Superconducting Division

Lecture II

Superconductivity

Ramesh Gupta Division Brookhaven National Laboratory

US School University of California – Santa Barbara June 23-27, 2003

USPAS Course on Superconducting Accelerator , June 23-27, 2003 Slide No. 1 of Lecture II Ramesh Gupta, BNL Basic Superconducting Magnet Division

An Introduction to Superconductivity

• It will not be a general course on superconductivity

•The purpose of this lecture is to give you a brief introduction to the parts that are relevant to designing superconducting accelerator magnets

USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 2 of Lecture II Ramesh Gupta, BNL The Superconductivity Superconducting Magnet Division Resistivity of Cu as a function First observation of “Superconductivity” by Onnes (1911) of Resistance of Mercury falls suddenly below measurement accuracy at very low temperature has larger RRR Resistance (Ohms) (~4K) ρ (273K)/ ρ High purity High RRR= Temperature (K)

USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 3 of Lecture II Ramesh Gupta, BNL Superconducting Accelerator Magnets Superconducting A Brief History Magnet Division 1908 Heinke Kemerlingh Onnes achieves very low temperature (<4.2 K) 1911 Onnes and Holst observe sudden drop in resistivity to essentially zero Superconductivity is born ! 1914 experiments 1933 Meissner-Ochsenfeld effect observed 1935 Fritz and London theory 1950 Ginsburg - Landau theory 1957 BCS Theory 1967 Observation of Flux Tubes in Type II superconductors 1980 : The first accelerator using superconducting magnets 1986 First observation of High Temperature Superconductors It took ~70 years to get first accelerator from conventional superconductors. How long will it take for HTS to get to accelerator magnets? Have patience! USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 4 of Lecture II Ramesh Gupta, BNL Critical Surface of Nb-Ti Superconducting Magnet Division Critical Surface The surface on 3-d (J,T,B) volume within which the material remain superconducting.

Operating point of the magnet must stay within this volume with a suitable margin. What a magnet designer always dreams for ?: A material that remains superconducting at higher and at higher fields.

USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 5 of Lecture II Ramesh Gupta, BNL Superconducting Magnet Division A remarkable observation in superconductors: They exclude the magnet flux lines from going through it.

Meissner and Ochsenfeld (1933)

Courtesy: Schmuser

Normal Conductor Superconductor Attenuation of and Courtesy: Wilson shielding currents in Type I superconductors

USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 6 of Lecture II Ramesh Gupta, BNL Type I and Type II Superconductors Superconducting Magnet Division

Normal phase

Courtesy: Schmuser

Type I: Type II: Also known as the Also known as the “hard superconductors”. “soft superconductors”. Completely exclude flux lines up to Bc1 Completely exclude the flux lines. but then part of the flux enters till Bc2 Allow only small field (< 0.1 T). Important plus: Allow much higher fields. Not good for accelerator magnets. Examples: NbTi, Nb3Sn

USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 7 of Lecture II Ramesh Gupta, BNL Critical Surface of Superconducting Type I Superconductors Magnet Division

0.9

(T) Type I c 0.6 superconductors are obviously NOT suitable for high field magnet applications. 0.3 Critical Field B Critical

0.0 Critical Temperature (K)

USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 8 of Lecture II Ramesh Gupta, BNL Critical Surface of Type II Low Superconducting Temperature Superconductors (LTS) Magnet Division

Not shown here:

MgB2 (39 K)

• Conductors that are currently being used in building accelerator magnets are Type II Low Temperature Superconductors. • NbTi, a ductile material, has been the conductor of choice so far. All accelerator machine magnets have been and are being built with this superconductor.

• For future high field magnet applications one must turn to Nb3Sn, etc.(higher Bc2). However, Nb3Sn is brittle nature, and presents many challenge in building magnets. USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 9 of Lecture II Ramesh Gupta, BNL (MgB ) Superconducting 2 Magnet Division

Magnesium Diboride (MgB2) Discovered 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.

USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 10 of Lecture II Ramesh Gupta, BNL London Penetration Depth Superconducting and Coherence Length Magnet Division

Ginzburg-Landau Parameter

κ = λL/ξ

Courtesy: Schmuser

• “London Penetration Depth” tells how field falls Nb is type II superconductor • “Coherence Length” tells how does cooper pair density increases USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 11 of Lecture II Ramesh Gupta, BNL Current Transport in Superconducting Bulk Superconductors Magnet Division

Courtesy: Schmuser Motion of these fluxoids generates heat.

USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 12 of Lecture II Ramesh Gupta, BNL Nb-Ti Microstructure Superconducting Magnet Division

A high critical microstructure in a conventionally processed Nb-Ti microstructure (UW strand). Courtesy: P.J. Lee (University of Wisconsin-Madison)

USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 13 of Lecture II Ramesh Gupta, BNL Difference Between the Superconductor Requirements for Superconducting RF Cavities and Superconducting Superconducting Magnets for Particle Accelerators Magnet Division

• For superconducting RF cavities, one needs very high purity materials, with no defects.

• For superconducting magnets, the presence of certain defects is essential, as without those defects, it can not stand those high fields.

USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 14 of Lecture II Ramesh Gupta, BNL Flux Jumping Superconducting Magnet Division Initially, when the field is raised, large screening current are generated to oppose the changes. These current densities may be much larger than Jc which will create . However, these large currents soon die and attenuate to Jc, which persist.

USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 15 of Lecture II Ramesh Gupta, BNL Instability from Flux Jumping Superconducting Magnet Division

Courtesy: Wilson

USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 16 of Lecture II Ramesh Gupta, BNL Stability Criteria Against Flux Jumping Superconducting Magnet Division

∆Q heat increases temperature ∆T and reduces Jc by ∆Jc Calculate if this creates an unstable (runaway) situation?

B(x) = Bo - µo Jc (a-x) h 2 φ(x)= Bo x - µo Jc (ax-x /2) h 2 Change in flux due to change in Jc: ∆φ(x)= µo ∆J (ax-x /2)h 2 Additional heat due to flux motion: ∆q = x = µo Jc ∆Jc a /3 ∆φ(x) Jc dx ∫0 2 2 Assignment: To first order ∆Jc = Jc ∆T / (Tc-To), thus ∆q = µo J c a /[3(Tc-To)] ∆T Go through the Total heat to raise the temperature: ∆Q + ∆q = C ∆T expressions. where C is specific heat per unit volume 2 2 ∆Q = C ∆T - ∆q = {C- µo J c a /[3(Tc-To)] }∆T = C’ ∆T 3CT()c − To 2 2 a < where C’ = {C- µo J c a /[3(Tc-To)] } is the effective specific heat. 2 µo J c For stability condition, the effective specific heat must be positive. This determines the maximum slab thickness “a” for stability Similarly determine condition for filament of diameter r. π 3CT()c − To r < 2 The computed filament diameter for flux stability in NbTi is < 40 µ; 4 µo J c for safety margin use ~ 20 µ. USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 17 of Lecture II Ramesh Gupta, BNL Effects in Superconducting Superconducting Filaments Magnet Division

The above magnetization creates persistent current, a major issue in SC magnets.

Persistent current induced magnetization: Courtesy: Schmuser

USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 18 of Lecture II Ramesh Gupta, BNL Persistent Current-induced Harmonics Superconducting in High Field (Nb Sn Magnets) Magnet Division 3 Persistent current induced magnetization : Measured magnetization (NbTi)

Problem in Nb Sn Magnets because 3 Courtesy: Ghosh (a) Jc is higher by several times (b) Filament size is big and gets bigger after reaction due to sintering

In most Nb3Sn available today, the effective filament diameter is an order of magnitude larger than that in NbTi. The obvious solution is to reduce filament diameter; however, in some cases it also reduces Jc. A small filament diameter is important for : • increasing stability • reducing persistent currents

USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 19 of Lecture II Ramesh Gupta, BNL Persistent Current-induced Harmonics

Superconducting (may be a problem in Nb3Sn magnets, if done nothing) Magnet Division

Nb3Sn superconductor, with the technology under use now, is expected to generate persistent current- induced harmonics which are a factor of 10-100 worse than those measured in Nb-Ti magnets. In addition, a snap-back problem is observed when the acceleration starts (ramp-up) after injection at steady state (constant field). Measured sextupole harmonic Measured sextupole harmonic in a Nb Sn magnet in a Nb-Ti magnet 3

