Superconducting magnets for the LHC · Superconducting magnets are first used to guide the particles scheduled for collision through the accelerator, and then to observe the events

CLEFS CEA - No. 56 - WINTER 2007-20084

Magnets and magnetic materials

The Large Hadron Collider (LHC), the world's largest highest-energy particle collider thatthe CERN plans to commission in 2008, gets a double boost from superconducting magnettechnology. Superconducting magnets are first used to guide the particles scheduled forcollision through the accelerator, and then to observe the events triggered by the collisioninside giant detectors in a known magnetic field. Despite the installation's massivedimensions, all this is done with minimal expenditure of energy.

Superconducting magnetsfor the LHC

The tunnel housing theLHC (Large Hadron

Collider), the world'slargest and highest-

energy proton-protoncollider installed at the

CERN site. The LHC has acircumference of 27 km

and is fully equipped withsuperconducting

magnets designed toguide and focus protonbeams along a circular

trajectory. The CEA isinvolved in building the

LHC by deploying itsexpertise in the design oftwo of the four detectors

and the construction ofcertain key machines

such as thesuperconducting dipoles

and quadrupoles.

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Physicists are continuously pushing back theboundaries of research into the structure of mat-

ter using increasingly powerful resolution tech-niques. The primary focus of high-energy nuclearphysics is to identify the elementary constituentsof matter and understand how they interact. Theparticle accelerators used in this research act likemicroscopes, probing matter with a spatial reso-lution that improves as the energy of the accelera-ted particles increases(1). Indeed, since the 1950s,physicists have been steadily progressing in the cons-

truction of ever more powerful accelerators usedin the field of nuclear physics (Figure 1).Technological advances, particularly in the field ofsuperconducting electromagnets (Focus B,Superconductivity and superconductors, p. 16),have enabled physicists to design and build themagnetic systems equipping the Large HadronCollider (LHC)(2) currently being installed at theCERN "European Organization for NuclearResearch" site near Geneva. A magnetic field isdeployed to bend particle beams, either to steerthem through the accelerator on orbits with a highlyspecific geometry, or to analyse the products ofhead-on proton-proton collisions between the detec-tors.

The main components of a circularcollider

Particles travel in a circular vacuum chamber sur-rounded by a guiding sequence of electromagneticsystems, and are accelerated via electric fields in

(1) A resolution of 10-19 m (at quark scale) requires 1 TeV(1012 electronvolts).

(2) Hadrons: subatomic particles composed of quarks(or antiquarks) that are subject to strong nuclear interactions.Protons and neutrons are both hadrons.

(3) Livingston plot: diagram developed in the 1960s by the American physicist Stanley Livingston, who demonstratedthe exponential increase in beam energy (as an eV multipleassuming a collision with a proton or an electron at rest)during centre-of-mass acceleration in particle accelerators,together with the increase in cost per eV of beam energy as a function of time (years).

CLEFS CEA - No. 56 - WINTER 2007-2008 5

high-power radio-frequency cavities. To make themost effective use of a limited number of RF cavi-ties, the accelerator designers force the particle beamthrough these cavities many times by creating a clo-sed-loop beam trajectory. The circular path of theproton beam axis is obtained by passing it througha series of ring sections with a uniform magneticfield created by dipole magnets; higher particleenergies require stronger fields to bend their path(see Box). Quadrupole focusing magnets are intro-duced to focus the beam, prevent it scattering andconstrain its width within reasonable bounds eitherside of the beam axis. In this type of component,the magnetic field increases linearly with increa-sing distance from its axis, while the focal length isinversely proportional to the transverse inductiongradient. Storage rings are principally designed toproduce head-on collisions between two counter-rotating beams of protons. These collisions takeplace at carefully chosen points on the machine'scircular frame, these points being surrounded bydetectors designed to track and identify the eventstriggered when two beams collide. Particle move-ment is quantified by measuring the bending oftheir trajectories within a known magnetic field,while their energy is measured by calorimeters.The CEA is involved in building the LHC, the world'slargest and highest-energy proton-proton collider,at the CERN, by deploying its expertise in the designof two of the four detectors and in the construc-tion of certain key machines such as the quadru-poles. The collider will be used to accelerate twocounter-rotating beams of protons around a 27-kmcircumference circular tunnel embedded under-ground at a depth of between 50 m and 170 m.These beams will travel at a speed close to the speedof light, producing violent head-on proton-protoncollisions with energies of 14 TeV at the points wherethe beams intersect. This immense scientific chal-lenge required the technological and industrial prowess to build 1,200 superconducting dipolesproducing a magnetic field of 8.4 T, 400 supercon-ducting quadrupoles providing a magnetic fieldgradient of 223 T/m, a superfluid helium cryoge-nic system which cools the magnets down to 1.9 K,and two gigantic detector systems, named Atlas (AToroidal LHC Apparatus) and CMS (Compact MuonSolenoid).

