Introduction to particle accelerators Walter Scandale CERN - AT department Roma, marzo 2006

1. Introduction to particle accelerators Walter Scandale CERN - AT department Roma, marzo 2006

2. Lecture III - superconducting devices topics • Limitations of normal conducting dipoles • Superconducting material properties • Critical temperature • Type I and type II superconductors • Theoretical approaches • Meissner effect • Cooper pairs and BCS theory • MgB2 and HTS • SC dipoles • Current density • Magnetization • Flux jumping • Quenches • Wires and cables • SC-RF

3. Dipoles • Iron yoke reduces magnetic reluctance(reduced power and ampere-turns) -> small gap height • Field quality -> determined by the pole shape • Field saturation -> 2 Tesla (BEarth= 3 10-5 Tesla) • B > 2 Tesla -> use SC magnets BLHC = 8.4 Tesla • Abolish Ohm’s Law! • no power consumption (although do need refrigeration power) • high current density • ampere turns are cheap, so we don’t need iron (although often use it for shielding) Consequences • lower power bills • higher magnetic fields -> reduced bending radius • smaller rings • reduced capital cost • new technical possibilities (eg muon collider) • higher quadrupole gradients • higher luminosity Powering a resistive magnet • I ≈ 5 kA for 1.8 T • I ≈ 3·105 A for 10 T • R ≈ 1 m • P = R·I2 • PLEP = 20 kW/magnet • PLHC = 100 MW/magnet (if resistive)

4. What is a superconductor K. Onnes 1911 Resistance of Mercury falls suddenly below measurement accuracy at very low temperature

5. Short history of superconductivity • 1908 Heinke Kemerlingh Onnes achieves very low temperature producing liquid He (< 4.2 K) • 1911 Onnes and Holst observe sudden drop in resistivity to essentially zero SC era starts • 1914 Persistent current experiments (Onnes) • 1933 Meissner-Ochsenfeld effect observed • 1935 Fritz and London theory • 1950 Ginsburg - Landau theory • 1957 BCS Theory (Bardeen, Coper, Schrieffer) • 1962 Josephson effect is observed • 1967 Observation of Flux Tubes in Type II superconductors (Abrikosov, Ginzburg, Leggett) • 1980 Tevatron: The first accelerator using superconducting magnets • 1986 First observation of Ceramic Superconductor at 35 K (Bednorz, Muller) • 1987 first ceramic superconductor at 92 K (above liquid Nitrogen at 77 K !) HTS era starts • 2003 discovery of a metallic compound the B2Mg superconducting at 39 K (x2 Tc of Nb3Sn) • It took ~70 years to get first accelerator from conventional superconductors. • How long will it take for HTS or B2Mg to get to accelerator magnets? Have patience!

6. What is a superconductor Meissner 1933 B = 0 T < Tc B < Bc Below the critical temperature Tc the resistivity drops Below Tc the B-field lines are expelled out of a superconductor (perfect diamagnetic behaviour) Cooper pair appearance phonon-e- interaction Type I superconductors the superconductivity disappears as T > Tc | B > Bc | J > Jc Type II superconductors For Bc1 < B < Bc2 there is a partial flux penetration through fluxoid vortexes and a mixed phase

7. Meissner effect and magnetization • Inside the SC material one has B = 0 E = 0 (otherwise there is an infinite current flowing !) • There is a superficial screening current inducing a diamagnetic polarization M = -H/4p = cH • The B field penetrate with an exponentially decaying intensity B(s) = B(0)exp(-s/lL)

8. BCS theory Normal conducting state Superconducting state • Tc ~ 1/ √Misotopic -> phonons should play a role in superconductivity • Creation of Cooper pairs (over-screening effect) • An e- attracts the surrounding ion creating a region of increased positive charge • The lattice oscillations enhance the attraction of another passing by e- (Cooper pair) • The interaction is strengthened by the surrounding sphere of conduction e- (Pauli principle) • In a superconductor the net effect of e-e- attraction through phonon interaction and the e-e- coulombian repulsion is attractive and the Cooper pair becomes a singlet state with zero momentum and zero spin • To break a pair the excitation energy is ∆E = 2∆

