Introduction to Superconducting RF (srf)
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1 Introduction to Superconducting RF (srf) Training Course on Particle Accelerator Technology May Mol, Belgium Holger J. Podlech Institut für Angewandte Physik J.W.-Goethe-Universität, Frankfurt am Main, Germany H. Podlech, IAP Frankfurt 1 ENEN Course on Particle Accelerator Technology
2 Overview Introduction to DC/RF superconductivity History, materials, fundamentals RF figures of merit Q-value, gradient, surface resistance, impedance, R/Q, G, power coupling Measurerements of sc cavities Limitations and phenomena of sc cavities Trapped magnetic flux, thermal break-down, field emission, multi-pacting, LFD, Microphonics H. Podlech, IAP Frankfurt 2 ENEN Course on Particle Accelerator Technology
3 Discovery of Superconductivity Heike Kamerlingh Onnes: 1908 Liquification of Helium 1911 Dicsovery of superconductivity Mercury Nobel Prize 1913 (He-Liquification) Destillation of mercury extreme pure R should vanish at T=0 H. Podlech, IAP Frankfurt 3 ENEN Course on Particle Accelerator Technology
4 Difficulties in Understanding Superconductivity Assumption: Ordering state of the electron system Fermi energies are typically ev T=0 T between 10 4 und 10 5 K T>0 Transition (critical) temperature < 10 K (elements) ΔE mev We need an interaction, which leads to an ordered electron system inspite of high Fermi energies H. Podlech, IAP Frankfurt 4 ENEN Course on Particle Accelerator Technology
5 Isotope Effect Depending on lattice properties Tin-isotopes H. Podlech, IAP Frankfurt 5 ENEN Course on Particle Accelerator Technology
6 Polarisation of the Atomic Lattice Atoms are elastically bounded polarization by an electron Second electron feels polarization Attraction and decrease of energy (under certain conditions) Microscopic theory: 1957 BCS-Theory Cooper-pairs H. Podlech, IAP Frankfurt 6 ENEN Course on Particle Accelerator Technology
7 Coherence length Coherence length ξ 0 Range of pair correlation dimension of a Cooper-pair ξ 0 is typically some 100 nm large compared with distance of normal electrons Uncertainty principle Very small compared with Fermi energy Low critical temperature can be partly understood H. Podlech, IAP Frankfurt 7 ENEN Course on Particle Accelerator Technology
8 Loss Free Charge Transport The pair correlation decreases the electron energy Creation of Cooper-pairs (decreases total system energy) Cooper-pairs can be considered a bosons. All Cooper-pairs are in the same bosonic state. The system wave function is the product of the identical 2-electrons-wave functions. The BCS-theory predicts the existence of an energy gap 2Δ around the Fermi energy. The width 2Δ depends from the temperature and the material. 2Δ can be considered as the binding energy of a Cooper-pair. If this energy is not available for the Cooper-pairs, there is no possibility to change the state. No scattering loss free H. Podlech, IAP Frankfurt 8 ENEN Course on Particle Accelerator Technology
9 Fermi Distribution T>0 T=0 Electrons are fermions Pauli Fermi-liquid (electron gas) All states are filled up to the Fermi-energy (T=0) For T>0: broadening around E F Only e - close to E F contribute to scattering Only these electrons can form Cooper pairs H. Podlech, IAP Frankfurt 9 ENEN Course on Particle Accelerator Technology
10 Energy Gap The energy gap is a function of temperature Energy gap for T=0 K energy Normal electrons Fermi energy Energy gap Cooper-pairs Fermi liquid of normal conducting but loss free electrons H. Podlech, IAP Frankfurt 10 ENEN Course on Particle Accelerator Technology
11 Magnetical Properties of Superconductors A superconductor behaves like an ideal diamagnet A superconductor expells a magnetic field when reaching the superconducting state Meissner-Ochsenfeld-Effect μ=0 These property CANNOT be derived from vanishing ohmic resistance!!! H. Podlech, IAP Frankfurt 11 ENEN Course on Particle Accelerator Technology
