Acceleratorsepweb2.ph.bham.ac.uk/user/newman/appt10/Accelerators... · 2010-11-14 · Particle Detection UVA/VU 2003 III 14 Linear Drift Tube accelerator, Alvarez type ~ small antenna

Particle Detection UVA/VU 2003 III 1

Accelerators• The following are extracts from a lecture course at Nikhef (Amsterdam).

• You are not required to know this information for this course, but you will find it interesting as background information

• There are, of course, many other good resources for this subject on the web!


Force on charged particle due to electric and magnetic fields:

dpdt

= q(E + v × B)

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


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 CockroftNobel Prize 1951

Ernest Walton


Cockroft Walton generatorat Fermilab

High voltage = 750 kV

Structure in the foreground:ion (H-) source

CERN had a similar 750 kV setup,this has been replaced by a RFQ(Radio-Frequency Quadrupole)


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



Beam pipe


Tandem Van de Graaff accelerator: doubling of beam energy



6 MV tandem Van de Graaff accelerator, University of Utrecht


Betatron: "beam transformer": increasingmagnetic field accelerates particles (electrons)


Curved magnetic fieldfocuses electrons


"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/


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


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


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


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"


Inside the tank of theFermilab Alvarez type200 MeV proton linac

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


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


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


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".


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


Direct acceleration with e.m. waves in cavities(i.e. without using drift tubes)

Consider an e.m. wave in a cylindrical conducting enclosure.The phase velocity of the wave will be larger than the speed of light, i.e. maximaand minima in electric field strength will move faster than light (not in conflictwith relativity, as energy does not propagate faster than light)

Explanation: the e.m. wave can beregarded as a superposition of e.m.waves bouncing from the walls, eachmoving with the speed of light

wave crest 2interfering waves

wave crest 1resultant wave crest travels over largerdistance than original wave crests in the same time


αwave

wall

Energy propagates with group velocity, vg = c sin α

TM waves: magnetic field transversal, electric field longitudinalTE waves: electric field transversal, magnetic field longitudinal,unless distorted not usable for acceleration

The phase velocity needs to be < c to make acceleration possible. Thisis possible with a disc loaded cylindrical cavity with holes ("irisses")in the centre of the discs.

r.f. energy in r.f. energy out

part of cavity (cut open) used inSLAC linear accelerator


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

Cavities in cryostat in LEP

"iris"


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


Collider: two beams are collided to obtain a high 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 σnumber of events /s cross-section

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


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.


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"


s zρ

θ

θ=0x

qvBz(r) < γmv2/r for r<ρqvBz(r) > γmv2/r for r>ρ

Lorentzforce

centrifugalforce

In-plane stability:

Assume x<<ρ:With: r= ρ+x= ρ(1+x/ρ) we write: γmv2/r ≈ (1-x/ρ) γmv2/ρ

Bz r( )= B0 1+x

B0

∂Bz

∂r⎛ ⎝ ⎜

⎞ ⎠ ⎟

r=ρ

⎛

⎝ ⎜

⎞

⎠ ⎟ = B0 1− n x

ρ

⎛

⎝ ⎜

⎞

⎠ ⎟ n = "field index"

The conditions now become:1-nx/ρ < (1-x/ρ) for x<01-nx/ρ > (1-x/ρ) for x>0

n<1


s zρ

θ

θ=0x

Bx = -Cz (C is a constant)Out-of-plane stability:

∇ × B = 0∂Bx

∂z=

∂Bz

∂x= −C

-> Bz has to decrease with increasing x, therefore: n > 0. Note: C=0 for n=0, which corresponds to Bz being independent of x

For small n the amplitude of the vertical oscillations aroundthe design orbit can be large, i.e. a large vacuum chamber willbe required to contain the beam

=> a large value of n is desirable, but n < 1 for horizontal stability


poleshoe

poleshoe

poleshoe

poleshoe

Here is themagnetic fieldnot strong enough for stability if n≥1and if the orientationof all magnets in thering is the same

=> Alternate magnets with field linesbending to outside and bending toinside, |n| can be much larger than 1,and the amplitude for oscillations aroundthe design orbit is much smaller.This is "strong focusing"

The inventors

and anotherindependentinventor


CERN proton synchrotron (28 GeV protons), photographtaken in 1959 clearly shows the alternation of the combinedfunction magnets


The Cosmotron at Brookhaven, a 3.3 GeVproton synchrotron, weak- focusing, inoperation from 1952 - 1966 (photographtaken before concrete shielding wasinstalled)

Size comparison betweenCosmotron and AGS magnet.AGS = Alternating GradientSynchrotron, a strong-focusing,33 GeV proton synchrotron,in operation from 1960 atBrookhaven

The AGS: the field gradient is alternatingbetween successive magnets (240 in total)


The field of the combined function magnets used in the PS and in the AGS is a combination of a dipole field (for bending) and a quadrupole field (for focusing). In modern machines these functions are separated.