The advantages of using superconductingelectromagnets

A key property of superconductive bodies is thattheir electrical resistivity drops to zero below a cer-tain critical temperature, meaning that there is noenergy loss via a Joule effect. Some of these materials, such as niobium-titanium, can carry currentdensities of around 3,000 A/mm2 in induction fieldsof 5 T to 4.2 K. By comparison, the materials usedto make the coils for conventional electromagnets,typically copper or aluminium, can only producecurrent densities of between 5 and 50 A/mm2 depen-ding on the cooling method. Their very high currentdensities mean superconducting electromagnets areable to produce ultra-high magnetic fields via a sys-tem of compact coil assemblies, which significantly

Figure 1.Livingston plot(3) giving a timeline of energy levels increasing from 100 MeV in 1950 to several tens of GeV in 1975 and then to several hundred GeV in 1990. The LHC, which is scheduled to begin operations in 2008, will be the world's highest-energy particleaccelerator, with a proton-proton head-on collision energy of 14 TeV.

How does an electromagnetic field act on a charged particle?

Electrically charged particles are subject to the action of an electric fieldE or a magnetic field B. The force, called the Lorentz force, experiencedby a charged particle with charge q moving at velocity v in an electro magneticfield is expressed as:

E and B act very differently on the particle's movement. The particle acce-lerates as it moves through an electric field E, thus gaining kinetic energy:the electric force (qE) is an accelerating force. This is the fundamental prin-ciple of accelerator cavities. Conversely, when moving through a mag neticinduction field B, the magnetic force or Laplace force (qv ∧ B) is perpendi-cular to v and B and does not cause any change in kinetic energy. This is abending force used to guide particle beams. In a uniform magnetic induc-tion field B, a particle with mass m moving at velocity v follows a circulartrajectory with an average radius R, such that:

where mv represents the momentum of the particle.

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ference of 120 km in order to achieve the same col-lision energy, and would use 40 times more elec-tricity.Ordinary electromagnets comprise pure iron polespositioned around conductive coils. The magneticinductions created in the air gap between these devi-ces rarely exceed 2 T, as the saturation magnetisa-tion of iron is reached. Conversely, iron has only anegligible effect in superconducting magnets andis mainly used to provide magnetic shielding withregard to the outside world. The usable field is pro-duced directly via the superconducting conductorcoils while current densities are distributed through-out the coils in a specific pattern in order to obtainthe exact morphology required for the dipole andquadrupole magnetic fields (Figure 2).It is essential to set the nominal operating point ofa superconducting conductor below its critical valuesfor temperature, magnetic induction and currentdensity (Figure 3). Superconducting materials pro-viding ultra-high critical fields (up to 20 T) andhigh current densities are referred to as type IIsuperconductors (niobium-titanium, niobium-tin) and exhibit critical temperatures of below 20 K(Figure 4). The coils have to be cooled and main-tained at their operating temperature using a cryo-genic fluid such as liquid helium, which has a boi-ling point of 4.2 K at atmospheric pressure. At thisvery low temperature, the coils react to the slight -est thermal disturbance due to the material's verylow heat capacities, which are about 2,000 timesless than at ambient temperature; a movement ofjust 10 micrometers (1 μm = 10-6 m) in the conduc-tor can generate an energy loss sufficient to heatthe conductor by 3 K, which would lift the super-conductor's temperature above its critical point.When employing superconducting electromagnets,it is vital to be able to control and prevent quench,which occurs when all or part of a superconduc-ting coil suddenly and accidentally reverts from asuperconducting state to a normal state.Superconducting magnets are therefore fitted withsafety systems designed to act on quench and pre-vent coils being damaged by the generation of heat.

reduces the overall dimensions and cost involvedin constructing a ring collider. Operating costs arealso minimized by reducing the consumption ofelectrical power, which is only needed to run themagnet cooling facilities. If the LHC used conven-tional ‘warm’ magnets instead of superconductingmagnets, the ring would have to have a circum -

Figure 2.Distribution of the current density J(θ) and associated magnetic field lines in a superconducting dipole and quadrupole.

Figure 3.Niobium-titanium phase diagram. The hatched area gives the curve Jc(B) at 4 K, i.e. the maximum current density in the superconductor cooled to the temperature ofliquid helium and subjected to a magnetic induction field B.

