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ACCELERATORS

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Topics

types of accelerators relativistic effects Fermilab accelerators Fermilab proton-antiproton collider beam coolingCERN -- LHC summary

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Luminosity and cross section

Luminosity is a measure of the beam intensity (particles per area per second) ( L~1031/cm2/s )

“integrated luminosity” is a measure of the amount of data collected (e.g. ~100 pb-1)

cross section s is measure of effective interaction area, proportional to the probability that a given process will occur.

o 1 barn = 10-24 cm2

o 1 pb = 10-12 b = 10-36 cm2 = 10-40 m2

interaction rate:

LdtnLdtdn /

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How to make qq collisions Quarks are not found free in nature! But (anti)quarks are elements of (anti)protons. So, if we collide protons and anti-protons we should get some qq

collisions.

Proton structure functions give the probability that a single quark (or gluon) carries a fraction x of the proton momentum (which is 980 GeV/c at the Tevatron)

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ACCELERATORS are devices to increase the energy of charged particles;

use magnetic fields to shape (focus and bend) the trajectory of the particles;

use electric fields for acceleration. types of accelerators:

DC)acceleratorso Cockcroft-Walton accelerator (protons up to 2 MeV)o Van de Graaff accelerator (protons up to 10 MeV)o Tandem Van de Graaff accelerator (protons up to 20 MeV)

resonance acceleratorso cyclotron (protons up to 25 MeV)o linear accelerators

electron linac: 100 MeV to 50 GeV proton linac: up to 70 MeV

synchronous accelerators o synchrocyclotron (protons up to 750 MeV)o proton synchrotron (protons up to 900 GeV)o electron synchrotron (electrons from 50 MeV to 90 GeV)

storage ring accelerators (colliders)

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DC Accelerators

electrostatic accelerators: generate high voltage between two

electrodes charged particles move in electric field, energy gain = charge times voltage drop;

Cockcroft-Walton and Van de Graaff accelerators differ in method to achieve high voltage.

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Cockcroft-Walton generator C-W generator uses diodes and capacitors in a

rectifier and voltage-multiplier circuit

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Van de Graaff accelerator

use power supply to deposit charges on belt; pick charges off at other end of belt and deposit on “terminal”

now rubber belt replaced by “pellet” chain – “pelletron”

http://www.pelletron.com/charging.htm

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Van de Graaff accelerator -- 2

tandem – VdG: use potential difference twice, with change of charges in the middle (strip off electrons)

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Proton Linac proton linac (drift tube accelerator):

cylindrical metal tubes (drift tubes) along axis of large vacuum tank

successive drift tubes connected to opposite terminals of AC voltage source

no electric field inside drift tube while in drift tube, protons move with constant velocity

AC frequency such that protons always find accelerating field when reaching gap between drift tubes

length of drift tubes increases to keep drift time constant for very high velocities, drift tubes nearly of same length

(nearly no velocity increase when approaching speed of light)

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CYCLOTRON cyclotron

consists of two hollow metal chambers called (“dees” for their shape, with open sides which are parallel, slightly apart from each other (“gap”)

dees connected to AC voltage source - always one dee positive when other negative electric field in gap between dees, but no electric field inside the dees;

source of protons in center, everything in vacuum chamber; whole apparatus in magnetic field perpendicular to plane of dees; frequency of AC voltage such that particles always accelerated when

reaching the gap between the dees; in magnetic field, particles are deflected: p = qBR

p = momentum, q = charge, B = magnetic field strength, R = radius of curvature

radius of path increases as momentum of proton increases time for passage always the same as long as momentum proportional to velocity; this is not true when velocity becomes too big (relativistic effects)

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Cyclotron

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Accelerators: “relativistic effects”

“relativistic effects” special relativity tells us that certain approximations made in

