dipole

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proton-proton collider

• Crossing angle to avoid long range beam beam interaction

• R ~4 km, E ~ 7 TeV (2x!) B ~ 7 T!

Interaction point

Large Hadron Collider LHC:

Bunch size squeezednear interaction point

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Superconducting magnets: no pole shoes

Current distributions

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LHC dipoles

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pp collisions

2) heavy collisions: A proton is a bag filled with quarks en gluons

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With van de Graaff accelerator: simple:

E = q V, so E = V eV

From Einstein’s Special Theory on Relativity:

E2 = mo2 c4 + p2c2

With:

= v / c, and the Lorentz factor γ:

relativistic mass mr = γ m0

γ = 1 / sqrt(1- 2), and = sqrt(γ2 -1) / γ

So: total energy E = m0 c2 sqrt(1+ 2 γ2) [= rest mass eq. + kinetic energy]

= γ m0 c2 = mr c2 42

Remember:

TOTAL energy E2 = mo2 c4 + p2c2

Note ‘restmass’ term and ‘kinetic’ term (squared!)

relativistic mass mr = γ m0

p = m v = γ m0 v (for high energy particles: p = γ m0 c)

γ = 1 / sqrt(1- 2)

For high-energy particles (E >> m0c2):

E2 = mo2 c4 + p2c2 = E2 = p2c2 E = pc p = E/c

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Examples: electron: rust mass m0 = 511 keV

With total energy 1 GeV: kinetic energy = 1 GeVMomentum p: 1GeV/c

Other example: electron with [kinetic] energy of 1 MeV (~1/2 m0 c2)

Total energy ET = 1 MeV + 511 keV = 1511 keVMomentum p follows from ET

2 = mo2 c4 + p2c2

Gamma factor γ = ET / moc2

Speed follows from γ = 1 / sqrt(1- 2), and = sqrt(γ2 -1) / γ

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