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Design issues that need to be addressedearly on

Cryomagnet design must ensure the system coversdesign imperatives regarding issues such as super-conductor use, quench protection, mechanical designand the cooling system. Once designers have selec-ted the appropriate operating temperature for thetarget magnetic field and have identified which pro-perties will be exhibited by the superconductingmaterial at this temperature, they can then deter-mine an average current density that takes accountof the amount of stabilising material, the thick-nesses of the electric insulators and the empty spaces.This average current density is then used to pre-size the magnetic system allowing designers to definethe characteristics of the superconducting conduc-tor and, where necessary, adjust coil dimensions toobtain the target magnetic field.Quench is an adverse event, which cannot be igno-red and must be factored into the design of themagnet. As the superconductor becomes resistiveduring quench, the current is diverted into the sta-bilising material which then dissipates the energyin the form of heat via a Joule effect. The heat gene-rated allows the quench to spread to neighbouringsections and an electrical voltage appears at the ter-minals of the newly-resistive area. Superconductingmagnets are quench-protected by setting up a rapidquench detection system, and by dissipating partof the energy stored within the magnet to outsideresistors. Heaters may be used to deliberately spreadthe quench to all magnets in order to limit the tem-perature rise at the quench source location. Thiseffectively minimizes the amount of energy depo-sited per unit of volume and also curbs the electricvoltage at the magnet's terminals, which coulddamage the insulation.Mechanics is another key issue in cryomagnet design.The Lorentz forces acting on any conductor pla-ced in a magnetic field generate enormous stresseson superconducting magnet coils. As the materialsmaking up the coils, in particular insulating mater-ials, have fairly low mechanical strength, the mecha-

nical stresses have to be kept within acceptable valuesthroughout the coil's lifetime. Designers also haveto limit any potential movement of the conductorsin the magnetic field as this would generate the localheating likely to result in quench. Furthermore, themagnet's structure not only has to withstand theoverall stresses but also limit distortions that couldmodify the magnetic field lines and, therefore, thequality of the field.One feature of superconductors is that they ope-rate at very low temperatures, an aspect that mustbe carefully calculated in order to reduce the mecha-nical stresses generated by differences in thermalcontraction(4) between the various materials. Inaddition, any heat likely to raise magnet tempera-ture must be evacuated: this heat is usually generatedwhen the cryostat containing the magnet transmitsheat through its support posts, instruments andcurrent feeders. This rise in temperature may alsobe generated by the energy deposited within themagnet itself, produced by non-static operation orby beam radiation.Although they bring a number of different specia-list areas into play, all these aspects must be dealtwith jointly, taking account of the manufacturingtechnology used to achieve a design that meets allthe requirements. Successful design also dependson running comprehensive tests to validate physi-cal quantities or technological preferences.

Four hundred quadrupole magnets for the LHC

A preliminary study carried out between 1989 and1993 at the Saclay CEA centre (Essonne) as part ofa joint CEA-CERN project led to the constructionand testing of two quadrupole cold masses with amagnetic field gradient of 250 T/m. These twomagnets were then inserted into a chain of magnetsbuilt to validate the design of the LHC system. Aspart of France's contribution to the LHC project,the CEA was commissioned to design, build and testthree new cold mass prototypes with a magneticfield gradient of just 223 T/m, which have successfullyvalidated the design choices. These quadrupolemagnets are 3.2 m long and operate at 1.8 K, a tem-perature at which helium is superfluid. It was the

Figure 4.Cross-sections through superconducting conductors. Current technology deployed in superconducting electromagnets usesmonolithic conductors or cabled conductors that employ composite strands comprised of thousands of extremely finesuperconducting filaments (around ten microns) embedded in a copper matrix.

(4) Thermal contraction: decrease in the dimensions of amaterial as its temperature drops.

CEA

superconducting cable for the LHCquadrupoles (15 mm x 1.6 mm)

conductor for the CMS superconductingsolenoid (64 mm x 22 mm)

NbTi+Cu composite strand (ø 1 mm)

cable comprising 32 NbTi+Cu compositestrands

pure aluminium

aluminium alloy



CEA's expertise in designing and building super-conducting magnets, experience acquired when wor-king on the Tore Supra project, that paved the wayfor using superfluid helium in the LHC system.Two quadrupole magnets, built as separate mecha-nical units, are carefully placed in a magnetic yokemade out of carbon steel. Each quadrupole is ableto withstand huge electromagnetic burst forces of110 tons per metre of magnet. These forces areabsorbed by non-magnetic stainless steel collars.Along with other beam-correction magnets, thedouble-quadrupole magnet is mounted in the cold

mass, which measures some 6 m in length andcontains superfluid helium. The coils have to bebuilt to a precision of twenty microns and with ayield strength that keeps deformation down to0.1 mm in order to ensure the magnetic field hasthe required quality.The CEA took on the technology transfer and pro-duction follow-up during series fabrication at theGerman manufacturer Accel Instruments, whichbuilt 400 cold mass units. Production was success-fully completed in late 2006, and out of all the magnetsproduced, only one cold mass was actually rejected.Once they had been assembled in their cryostat hou-sings at the CERN, all the components were loweredinto the LHC tunnel and connected up to their neigh-bouring magnets. The LHC accelerator is scheduledto officially begin operation before summer 2008.

