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Superconductivity Lecture II Superconducting Magnet Division Lecture II Superconductivity Ramesh Gupta Superconducting Magnet Division Brookhaven National Laboratory US Particle Accelerator School University of California – Santa Barbara June 23-27, 2003 USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 1 of Lecture II Ramesh Gupta, BNL Basic Superconductivity 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 Temperature Resistance of Mercury falls suddenly below measurement accuracy at very low temperature has larger RRR Resistance (Ohms) (~4K) ρ (273K)/ ρ High purity copper 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 Persistent current 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 Tevatron: 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 temperatures and at higher fields. USPAS Course on Superconducting Accelerator Magnets, June 23-27, 2003 Slide No. 5 of Lecture II Ramesh Gupta, BNL Meissner Effect 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 magnetic field 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 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 Magnesium Diboride (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 current density 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 Joule heating. 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 Magnetization 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
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