Introduction to particle accelerators

Walter Scandale

CERN - AT department

Roma, marzo 2006

Lecture I - what are accelerators ?

topics Fundamental discoveries in accelerator physics and technology

Historical perspective

Accelerator typologies Sources Linear accelerators Circular accelerators Special accelerators Synchrotrons

Fixed target versus colliders

Lepton versus hadron colliders

Some relevant numbers

Introductory remarks

Particle accelerators are black boxes producing either flux of particles impinging on a fixed target or debris of interactions emerging from colliding particles

In trying to clarify what the black boxes are one can list the technological problems describe the basic physics and mathematics involved

Most of the phenomena in a particle accelerator can be described in terms of classical mechanics, electro-dynamics and restricted relativityquantum mechanic is required in a couple of cases just for leptons (synchrotron radiation, pinch effect)However there are some complications: many non-linear phenomena many particles interacting to each other and with a complex

surroundings the observables are averaged over large ensembles of particles to handle high energy high intensity beams a complex technology

is requiredIn ten hours we can only superficially fly over the problems just to have a preliminary feeling of them

The everyone’s accelerator

Important discoveries

1900 to 1925 radioactive source experiments à la Rutherford -> request for higher energy beams;

1928 to 1932 electrostatic acceleration -> Cockcroft & Walton -> voltage multiplication using diodes and oscillating voltage (700

kV); Van der Graaf -> voltage charging through mechanical belt (1.2 MV);

1928 resonant acceleration -> Ising establish the concept, Wideroe builds the first linac;

1929 cyclotron -> small prototype by Livingstone (PhD thesis), large scale by Lawrence;

1942 magnetic induction -> Kerst build the betatron; 1944 synchrotron -> MacMillan, Oliphant and Veksel invent the RF phase stability

(longitudinal focusing); 1946 proton linac -> Alvarez build an RF structure with drift tubes (progressive

wave in 2 mode); 1950 strong focusing -> Christofilos patent the alternate gradient concept

(transverse strong focusing); 1951 tandem -> Alvarez upgrade the electrostatic acceleration concept and build a

tandem; 1955 AGS -> Courant, Snider and Livingstone build the alternate gradient

Cosmotron in Brookhaven; 1956 collider -> Kerst discuss the concept of colliding beams; 1961 e+e- collider -> Touschek invent the concept of particle-antiparticle

collider; 1967 electron cooling -> Budker proposes the e-cooling to increase the proton

beam density; 1968 stochastic cooling -> Van der Meer proposes the stochastic cooling to

compress the phase space; 1970 RFQ -> Kapchinski & Telyakov build the radiofrequency quadrupole; 1980 to now superconducting magnets -> developed in various laboratories to

increase the beam energy; 1980 to now superconducting RF -> developed in various lab to increase the RF

gradient.

The Livingstone’s diagram

In 1950 Livingstone plotted the accelerator energy expressed in a semi-logarithmic scale as a function of the year of construction observing a linear growth.

The energy increase by a factor 33 every decade, mostly due to discoveries and technological advances.

Recent signs of saturation ?

Ion sources: positive ions sources

formed from electron bombardment of a gas extracted from the resulting plasma: species ranging from H to U (multiply charged)

negative ion sources: principal interest is in H-, for charge exchange injection surface sources: in a plasma, H picks up electrons from an activated surface

volume sources: electron attachment or recombination in H plasma polarized ion sources: e.g., optically pumped source -> some penalty in intensity, relatively high (> 65 %) polarization

Sources (1/3)

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Penning source

Surface source

Volume source

Magnetron source

Electron sources electron production mechanism:

thermo ionic emission (pulse duration controlled by a pulsed grid)

photocathode irradiation by pulsed laser (laser pulse width determines the pulse duration)

initial acceleration methods DC HV guns -> 50-500 keV acceleration RF guns: cathode forms one wall of the RF cavity -> rapid acceleration to > 10 MeV in a few cells-> mitigates space charge effects, -> makes for low emittance

