APPEAL-9:

How to Build the Biggest and Most Complex Discovery Machines

Lecture 1: Introduction to Particle Accelerators

Professor Emmanuel Tsesmelis

CERN & University of Oxford

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Introduction

Accelerators and beams are tools of discovery. They include light sources, neutron sources, medical accelerators, ion implanters, industrial accelerators and colliders. They are involved in the biological sciences, medicine, education, energy, national security, industry, investigation of the fundamental building blocks of nature and original elements, creation and investigation of advanced materials.

Particle accelerators are used to study the macro and micro world. This includes investigating the history of the universe, the lifecycle of stars, structure and function of molecules, subatomic particles (known matter), dark matter and dark energy (unknown matter).

The Three Frontiers of research are the energy frontier, the intensity frontier and the cosmic frontier. All three are involved in the investigation into the origin of the universe, unification of forces and new physics beyond the standard model. The cosmic frontier of research investigates cosmic particles, dark energy and dark matter. The intensity frontier of research investigates proton decay, neutrino physics and matter/anti-matter asymmetry. The energy frontier of research investigates the matter/anti-matter asymmetry, the origin of mass and dark energy.

Our Scientific Challenge: to understand the very first moments of our Universe after the Big Bang.

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http://guava.physics.uiuc.edu/~nigel/courses/569/Essays_Fall2011/Files/banerjee.pdf

In the Standard Model, it is generally accepted that elementary particles get their masses via the Higgs mechanism, which involves a phase transition from the symmetric phase at higher temperatures (close to the Big Bang) to a phase in which the symmetry has been spontaneously broken. One of the outstanding problems in particle physics is to explain the origin of the observed matter-antimatter asymmetry (baryogenesis) which we observe in today’s universe. It is believed that the Standard Model, along with the mechanism of electroweak phase transition provides a model for baryon number asymmetry.

The standard model is the name given in the 1970s to a theory of fundamental particles and how they interact. It incorporated all that was known about subatomic particles at the time and predicted the existence of additional particles as well.

https://physics.info/standard/

There are seventeen named particles in the standard model, organized into the chart shown below. The last particles discovered were the W and Z bosons in 1983, the top quark in 1995, the tau neutrino in 2000, and the Higgs boson in 2012.

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Fundamental particles are either the building blocks of matter, called fermions, or the mediators of interactions, called bosons. There are twelve named fermions and five named bosons in the standard model.

Up (u), down (d), charm (c), strange (s), top (t) and bottom (b) are quarks

Electron (e), electron neutrino (ne), muon (m), muon neutrino (nm), tau (t) and tau neutrino (nt) are leptons

Fundamental particles are either the building blocks of matter, called fermions, or the mediators of interactions, called bosons. There are twelve named fermions and five named bosons in the standard model.

Fermions obey a statistical rule described by Enrico Fermi (1901–1954) of Italy, Paul Dirac (1902–1984) of England, and Wolfgang Pauli (1900–1958) of Austria called the exclusion principle. Simply stated, fermions cannot occupy the same place at the same time. (More formally, no two fermions may be described by the same quantum numbers.) Leptons and quarks are fermions, but so are things made from them like protons, neutrons, atoms, molecules, people, and walls. This agrees with our macroscopic observations of matter in everyday life. People cannot walk through walls unless the wall gets out of the way.

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Bosons have no problem occupying the same place at the same time. (More formally, two or more bosons may be described by the same quantum numbers.) The statistical rules that bosons obey were first described by Satyendra Bose (1894–1974) of India and Albert Einstein (1879–1955) of Germany. Gluons,

photons, and the W, Z and Higgs are all bosons (gauge particles). As the particles that make up light and other forms of electromagnetic radiation, photons (electromagnetic force) are the bosons we have the most direct experience with. In our everyday experience, we never see beams of light crash into one another. Photons are like phantoms. One may pass through the other with no effect. Gluons are involved with the strong force; W+, W and Z particles are involved with weak force and the Higgs is a scalar particle.

Elementary particles have an intrinsic spin angular momentum S. Every elementary particle has associated with it a spin quantum number s.

Quarks are known to bind into triplets and doublets. The triplets are called baryons and the doublets are called mesons.

A proton (p) is made up of two ups and one down quark. It was predicted in 1815 and discovered in 1917. Spin number = 1/2, charge = +1e, no colours and mass = 938.272081 MeVc-2

A neutron (n) is made up of two downs and one up quark. It was predicted in 1920 and discovered in 1932. Spin number = 1/2, charge = 0e, no colours and mass = 939.565413 MeVc-2

Microscopic cosmic ruler

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The Large Hadron Collider (LHC) produces quarks and studies them.

https://home.cern/science/accelerators/large-hadron-collider

The Alpha Magnetic Spectrometer also designated AMS-02, is a particle physics experiment module that is mounted on the International Space Station (ISS). The module is a detector that measures antimatter in cosmic rays; this information is needed to understand the formation of the Universe and search for evidence of dark matter. It looks at smaller scales than the LHC.