Snap back

Either reduce the effective filament diameter or come up with a magnetic design that minimizes the effect of magnetization in the magnets (LBL, FNAL, TAMU). USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 20 of Lecture II Ramesh Gupta, BNL Manufacturing of Nb-Ti Wires Superconducting Magnet Division

USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 21 of Lecture II Ramesh Gupta, BNL Superconducting A Typical Superconducting Cable Magnet Division

Filaments in an actual cable (Filament size in SSC/RHIC magnets: 6 micron)

USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 22 of Lecture II Ramesh Gupta, BNL Stability of Superconducting (Wire is Made of Many Filaments) Magnet Division

Filaments not coupled Coupled filaments

Courtesy: Wilson

Rutherford cable

A wire composed of twisted filaments

USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 23 of Lecture II Ramesh Gupta, BNL Interstrand Coupling Superconducting Magnet Division

Courtesy: Devred

USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 24 of Lecture II Ramesh Gupta, BNL Influence of Interstrand Coupling Superconducting Magnet Division

Courtesy: Devred USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 25 of Lecture II Ramesh Gupta, BNL Nb-Ti Alloys at 4.2 K and 1.8 K Superconducting Magnet Division LHC will operate at 1.8 K; all current accelerators operate at ~4.5 K. All use Nb-Ti.

A Reasonable Assumption: 3 T increase between 4.2 K and 1.8 K

Courtesy: P. Lee (U Of W-M)

USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 26 of Lecture II Ramesh Gupta, BNL Cable Measurement Set-up Superconducting Magnet Division

Courtesy: Ghosh

USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 27 of Lecture II Ramesh Gupta, BNL Superconducting Nb3Sn Cable in Cu- Channel Magnet Division

40

30

20 n V ∝ (I/Ic) LOCALLY DAMAGED CABLE.

10 n-value: Vs (µV) Vs A good indicator of the quality of cable. 0 A lower “n-value” means a slow transition from superconducting to -10 SMOOTH CABLE normal phase, which Courtesy: Ghosh generally indicates some sort of damage in the -20 cable. 2000 3000 4000 5000 6000 7000 8000 Is (A)

USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 28 of Lecture II Ramesh Gupta, BNL The Conventional Low Temperature Superconductors (LTS)

Superconducting and the New High Temperature Superconductors (HTS) Magnet Division Low Temperature Superconductor Onnes (1911) Resistance of Mercury falls suddenly below meas. accuracy at very low (4.2) temperature New materials (ceramics) loose their resistance at NOT so low temperature ()! High Temperature Superconductors (HTS) Resistance (Ohms) Resistance

Temperature (K) USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 29 of Lecture II Ramesh Gupta, BNL Critical Surface of High Superconducting Temperature Superconductors (HTS) Magnet Division HTS (this example, BSCCO2212) can operate at a temperature much higher than ~4 K required for conventional LTS; say 20K (or even more). Field perpendicular

USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 30 of Lecture II Ramesh Gupta, BNL Critical Surface of High Superconducting Temperature Superconductors (HTS) Magnet Division HTS (this example, BSCCO2212) can operate at a temperature much higher than ~4 K required for conventional LTS; say 20K (or even more). Field parallel case is betterField parallel case (lower drop in Jc) C.M. Friend et al., Physica C (1996)

USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 31 of Lecture II Ramesh Gupta, BNL Popular HTS Materials of Today Superconducting Magnet Division

•BSCCO 2223 (Bi,Pb)2Sr2Ca2Cu3Ox •BSCCO 2212 •YBCCO

•MgB2 is technically a low temperature superconductor (LTS) with critical temperature ~39 K.

Of these only BSCCO2212 and BSCCO2223 are now available in sufficient quantity to make accelerator magnets.

USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 32 of Lecture II Ramesh Gupta, BNL Some Remarkable Properties of HTS Superconducting (High Temperature Superconductors) Magnet Division HTS retain superconductivity to Superconductor Critical Currents DeDe ce ce mbe mbe r r12 12thth20022002 - - Compiled Compiled by by Peter Peter J.J. LeeLee -- jcprog_02bl.ppt, jcprog_02bl.ppt, jcprog_02.xlsjcprog_02.xls Superconductor Critical Currents Legend on next slide higher temperature 100,000

At 4.2 K Unless R vs. T Otherwise Stated

Nb-Ti Multilayer YBCO µbridge H||c 10,000

2212 Tape YBCO HTS 75 K H||a-b

Nb Sn Internal Sn ASC Nb3Sn 3 2212 Round wire 1,000 ITER 2223

Tape B|_ 2223 Nb3Al Tape B|| ITER Nb3Sn Tape

from (Nb,Ta) 6 Sn 5 2 Nb-Ti HT 1.8 K

Nb3Al RQHT+Cu Also compare the high A/mm² Density, Current Critical Nb-Ti-Ta

100 Nb-Ti APC field performance of 1.8 K YBCO Nb-Ti

“High Temperature , A/mm 75 K H||c

c MgB2 Film Superconductors (HTS)” J PbSnMo6S8 Nb3Sn 1.8 K Bronze as compared to that of 10 0 5 10 15 20 25 30 “Low Temperature University of Wisconsin-Madison Univers ity of Wis co ns in-Madiso n Applied Field, T Superconductors (LTS)”. AppliedApplied SuperconductivitySuperconductivity CenterCenter Applied Field, T

USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 33 of Lecture II Ramesh Gupta, BNL High Field Superconductors Superconducting Magnet Division Differences between Low field and high field superconductors:

Low field superconductors (NbTi) are ductile. The coils can be wound without significantly damaging the conductors.

High field superconductors (Nb3Sn and HTS) are brittle!

One has to be very careful in winding coil with these brittle material or use alternate design to minimize the damage on conductors.

One can also wind the coil before they become brittle (& superconducting) and react the material after winding to make them superconductor. This is referred to as “Wind and React” technique and it requires everything in the coil to go through the high temperature (650 C or more) reaction process. One has to be careful in choosing material, etc. USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 34 of Lecture II Ramesh Gupta, BNL Superconducting Usable Current Densities in Coils Magnet Division

J Vs. B curve in NbTi Even though the superconductor may be capable of c carrying a current density of 3000 A/mm2 or so, only a fraction of that is available to power the magnet. Here is why? • There should be enough copper within the wire to provide stability against transient heat loads and to carry the current in the event superconductor turns normal. Usually copper content is more than superconductor. In most NbTi medium field production magnets, the maximum current density in copper is 1000 A/mm2 or less at the design field. In high field

Nb3Sn R&D magnets, we are allowing it to be twice that. • The trapezoidal “Rutherford cable” is made of several round wire. The fill factor may be 90% or so. • The coil is consisted of many turns. There must be a turn-to- turn insulation taking ~15% of the volume.

USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 35 of Lecture II Ramesh Gupta, BNL Superconducting Usable Current Densities in Coils Magnet Division

8000

The example on the right is for a ) 7000 Jc (A/mm2) 6000 Nb3Sn superconducting cable Jwire 5000 Joverall with Cu/Sc ratio fixed at 1.7. 4000 3000 Note that overall current density 2000 in the coil is only ¼ of the Jc, Jw, Jo (A/mm2 1000 0 superconductor current density. 5 6 7 8 9 101112131415 B(T)

1.2 Joverall for various Jcu 1.1 1.0 0.9 In the example on the right, the 0.8 0.7 overall current density is 0.6 0.5 1.0 computed to keep current 0.4 1.2 0.3 Jcu= 1.4 density in copper at a given Joverall(kA/mm2) 0.2 1.6 0.1 1.8 value. 0.0 2.0 012345678910

Jsc(kA/mm2)

USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 36 of Lecture II Ramesh Gupta, BNL Usable Current Density in Magnet Design

Superconducting (A case study of Nb3Sn for fix Jcu at quench) Magnet Division

2 Jsc(12T,4.3K) Jcu(A/mm ) 2500 1500 Critical Current Density in Superconductor: Jsc(at 4.3 K) Also Wire & Overall Current Densities Normalized for a Given Jcu