Sources (2/3)

NLC Electron Source layout, for polarized and un-polarized sources

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Positron sources “conventional” positron source: can get from 10-3 :1 up to ~1:1 positron/electron as electron energy rises from 0.2 to 20 GeV

positron production through high energy photons:

RF linac

solenoidhelical undulatorsweep

magnetconverter

high energy e-

e-e-

e+ e+

Antiproton sources

matching solenoid

RF linac

solenoid

target0.2 to 20 GeV e- e+ e+

horn lens80÷150 GeV p+

targetp- To a storage ring with stochastic cooling

p+/p- yield typically ≈ 10-5

Sources (3/3)

source is similar to p- source

Linear accelerators (1/2) electrostatic accelerators

positive ion beamenergy = 2qV n+

AnalysingMagnet

Charging beltnegative

ion source

high voltage terminal V ≤ 10 MV

Stripping foil

- n+

(n-1)+

(n+1)+

RF linac

tandem Van der Graaf, pelletron

Wideroe (1928)V=V0*sin(t)

Alvarez (1946)

V=V0*sin(t)

Focusing magnets

RFQ (RF quadrupole) electric quadrupole, with a sinusoidal varying voltage on its electrodes;

the electrode tips are modulated in the longitudinal direction; this modulation results in a longitudinal accelerating field; it is a capable of a few MeV of acceleration; typically used between the ion source and the Alvarez linac in proton RF linacs.

Induction linac: the beam forms the secondary circuit of a high-current pulse transformer very low rep rates (a few Hz) intermediate voltages (30-50 MeV) very high peak currents (>10 kA) in short (0.1÷1 µs) pulses

solenoid

pulser

accelerating gaps

magnetic core

Linear accelerators (2/2)

Klystron - a microwave generator

The e- beam enters in an RF cavity with Lcavity ≈ RF In the cavity there is a velocity modulation of the e- beam In the drift region the velocity modulation induces a beam bunching The bunched beam induces a wake modulation in the second cavity The initial RF power is amplified in the second cavity The residual e- beam is absorbed in a stopper If the two cavities are coupled we have instead an oscillator

velocity modulation -> e- beam bunching -> coherent emission

Other RF power amplifier:

the magnetron, the travelling wave tube (TWT)

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A microwave oven magnetron

Circular accelerators (1/4) Betatron

The betatron accelerate e- at relativistic speeds It is essentially a transformer with a doughnut shaped vacuum tube as its secondary coil

The magnetic field B0 makes the electrons moving in a circle, The change of magnetic flux within the orbit ∆ = π2∆ <B> produces an accelerating electric field E

<B> = 2·B0 -> stable obit along a fixed radius at all energies (Wideroe condition)

Energies up to 300 MeV have been obtained. Betatrons are still used in industry and medicine as they are the very compact accelerators for electrons. Cyclotrons are similarly compact but cannot accelerate electrons to useful energies.

Principle of Betatron AccelerationCross section of a Betatron

Bguide= <B>/2p=erBguide

Bguide = 1/2 Baverage

CoilSteel

Vacuum chamber

<B>B0

€

p = erB0 ⇔ dp = eρdB0

p = eE ⇔ dp = edE = 12 eρd B

⎧ ⎨ ⎩

⇒ B0 = 12 B

€

E = −U

2πρ=

1

2πρ

dφ

dt=ρ

2

d B

dt

Cyclotron The cyclotron accelerate ions at non-relativistic speeds

A constant magnetic field imposes circular orbits;

The RF accelerating field in the Dee’s gap can be substantially reduced respect to a linear accelerator;

The acceleration process is resonant and similar to a parametric resonator.