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AMS-02 installed on the ISS.

https://en.wikipedia.org/wiki/Alpha_Magnetic_Spectrometer (AMS)

Atacama Large Millimeter/submillimeter Array (ALMA), currently the largest radio telescope in the world, is used to investigate millimetric and submillimetric wavelengths of electromagnetic radiation. It is well-known that these waves are full of information about our cosmic origins.

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https://www.almaobservatory.org/en/home/

The Very Large Telescope (VLT) is a telescope facility operated by the European Southern Observatory on Cerro Paranal in the Atacama Desert of northern Chile. The VLT consists of four individual telescopes, each with a primary mirror 8.2 m across, which are generally used separately but can be used together to achieve very high angular resolution.

The VLT operates at visible and infrared wavelengths. Each individual telescope can detect objects roughly four billion times fainter than can be detected with the naked eye, and when all the telescopes are combined, the facility can achieve an angular resolution of about 0.001 arc-second. In single telescope mode of operation angular resolution is about 0.05 arc-second.

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https://en.wikipedia.org/wiki/Very_Large_Telescope (VLT)

Investigating the structure of matter

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The Study of Elementary Particles & Fields & Their Interactions using CERN Accelerator Complex

The next big challenge is to link gravity and quantum mechanics. Some of this work will take place at the CERN accelerator complex (LHC)

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With p-p collisions you need start with hydrogen atoms. Rip off the electron from each atom and accelerate the resultant proton close to the speed of light.

The biggest engineering challenge was to dig down to create the LHC.

The Large Hadron Collider (LHC)

Everything was built specifically for a particular job. The result of 25 years of research and development.

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High energy beams of particles are kept in line with dipole magnets, 15m in length and a mass of 35 tonnes.

Pipes around the magnets (superconducting coils) transports very low temperature liquid helium to produce the superconductors necessary to produce the required magnetic fields (up to 9 Tesla).

The vacuum in the apparatus can be 10-8 torr. Residual water vapour is sucked out. The coils sit in the liquid Helium.

Accelerator Development was characterised by rapid progress for over a century. Initially from cathode-ray tubes that aided in the discovery of the electron to the LHC that aided the discovery of the Higgs boson.

https://en.wikipedia.org/wiki/J._J._Thomson

Sir Joseph John Thomson OM PRS (18 December 1856 – 30 August 1940) was an English physicist and Nobel Laureate in Physics, credited with the discovery and identification of the electron; and with the discovery of the first subatomic particle.

https://www.phy.cam.ac.uk/history/electron/autobiography

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The basic features of Thomson’s apparatus are shown in the diagram above. The cathode C is at a negative potential of several hundred volts, and the anode S1 is earthed. The cathode rays travel towards the anode and pass through a slit in it. They continue through a second slit in the plug S2, and travelling in a straight line (shown black in the diagram) strike the end of the tube at the point O, where they produce a narrow well-defined phosphorescent patch. P1 and P2 are a pair of parallel metal plates across which a potential difference may be applied. This gives rise to an electric field in the space between them along which the cathode rays are travelling. If the plate P1 is positive the cathode rays are deflected upwards. They follow the path shown in red and produce a phosphorescent patch at the point A. A scale is pasted on the outside of the tube to measure the amount of the deflection.

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The image above right shows the cathode ray tube by which J.J. Thomson demonstrated that cathode rays could be deflected by a magnetic field, and that their negative charge was not a separate phenomenon.

https://atlas.cern/

ATLAS observes elusive Higgs boson decay to a pair of bottom quarks

https://home.cern/science/experiments/lhcb

The LHCb experiment will shed light on why we live in a universe that appears to be composed almost entirely of matter, but no antimatter

https://home.cern/science/experiments/alice

ALICE detects quark-gluon plasma, a state of matter thought to have formed just after the big bang

https://home.cern/science/experiments/cms

The CMS detector uses a huge solenoid magnet to bend the paths of particles from collisions in the LHC

Advances in accelerators require corresponding advances in accelerator technologies. These include magnets, vacuum systems, RF systems, diagnostics,…

But timelines become long, requiring: Long-term planning; Long-term resources; Global collaboration.

Livingston Plot

Accelerators have their own version of Moores’ law known as a Livingston plot. The energy of accelerators has increased by a factor of 10 every 10 years.

