DEVELOPMENT OF SSR2 FOCUSING LENSES FOR PIP-II Electromagnetic Application Section Electromagnetic Applications & Instrumentation Division Team members: Kumud Singh, Janvin Itteera, Mahima, R R Singh , Rajesh Jalan & Sanjay Malhotra
OUTLINE Design Work carried out for PIP-II superconducting focusing lenses for Spoke resonator cryomodule (SSR2). EM design of SSR2 superconducting focusing lens. Quench Analysis. Engineering development January 31, 2019 IIFC Magnet meeting presentation | SSR2 lenses For PIP-II
FUNCTIONAL REQUIRMENT SPECIFICATIONS A new design is suggested and verified to meet Parameters Values the main requirements because of increased beam aperture and focusing strength for SSR2. Focusing Strength 5 T 2 m Focusing strength and Fringe field on the SSR2 cavity surface has been optimized for PIP-II Bending strength of Dipole correctors 5 mT-m requirements. Beam pipe aperture 40 mm Uncertainty in the location of magnetic axis <0.1mm RMS w.r.t Reference points (Transverse and <0.5 mrad RMS angular alignment) Effective length of solenoid (FWHM) <15 cm Active magnetic shielding requirements 0.5Q 0 criterion Maximum current in the solenoid 100A Maximum current in the dipole correctors 50 A January 31, 2019 IIFC Magnet meeting presentation | SSR2 lenses For PIP-II
EM DESIGN AND PARAMETERS (Design date: Jan’2016) Sr. no Parameter Value Unit 44.4mm 44.4mm T 2 m 1. Designed value of focusing strength 5.33 Magnetic Field Integral 1.01 T-m 2. 60.6 mm Peak transverse Magnetic field in the lens 3. 6.22 T aperture 4. Peak Magnetic field on the wire strand 6.878 T Nominal current 77.4 A 5. 145 mm 105.5 mm 50 mm Beam pipe aperture 40 mm A/mm 2 6. Nominal Current Density 260 169 mm B max at the cavity Surface 0.179 Gauss 7. Field Integral (along the radial line 0 to 0.3m) 8. 3.9 G-cm 150 mm at axial Distance of 0.5 mm 52.5 mm Objective function : 2 . 𝑒𝑨 ≥ 5 T 2 m 𝐶 𝑨 𝑠=0.3 𝐶. 𝑒𝑚 Minimize at z= 0.5m 𝑠=0 Constraints: 𝐶 𝑨 ∗𝑒𝑨 ≤ 150 cm 𝐶 0 I exc < 100A Optimization Parameters: N main , L main , R main N BC , L MC , R MC , Z center-BC January 31, 2019 IIFC Magnet meeting presentation | SSR2 lenses For PIP-II
ACTIVE MAGNETIC SHIELDING REQUIRMENTS Power loss in superconducting RF cavities is a major source of heat influx in the cryomodules. Power loss can be affected by magnetic field trapped in superconducting walls of the cavities. Diamagnetism of superconducting niobium shield the cavities . But this protection is broken when the cavity quenches as part of its surface warms up above the superconductivity threshold . During quenching, magnetic flux penetrates inside the cavity through the normally conducting opening and becomes trapped in the cavity Trapped magnetic flux that reduces the unloaded quality factor of a cavity Q 0 to the level Q 1 = η∙Q 0 ( η ≤1) can be calculated as Φ tr = 2 μ 0 Φ 0 2 ) * f ∙V * ( 1− η) η (Rs∙ ξ 0 ( ΛQ 0 ) μ 0 =4π∙10 -7 H/m is the permeability of empty space ; Φ 0 =2 ∙ 10 -15 Wb is the magnetic flux quant, ξ 0 =3.9 ∙ 10 -8 m is the coherent length in Nb, f is the frequency of the cavity, Rs is the surface resistance of Nb at this frequency, V is the volume of the cavity, and Λ is a dimension -free coefficient that defines magnetic energy density at the location of the quench relative to the average energy density in the cavity First multiplier is fully defined by the properties of superconducting material. The second one is cavity specific with Λ depending on quench location. The last multiplier relates the acceptable degree of degradation η with allowed amount of the trapped flux. Corresponding choice of η can be made taking into account available cooling power and distribution of RF magnetic field (or the energy density factor Λ ) and expected static magnetic field on the cavity surface. (0.5Q 0 for PIP-II SSR cavities) January 31, 2019 IIFC Magnet meeting presentation | SSR2 lenses For PIP-II
FRINGE FIELD ON CAVITY SURFACE The magnetic field generated by magnetic elements inside cryomodule must be sufficiently small to limit the degradation in Q . 𝑆 𝑡𝑣𝑠𝑔 = 𝑆 𝐶𝐷𝑇 (ν, 𝑈) + 𝑆 𝑠𝑓𝑡 + 𝑆 𝑛𝑏 ( 𝐼 𝑓𝑦𝑢) External DC magnetic field on the cavity surface due to fringing field of the solenoid magnet has been restricted to below 1 mT (10 Gauss). January 31, 2019 IIFC Magnet meeting presentation | SSR2 lenses For PIP-II
TOLERANCE STUDIES ON BUCKING COIL GEOMETRICAL PARAMETERS Tight tolerance is required for the bucking coil winding dimensions and its placement w.r.t main coil. The positional inaccuracy of the Bucking coil effects the fringe magnetic field on the cavity surface. January 31, 2019 IIFC Magnet meeting presentation | SSR2 lenses For PIP-II