The magnets equipping two large LHCdetectors

The Atlas and CMS detectors use single magnet sys-tems which both operate at a temperature close tothat of liquid helium and have their own separatehelium liquefaction system. While these magnetsgenerate weaker magnetic fields than the quadru-poles, they magnetise far greater volumes. Rapidextraction of the stored energy is, however, imposs-ible, meaning that the conductor has to be built towithstand a high current for a period of severalminutes without suffering damage (compared to afew tens of milliseconds for a quadrupole magnet).Although physicists were confronted with the samedesign issues during construction of the quadru-poles and the detector magnets, they had to find andapply a different set of solutions in each case. TheCEA has been working on the design studies for themain toroidal magnet for the Atlas detector and the

Central toroid of the Atlas detector in its cavern at the CERN facility. The eight superconducting coils are laid out in a star-shaped configuration, resemble ellipses 25 m long and 5 m wide, and are powered by a 20,500 A current.

The LHC's double-aperture quadrupoles share the same magnetic and cryogenicstructure. Key magnet features are a length of 3.2 m, an aperture of 56 mm and a magnetic field gradient of 223 T/m.

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solenoid for the CMS detector since the late 1980s.They are scheduled to begin operation during 2008.

The toroidal magnet system equipping the Atlas detectorThe central toroid of the Atlas system comprises8 superconducting coils 25 m long and 5 m widearranged like a torus around the collision point ofthe two particle beams. The system has a storedenergy of 1,100 MJ for a field strength of 0.4 T atthe centre of the toroid and 3.9 T at the supercon-ductor. The Saclay Centre first developed a proto-type coil at 1/3 of the full length that was tested atthe CERN in 2001, successfully validating the designchoices. The final coils were assembled at the CERNusing components provided by European indus-trial partners. The CEA monitored industrial manu-facture of most of the components, in addition totechnical monitoring of their assembly and indivi-dual testing at CERN surface test facilities, and wenton to monitor their assembly in the Atlas experi-ment cavern. In November 2006, the toroid assem-bly successfully completed the planned test series,effectively carrying a 21,000 A current (i.e. 500 Amore than the nominal current) with zero quench.Assembly of the other magnets and detectors is cur-rently in process, with the Atlas experiment sched -uled to be up and running sometime during thefirst six months of 2008.

The superconducting solenoid of the CMSdetectorAt 7 m in diameter, 12.5 m in length and with amagnetic field strength of 4 T, the superconductingsolenoid for the CMS experiment holds the recordfor total stored magnetic energy with an impress -

ive 2.6 GJ as well as the record for the amount ofmagnetic energy stored per coil mass unit. The sole-noid comprises 5 modules formed of 4 conductorlayers stabilised by pure aluminium mechanicallyreinforced by an aluminium alloy (a new conceptpioneered by the CEA). The conductor is woundinside an external cylinder which provides supportand cools the system using helium circulated natu-rally via a thermosiphon heat exchanger. The5 modules manufactured by European industrialpartners were delivered and assembled in verticalposition at the CERN's surface testing facility wherethey were successfully tested during summer 2006.The magnet was then dismantled and lowered intothe CMS experiment cavern where it is currentlybeing reassembled. It is scheduled to be commis-sioned during the first six months of 2008. The CEAplayed a central role in the design and industrialmanufacture of the superconducting magnet andthe subsequent assembly and cold testing opera-tions carried out at the CERN facility.

Planned upgrades

Even though the LHC has yet to go into operation,physicists have already started discussing optionsfor future improvements, in particular on how toincrease the machine's luminosity(5) tenfold. Projectsare underway to manufacture new large-aperture(130 mm) niobium-titanium quadrupoles, produceniobium-tin dipoles supplying a field strength of13 T within an aperture of 100 mm, and even insertsusing high-critical-temperature superconductors(Bi2212 or YBCO). All these projects will require asignificant R&D input which the CEA will providethrough its solid expertise in the field.

> Chantal Meuris and Jean-Michel Rifflet Institute of Research

into the Fundamental Laws of the Universe (IRFU)Physical Sciences Division

CEA Saclay Centre

(5) Luminosity: along with the beam energy range, one of the two fundamental parameters that sets the boundariesof particle collider design. It is given by the formula L = f 2n2k2/A(in cm-2·s-1), where k is the number of particles making up abunch in each beam, n the number of bunches, A is the beamcross-section, and f is the beam-crossing frequency.