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Around 1950, Livingston made following observation:

Plotting energy of accelerator as a function of year of commissioning, on semi-log scale, the energy gain has linear dependence.

Observations today:

Exhibition of saturation effect so new technologies needed;

Overall project cost increased – Project cost increased by factor of 200 over last 40 years;

Cost per proton-proton ECM energy decreased by factor of 10 over last 40 years. The decrease is not enough. Research is in trouble as the energy required to continue the research needs to increase.

Accelerator Parameters (I)

Particle colliders designed to deliver two basic parameters to HEP user.

I. Centre-of-Mass Energy ECM

Why Colliders?

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Only a tiny fraction of energy converted into mass of new particles (due to energy and momentum conservation)

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Entire energy converted into the mass of new particles

https://en.wikipedia.org/wiki/Louis_de_Broglie

Louis Victor Pierre Raymond de Broglie, duc de Broglie (15 August 1891 – 19 March 1987) was a French physicist who made ground breaking contributions to quantum theory. In his 1924 PhD thesis, he postulated the wave nature of electrons and suggested that all matter has wave properties. This concept is known as the de Broglie hypothesis, an example of  wave–particle duality, and forms a central part of the theory of quantum mechanics.

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De Broglie won the Nobel Prize for Physics in 1929, after the wave-like behaviour of matter was first experimentally demonstrated in 1927.

The De Broglie Wavelength is the wavelength associated with the wave like behaviour of matter

l = h/p (1.2fm/p[GeV/c])

where l = De Broglie wavelength, h = Planck constant and p = momentum

Wave-particle duality requires higher energies in order to probe shorter distances inside matter. In other words the shorter the De Broglie wavelength the greater the energy required.

l = h/√(2Em) where E is the energy and m is the mass of the particle

Accelerator Parameters (II)

Particle colliders designed to deliver two basic parameters to the high energy physics user.

https://en.wikipedia.org/wiki/Particle_physics

II. Luminosity:

Measure of collision rate per unit area;

Event rate for given event probability (“cross-section”)

R = ℓs

σ = cross section and ℓ = instantaneous luminosity

For a Collider, instantaneous luminosity ℓ is given by

N+Nfc/4psx*sy*

N+, N = numbers of particles per bunch

fc = crossing frequency

σx,y = transverse profiles of beams (4πσxσy = transverse area)

–> Require intense beams, high bunch frequency and small beam sizes at the interaction point (IP).

http://sns.ias.edu/~pgl/SMB/529/Lecture_notes/LN13_collider.pdf

Cross-sections at the LHC

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https://www.lhc-closer.es/taking_a_closer_look_at_lhc/0.cross_section

Cross section (σ) is a measurement of the probability that an event occurs. It´s measured in “barn” – 1 b = 10-24 cm2

Collider Types: Hadron Colliders

Desire high energy

Only ~10% of beam energy available for hard collisions producing new particles. You need O(10 TeV) Collider to probe 1 TeV mass scale.

High-energy beam requires strong magnets to store and focus the beam in a reasonable-sized ring.

Desire high luminosity

Use proton-proton collisions. High bunch population and high bunch frequency. Anti-protons are difficult to produce if beam is lost c.f. SPS Collider and Tevatron

https://en.wikipedia.org/wiki/Super_Proton%E2%80%93Antiproton_Synchrotron

https://en.wikipedia.org/wiki/Tevatron

Collider Types: Lepton Colliders (e+e)

Synchrotron radiation causing undesired energy loss is the most serious challenge

https://en.wikipedia.org/wiki/Synchrotron_radiation

Synchrotron radiation (also known as magnetobremsstrahlung radiation) is the electromagnetic radiation emitted when charged particles are accelerated radially, i.e., when they are subject to an acceleration perpendicular to their velocity.

Energy loss of a particle per turn is given by

U0 = 4preg4[mc2]/3R where re is classical electron radius, g the ratio of energy over rest mass of the electron and R is the radius of the circular collider.

Emitted power in a circular machine is

PSR[kW] = 88.5E4[GeV]I[A]/r[m] where I is the total beam current, r is the particle bending radius and E4 is the 4th power of the energy

https://fcc.web.cern.ch/Documents/Public%20Information/FCC-1401201640-JWE_LeptonColliderParameters_V0200.pdf

http://pdg.lbl.gov/2002/accelrpp.pdf

https://indico.desy.de/indico/event/699/session/6/contribution/6/material/slides/0.pdf

For a collider with ECM (centre of mass energy) = 1 TeV in the LHC tunnel with a 1 mA beam, radiated the power would be 2 GW. You would need to replenish the radiated power with RF (radio frequency energy) and remove it from the vacuum chamber.

https://arxiv.org/ftp/arxiv/papers/1205/1205.3087.pdf

The approach for high energies is a Linear Collider.