Used in the industry and medicine to accelerate protons and ions The centripetal force is the

Lorenz force: F = eE+evB The instantaneous radius of curvature is: evB = mv2/ -> = p/eB

The cyclotron frequency is: = v/ = eB/m

The maximal kinetic energy depends on the magnetic field and radius: Ecin = 1/2 mv2 = 1/2 e2B22/m

Circular accelerators (2/4)

Isochronous cyclotron The isochronous cyclotron (sector cyclotron) accelerate ions at relativistic speeds

B varies with the azimuth: mimic the alternate gradient principle, focusing the beam also in the vertical direction

B varies with shape B() to keep constant whilst m and the kinetic energy Ecin increase above the relativistic limit

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The PSI Ring Cyclotron: a separated sector cyclotron with a fixed beam energy of 590 MeV, commissioned in 1974, produces a proton beam with the highest power in the world.

The protons are accelerated in the ring cyclotron to almost 0.8c, corresponding to an energy of 590 MeV.

The proton current amounts presently to almost 2 mA, which results in a beam power of over 1 MW.

The principle components of the ring cyclotron are eight sector magnets, with a total weight of 2000 t, and four accelerator cavities (50 MHz frequency) each having a peak voltage of 730 kV.

Circular accelerators (3/4)

Synchro-cyclotron A synchrocyclotron accelerate ions at relativistic speed It is simply a cyclotron with the accelerating supply frequency decreasing as the particles become relativistic and begin to lag behind.

Although in principle they can be scaled up to any energy they are not built any more as the synchrotron is a more versatile machine at high energies.

Circular accelerators (4/4)

€

Trev =2πr

v=

2πm0γ

eB

The revolution period increases with the energy since the path length increases faster than the speed

€

RF =ec 2B

m0c2 + Ecin

The radiofrequency decreases with the energy: a variable capacity modifies the RF resonant circuit

Special accelerators Microtron

A microtron accelerate e- at relativistic speed It is simply a cyclotron for e- containing an RF linac and a bending field region

Turn after turn Trev increases by a multiple of TRF so that the e- are always in phase with the accelerating RF

€

Trev ,1 =2π

ec 2Bm0c

2 + ΔEcin( ) = hTRF

ΔTrev =2π

ec 2BΔEcin = kTRF

⎧

⎨ ⎪

⎩ ⎪

first turn

change per turn

€

TRF =2πm0

eB h − k( )

ΔEcin = m0c2 h

h − k

⎧

⎨ ⎪ ⎪

⎩ ⎪ ⎪

Cebaf concept: disentangle RF for magnet The orbits are separated by large space A magnetic system for each consecutive orbit Orbit lengths shaped to keep synchronicity for an optimal RF system (large k) within limited space and costs

Special accelerators FFAG Fixed Field Alternate Gradient

A FFAG accelerate e- at relativistic speed recent versions accelerate p or beams at high rate

It allows strong focussing, RF synchronisation, fixed B field -> fast cycling

complex

A modern synchrotron

Extraction devices special magnets high voltage septa high power targets

Main components of a modern accelerator Source of charged particles; Acceleration element (RF cavities); Guiding magnets (quadrupole, dipoles, correctors); Vacuum system; Beam diagnostics; Physics detectors in an experimental area

Fixed target versus collider rings

N1 particlesbeam population N1

target density cross section no. of target particles N2 = lAeffective interaction area Aeff = N2 = lAprobability of interaction P = Aeff/A = lreaction rate R = P•dN1/dt = l•dN1/dt

Fixed target

A

l

Collider

Advantage

Luminositybunch population in beam 1 N1

bunch population in beam 2 N2

rms beam radius beam area 2

L = R/ = l•dN1/dt = N2/A•dN1/dt L = fN1N2/42

Synchrotron radiation

€

U =e2

3ε0

β 3γ 4

ρ

U MeV[ ] = 0.0885E 4 GeV[ ]ρ m[ ]

Energy loss per turn

Polarized light Fan in the bending plane

Lepton versus hadron circular colliders

->

(At the parton level )

RF is a major concern

magnets are a major concern

Type of accelerators (1990)