OPERATING CURVE FOR THE SSR2 FOCUSING LENS Predicted performance of main coil for SSR2 Magnets 293 243 Current [A] 193 143 93 43 4 5 6 7 8 9 10 Max magnetic Field on Sc strand [T] 2K 4K Operating curve we expect the magnet to go resistive 'quench' where the peak field load line crosses the critical current line January 31, 2019 IIFC Magnet meeting presentation | SSR2 lenses For PIP-II
DIPOLE CORRECTOR COIL Sr. no Parameter Value Unit 1. Designed value of Bending strength of corrector coils 5.25 mT-m 2. Designed value of integrated Gradient of focusing quadrupole 0.2 T 3. Nominal current ~39.2 A January 31, 2019 IIFC Magnet meeting presentation | SSR2 lenses For PIP-II
COMBINED FIELD SIMULATION Fringe field on the cavity surface increases slightly when DC coil powered on with MC coil but field values are still within the acceptable limits January 31, 2019 IIFC Magnet meeting presentation | SSR2 lenses For PIP-II
WINDING CONDUCTOR LUVATA make OK 54 Conductor Wire Specifications: Sr. No. Parameter Value 0.540 ± 0.15 1. Diameter, nominal 2. Diameter (bare ,nominal) 0.5 mm 3. Insulation PVA, Formvar 4. Number of filaments 54 (filament dia : 45 µm) 5. Cu/Sc (nominal) 1.3 Ic (A) Jc (A/mm 2 ) 6. Critical Currents @3T 252 3645 @6T 134 2173 Magnetization measurements have been carried out on the wire samples to derive critical current density data. Measured data shall be fitted to Bottura fit. Wire DC resistivity vs temperature is being measured to fit the measured data into simulations. January 31, 2019 IIFC Magnet meeting presentation | SSR2 lenses For PIP-II
WINDING CONDUCTOR The magnetization was measured at various temperature and magnetization data were normalised to the volume of sample calculated from mass and the density of wire. For calibration of the magnetometer nickel standard sample is used. Factors which influence the magnetization can be derived from the Bean Model. According to this the magnetization of a strand in the hysteresis loop is: λ 3/2 λ 3/2 2 2 3𝜌 √𝑂 𝑔 𝐾 𝑑 d , 𝑝𝑠 𝑁 = √𝑂 𝑔 𝐾 𝑑 D 3𝜌 M = magnetic moment per unit volume, λ = Ratio of superconductor to strand volume, J c = Critical current density, 𝑂 𝑔 = Number of filaments, d = Filament diameter D = Strand diameter January 31, 2019 IIFC Magnet meeting presentation | SSR2 lenses For PIP-II
QUENCH ANALYSIS • Although the total stored magnet Energy of 14KJ is small, the Quench analysis needs to be carried out to verify the maximum hot spot temperature and the maximum coil to ground voltage are within safe limits. • A quench circuit is defined to include main coil, bucking coils, dump resistance and coil-diodes. An inductance matrix is needed in the quench circuit for QUENCH analysis. • Inductance matrix of the sub-coils 4.82𝐼 −0.59𝐼 −0.59𝐼 • 𝐽 = −0.59𝐼 0.694𝐼 0.082𝐼 −0.59𝐼 0.082𝐼 0.694𝐼 • To compute the maximum temperature after quench, a heat flux is introduced at the point of maximum magnetic field to initialize a quench. January 31, 2019 IIFC Magnet meeting presentation | SSR2 lenses For PIP-II
QUENCH ANALYSIS • Material properties for quench analysis: • In the present case an external heat source has been defined at peak magnetic field location to study the effect of quench. • Resistance growth and peak voltage was derived from the loops defined in the circuit. • To simplify quench analysis, existence of liquid helium, insulation between the bobbin and the coil, and the stainless steel keys around the coil were ignored, which is a conservative assumption because in reality they will absorb heat from the coil when quench happens. The actual maximum temperature due to quench should be lower than calculated. In the event of quench, the coil is protected by an external dump resistor. The dump resistance is 0.010 Ω for both the main coil and the bucking coil. The overall resistance of the connections, including the internal bus bars, current leads, and external connections with the dump resistor, is assumed to be 2.0x 10 -4 Ω . January 31, 2019 IIFC Magnet meeting presentation | SSR2 lenses For PIP-II
QUENCH INITIATED IN MAIN COIL Quench initiated at t=0.1s Quench propagation at t=0.105s Quench propagation at t=0.175s Quench propagation at t=0.3s Quench propagation at t=0.5s Quench propagation at t= 20 s January 31, 2019 IIFC Magnet meeting presentation | SSR2 lenses For PIP-II
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