9. Predictions of the BCS theory BCS theory NOT valid in the ceramic SC. Problems with SC type II Energy bond of a Cooper pair Size of a Cooper pair 100 nm Lattice spacing 0.1 ÷ 0.4 nm

10. More on type I and II superconductors Note: of all the metallic superconductors, only NbTi is ductile. All the rest are brittle intermetallic compounds • Type I: not good for accelerator magnets • Also known as the “soft superconductors”. • Completely exclude the flux lines. • Allow only small field (Bc < 0.1 T). • Type II: allow much higher fields • Also known as the “hard superconductors”. • Completely exclude flux lines up to Bc1 • but then part of the flux enters till Bc2 • Examples: NbTi, Nb3Sn • In accelerator magnets only Type II Low Temperature Superconductors are used. • NbTi, a ductile material, is the conductor of choice so far to build SC accelerator magnets. • Nb3Sn (higher Bc2) is the only very promising conductor for future higher field magnet. However, Nb3Sn is brittle nature and presents many challenge in building accelerator magnets.

11. Physics of type I and II superconductors • “London Penetration Depth”lL is the e-fold decay length of the magnetic field from the superconductor skin due to the Meissner effect (in the range of 10 to 103 nm) • “Coherence Length”x the average size of Cooper in the superconductor (in the range of 10 to 100 nm, I.e. much larger than the inter-atomic distance typically of 0.1 to 0.3 nm. Ginzburg-Landau Parameter k

12. More on fluxoids Fluxoids consist of resistive cores with super-currents circulating round them. a single fluxoid encloses flux spacing between the fluxoids Fluxoid patter in Nb Fluxoid motion due to current flow in Nb (SC type II)

13. The Magnesium Diboride MgB2 The magnesium diboride MgBDiscovered in January 2001 (Akimitsu)LTS with Tc: ~39 K A low temperature superconductor with high Tc • The basic powder is very cheap, and abundantly available. • The champion performance is continuously improving in terms of Jc and Bc. • However, it is still not available in sufficient lengths for making little test coils.

14. The high temperature SC (HTC) metallic HTS • many superconductors with critical temperature above 90K - BSCCO and YBCO • operate in liquid nitrogen? • Unlike the metallic superconductors, HTS do not have a sharply defined critical current. • At higher temperatures and fields, there is an 'flux flow' region, where the material is resistive - although still superconducting • The boundary between flux pinning and flux flow is called the irreversibility line

15. SC dipole d -J +J I I I B simplest winding uses racetrack coils real x-section • saddle shaped long dipole coils to make more uniform fields • some iron - but field shape is set mainly by the winding • for good uniformity need special winding cross sections

16. Current density insulation NbTi Cu • In pure SC filament -> J ~ 3 kA/mm2 • In the real world replace J -> Jeng the 'engineering' current density • Wire: enough copper to provide stability (Cu/SC ≈ 1.7) • against transient heat loads • to carry the current in the event superconductor turns normal. • Cable: the trapezoidal “Rutherford cable” is made of several round wires (filling factor ~ 0.9) • Coil: it consists of many turns. There must be a turn-to turn insulation (filling factor ~ 0.85) Current density in wires and cables of Nb3Sn

17. Flux jumping a problem solved using fine SC filaments  • When the B-field raises, large screening current are generated to oppose the changes. • The current densities are initially much larger than Jc which will create Joule heating. • The large current soon dies and attenuates to Jc, which persist. • Screening currents are in addition to the transport current, which comes from the power supply. • They are like eddy currents but, because there is no resistance, they don't decay. • Unstable behaviour is shown by all type II and HT superconductors.The unstable loop is: • reduction in screening currents allows flux to move into the superconductor • flux motion dissipates energy • thermal diffusivity in superconductors is low, so energy dissipation causes local temperature rise • critical current density falls with increasing temperature • Cure flux jumping by making superconductor in the form of fine filaments • –--> weakens DJcDT DQ