Assembly of thesuperconducting solenoid forthe CMS detector at the CERNfacility. The magnetic yoke (in red), housing the vacuumchamber, is slid into placearound the solenoid which is encircled by its thermalscreens. In yellow, the platform used to assemble the coil and tilt it from the vertical to the horizontal position.C

ERN

Some historical backgroundTrains "flying" above the track usingmagnetic levitation, electricity storagefinally resolved using giant magneticcoils, electrotechnical instruments andelectric power transmission cables withno joule losses, magnetic fields that canbe used to explore the human body anddeliver even higher resolution images.People have been marvelling at thepotential uses of superconductivity since1911 when Dutch physicist HeikeKammerlingh-Onnes first discovered theextraordinary property exhibited bysuperconducting materials; their elec-trical resistance drops to zero below acertain critical temperature (which varieswith their isotopic mass). This discoverywon him the Nobel Prize in Physicsin 1913.Apart from zero electrical resistanceand optimal electrical conductivity, thesuperconductors discovered by Kam -merlingh-Onnes (later named type Isuperconductors) possess anotherremarkable property manifested by theMeissner effect, discovered in 1933 byGerman physicists Walter Meissner and

Robert Ochsenfeld. If we ignore theLondon penetration depth(1), supercon-ductors can be said to exhibit perfect dia-magnetism, i.e. the superconductingmaterial fully expulses its internalmagnetic field up to a certain criticalfield value whereas, in theory, themagnetic field of a material with perfectconduction of electricity should equalthat of the externally applied field.Herein lies the second obstacle thatcontinues to hamper superconductorapplications: superconductivity is lost atabove a critical magnetic field strength.For many years physicists thought therewas only one type of superconductivityand that the magnetic anomalies ob -served in some samples were due solelyto the presence of impurities. Inthe 1950s, however, Russian physicistsVitaly L. Ginzburg and Lev DavidovitchLandau came up with the theory that

there were actually two types of super-conductors.In 1957, the Russian-American physi-cist Alexei A. Abrikosov finally confirmedtype II superconductivity. Type II super-conductors exhibit a completely differenttype of magnetisation characterised bya mixed state that allows them to retaintheir superconducting state even inintense magnetic fields. This means theyare not subject to the Meissner effect.In 2003, Abrikosov, Ginzburg and theAnglo-American physicist Anthony J.Leggett were awarded the Nobel Prizein Physics for their research into super-conductors.It was also in 1957 that American phy-sicists John Bardeen, Leon N. Cooperand John R. Schrieffer published theirtheory of superconductivity, which wonthem the 1972 Nobel Prize in Physics.This BCS theory (named after the firstletter of their surnames) postulates thatelectrons move through a conductor asCooper pairs (two electrons with oppo-site spin). These pairs act like spin-zerobosons and condense into a single quan-tum state via a phonon interaction, which

Superconductivity and superconductorsBFOCUS

One of the main fields of application of superconductivity is medical imaging. This is the 3-tesla magnetic resonance imager at the SHFJ hospital in Orsay (Essonne).

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(1) In 1935, Fritz and Heinz London proposedanother explanation for the Meissner effect by claiming that the magnetic field decreases with depth from the surface of a superconductingmaterial over a characteristic length λL known as the penetration depth.

is also a quantized mode of vibration. Itis this electron-phonon interaction thatunderpins resistivity and superconducti-vity. Ions move in response to the ultra-fast passage of an electron (106 m/s), thereby creating an area of positive elec-trical charge which is held after the passage of the electron. This attracts an -other electron that pairs up with the firstelectron thereby resisting the Coulombrepulsion but not thermal agitation, whichexplains why temperature has such anadverse effect on superconductivity.The BCS theory, which applies to 'conventional' superconductors, did nothowever provide for the appearance ofsuperconductivity at fairly high tempera-tures, i.e. higher than the temperature ofliquid nitrogen (77 K, i.e. – 196 °C), and afortiori at ambient temperature. This 77 Kthreshold was reached by using compoundssuch as Y-Ba-Cu-O (current records standat around 165 K, at high pressure, and138 K, i.e. – 135 °C, at standard pressure).German physicist Johannes GeorgBednorz and Swiss physicist KarlAlexander Müller were awarded the NobelPrize in Physics in 1987 for their work onunconventional superconductors. Theydiscovered a lanthanum-based copperoxide perovskite material that exhibitedsuperconducting properties at a tempe-rature of 35 K (- 238 °C). By replacing lan-thanum with yttrium, particularly inYBa2Cu3O7, they were able to significantlyraise the critical temperature thus developing the cuprate family of super-conductors. Although these are highlyeffective superconductors, the fact thatthey are ceramics makes them difficult touse in electrotechnical applications. Allhigh-critical-temperature superconduc-tors are type II superconductors.

