The linear 2D interpolation is utilized to map the magnetic field calculated from the FEM analysis into the thermal and quench analysis. To find a value at position (x, y) in
Appendix A. Numerical Treatments
a 2D plane, firstly, four points surrounding the point of (x, y) is found to be (x0, y0), (x1, y0), (x1, y1) and (x0, y1). Then, the weight along the x-axis can be calculated as
w1(x) =u(x0, y0) + u(x1, y0)−u(x0, y0)
y1−y0 ·(x−x0) (A.11) w2(x) =u(x0, y1) + u(x1, y1)−u(x0, y1)
y1−y0 ·(x−x0) (A.12) where u(x, y) is the value at position of (x, y). Using these weights, the value at position (x,y) can be determined as
u(x, y) =w1(x) + w2(x)−w1(x)
y1−y0 ·(y−y0) (A.13)
Appendix B
Critical Current of ReBCO coated HTS Tape
The critical current of ReBCO tape (SuperPower, SCS4050) is measured with an applied magnetic field until 15.5 Tesla in the Institute for Materials Research (IMR) at Tohoku University. The critical current has been measured when the magnetic field is parallel to the c-axis of ReBCO tape, and the experiment is still ongoing, thus the detail of the experiment will not be presented in this thesis besides the data analysis.
Magnetic Field [Tesla]
0 2 4 6 8 10 12 14
Critical Current [A]
0 50 100 150 200 250 300 350 400 450 500
77 K 80 K
83 K 73 K
67 K 40 K
20 K 5 K
Magnetic Field [Tesla]
0 2 4 6 8 10 12 14
n-value
0 20 40 60 80 100
120 77 K 80 K
83 K 73 K
67 K 40 K
20 K 5 K
Figure B.1: The measurement data of critical current (left) andn-value (right). The solid line is the function fitted with the measurement data.
Table B.1: Fit parameters for ReBCO tape.
Item Tc0 [K] Bc20 [Tesla] C0 α β γ n
Critical current 91.66 53662.99 12442497.34 0.8637 4102.04 2.384 0.996 n-value 91.66 150 9658.6 0.891 0.813 1.522 0.274 Figure B.1 shows the measured data of critical current with various magnetic field and n-value. Each critical current and n-value is extracted by fitting the V-I characteristic with the fit function (D.1). Same with the NbTi, the equation (3.17) is employed to fit
Appendix B. Critical Current of ReBCO coated HTS Tape
the measured data for ReBCO tape, and the fit parameters are listed in Table B.1. Since the n-value is also a function of magnetic field and temperature, it is fitted with the same function. It is noted that the critical current Ic is directly fitted with the equation (3.17), therefore, there are no meanings for the fit parameters given in Table B.1.
Appendix C
Quench Simulation for ATLAS Central Solenoid
In Chapter 5, the quench characteristics is studied for a conduction-cooled solenoid. As for the quench simulation for the accelerator, the adiabatic condition is usually considered to estimate the maximum temperature after the magnet quench. However, the effect of the aluminum strips plays a significant role in the case that the aluminum strips are inserted since the quench propagation is accelerated. In our case, the quench propagation in a coil cannot be treated as an adiabatic condition, and the effect of heat transfer is considered.
For the prior study of the quench in the aluminum strip based solenoid, M. Wake et al.
has compared the quench simulation with the experimental measurement for the ATLAS central solenoid [119]. However, the simulation model is not clear in their study, in which the effect of aluminum strip is not include and the current sharing is not considered. In this work, we also simulated with a model of the ATLAS central solenoid to validate and debug the simulation code.
C.1 Simulation Model
In this simulation, the main coil parameters are derived from the quench test for the ATLAS central solenoid as described in Ref. [106]. As shown in Fig. C.1, the solenoid is wound with an aluminum-stabilized NbTi superconducting cable, and the pure aluminum strips attached to the inner surface of solenoid are employed as the quench propagators, which is similar to the magnets in the COMET experiment.
The aluminum-stabilized conductor with size of 30 × 4.25 mm2 is insulated with two layers of UG (Upilex / glass-EPP) insulation tape impregnated with the epoxy resin (XD911). The aluminum strip with a thickness of 1.2 mm and RRR of 3000 is
ground-insulated with two layers of GUG (glass / Upilex / glass) insulation. All the material of insulation is assumed to be polyimide (Kapton) in this simulation. Along the azimuthal direction, totally 72 pieces of aluminum strip with a width of 100 mm are inserted.