Collider Characteristics

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Circular versus Linear Collider

Circular Collider
many magnets, few cavities, stored beam

higher energy → stronger magnetic field → higher synchrotron radiation losses (E4/m4R)

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Linear Collider
few magnets, many cavities, single pass beam higher energy → higher accelerating gradient higher luminosity → higher beam power (high bunch repetition)

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Rutherford fired the starting pistol

https://en.wikipedia.org/wiki/Ernest_Rutherford

Ernest Rutherford, 1st Baron Rutherford of Nelson, OM, FRS HFRSE LLD (30 August 1871 – 19 October 1937), was a New Zealand-born British physicist who came to be known as the father of nuclear physics.

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At the Royal Society in 1928 he said:

“I have long hoped for a source of positive particles more energetic than those emitted from natural radioactive substances”.

Lightning: requires > MV/m over many tens of metres to initiate it

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Your (old CRT) TV is an accelerator

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https://en.wikipedia.org/wiki/Cathode_ray_tube

The cathode ray tube (CRT) is a vacuum tube that contains one or more electron guns and a phosphorescent screen, and is used to display images. It modulates, accelerates, and deflects electron beam(s) onto the screen to create the images. The images may represent electrical waveforms (oscilloscope), pictures (television, computer monitor), radar targets, or other phenomena. CRTs have also been used as memory devices, in which case the visible light emitted from the fluorescent material (if any) is not intended to have significant meaning to a visual observer (though the visible pattern on the tube face may cryptically represent the stored data). In all modern CRT monitors and televisions, the beams are bent by magnetic deflection, a varying magnetic field generated by coils and driven by electronic circuits around the neck of the tube, although electrostatic deflection is commonly used in oscilloscopes, a type of electronic test instrument. A CRT is constructed from a glass envelope which is large, deep (i.e., long from front screen face to rear end), fairly heavy, and relatively fragile. The interior of a CRT is evacuated to approximately 0.01 pascals (9.9 x 10−8 atm) to 133 nanopascals (1.31 x 10−12 atm), evacuation being necessary to facilitate the free flight of electrons from the gun(s) to the tube’s face.

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Electrostatic Accelerators
The Cockcroft-Walton

https://en.wikipedia.org/wiki/Cockcroft%E2%80%93Walton_generator

The Cockcroft–Walton (CW) generator, or multiplier, is an electric circuit that generates a high DC voltage from a low-voltage AC or pulsing DC input. It was named after the British and Irish physicists John Douglas Cockcroft and Ernest Thomas Sinton Walton, who in 1932 used this circuit design to power their particle accelerator, performing the first artificial nuclear disintegration in history. They used this voltage multiplier cascade for most of their research, which in 1951 won them the Nobel Prize in Physics for “Transmutation of atomic nuclei by artificially accelerated atomic particles”. The circuit was discovered in 1919, by Heinrich Greinacher, a Swiss physicist. For this reason, this doubler cascade is sometimes also referred to as the Greinacher multiplier. Cockcroft–Walton circuits are still used in particle accelerators. They also are used in everyday electronic devices that require high voltages, such as X-ray machines, television sets, microwave ovens and photocopiers.

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This Cockcroft–Walton voltage multiplier was part of one of the early particle accelerators responsible for development of the atomic bomb. Built in 1937 by Philips of Eindhoven it is now in the National Science Museum in London, England.

Based on a system of multiple rectifiers a voltage is generated by cascade circuit

Utot = 2Un – (2pI/wC)((2n3/3) + (n2/4) + (n/12))

I = current, C = capacitance

https://en.wikipedia.org/wiki/John_Cockcroft (bottom left)

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Sir John Douglas Cockcroft, OM, KCB, CBE, FRS (27 May 1897 – 18 September 1967) was a British physicist who shared with Ernest Walton the Nobel Prize in Physics in 1951 for splitting the atomic nucleus, and was instrumental in the development of nuclear power.

https://en.wikipedia.org/wiki/Ernest_Walton (above right)

Ernest Thomas Sinton Walton (6 October 1903 – 25 June 1995) was an Irish physicist and Nobel laureate for his work with John Cockcroft with “atom-smashing” experiments done at Cambridge University in the early 1930s, and so became the first person in history to split the atom.

Modern CWs have voltages up to ~4 MV. Beam currents of several hundred mA with pulsed particle beams of few ms pulse length.