Main accelerators for research

Colliders in operation (2001)

Type Facility Ecm (GeV) Luminosity (1033cm-2 s-1)e+e- two rings DAFNE (It aly) 1.05 0.01e+e- single ring BEPC (China) 3.1 0.05e+e- single ring CESR (US) 10.4 0.8e+e- two rings SLAC PEP-II ( US) 10.4 0.6e+e- two rings KEK-B (Ja pan) 10.4 0.3e+e- single ring CERN LEP (Europe) 200 0.05Pbar-p single ring Fermilab Tevatron (US) 1800 0.02ep two rings DESY HERA (Germany) 300 0.02e+e- linear collider SLAC SLC (US) 100 0.002

Main accelerators for research

Colliders under investigation or in construction (2006)

Type Facility Ecm (GeV) Luminosity (1033cm-2 s-1)pp two rings CERN LHC 14000 10e+-e- linear collider NLC – JL C -TESLA - CLI C 500-3000 10µ+-µ- single ring Muon collider 100-3000 0.1-100pp two rings VLHC 100000 10

Type Facility Ecm (GeV) Luminosity (1033cm-2 s-1)AuAu two ring collider BNL RHI C (US) 100/nucleon 10-6Electron Microtron CEBAF (US) 4 -Electron linac Bates (US) 0.3-1.1 -Proton synchrotron I UCF (US) 0.5 -Is ochronous heavy-ion cyclotron MSU NSCL (US.) 0.5Is ochronous cyclotron TRI UMF(Canada) 0.5 -Is ochronous cyclotron PSI (Switzerland) 0.5 -

Accelerators in operation for nuclear physics research (2006)

Other applications

Field Accelerator Topics of study

Atomic Physics Low energy ion beams Atomic collision processes - study of excitedstates - electron-ion collisions - electronicstopping power in solids

Condensed matterphysics

Synchrotron radiationsources

X-ray studies of crystal structure

Condensed matterphysics

Spallation neutronsources

Neutron scattering studies of metals andcrystals - liquids and amorphous materials

Material science I on beams Proton and X-ray activation analysis ofmaterials - X- ray emission studies -accelerator mass spectrometry

Chemistry andbiology

Synchrotron radiationsources

Chemical bonding studies: dynamics andkinetics - protein and virus crystallography -biological dynamics

Other applications

Oil well logging with neutron sources from small linacs Archaeological dating with accelerator mass spectrometry Medical diagnostics using accelerator-produced radioisotopes

Radiation therapy for cancer: X-rays from electron linacs, neutron-therapy from proton linacs, proton therapy; pion and heavy-ion therapy

Ion implantation with positive ion beams Radiation processing with proton or electron beams: polymerization,vulcanization and curing, sterilization of food, insect sterilization,production of micro-porous membranes

X-ray microlithography using synchrotron radiation Inertial confinement fusion using heavy-ion beams as the driver

Muon-catalyzed fusion Tritium production, and radioactive waste incineration, using high energy proton beams

CATEGORY NUMBERIon implanters and surface modifications 7'000Accelerators in industry 1'500Accelerators in non-nuclear research 1'000Radiotherapy 5'000Medical isotopes production 200Hadrontherapy 20Synchrotron radiation sources 70Research in nuclear and particle physics 110TOTAL        15'000

How many accelerators today?

Lecture I - what are accelerators ?

reminder The accelerators are basic tools for physics

discovery: new ideas and technological breakthrough sustained an impressive exponential progress of their performance for more than 80 years

Many different type of accelerator are used for particle and nuclear physics research, however the large majority of the existing accelerators is used for a multitude of practical applications

The synchrotrons are the backbone of accelerator complex, however old ideas and concepts are still revisited and upgraded to achieve more demanding requirements

Colliders are the master tool in the quest of the highest energy, whilst fixed target operation allow reaching the highest rates

Hadron and lepton colliders play complementary roles