The strange magnetic propertiesof type II superconductorsIn the presence of a magnetic field, typeII superconductors exhibit perfect dia-magnetism up to certain field Hc1 just liketype I superconductors. Beyond Hc1, how -ever, type II superconductors enter a mixedstate that allows partial field penetrationup to Hc2 (Figure 1), thereby permitting amaterial to be superconducting under ahigh magnetic field.This mixed state resembles an array ofnormal-state cores that start to fill thesuperconducting material at Hc1 and over.Each region contains a flux quantum(2.07·10-15 weber) and is surrounded by avortex of superconducting currents(Figure 2). When the magnetic field increa-ses, the network densifies until it com-pletely fills the superconducting materialat Hc2.The distinction between the two types ofsuperconductivity is coupled to theconcepts of coherence length � and pene-

tration depth �L, which characterise theinterface between a normal region and asuperconducting region. � represents thespatial variation of the superconductingstate (i.e. the density of the supercon-ducting electrons) and �L the London pene-tration depth of the magnetic field. It isthe ratio of these two characteristiclengths, known as the Ginzburg-Landauparameter and written as � (� = �L/�),that determines which type of supercon-ductivity is involved. If � < �2/2, the super-conductor is type I, and if � > �2/2, thesuperconductor is type II.At the interface, the penetration of themagnetic field, as defined by �L, cor-responds to an increase in free energy inthe superconducting material, while theformation of the superconducting state,characterised by the coherence length, isrelated to a decline in free energy. Theinterface's energy balance varies with theratio �. In type II superconductors, the

Magnetic pattern on the surface of a superconductor in mixed state.

Figure 2.Diagram of a vortex illustrating penetration depth and coherence length.

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Potential avenues for applicationType I superconductivity does not pre-sent any great potential for new areasof application. Unfortunately, the criti-cal temperature that limits supercon-ductivity applications is very low in thetwo superconducting materials thatcurrently offer real-world applicationsi.e. niobium-titanium, NbTi (9.2 K) - thefirst superconducting cables in niobium-titanium alloy were developed in theearly 1960s - and niobium-tin, Nb3Sn(18 K). These materials have to becooled to the temperature of liquidhelium (4.2 K)(2) in order to activate

their superconducting properties. This temperature was the first importantmilestone towards achieving super-conductivity at ambient temperature,which is the ultimate goal.Type II superconductors can withstandvery strong magnetic fields, and arealso able to carry extraordinarily highcurrent densities, up to another criti-cal value that varies with the magneticfield (Figure 3). This fact heralded thedevelopment of the first superconduc-ting magnets. The current densities thatcan be generated under these condi-tions are huge in comparison with whatcan be achieved with domestic or indus-trial electrotechnical applications(around 10 A/mm2).Since the 1970s, the CEA has been focu-sing its research on the production oflarge-scale intense permanent mag -netic fields (magnetic confinement offusion plasmas, particle physics, medi-cal imaging). In fact, these are the pre-

dominant applications of type II super-conductors, mainly NbTi(3), wheresuperconductivity significantly cutsdown on electric power consumptiondespite the cryogenic efficiency of thefacilities - in fact, one watt dissipatedat 4.2 K requires a minimum consump-tion of 300 W at ambient temperaturein the largest industrial power plants.While researchers the world over stilldream of developing superconductingmaterials that function at room tem-perature, it would seem that appliedsuperconductivity will still have to relyon the use of very low temperaturecooling for the foreseeable future.

BFOCUS

(2) The history of superconductivity actuallygoes as far back as William Ramsay who, in1895, was the first person to isolate helium.Indeed, where would the science of superconductivity be today if it wasn't for helium which is the key component of the ultra-low cooling process? Note also that Kammerlingh-Onnes finally succeeded inproducing liquid helium in 1908 followingunsuccessful attempts by James Dewar in the late 19th century, thus paving the way to the discovery of superconductivity.

(3) Produced in quantities of around 1,500 to 2,000 tons per year.

The discovery of high-critical-temperaturesuperconductivity made it possible to see how superconductivity manifests inthe open air in the form of a magnet floatingabove a pellet of liquid-nitrogen cooledYBaCuO, which is now a famous example of the effect.