Cross-section of quadrupole magnet

By = gx and Bx = gy,where g is a constant

The quadrupole focuses inone plane, but defocusesin the perpendicular plane. Two quadrupoles, rotatedover 900 with respect toeach other have a netfocusing effect

Hyperbolic polecontour

Coil

yx

Magnetic field lines

S

S

N

N


Dipoles and quadrupoles in LEP

Quadrupole Dipole


Focusing of a system of two lenses for both planes

d = 50 m

horizontal plane

vertical plane

f1 100 m:=

f2 100− m:=

d 50m:=

F 1f1

1f2

+d

f1 f2⋅−⎛

⎜⎝

⎞⎟⎠

1−:=

F 200 m=

To focuse the beams in both planes, a succession of focusing and defocusing quadrupole magnets is required: FODO structure

http://www.ippp.dur.ac.uk/sussp57/LectureNotes/Schmidt1.ppt


Dipole- und Quadrupol magnets– Particle trajectory stable for particles with nominal momentum

Sextupole magnets– To correct the trajectories for off momentum particles – Particle trajectories stable for small amplitudes (about 10 mm)

Multipole-corrector magnets– Sextupole - and decapole corrector magnets at end of dipoles– Particle trajectories can become instable after many turns (even after,

say, 106 turns)

QF QD QFdipolemagnets

small sextupolecorrector magnets

decapolemagnets

LHC Cell - Length about 110 m (schematic layout)

sextupolemagnets

LHC FODO structure



Superconducting magnets: no pole shoes

Current distributions



LHC string under test


Calculation of the luminosity in a circular collider for head-on collisions

• k particle bunches moving in same direction simultaneously present in ring• n particles per bunch• surface of bunch is A• one bunch is circling the machine with frequency f• Interaction cross-section is σ

For a particle in the left bunch the probability for an interaction with a particlein the right bunch is: nσ/A. For one bunch-bunch encounter the probability is n2σ/A. There are fk bunch-encounters per second in one interaction region

With L = (# of interactions/s) / σ we find: L = fkn2/A-> minimizing the beam size and many bunches help to maximize the luminosity


Luminosity can be increased by increasing n1 and n2, butthe counterrotating beams interact electro-magnetically:"beam-beam" interactions

Beam size 16 μmf = 11246 Hz

Number of protons per bunch limited to about 1011

L = n1n2 f k / 4π σ x σ y = 3.5 1030 [cm-2 s-1]

with one bunchwith 2808 bunches (every 25 ns one bunch) L = 1034 [cm-2s-1]

LHC:


L =f kn1n2

4πσxσy

Assume the probability distribution to be Gaussian:


Large number of bunches

• Crossing angle to avoid long range beam beam interaction• Interaction region quadrupoles with gradient of

250 T/m and 70 mm aperture

Interaction point

Bunch size squeezednear interaction point


LHC:


SLAC accelerator complex

Present lay-out,showing the Babarexperiment :

Damping rings:see section 3.3



DESY accelerator complex(Hamburg)

8 kmcircumference


to Gran-Sasso (730 km)

CERN accelerator complex



ESRF: European Synchrotron Radiation Facility, Grenoble, France

16 m linac, 200 MeV

300 m circumference booster synchrotron, 6 GeV


Photon beams

• From electron beam by bremsstrahlung, using thin, high Z target.By measuring the energy and the direction of the electron before and aftercreation of the photon, the photon energy can be determined ("tagged" photonbeam).

• From proton beam via π0 decays. The beam may contain a significantfraction of neutrons, passing the beam through deuterium may improvethe photon / neutron ratio.

• Charged particles are removed with bending magnets.


π, K and anti-proton beams

Production by interactions of primary protons from a proton acceleratorwith a suitable target. Typical fractions of particles for 400 GeV/c primaryprotons:

Positive beam: 83.5 % p, 14.0 % π+, 2.5% K+

Negative beam: 95.7% π−, 3.5% K-, 0.8 % anti-proton

At low energy electrostatic separators can be used for improving purity beamIt may be possible to use Cerenkov counters in the beam to determine the beamcomposition on an event-by-event basis


μ beams

From decays of pions, hadrons absorbed in low Z absorber to minimizemultiple scattering of muons

Absorber: 9.9 m Be

High-intensitymuon beam atCERN


Electron or positron beams

From pair production in thin high Z radiator by photons produced bydecays of neutral pions.

Neutron, anti-neutron and K0 beams

From proton interactions in a production target, charged particlescan be removed with magnetic fields, photons can be removed by passingthe beam through a radiator, leading to conversion into e+e- pairs.

Spallation source: accelerator + production target optimized for neutronbeam production, example: ISIS, Rutherford lab, UK (800 MeV protonsynchrotron and Ta target, see http://www.isis.rl.ac.uk/)

Hyperon (Λ, Σ±,Ξ-, Ξ0, Ω-) beams

Particles have short lifetimes -> short beamlines. Production with protoninteractions, "tagging" of particles (e.g. using Cerenkov detector) in beam essential


Neutrino beams

From decays of charged pions and K-mesons:

π+ -> μ+νμπ− -> μ−νμ

Electron neutrino flux ~ 1% of muon neutrino flux

Beamline: thin production target, decay region and massive absorber(earth, iron) for removing everything else than neutrinos from beam.

Wide band beam: collection of π's and K's from productiontarget over wide range of momenta and large solid angle ->broad energy spectrum, high neutrino flux

Narrow band beam: momentum (and charge) selection of π's and K's ->neutrino's or anti-neutrino's, lower intensity, better defined energy than inwide band beam.

Κ+ -> μ+νμΚ− -> μ−νμ

Κ+ -> e+π0νμΚ− -> e−π0νμ


The future CNGS neutrino beam line at CERN, pointing to Gran Sasso

Horn: pulsed magnet focusing particles produced

Documents

Acceleratorsepweb2.ph.bham.ac.uk/user/newman/appt10/Accelerators... · 2010-11-14 · Particle Detection UVA/VU 2003 III 14 Linear Drift Tube accelerator, Alvarez type ~ small antenna