Newtonian mechanics break down at very high speeds; relation between momentum and velocity in “old” (Newtonian)

mechanics: p = m v relativistically this becomes p = mv , with = 1/1 - (v/c)2

m = “rest mass”, i.e. mass is replaced by rest mass times - “relativistic growth of mass”

factor often called “Lorentz factor”; ubiquitous in relations from special relativity; energy: E = mc2

acceleration in a cyclotron is possible as long as relativistic effects are negligibly small, i.e. only for small speeds, where momentum is still proportional to speed; at higher speeds, particles not in resonance with accelerating frequency; for acceleration, need to change magnetic field B or accelerating frequency f or both;

________

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more types of Accelerators

electron linac electrons reach nearly speed of light at small

energies (at 2 MeV, electrons have 98% of speed of light); no drift tubes; use travelling e.m. wave inside resonant cavities for acceleration.

synchrocyclotron: B kept constant, f decreases;

synchrotron : B increases during acceleration, f fixed (electron

synchrotron) or varied (proton synchrotron); radius of orbit fixed.

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Fermilab

Fermi National Accelerator Laboratory (http://www.fnal.gov/) Founded 1972 One of the top laboratories for high energy

physics Near Batavia, Illinois (45 mi West of Chicago) Until 2009 world’s highest energy accelerator:

Tevatron = proton synchrotron, Emax=980GeV

Operated as collider: proton – antiproton collisions at Ecm = 1.96 TeV

collider operation ended 30 Sept 2011 Physics Program

Collider experiments CDF, DØ, CMS neutrino physics: Minos, Mini-Boone,.. Astrophysics: Auger Observatory, Sloan Sky

Survey, DES,.. ………….

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The TeVatron Collider

Tevatron collider Colliding bunches of protons and anti-

protons; bunches meet each other every 396 ns

in the center of two detectors (DØ and CDF)

steered apart at other places Each particle has ~ 980 GeV of energy,

so the total energy in the center of massis 1960 GeV = 1.96 TeV

About 2,500,000 beam bunch crossings per second

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Fermilab aerial view

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Fermilab accelerator chain: 0 to 400 MeV

Plasma ion source: H- ions, 18keVCockroft-Walton H- ions, 18keV to 750keV

Linac :H- ions, 750keV to 400 MeV

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FNAL Cockcroft-Walton acc.

The Cockcroft-Walton pre-accelerator provides the first stage of acceleration; hydrogen gas is ionized to create negative ions, each consisting of two electrons and one proton.

ions are accelerated by a positive voltage and reach an energy of 750,000 electron volts (750 keV). (about 30 times the energy of the electron beam in a television's picture tube.)

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FNAL Linac Next, the negative

hydrogen ions enter a linear accelerator, approximately 500 feet long.

Oscillating electric fields accelerate the negative hydrogen ions to 400 million electron volts (400 MeV).

Before entering the third stage, the ions pass through a carbon foil, which removes the electrons, leaving only the positively charged protons.

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Fermilab Linac

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Fermilab accelerator chain: 400 MeV to 980

GeV Booster: H- ions, stripped to p 400 MeV to 8 GeV

Main Injector:Protons, 8GeV to 150GeV

TeVatronProtons and Antiprotons150GeV to 980GeV

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Main Injector and recycler recycler:

antiproton storage ring fixed momentum

(8.9 GeV/c), permanent magnets

Main Injector: proton synchrotron;

cycle period 1.6-3 seconds;

delivers 120 GeV protons to pbar production target.

Also delivers beam to a number of fixed target experiments.