12 London Penetration Depth Maxwell: B=0 j s?? Field expulsion incomplete London depth λ 0 Mass Cooper-pair λ nm H. Podlech, IAP Frankfurt 12 ENEN Course on Particle Accelerator Technology
13 Magnetic Properties of Superconductors Sufficient high magnetic fields destroy the superconducting state Existence of a temperature depending critical magnetic field H c H. Podlech, IAP Frankfurt 13 ENEN Course on Particle Accelerator Technology
14 Type I und Type II Superconductors Complete Meissner-Effect Type I Type II Incomplete Meissner- Effect Hard superconductors (I) (II) Parameter Pb Nb NbTi Nb 3 Sn Material In Pb Sn Nb T c (K) B c (T) Application RF RF DC DC λ 0 (nm) ξ 0 (nm) κ Type I I I II H. Podlech, IAP Frankfurt 14 ENEN Course on Particle Accelerator Technology
15 H. Podlech, IAP Frankfurt 15 ENEN Course on Particle Accelerator Technology
16 RF parameter RF figures of merit Gradient E a and transit time factor T Peak fields Surface resistance R s Stored energy W Cavity losses P c Quality factor Q 0 (Shunt-)Impedance R a Geometrical factor G Geometrical impedance R a /Q 0 H. Podlech, IAP Frankfurt 16 ENEN Course on Particle Accelerator Technology
17 Voltage, Gradient and Transit Time Factor Accelerating (effective) voltage Transit time factor Accelerating gradient H. Podlech, IAP Frankfurt 17 ENEN Course on Particle Accelerator Technology
18 Peak Fields E p /E a and B p /E a Maximum fields E p inside the cavity are always higher than the accelerating gradient E a There are magnetic fields related to the surface currents Depending on the geometry there is a level independent ratio E p /E a >1 E 0 E = E T = E T = a E p a E 0 p p = π π p = 3 E ( ) B E a mt MV / m E-Field distribution Pillbox TM 010 Goal: Minimisation of peak fields to increase performance of s.c. cavities H. Podlech, IAP Frankfurt 18 ENEN Course on Particle Accelerator Technology
19 Surface Resistance R s Room temperature Skin depth δ 12 μm (350 MHz, Cu) R s mω H. Podlech, IAP Frankfurt 19 ENEN Course on Particle Accelerator Technology
20 Surface Resistance R s R s is independent of the surface area H. Podlech, IAP Frankfurt 20 ENEN Course on Particle Accelerator Technology
21 Surface Resistance R s superconducting Cooper pairs have inertia can t follow immediately RF fields Unpaired electrons feel electric field RF losses proportional to n n R s nω H. Podlech, IAP Frankfurt 21 ENEN Course on Particle Accelerator Technology
22 RF Surface Resistance (BCS) as function of frequency as function of temperature Low frequency 4K high frequency 2K H. Podlech, IAP Frankfurt 22 ENEN Course on Particle Accelerator Technology
23 Stored Energy W and Dissipated Power P c Power dissipation is reduced because of low BCS-value H. Podlech, IAP Frankfurt 23 ENEN Course on Particle Accelerator Technology
24 Quality factor Q 0 Lorentz-Curve Quality-factor, Q-value H. Podlech, IAP Frankfurt 24 ENEN Course on Particle Accelerator Technology
25 Quality factor Q 0 Measured resonance curve with network analyser H. Podlech, IAP Frankfurt 25 ENEN Course on Particle Accelerator Technology
26 Quality factor Q 0 r.t.: s.c.: Stored energy Number of RF periods until stored energy is dissipated Energy dissipated in one RF period H. Podlech, IAP Frankfurt 26 ENEN Course on Particle Accelerator Technology
27 (Shunt-)-Impedance R Cavity can described with a parallel circuit model H. Podlech, IAP Frankfurt 27 ENEN Course on Particle Accelerator Technology