18. Stabilization of flux jumping criterion for stability against flux jumping a = half width of filament • typical figures for NbTi at 4.2 K and 1 T • Jc critical current density = 7.5 x 10 9 Am-2 • g density = 6.2 x 10 3 kg·m3 • C specific heat = 0.89 J·kg-1K-1 • q c critical temperature = 9.0 K • so a = 33 mm, ie 66 mm diameter filaments • Less stable • at low field -> Jc is highest • when decreasing T -> Jc up and C down

19. Magnetization J J J B B When viewed from outside the sample, the persistent currents produce a magnetic moment. Problem for accelerators because it spoils the precise field shape We can define a magnetization (magnetic moment per unit volume) as: for cylindrical filaments the inner current boundary is roughly elliptical for a fully penetrated slab down-ramp branch when fully penetrated, the magnetization per unit volume of filament is up-ramp branch where a = filament radius

20. Synchrotron injection and field errors don't inject here! M B much better here! • synchrotron injects at low field, ramps to high field and then back down again • note how quickly the magnetization changes when we start the ramp up • so better to ramp up a little way, then stop to inject • Magnetization also produces field error. • The effect is worst at injection because • DB/B is greatest • magnetization, ie DB is greatest at low field

21. Degraded performance and 'training' LHC short model dipole training histories: data from Andrzej Siemko * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * • most magnets do not go straight to the expected quench point *, instead they go resistive - quench - at lower currents • at quench, the stored energy 1/2LI2 of the magnet is dissipated in the magnet, raising its temperature way above critical - must wait for it to cool down and then try again • second try usually goes to higher current and so - known as training

22. Causes of training and some cures • Low Specific Heat: at 4.2K the specific heat of all substances is ~2,000 times less than at room temperature – so the smallest energy release can produce a catastrophic temperature rise. • Cure: work at higher temperatures – but HTS materials don’t yet work in magnets • Jc decreases with temperature: so a temperature rise drives the conductor resistive. • Cure: there isn’t one. • Conductor motion: JB force makes conductor move, which releases heat by friction - even 10µm movement can raise the temperature by 3K: • Cures: i)make the coils fit together very tightly, pre-compress them ii) vacuum impregnate with epoxy resin – but………………. • Resin cracks: organic materials become brittle at low temperature, because of differential thermal contraction they are often under tension – cracking releases heat. • Cure: fill the epoxy with low contraction (inorganic) material, eg silica powder or glass fibre. • Point quenching: even if only a very small section of conductor is driven resistive, the resistive zone will grow by Ohmic heating until it has quenched the magnet. • Cure: make the conductor such that a resistive zone will not grow until a large section has been driven resistive.

23. Causes of training and some cures • make thermal conductivity k large • make resistivity r small • make heat transfer term hP/A large • NbTi has high r and low k • copper has low r and high k • mix copper and NbTi in a filamentary composite wire • NbTi in fine filaments for intimate mixing • make the windings porous to liquid helium --> superfluid is best

24. Superconducting wires & cables twisted filaments coupled filament uncoupled filament • all superconducting accelerators to date still use NbTi (45 years after its discovery) • performance of superconductors is described by the critical surface in B J T space, • magnet performance is often degraded and shows ‘training’ • SC stability requires making superconductor as fine filaments embedded in a matrix of copper • magnetic fields induce persistent screening currents in superconductor • flux jumping occurs when screening currents go unstable  quenches magnet - avoid by fine filaments - solved problem • screening currents produce magnetization  field errors - reduce by fine filaments • in changing fields, filaments become coupled  increased magnetization - reduce by twisting • accelerator magnets need high currents cables - cables must be fully transposedie every wire must change places with every other wire along the length of the cable - Rutherford cable used in all accelerators to date • can get coupling between strands in cables - causes additional magnetization  field error - control coupling by oxide layers on wires or resistive core foils fully transposed cables Rutherford cable