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Fermilab TeVatron tunnel

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Antiproton manufacture

when enough antiprotons: extract from

accumulator or recycler

transfer to Main Injector

accelerate to 150 GeV

transfer to Tevatron

120 GeV protons from Main Injector

extract, shoot on target (Ni)

collect with Lithium lens

select 8GeV antiprotons

transfer to debuncher reduce beam spread

by stochastic cooling store in accumulator

(“stacking”) transfer to “recycler”

when stack reaches 1012 pbars

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Antiprotons -- target and collection pbars from target have wide angular distribution; Li lens focuses bend magnet selects 8 GeV pbars efficiency: 8 pbars per 1 M protons hitting target make it into accumulator

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Debuncher

pbars from target are in “bunches” (small time spread), wide energy spread (4%);

debuncher performs “bunch rotation” to swap large energy spread and small time spread into narrow energy spread and large time spread

low momentum pbars have shorter path arrive earlier at RF cavity get stronger accelerating kick

after sufficient turns, energy spread reduced

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Debuncher and accumulator

debuncher accumulator

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Accumulator

accumulates antiprotons successive pulses of antiprotons from

debuncher stacked over a day or so momentum stacking: newly injected

pbars are decelerated by RF cavity to edge of stack

stack tail cooling system sweeps beam deposited by RF towards core of the stack

additional core cooling systems keep antiprotons in core at desired energy and minimize beam size

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Beam Cooling Beam cooling: reduce size and energy spread

of a particle beam circulating in a storage ring (without any accompanying beam loss)

motion of individual beam particles deviate from motion of beam center (ideal orbit) transverse deviations in position and angle –

“betatron oscillations” longitudinal deviations due to energy

(momentum) spread -- “synchrotron oscillations”

motions of particles with respect to beam center similar to random motion of particles in a gas beam temperature = measure of average

energy corresponding to these relative motions

“beam cooling” = reduction of these motions -- decrease of beam temperatures

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Phase space Phase Space = space defined by

coordinates describing motion wrt beam center

Emittance = region of phase space where particles can orbit, also its size (phase space volume)

Liouville’s Theorem: phase space volume = constant (cannot be changed by conservative forces)

L.T. only for continous particle stream (liquid) – discrete particles can swap particles and empty phase space – reduce area occupied by beam

Transverse Phase space

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x

x’

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Beam cooling -- 2

beam cooling beats constraints of Liouville theorem (phase space volume is constant) because phase space volume is not reduced, only occupancy (distribution of particles) within phase space volume is changed

Cooling is, by definition, not a conservative process. The cooling electronics act on the beam through a feedback loop to alter the beam's momentum or transverse oscillations.

Two types of beam cooling have been demonstrated and used at various laboratories: electron cooling which was pioneered by G. I. Budker, et. al., at Novosibirsk, and stochastic cooling, developed by Simon van der Meer of CERN.

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Stochastic cooling -- 1

Stochastic cooling: pick-up electrode

detects excursions of a particle from its central orbit

sends signal to a “kicker” downstream

kicker applies a correction field to reduce this amplitude.

Short cut, (n+¼)

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Stochastic cooling - 2

The cooling process can be looked at as a competition between two terms:

(a) the coherent term which is generated by the single particle,

(b) the incoherent term which results from disturbances to the single particle.

(a)=linear with gain (b)=quadratic

by suitable choice of gain, overall cooling can be achieved

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Stochastic Cooling - 3 Particle beams are not just a single particle,

but rather, a distribution of particles around the circumference of the storage ring. Each particle oscillates with a unique amplitude and random initial phase. The cooling system acts on a sample of particles within the beam rather than on a single particle.

Since stochastic cooling systems cannot resolve the motion of a single antiproton, only a phenomenon called mixing makes cooling possible. Mixing arises because particles with different momenta take different times to travel around the ring, and get spread out over the beam. After a few turns around the ring, the noise averages to zero for accumulating antiprotons.

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Stochastic Cooling in the Pbar Source

Standard Debuncher operation: 108 pbars, uniformly distributed ~600 kHz revolution frequency

To individually sample particles to resolve 10-14 seconds, would need 100

THz bandwidth Don’t have good pickups, kickers, amplifiers in

the 100 THz range Sample Ns particles -> Stochastic process

o Ns = N/2TW where T is revolution time and W bandwidth

o Measure <x> deviations for Ns particles

The higher the bandwidth the better the cooling

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Betatron Cooling With correction ~ g<x>, where g is gain of system

New position: x - g<x> Emittance Reduction: RMS of kth particle

(W = bandwidth and N = number of circulating particles),

Must also consider noise (characterized by U = Noise/Signal) Mixing:

Randomization effects M = number of turns to completely randomize sample

Net cooling effect if g sufficiently small

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rate Cooling

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algebra of lots do and particles allover Average

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Momentum cooling Momentum cooling systems reduce the longitudinal

energy spread of a beam by accelerating or decelerating particles in the beam distribution towards a central momentum.