Electrostatic Accelerators – van de Graaff

With any electrostatic accelerator, it is difficult to achieve energy higher than ~20 MeV (e.g. due to practical limitations of the size of the vessels).

https://en.wikipedia.org/wiki/Van_de_Graaff_generator

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Tandem is a version with charge exchange in the middle (~1000 MeV).

A Van de Graaff generator is an electrostatic generator which uses a moving belt to accumulate electric charge on a hollow metal globe on the top of an insulated column, creating very high electric potentials. It produces very high voltage direct current (DC) electricity at low current levels.

https://en.wikipedia.org/wiki/Robert_J._Van_de_Graaff

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Robert Jemison Van de Graaff (December 20, 1901 – January 16, 1967) was an American engineer, physicist, and noted for his design and construction of high-voltage Van de Graaff generators

https://en.wikipedia.org/wiki/Tandem_accelerator

Linear Accelerators

Principle:

Use rapidly-changing high frequency voltages instead of direct voltages (Ising); Energy is proportional to the number of stages i traversed by a particle; The largest voltage in the entire system is never greater than Vmax

Arbitrary high energies without voltage discharge.

https://en.wikipedia.org/wiki/Rolf_Wider%C3%B8e

Rolf Widerøe (11 July 1902 – 11 October 1996), was a Norwegian accelerator physicist who was the originator of many particle acceleration concepts, including the resonance accelerator and the betatron accelerator.

https://en.wikipedia.org/wiki/Linear_particle_accelerator

A linear particle accelerator (often shortened to linac) is a type of particle accelerator that accelerates charged subatomic particles or ions to a high speed by subjecting them to a series of oscillating electric potentials along a linear beamline. The principles for such machines were proposed by Gustav Ising in 1924, while the first machine that worked was constructed by Rolf Widerøe in 1928 at the RWTH Aachen University. Linacs have many applications: they generate X-rays and high energy electrons for medicinal purposes in radiation therapy, serve as particle injectors for higher-energy accelerators, and are used directly to achieve the highest kinetic energy for light particles (electrons and positrons) for particle physics.

The design of a linac depends on the type of particle that is being accelerated: electrons, protons or ions. Linacs range in size from a cathode ray tube (which is a type of linac) to the 3.2-kilometre-long (2.0 mi) linac at the SLAC National Accelerator Laboratory in Menlo Park, California.

https://en.wikipedia.org/wiki/File:Linear_accelerator_animation_16frames_1.6sec.gif

The above link is an animation showing how a linear accelerator works. In this example the particles accelerated (red dots) are assumed to have a positive charge. The animation shows a single particle being accelerated each cycle; in actual linacs a large number of particles are injected and accelerated each cycle. The graph V(x) shows the electrical potential along the axis of the accelerator at each point in time. The polarity of the RF voltage reverses as the particle passes through each electrode, so when the particle crosses each gap the electric field (E, arrows) has the correct direction to accelerate it. The action is shown slowed down enormously.

The particles move down a vacuum tube under the influence of a travelling wave, which appears regularly with correct phase at the electrode gaps. As the particles reach each gap they are given a “kick” by the accelerating field.

Alternate pairs of electrodes are connected together and an a.c. signal applied to them.

The electrodes have to get longer as the particle gets further down the tube, since the particles will travel further during each cycle of the field. At very high velocities relativistic effects have to be allowed for.

With electron linear accelerators the particles are injected at about 4 MeV from a small electrostatic accelerator, and in the Stanford machine they are accelerated to energies in excess of 10 GeV (1000 MeV). The average beam current is about 15 mA.

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Phase focusing in linacs

In 1945 Veksler (UDSSR) and McMillan (USA) realised the importance of phase focusing. With the RF accelerator the energy gain depends critically on the voltage Vmax and the nominal accelerating phase Ψ0 therefore ΔE = qVmax sin(Ψ0).

A small error in Vmax or Ψ0 means the particle velocity no longer matches the design velocity fixed by the length of drift tube leasing to a phase shift relative to design Ψ0 phase in subsequent stages. This creates a longitudinal instability and a large energy error.