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Table.Characteristics of some type I and type II superconductors. μ0·Hc1 and μ0·Hc2 represent magnetic inductions, where μ0 is the magnetic permeabilityof a vacuum (and of the material in this particular case).

material � (μm) �L (μm) � Tc (K) μ0 · Hc1 (teslas) μ0 · Hc2 (teslas)0 K 0 K 0 K 0 K

type I Al 1.36 0.05 0.04 1.18 0.010 5Pb 0.083 0.037 0.5 7.18 0.080 3

type II NbTi 0.005 0.3 60 9.25 0.01 14Nb3Sn 0.003 6 0.065 18 18 0.017 25.5

YBaCuO plane 0.003 plane 0.8 � 300 93 140axis c 0.000 6 axis c 0.2

page 17 cont’d

Figure 3. Characteristic critical current densities in relation to a 4.2-K magnetic field for the two superconducting materials most widely used, particularly in the manufacture of superconducting magnets.

criti

cal c

urre

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ensi

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/mm

2 )

magnetic field (teslas)

10,000

1,000

100

100 5 10 15 20

niobium-tin

niobium-titanium

The origins of magnetism lie in theproperties of electrons as explained

by the laws of quantum physics. Part ofan electron's magnetic properties (spinmagnetism) results from its quantum-mechanical spin state, while another partresults from the orbital motion of elec-trons around an atom's nucleus (orbitalmagnetism) and from the magnetism ofthe nucleus itself (nuclear magnetism).This is put to use, in particular, for nuclearmagnetic resonance imaging in the medi-cal field. Magnetism is therefore produ-ced by electric charges in motion. Theforce acting on these charges, called theLorentz force, demonstrates the pre-sence of a magnetic field.Electrons have an intrinsic magneticdipole moment (the magnetic quantumstate being the Bohr magneton), whichcan be pictured as an electron's rotatio-nal motion of spin around itself in onedirection or another, oriented eitherupwards or downwards. The spin quan-tum number (one of the four numbers that'quantifies' the properties of an electron)equals 1/2 (+ 1/2 or - 1/2). A pair of elec-trons can only occupy the same orbital ifthey have opposite magnetic dipolemoments.Each atom acts like a tiny magnet car-rying an intrinsic magnetic dipolemoment. A nucleus (the neutron andproton individually have a half-integerspin) will have a half-integer spin if it hasan odd atomic mass number; zero spinif the atomic mass number and chargeare even, and an integer spin if the ato-mic mass number is even and the chargeodd.On a larger scale, several magneticmoments can together form magnetic

domains in which all these moments arealigned in the same direction. These spa-tial regions are separated by domainwalls. When grouped together, thesedomains can themselves form a macro-scopic-scale magnet (Figure E1). The type of magnetism that comes intoplay is determined by how these ele-mentary constituents are ordered, and isgenerally associated with three maincategories of material: ferromagnetic,paramagnetic and diamagnetic. Any material that is not diamagnetic isby definition paramagnetic provided thatits magnetic susceptibility is positive.However, ferromagnetic materials haveparticularly high magnetic susceptibilityand therefore form a separate category.1. Ferromagnetic materials are formedof tiny domains inside which atoms exhi-biting parallel magnetisation tend to alignthemselves in the direction of an exter-nal magnetic field like elementary dipo-les. In fact, the magnetic moments ofeach atom can align themselves sponta-neously within these domains, even inthe absence of an external magnetic field.Applying an external field triggers domainwall movement that tends to strengthenthe applied field. If this field exceeds acertain value, the domain most closelyoriented with the direction of the appliedfield will tend to grow at the expense ofthe other domains, eventually occupyingthe material's whole volume. If the fielddiminishes, the domain walls will move,but not symmetrically as the walls can-not fully reverse back to their originalpositions. This results in remanentmagnetisation, which is an important fea-ture of naturally occurring magnetite, orof magnets themselves.

The whole process forms a hysteresisloop, i.e. when the induced field is plot-ted against the applied field it traces outa hysteresis curve or loop where the sur-face area represents the amount ofenergy lost during the irreversible partof the process (Figure E2). In order tocancel out the induced field, a coercivefield has to be applied: the materials usedto make artificial permanent magnetshave a high coercivity. Ferromagnetic materials generally havea zero total magnetic moment as thedomains are all oriented in different direc-tions. This ferromagnetism disappearsabove a certain temperature, which isknown as the Curie Temperature or Curiepoint.The magnetic properties of a given mate-rial stem from the way the electrons inthe metallic cores of a material or of atransition metal complex collectively cou-ple their spins as this results in all theirspin moments being aligned in the samedirection. Materials whose atoms are widely dis-tributed throughout their crystal struc-ture tend to better align these elemen-tary magnets via a coupling effect. Thiscategory of materials, which is charac-terised by a very high positive magnetic

The different types of magnetismAFOCUS

Figure E2. The induction B of a magnetic material by a coilis not proportional to its magnetic excitation(field H). While the initial magnetisation formsan OsS-type curve, shown in blue in the figure,it reaches saturation at point s. Only a partialinduction is retained if the field approacheszero; this remanent induction can only becancelled out by reversing the magnetic field to a "coercive" field value. This hysteresis loopillustrates the losses due to "friction" betweenthe magnetic domains shown on the areabounded by the magnetisation anddemagnetisation curves.