The solenoid is operated at 4.5 K with nominal current flowing of 7600 A. The peak field in winding is given in Ref. [80] to be 2.6 Tesla at operating current of 7730 A and 2.7 Tesla at operating current of 8400 A. The field is assumed to be uniform to be 2.6 Tesla
Appendix C. Quench Simulation for ATLAS Central Solenoid
IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 16, NO. 2, JUNE 2006 533
Quench Characteristics of the ATLAS Central Solenoid
R. J. M. Y. Ruber, Y. Makida, M. Kawai, S. Mizumaki, G. Olesen, H. H. J. ten Kate, and A. Yamamoto
Abstract—A thin superconducting solenoid has been constructed for ATLAS, one of the four LHC experiments at CERN. The single layer coil wound with an Al stabilized NbTi superconductor, with overall dimensions of 5.3 m length and 2.6 m diameter and oper-ating at 7.6 kA provides the 2 T magnetic field for the inner de-tector. The coil was successfully tested at the company before ship-ment and re-tested at CERN on surface in its final configuration before commencing the installation in the ATLAS cavern 100 m underground. The tests include an extensive study of the quench evolution and in particular the normal zone propagation through the coil windings and in the superconducting bus-lines. A special feature of this coil is the use of aluminum quench propagation strips glued to the windings inner surface. This design enhances the turn-to-turn normal zone propagation velocity, reaching up to 0.8 m/s, and limits the hot spot temperature to 110 K. Along the conductor, normal zone propagation reaches velocities up to 14 m/s at nominal current.
Index Terms—Detector magnet, hot spot temperature, NbTi/Al superconductors, normal zone propagation, quench.
I. INTRODUCTION
T
HE CENTRAL Solenoid provides an axial magnetic field of 2 T in a 2.3 m diameter warm-bore for the ATLAS inner detector trackers [1]. The main parameters of the Cen-tral Solenoid are listed in Table I. The solenoid has a stored energy of 39 MJ, a cold mass of 5.6 tonnes and a thickness of 45 mm equivalent to 0.66 radiation length. For the coil to be this thin, it is wound with a single layer of specially devel-oped high-strength aluminum stabilized NbTi superconductor [2]. A cross-section of the coil design is shown in Fig. 1. The coil is installed in the same cryostat as the barrel electro-mag-netic calorimeter, the so-called barrel cryostat. It is attached to the inner warm vessel of the barrel cryostat by 23 triangular sup-ports made of GFRP. These are arranged in such a way that one side of the coil is fixed and the other sliding in axial direction [3]. The cryostat is surrounded by the hadron calorimeter which also serves as a return yoke for the magnetic flux.II. AIR-CORETESTSET-UP
The Central Solenoid has been tested twice: at the factory site in Japan [4] and at the integration hall in CERN [5]. These tests were always performed in an air-core environment, whereas the final installation in the ATLAS detector will include an iron
Manuscript received September 20, 2005.
R. J. M. Y. Ruber, G. Olesen, and H. H. J. ten Kate are with CERN, CH-1211 Geneva 23, Switzerland (e-mail: ruber@cern.ch).
Y. Makida, M. Kawai, and A. Yamamoto are with KEK, Tsukuba 305-0801, Japan.
S. Mizumaki is with Toshiba Co., Tsurumi, Yokohama 230-0045, Japan.
Digital Object Identifier 10.1109/TASC.2006.873349
TABLE I
MAINPARAMETERS OF THECENTRALSOLENOID
Fig. 1. Cross-section of the coil, showing support cylinder, end flange, con-ductor turns, insulation and pure aluminum strip quench propagators.
calorimeter that functions as a magnetic flux return yoke. For the test at the factory site, the solenoid was installed in a temporary cryostat, while the test at CERN was done with the final cryostat including the surrounding liquid argon calorimeter that func-tioned as part of the thermal screen. For both tests, the chimney (transfer line) connecting coil to proximity cryogenics and cur-rent leads was mounted horizontally, as opposed to its final ver-tical mounting position.
The main purpose of these tests was to verify operation of the solenoid at nominal field and study of the intrinsic safety of the design. In the ATLAS detector set-up the nominal operational field of the solenoid is 2.0 T at a current of 7.6 kA. In the air-core test set-up, a current of 8.0 kA is required to reach the 2.0 T field.
The maximum applied test current is 8.4 kA.
III. INSTRUMENTATION ANDQUENCHPROTECTION
The solenoid is equipped with voltage taps, temperature sen-sors, superconducting quench detectors and pick-up coils [4].
Quench protection heaters (QPHT, ) are installed
1051-8223/$20.00 © 2006 IEEE
Figure C.1: Cross-sectional view of the ATLAS central solenoid [120].
in our simulation. A hot spot is set in the middle of coil with the heat generation of 6.4 W in a duration of 1 sec. Table C.1 shows the coil parameters used in this quench simulation. The quench test for ATLAS central solenoid has been preformed with and without a protection of quench back heater. Here, we only compare the case without the protection of quench back heater. The algorithm of quench simulation is same as the description in Chapter 5.