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Phase focusing is required in any RF accelerator to bring particles back to nominal phase!

https://www.classe.cornell.edu/~liepe/webpage/docs/P4456L2.pdf

Drift Tube Linac: Higher Integrated Field

https://www.researchgate.net/publication/47549724_Production_design_of_the_drift_tube_Linac_for_the_CERN_Linac4

The Drift Tube Linac (DTL) for the new linear accelerator Linac4 at CERN will accelerate H–ion beams of up to 40 mA average pulse current from 3 to 50 MeV. It is designed to operate at 352.2 MHz and at duty cycles of up to 10 %, if required by future physics programmes. The accelerating field is 3.2 MV/m over the entire length. Permanent magnet quadrupoles (PMQs) are used as focusing elements. The 3 DTL cavities consist of 2, 4 and 4 section of about 1.8 m each, are equipped with 35, 41 and 29 drift tubes respectively, and are stabilized with post-couplers. Several new features have been incorporated in the basic design. The electro-magnetic design has been refined in order to reduce peak field levels in critical areas. The mechanical design aims at reducing the complexity of the mechanical structure and of the adjustment procedure. Drift tubes and holders on the tanks that are machined to tight tolerances do not require adjustment mechanisms like screws or bellows for drift tube positioning. A scaled cold model, an assembly model and a full-scale prototype of the first half section have been constructed to validate the design principles.

https://www.researchgate.net/publication/237077823_Drift_Tube_Linac_Design_and_Prototyping_for_the_CERN_Linac4

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Cyclic Accelerators

In 1931 Lawrence designed a “cyclotron”, a circular device made of two electrodes placed in a magnetic field.

https://en.wikipedia.org/wiki/Cyclotron

It accelerates charged particles outwards from the centre along a spiral path. The particles are held to a spiral trajectory by a static magnetic field and accelerated by a rapidly varying (radio frequency) electric field. Ernest O. Lawrence was awarded the 1939 Nobel Prize in physics for this invention.

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Above left shows a diagram of cyclotron operation from Lawrence’s 1934 patent

https://en.wikipedia.org/wiki/Ernest_Lawrence

Ernest Orlando Lawrence (August 8, 1901 – August 27, 1958) was a pioneering American nuclear scientist and winner of the Nobel Prize in Physics in 1939 for his invention of the cyclotron. He is known for his work on uranium-isotope separation for the Manhattan Project, as well as for founding the Lawrence Berkeley National Laboratory and the Lawrence Livermore National Laboratory.

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Cyclotrons can accelerate (e.g.) protons up to hundreds of MeV.

A cyclotron accelerates a charged particle beam using a high frequency alternating voltage which is applied between two hollow “D”-shaped sheet metal electrodes called “dees” inside a vacuum chamber.The dees are placed face to face with a narrow gap between them, creating a cylindrical space within them for the particles to move. The particles are injected into the centre of this space. The dees are located between the poles of a large electromagnet which applies a static magnetic field B perpendicular to the electrode plane. The magnetic field causes the particles’ path to bend in a circle due to the Lorentz force perpendicular to their direction of motion.

If the particles’ speeds were constant, they would travel in a circular path within the dees under the influence of the magnetic field. However a radio frequency (RF) alternating voltage of several thousand volts is applied between the dees. The frequency is set so that the particles make one circuit during a single cycle of the voltage. To achieve this, the frequency must match the particle’s cyclotron resonance frequency f = qB/2pm, where B is the magnetic field strength, q is the electric charge of the particle, and m is the relativistic mass of the charged particle. Each time after the particles pass to the other dee electrode the polarity of the RF voltage reverses. Therefore, each time the particles cross the gap from one dee electrode to the other, the electric field is in the correct direction to accelerate them. The particles’ increasing speed due to these pushes causes them to move in a larger radius circle with each rotation, so the particles move in a spiral path outward from the centre to the rim of the dees. When they reach the rim a small voltage on a metal plate deflects the beam so it exits the dees through a small gap between them, and hits a target located at the exit point at the rim of the chamber, or leaves the cyclotron through an evacuated beam tube to hit a remote target. Various materials may be used for the target, and the nuclear reactions due to the collisions will create secondary particles which may be guided outside of the cyclotron and into instruments for analysis.

Mark Oliphant & the Synchrotron

https://en.wikipedia.org/wiki/Mark_Oliphant

Sir Marcus Laurence Elwin “Mark” Oliphant AC KBE FRS FAA FTSE (8 October 1901 – 14 July 2000) was an Australian physicist and humanitarian who played an important role in the first experimental demonstration of nuclear fusion and in the development of nuclear weapons.

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Mark Oliphant with Ernest Rutherford in 1932

“Particles should be constrained to move in a circle of constant radius thus enabling the use of an annular ring of magnetic field…which would be varied in such a way that the radius of curvature remains constant as the particle gains energy through successive accelerations by an alternating electric field applied between coaxial hollow electrodes.” Mark Oliphant, Oak Ridge, 1943

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1 GeV machine at Birmingham University

Synchrotrons

https://en.wikipedia.org/wiki/Synchrotron

A synchrotron is a particular type of cyclic particle accelerator, descended from the cyclotron, in which the accelerating particle beam travels around a fixed closed-loop path. The magnetic field which bends the particle beam into its closed path increases with time during the accelerating process, being synchronized to the increasing kinetic energy of the particles.