Figure E1.Intrinsic magnetic dipole moments have parallel alignment in ferromagnetic materials (a), anti-parallel alignment but zero magnetisation in antiferromagnetic materials (b), and anti-parallelalignment with unequal moments in ferrimagnetic materials (c).

a b c

B

O

S

H

S’

s+BR

-BR

-HS -HC

+HC +HS

susceptibility, includes iron, cobalt andnickel and their alloys, steels in particu-lar, and some of their compounds, and, toa lesser extent, some rare earth metalsand alloys with large crystal lattices, andcertain combinations of elements that donot themselves belong to this category. Inferrimagnetic materials, the magneticdomains group into an anti-parallel align-ment but retain a non-zero magneticmoment even in the absence of an exter-nal field. Examples include magnetite,ilmenite and iron oxides. Ferrimagnetismis a feature of materials containing twotypes of atoms that behave as tiny magnetswith magnetic moments of unequal magni-tude and anti-parallel alignment. Anti-ferromagnetism occurs when the sum ofa material's parallel and anti-parallelmoments is zero (e.g. chromium or hae-matite). In fact, when atoms are in a closeconfiguration, the most stable magneticarrangement is an anti-parallel alignmentas each magnet balances out its neigh-bour so to speak (Figure E1). 2. Paramagnetic materials behave in asimilar way to ferromagnetic materials,although to a far lesser degree (they havea positive but very weak magnetic sus-ceptibility of around 10- 3). Each atom in aparamagnetic material has a non-zeromagnetic moment. In the presence of anexternal magnetic field, the magneticmoments align up, thus amplifying thisfield. However, this effect decreases astemperature rises since the thermal agi-tation disrupts the alignment of the ele-mentary dipoles. Paramagnetic materialslose their magnetisation as soon as theyare released from the magnetic field. Mostmetals, including alloys comprising ferro-magnetic elements are paramagnetic, as

are certain minerals such as pegmatite. 3. Diamagnetic materials exhibit a nega-tive and an extremely weak magnetic sus-ceptibility of around 10- 5. The magnetisa-tion induced by a magnetic field acts in theopposite direction to this field and tendsto head away from field lines towards areasof lower field strengths. A perfect diama-gnetic material would offer maximumresistance to an external magnetic fieldand exhibit zero permeability. Metals suchas silver, gold, copper, mercury or lead,plus quartz, graphite, the noble gases andthe majority of organic compounds are alldiamagnetic materials. In fact, all materials exhibit diamagneticproperties to a greater or lesser extent,resulting from changes in the orbitalmotion of electrons around atoms inresponse to an external magnetic field, aneffect that disappears once the externalfield is removed. As Michael Faraday sho-wed all that time ago, all substances canbe "magnetised" to a greater or lesserdegree provided that they are placed withina sufficiently intense magnetic field.

ElectromagnetismIt was the Danish physicist Hans ChristianØrsted, professor at the University ofCopenhagen, who, in 1820, was first to dis-cover the relationship between the hithertoseparate fields of electricity and magne-tism. Ørsted showed that a compass needlewas deflected when an electric currentpassed through a wire, before Faraday hadformulated the physical law that carrieshis name: the magnetic field produced isproportional to the intensity of the current.Magnetostatics is the study of staticmagnetic fields, i.e. fields which do notvary with time.

Magnetic and electric fields together formthe two components of electromagnetism.Electromagnetic waves can move freelythrough space, and also through mostmaterials at pretty much every frequencyband (radio waves, microwaves, infrared,visible light, ultraviolet light, X-rays andgamma rays). Electromagnetic fields the-refore combine electric and magnetic forcefields that may be natural (the Earth'smagnetic field) or man-made (low fre-quencies such as electric power trans-mission lines and cables, or higher fre-quencies such as radio waves (includingcell phones) or television.Mathematically speaking, the basic lawsof electromagnetism can be summarisedin the four Maxwell equations (or Maxwell-Lorentz equations) which can be used toprovide a coherent description of all elec-tromagnetic phenomena from electrosta-tics and magnetostatics to electromagne-tic wave propagation. James Clerk Maxwellset out these laws in 1873, thirty-two yearsbefore Albert Einstein incorporated thetheory of electromagnetism in his specialtheory of relativity, which explained theincompatibilities with the laws of classi-cal physics.

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A Transrapid train using magnetic levitation arriving at the Long Yang bus station in Shanghai (China).This German-built high-speed, monorail train was commissioned in 2004 to service the rail link

to Pudong international airport.

Close-up of the magnets used to guide and power the train.

Superconducting magnets for the LHC · Superconducting magnets are first used to guide the particles scheduled for collision through the accelerator, and then to observe the events

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