28 Geometrical Factor G and Geometrical Impedance R/Q Q 0 and R a depends on R s (material, surface preparation) For comparison of different cavities we need RF parameters which are independent on the surface resistance Geometrical Q-value Geometrical impedance CanbecalculatedwithEM simulations H. Podlech, IAP Frankfurt 28 ENEN Course on Particle Accelerator Technology
29 room temperature Plug Power P superconducting R/Q=4000 Q 0 =10000 U a =3 MV L=1 m P c = U R 2 a a = U R Q a 0 2 a Q 0 R/Q=3000 Q 0 =3E8 U a =3 MV L=1 m P c =225 kw η = 4K 300K 4K 0.25 P c =10 W +30 W static P plug =375 kw Klystron efficiency 60% P plug =12 kw H. Podlech, IAP Frankfurt 29 ENEN Course on Particle Accelerator Technology
30 Measurement of Cavities General Remarks amplifier Input coupler P f P r P c P f =forwarded power P r =reflected power P e =emitted power P i =input power P t =transmitted power P c =cavity losses P t control pickup Steady state H. Podlech, IAP Frankfurt 30 ENEN Course on Particle Accelerator Technology
31 Measurement of cavities RF Coupling We consider a cavity in steady state with a stored energy W 0 At t=0 we switch off the RF W decreases decay time of stored energy H. Podlech, IAP Frankfurt 31 ENEN Course on Particle Accelerator Technology
32 Measurement of cavities RF Coupling intrinsic Q loaded Q external Q external Q pickup H. Podlech, IAP Frankfurt 32 ENEN Course on Particle Accelerator Technology
33 Coupling Factor β Q 0 = Q L E7 1E8 1E9 Q e H. Podlech, IAP Frankfurt 33 ENEN Course on Particle Accelerator Technology
34 Generator + Coupler + Cavity We are interested in the time evolution of the stored energy depending on the coupling strength for different cases like RF switch on or RF switch off Some time consuming calculations Looking for a differential equation of the stored enery H. Podlech, IAP Frankfurt 34 ENEN Course on Particle Accelerator Technology
35 Differential Equation for the Stored Energy W 0 stored energy in steady state W time dependent stored energy ω resonance frequency Differerent cases Equilibrium Switch on Switch off H. Podlech, IAP Frankfurt 35 ENEN Course on Particle Accelerator Technology
36 Equilibrium (Steady State) 0 Stored energy in equilibrium H. Podlech, IAP Frankfurt 36 ENEN Course on Particle Accelerator Technology
37 Equilibrium (Steady State) β=1 zero reflection power meter network analyzer H. Podlech, IAP Frankfurt 37 ENEN Course on Particle Accelerator Technology
38 RF switch off Definition: W 0 is 0 for zero P f 0 H. Podlech, IAP Frankfurt 38 ENEN Course on Particle Accelerator Technology
39 Cavity losses RF switch off Decay of stored energy Power leaking through coupler measured as P r H. Podlech, IAP Frankfurt 39 ENEN Course on Particle Accelerator Technology
40 RF switch on W 0 H. Podlech, IAP Frankfurt 40 ENEN Course on Particle Accelerator Technology
41 RF switch on For t=0 P r =P f For t >>τ L P r =P f *(1-2β/(1+β)) 2 H. Podlech, IAP Frankfurt 41 ENEN Course on Particle Accelerator Technology
42 Rectangular RF pulses H. Podlech, IAP Frankfurt 42 ENEN Course on Particle Accelerator Technology
43 Rectangular Pulses P f P r P t P t Pr P on = P equilibrium f P = off P e H. Podlech, IAP Frankfurt 43 ENEN Course on Particle Accelerator Technology
44 Measurement of s.c. cavities What is the most important measurement? Problem: Q 0 depends on field level Exponent of e-function is time dependend Q=const. only Ohmic losses Additional non-ohmic losses H. Podlech, IAP Frankfurt 44 ENEN Course on Particle Accelerator Technology
45 Measurements of decay time τ H. Podlech, IAP Frankfurt 45 ENEN Course on Particle Accelerator Technology
46 P f Measurement of the coupling factor β cw operation (powermeter) P r Pulsed equilibrium (scope) P t Pulsed peak (scope) P on = P f P off = P e P r equilibrium H. Podlech, IAP Frankfurt 46 ENEN Course on Particle Accelerator Technology
47 Determination of Q 0 at low fields H. Podlech, IAP Frankfurt 47 ENEN Course on Particle Accelerator Technology