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There is a direct relationship between the speed of charged particles and their radius of curvature of the path. We will then get an acceleration of the particles from an electric field, according to:

F = qE where F is the force vector, q is the charge of the particle and E is the electric field intensity vector.

Now, the magnetic force is equal to the centripetal force of the circular movement (it is what makes it move in a circle!), so we get the cyclotron equation from equating the two: Centripetal force = mv2/r (m = mass of the particle, v = velocity of the particle and r = radius of curvature of the path of the particle) and Magnetic force = Bvq (B is the magnetic field and q is the charge on the particle) gives mv2/r = Bvq and simplifies to mv/r = Bq. Rearranging the equation gives r = mv/qB.

So for very large velocities we would need a very large circular path.

As r is fixed then increasing v requires an increasing magnetic field B because v/B must remain constant for constant r.

B increases synchronously with increasing v (and so does the energy as v is related to energy)

https://www.cyberphysics.co.uk/topics/atomic/Accelerators/Synchrotron/synchrotron.htm

Synchrotrons can accelerate to much higher energies. e.g., LHC is synchrotron

Limitation of synchrotrons (especially for electrons) is due to “synchrotron radiation”.

https://en.wikipedia.org/wiki/Synchrotron_radiation

Synchrotron radiation (also known as magnetobremsstrahlung radiation) is the electromagnetic radiation emitted when charged particles are accelerated radially, i.e., when they are subject to an acceleration perpendicular to their velocity. It is produced, for example, in synchrotrons using bending magnets, undulators and/or wigglers. If the particle is non-relativistic, then the emission is called cyclotron emission. If, on the other hand, the particles are relativistic, sometimes referred to as ultrarelativistic, the emission is called synchrotron emission. Synchrotron radiation may be achieved artificially in synchrotrons or storage rings, or naturally by fast electrons moving through magnetic fields. The radiation produced in this way has a characteristic polarization and the frequencies generated can range over the entire electromagnetic spectrum which is also called continuum radiation.

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Accelerator complexes start from a source of particles

Electron gun

https://en.wikipedia.org/wiki/Electron_gun

An electron gun (also called electron emitter) is an electrical component in some vacuum tubes that produces a narrow, collimated electron beam that has a precise kinetic energy.

Heated cathode releases electrons by thermionic emission. The electrons are extracted by an electric field.

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Photo electron gun

Laser kicks electrons out

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Ion Sources

A source of positive or negative ions can be produced using electric discharge in gas.

Atoms are stripped of their electron(s) and the ions are then extracted.

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RF Cavities are used in almost all modern accelerators…

In an RF cavity the particles “surf” on an electromagnetic wave that travels in the cavity.

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Focusing

Focusing is needed to confine the particles in their orbits.

First accelerators had “weak focusing” – focusing period is larger than the perimeter.

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10 GeV weak-focusing Synchrophasotron built in Dubna in 1957, the biggest and the most powerful of its time. Its magnets weigh 36,000 tons and it was registered in the Guinness Book of Records as the heaviest in the world.

“Strong focusing” alternates focusing-defocusing forces (provided by quadrupoles) to give overall focusing in both X & Y planes.

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Strong focusing allows use of more compact magnets, thus achieving many times larger energy with the same cost.

200-m diameter ring, weight of magnets 3,800 tons

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CERN’s Proton Synchrotron was the first operating strong-focusing accelerator.

Steering the Particle Beams

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http://lhc-machine-outreach.web.cern.ch

A magnetic field can be used to deflect the particles. The Lorentz force f = q(E + v x B). The LHC uses very strong magnets to keep its particles in a circular orbit.

https://en.wikipedia.org/wiki/Lorentz_force

In physics (particularly in electromagnetism) the Lorentz force is the combination of electric and magnetic force on a point charge due to electromagnetic fields.

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High-field Accelerator Magnets

Magnetic rigidity B used to describe motion of relativistic particle of charge e and momentum p in magnetic field of strength B and bending radius

B = p / e (in SI units)

B [T.m] ∼ 3.3356 p [GeV/c]

Two approaches for raising collision energy:

Increase magnetic field of bending magnets;

Increase ring circumference and hence radius

Final focus Quadrupoles

B Lq ≈ 1 / 𝛔*

Design quadrupoles for largest integrated field B Lq to obtain smallest beam size 𝛔* at IP

F0D0 Lattice

Quadrupole focuses in one plane and defocuses in the other.

To keep beam within envelope, quadrupoles arranged to focus alternately in each plane.