2 2 8000 Cu/Sc Ratio B(T) Jc(A/mm ) J wire (A/mm ) Joverall 6.30 5 9454 1295 911 7500 5.18 6 7766 1257 885 7000 4.29 7 6431 1216 856 3.56 8 5347 1171 825 6500 2.96 9 4446 1122 790 ) 6000 2.46 10 3689 1066 751 2 2.03 11 3048 1005 708 5500 1.67 12 2500 938 660 Jsc (A/mm 5000 1.35 13 2031 863 607 1.09 14 1631 781 550 4500 0.86 15 1289 693 488 4000 Scaled from TWCA Insulated Joverall Joverall 3500 1100 3000 y = -74.64x + 1824.1

1050 Jwire, R2 = 0.9956 2500 )

2 1000

Jsc, 2000 950 Jwire 1500 900 850 1000 500 Joverall (A/mm 800 Joverall 750 A Good "Linear Fit" 0 5 6 7 8 9 10 11 12 13 14 15 700 10 11 12 13 14 15 B(T) B(T)

Assignment: Obtain Jwire and Joverall curves for magnet designs at various short sample fields.

Assume the (Bc,Jc) relationship above and Jcu to be 1500 A/mm2 at quench. USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 37 of Lecture II Ramesh Gupta, BNL A Guide to Choosing the Maximum Superconducting Field in Superconducting Magnets Magnet Division

4.0 Dipole: B=-muo Jo/2 *t 3.6 Quad: G=-muo jo/2 ln(1+t/a) 3.2 t = coil thickness a = coil radius 2.8 Dipole Field 2.4 Relative Grad (quad) Grad Relative

2.0 1.6 1.2

0.8 Quadrupole Gradient 0.4

Relative Field (dip), 0.0 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 Coil thickness(dipole), coil thickness/coil radius [quadrupole]

To get maximum field keep increasing coil thickness (within practical limit) till you reach the maximum field in the coil where magnet quenches

USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 38 of Lecture II Ramesh Gupta, BNL Quadrupole Gradient for various coil radius Superconducting Magnet Division

1000 40 Dipole: B=-muo Jo/2 *t Quad: G=-muo Jo/2 ln(1+t/a) 2 900 35 t = coil thickness 800 30 a = coil radius 700 25

600 20

500 15

400 10 (current density in coil). Gradient (T/m) 300 radius, not aperture

200 Jo=700 A/mm2 at the given field. 100 Need Jc ~ 2000 or more. 0 0 5 10 15 20 25 30 35 40 45 50 55 60 Coil thickness mm

Important number is pole-tip field = Gradient * coil radius

In large aperture magnets, forces become large. Note: Legends are coil The plot scale linearly with Jo A reasonable range of Jc is 400-1000 A/mm USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 39 of Lecture II Ramesh Gupta, BNL Assignment Superconducting Magnet Division

Assume that a rectangular cable (Non-Keystone, Rutherford cable) is made of 30 wires (strands). The diameter of each wire is 1 mm. The width of the insulated cable is 17 mm and thickness is 2 mm. The insulation on each side of the cable is 0.2 mm. The critical current density of superconductor at 12 T is 2500 A/mm2. The wire has 40 % superconductor and you can assume that the rest is copper.

The magnet made with this cable operates at 12 T. Compute the current density in wire, in insulated cable and bare cable (cable without insulation) at 12 T. What will be the current density in copper if the magnet quenches (looses its superconductivity) at 12 T?

USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 40 of Lecture II Ramesh Gupta, BNL Why Use Superconducting Superconducting Magnets in Accelerators? Magnet Division

Use of superconductors in accelerator magnets generate field much higher than what can be achieved from the normal conductors. Two major reasons for using superconducting magnets in the accelerators: Cost advantage In high energy circular hadron , the superconducting magnets reduce the size of a machine. This usually translate in to a reduction in the overall machine cost. Superconducting magnets also lower the power consumption and hence the cost of operating a high energy machine. Performance advantage In interaction regions, a few high field and high field quality magnets may significantly enhance the luminosity of the machine. In Courtesy: Martin Wilson this case magnet costs may be large but the overall returns to experimentalists are high.

USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 41 of Lecture II Ramesh Gupta, BNL