48 Simulation Q-value at low fields Q 0 =5.7x10 8 R s =96 nω R BCS =49 nω B ext =2 μt R mag =4 nω R 0 =43 nω H. Podlech, IAP Frankfurt 48 ENEN Course on Particle Accelerator Technology
49 Determination of calibration point at low fields simulation Measured at low fields H. Podlech, IAP Frankfurt 49 ENEN Course on Particle Accelerator Technology
50 Determination of Q 0 at high fields H. Podlech, IAP Frankfurt 50 ENEN Course on Particle Accelerator Technology
51 Q 0 versus Gradient around the world Spoke, MSU CH-cavity, Frankfurt Spoke, IPN Orsay TESLA, DESY H. Podlech, IAP Frankfurt 51 ENEN Course on Particle Accelerator Technology
52 Q-value Q 0 (rt)= Δf 10 khz Q 0 (sc)= Δf 1 Hz r.t. r.t. s.c. s.c. H. Podlech, IAP Frankfurt 52 ENEN Course on Particle Accelerator Technology
53 circulator Bidirectional coupler P f P r P t power splitter power meter P t P f RF detector RF detector scope RF detector AMP P r P t scope power meter P f power meter P r NWA phase shifter phase detector Function generator VCO H. Podlech, IAP Frankfurt 53 ENEN Course on Particle Accelerator Technology
54 RF surface resistance (trapped magnetic flux) External magnetic flux is trapped and quantisized N normal conducting areas with πξ 0 2 additional losses f=352 MHz, T=4.2 K, B ext =38 μt R mag =89 nω, R BCS =38 nω H. Podlech, IAP Frankfurt 54 ENEN Course on Particle Accelerator Technology
55 Field Emission H. Podlech, IAP Frankfurt 55 ENEN Course on Particle Accelerator Technology
56 Field Emission X-ray emission (green) during RF pulse E p 25 MV/m H. Podlech, IAP Frankfurt 56 ENEN Course on Particle Accelerator Technology
57 Measurement of X-rays H. Podlech, IAP Frankfurt 57 ENEN Course on Particle Accelerator Technology
58 Coupling as Function of Field Level β=1 crit. coupled β>1 over coupled β<1 under coupled H. Podlech, IAP Frankfurt 58 ENEN Course on Particle Accelerator Technology
59 What to do against Field Emission? LEP-2 CERN Clean surface: BCP, HPR clean room technology Peak field reduction Clean room IAP H. Podlech, IAP Frankfurt 59 ENEN Course on Particle Accelerator Technology
60 Thermal Break Down Magnetic field and surface current are strongly related Ø=50 μm (A=4E-9 m 2 ) R s =5 mω (n.c.) H=34000 A/m=43 mt Break down of superconductivity: H>H c T>T c (related to defects) High RRR niobium (thermal conductivity) High quality material (defect free) Electron beam welding BCP Peak field reduction H. Podlech, IAP Frankfurt 60 ENEN Course on Particle Accelerator Technology
61 Microphonics Mechanical eigenmodes geometrical change Change of C and L frequency change Fast tuner Stiffener Strong coupling Frequency change >> bandwidth H. Podlech, IAP Frankfurt 61 ENEN Course on Particle Accelerator Technology
62 Lorentz Force Detuning (LFD) B-field E-field H. Podlech, IAP Frankfurt 62 ENEN Course on Particle Accelerator Technology
63 VCO-Signal k=-8 Hz/(MV/m) 2 cw no problem Pulse: fast tuner, stiffener Strong coupling H. Podlech, IAP Frankfurt 63 ENEN Course on Particle Accelerator Technology
64 Multipacting Resonant creation of an electron avalanche typically in the low electric field region H. Podlech, IAP Frankfurt 64 ENEN Course on Particle Accelerator Technology
65 Multipacting Conditioning Geometry Clean surface H. Podlech, IAP Frankfurt 65 ENEN Course on Particle Accelerator Technology
66 Summary Introduction to DC/RF superconductivity History, materials, fundamentals RF figures of merit Q-value, gradient, surface resistance, impedance, R/Q, G, power coupling Measurerements of sc cavities Limitations and phenomena of sc cavities Trapped magnetic flux, thermal break-down, field emission, multi-pacting, LFD, Microphonics H. Podlech, IAP Frankfurt 66 ENEN Course on Particle Accelerator Technology
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