25. What is an RF cavity A metallic box in which a resonant RF wave generate EM field modes to accelerate charged particles Equivalent circuit Acceleration mechanisms • There is a specific resonant frequency of the cavity that one wishes to drive the cavity • The capacitance C and the inductance L of the cavity affect the transfer efficiency of power between the RF amplifying system and the cavity • The most efficient transfer of power would occur when the impedance appears as a simple resistor to the RF amplifying system • The accelerating voltage is V(t) = d·E(t) where d is the effective cavity length • The resonant frequency is

26. What makes a good RF cavity • quality factor Q : it measures the ability of the cavity to store energy • power loss Pc • The high resistance Rskin of the cavity walls is the largest source of power loss. • In a superconducting RF cavityRskin is 106 times smaller than in a normal conducting cavity Stored energy Power loss in the cavity wall Shunt resistance • At the resonant frequency: • The shunt resistance Rsh is the resistive input impedance • The ratio Rsh/Q measures the acceleration efficiency per unit of stored energy

27. Super/normal conducting RF cavities RF power loss HOM RF power into the beam RF power into the cavity wall Eacc: accelerating field Lacc: accelerating length f : RF-wave phase Cavity at 700 MHz - ß = 0.65 - 5 cells - Lacc = 5·0.14 m Eacc = 10MV/m - f = 0 -> eVacc = eEaccLacc = 7 MeV

28. Plot à la ‘Livingstone’ for SRF cavities

29. SRF cavity limitations • Multipacting or resonant electron emission • Electrons emitted follow a trajectory such that they impact back at the surface of the cavity an integral number of RF cycles after emission, causing an avalanche effect, until all available power goes into this process. • Cure: change the cavity cross section from a rectangular to a spherical or elliptical shape. • Thermal breakdown, or quench • Twall > Tc, the cavity becomes normal conducting, rapidly dissipating all stored energy. A small, local "defect" in the RF surface dissipates power more rapidly than the surrounding walls can conduct away. • The quench field depends upon thermal conductivity of the bulk niobium, heat transfer from the niobium to liquid helium bath, and size and resistance of the defect. • Cure: improve the thermal conductivity of the niobium, improving the purity of the metal. Residual Resistivity Ratio (RRR), the ratio of the resistivity at 300 K / 4.2 K is a good indicator. • "Q virus" • a recently discovered phenomenon, in which excessive hydrogen in high purity niobium can condense onto the RF surface of the cavity, forming a niobium hydride with poor superconducting property. • The Q virus is characterized by an anomalously low cavity Q (high surface resistance) at low electric field, followed by a rapid Q decrease with increasing fields. • Cure: a vacuum bake to 900 degrees C is sufficient to remove the hydrogen from the niobium, while not damaging the cavity.

30. Lecture III - superconducting devices • reminder • The main reasons to introduce superconducting devices (magnets and RF cavities) in particle accelerators are power saving and increase of performance. • In a superconductor the resistivity drops below the critical temperature. • Type I SC cannot be penetrated by the B-field,instead, type II SC partially can. The latter are the only useful material for SC devices. • We miss full theoretical explanations for SC. Cooper pairs explains the resistivity drop in type I SC. Dynamics of fluxiods explains properties of type II SC. We have no explanations for HTS. • In SC dipoles we need maximizing the current density, and fighting magnetization, flux jumping and quenches (luckily training helps). This imply optimal design of wires and cables for SC coils. Presently SC improves field and gradient performance by a factor 4 respect to NC. • In SC RF we need high-purity Nb, with thermal treatment to deplete H2 and round or elliptic cavities. Presently SC improves Vacc by a factor 10 and Q by 6 orders of magnitude respect to NC.