Called `F0D0‘ (Focusing-Defocusing) lattice.

At the Collider, the lattice is slightly more complex as space needs to be created for experiments/utilities.

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Magnet layout http://ilc-china.ihep.ac.cn

Beam Size

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http://lhc-machine-outreach.web.cern.ch/

The beam size varies along the accelerator

At ISIS the beam can be as wide as 100mm

https://www.isis.stfc.ac.uk/Pages/home.aspx

In Diamond it is only a few hundred micrometres wide

https://www.diamond.ac.uk/Home.html

In the LHC, near the interaction points, the beam is only 64 micrometres wide (the size of a human hair)

https://home.cern/science/accelerators/large-hadron-collider

Charge and Current

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The LHC tunnel http://cds.cern.ch

The charge of one electron (or one proton) is 1.6 x 10-19 Coulombs. The LHC can store up to 3 x 1014 protons. This corresponds to a total charge of 4.8 x 10-5C. As it takes 90 microseconds for the particles to travel around the ring this corresponds to a current of 0.54 amps. Current = charge/duration

Stored Beam Energy

1 electron-volt is 1.6 x 10-19 joules. 3.5 TeV = 560nJ. Hence the full beam of 3 x 1014 protons contains 1.7 x 108J (170MJ)

This energy is comparable to that of an Airbus 380 flying with a speed of 100km/h

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The energy will double will double when the beam reaches 7TeV. Energy of 170MJ over 90 microseconds corresponds to a power of 2 petawatts (Power = energy/time).

Beam Lifetime

The beam does not stay in the ring forever. Some particles will scatter each other and be ejected from the beam.

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Particle scattering inside a bunch

Some particles “hit” the walls of the beampipe. In some rings the beam lifetime can be only a few minutes. In rings where stability was important (such as the LHC or Diamond) the beam lifetime will be several days.

High-Energy LHC (HE-LHC)

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Future Circular Collider (FCC) Study

Infrastructure in the Geneva area

Forming an international collaboration to study:

pp-collider (FCC-hh) –> defining infrastructure requirements

~16 T Þ 100 TeV pp in 100 km

~20 T Þ 100 TeV pp in 80 km

potential intermediate step p-e (FCC-he) option 80-100 km

The aim is to produce much higher mass particles, investigate dark matter and provide a hyper microscope.

We don’t have the technology at the moment to produce 16T or 20T magnetic systems.

A type of tin may be used in the superconductor.

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HE-LHC in the present LHC tunnel with FCC-hh technology

Alternatives to the LHC

CEPC/SppC in China

CEPC: Circular Electron Positron Collider; 50 -70 km ring, up to 100 km? 90-250 GeV; Z and Higgs factory

SppC: Super proton proton Collider with CM energies > 100 TeV; In the same ring as CEPC

Site Candidates:

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Proposals

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ILC

https://en.wikipedia.org/wiki/International_Linear_Collider

The International Linear Collider (ILC) is a proposed linear particle accelerator. It would collide electrons with positrons.

0.5 TeV CM, upgradable to 1 TeV

SC RF industrialized

mature design (TDR in 2012)

Possibility of hosting is evaluated by Japanese government

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CLIC

https://en.wikipedia.org/wiki/Compact_Linear_Collider

The Compact Linear Collider (CLIC) is a concept for a future linear particle accelerator that aims to explore the next energy frontier. CLIC would collide electrons with positrons and is currently the only mature option for a multi-TeV linear collider.

Two-beam scheme, 1-3 TeV CM

Option for 380 GeV explored (klystrons)

CTF3 facility – key R&D done

Ready for demonstrator project

image

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The LHC is expected to run until 2040

24 (+1) Nobel Prizes in Physics that had direct contribution from accelerators

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A.Chao and E. Haussecker “Impact of Accelerator Science on Physics Research”, published in ICFA Newsletter, Dec 2010; & submitted to the Physics in Perspective Journal, Dec 2010.

Nobel Prize in Physics 2013

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The Nobel Prize in Physics 2013 was awarded jointly to François Englert and Peter W. Higgs “for the theoretical discovery of a mechanism that contributes to our understanding of the origin of mass of subatomic particles, and which recently was confirmed through the discovery of the predicted fundamental particle, by the ATLAS and CMS experiments at CERN’s Large Hadron Collider”.

https://en.wikipedia.org/wiki/Fran%C3%A7ois_Englert

https://en.wikipedia.org/wiki/Peter_Higgs

End of lecture comments:

Vacuum insulation keeps the helium temperature constant

It takes 30 minutes to get the magnetic field to the constant high value required so low ramp

RF systems are well developed

Power converter is outside the LHC tunnel

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