The sum signal is used for longitudinal cooling and the difference for betatron cooling.

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AntiProton Source

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Electron cooling

invented by G.I. Budker (INP, Novosibirsk) in 1966 as a way to increase luminosity of p-p and p-pbar colliders.

first tested in 1974 with 68 MeV protons in the NAP-M ring at INP.

cooling of ion beams by a co-moving low emittance electron beam is a well-established technique for energies up to hundreds of MeV per nucleon

at higher energy, expect slower cooling, but may still give enhancement in the performance of high energy colliders as well. was used for cooling of 8 GeV antiprotons in the

Fermilab recycler ring GSI project for cooling antiprotons

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How does electron cooling work?

velocity of electrons made equal to velocity of ions (antiprotons)

ions undergo Coulomb scattering in the “electron gas” and lose energy which is transferred from the ions to the co-streaming electrons until thermal equilibrium is attained

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electron collector electron gun

high voltage platform

magnetic field electron beam

ion beam

Electron cooling

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CERN (Conseil Européen pour la Recherche Nucléaire)

European Laboratory

for Particle Physics,

near Geneva,

Switzerland

(about 9km West of

Geneva, between

Meyrin,

and St.Genis,

straddling the Swiss-

French border)http://www.cern.ch

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CERN accelerators

http://public.web.cern.ch/public/en/LHC/LHC-en.html

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Large Hadron Collider (LHC)

Proton beams travel around the 27 km ring

in opposite directions, separate beam pipes.

In ultrahigh vacuum, 10-10 Torr. time for a single orbit, 89.92 μs.

beams controlled by superconducting electromagnets

o 1232 dipole magnets, 15 m each, bends beam.

o 392 quadrupole magnets, 5-7 m, focus beams.

o 8 inner triplet magnets are used to 'squeeze' the particles closer for collisions. Similar to firing needles 10 km apart with enough precision to meet in the middle.

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LHC – some numbers

Circumference Dipole operating temperature Number of magnets Number of dipoles Number of quadrupoles Number of RF cavities Nominal energy, protons Nominal energy, ions Peak magnetic dipole field Min. distance between bunches Design luminosity No. of bunches per proton beam No. of protons per bunch (at

start) Number of turns per second Number of collisions per second

26 659 m1.9 K (-271.3°C)930012328588 per beam7 TeV2.76 TeV/nucleon8.33 T7 m1034 cm-2 s-l

28081.1 x 1011

11 245600 million

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LHC Experiments

Atlas

CMS

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LHC Detectors

ATLAS

CMS

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CMS Collaboration

Slovak Republic

CERN

France

Italy

UK

Switzerland

USA

Austria

Finland

Greece

Hungary

Belgium

Poland

Portugal

Spain

Pakistan

Georgia

Armenia

UkraineUzbekistan

CyprusCroatia

China, PR

TurkeyBelarus

Estonia

India

Germany

Korea

Russia

Bulgaria

China (Taiwan)

IranSerbia

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Summary

many different types of accelerators have been developed for nuclear and particle physics research

different acceleration techniques suitable for different particles and energy regimes

most accelerators in large research laboratories use several of these techniques in a chain of accelerators

beam cooling has become important tool in improving beam quality and luminosity

active research going on to develop new accelerating techniques for future applications

many types of accelerators have found applications in fields other than nuclear and particle physics (e.g. medicine, ion implantation for electronics chips, condensed matter research, biology,….)