Analysis of Uncertainties in Protection Heater Delay Time Measurements and Simulations in Nb₃Sn High-Field Accelerator Magnets

The quench protection of superconducting high-field accelerator magnets is presently based on protection heaters, which are activated upon quench detection to accelerate the quench propagation within the winding. Estimations of the heater delay to initiate a normal zone in the coil are essential for the protection design. During the development of Nb$_{3}$Sn magnets for the LHC luminosity upgrade, protection heater delays have been measured in several experiments, and a new computational tool CoHDA (Code for Heater Delay Analysis) has been developed for heater design. Several computational quench analyses suggest that the efficiency of the present heater technology is on the borderline of protecting the magnets. Quantifying the inevitable uncertainties related to the measured and simulated delays is therefore of pivotal importance. In this paper, we analyze the uncertainties in the heater delay measurements and simulations using data from five impregnated high-field Nb$_{3}$Sn magnets with different heater geometries. The results suggest that a minimum variation of 3 ms or 20% should be accounted in the heater design for coil outer surfaces and at least 10 ms or 40% in the inner surfaces due to more uncertain heater contact. We also propose a simulation criterion that gives an upper bound enclosing 90% of the measured delays for heaters on the coil outer surface

Analysis of Uncertainties in Protection Heater Delay Time Measurements and Simulations in Nb3_{3}Sn High-Field Accelerator Magnets

The quench protection of superconducting high-field accelerator magnets is presently based on protection heaters, which are activated upon quench detection to accelerate the quench propagation within the winding. Estimations of the heater delay to initiate a normal zone in the coil are essential for the protection design. During the development of Nb$_{3}$Sn magnets for the LHC luminosity upgrade, protection heater delays have been measured in several experiments, and a new computational tool CoHDA (Code for Heater Delay Analysis) has been developed for heater design. Several computational quench analyses suggest that the efficiency of the present heater technology is on the borderline of protecting the magnets. Quantifying the inevitable uncertainties related to the measured and simulated delays is therefore of pivotal importance. In this paper, we analyze the uncertainties in the heater delay measurements and simulations using data from five impregnated high-field Nb$_{3}$Sn magnets with different heater geometries. The results suggest that a minimum variation of 3 ms or 20% should be accounted in the heater design for coil outer surfaces and at least 10 ms or 40% in the inner surfaces due to more uncertain heater contact. We also propose a simulation criterion that gives an upper bound enclosing 90% of the measured delays for heaters on the coil outer surface

Measurements and Analysis of Dynamic Effects in the LARP Model Quadrupole HQ02b During Rapid Discharge

This paper presents the analysis of some quench tests addressed to study the dynamic effects in the 1-m-long 120-mm-aperture Nb$_{3}$Sn quadrupole magnet, i.e., HQ02b, designed, fabricated, and tested by the LHC Accelerator Research Program. The magnet has a short sample gradient of 205 T/m at 1.9 K and a peak field of 14.2 T. The test campaign has been performed at CERN in April 2014. In the specific tests, which were dedicated to the measurements of the dynamic inductance of the magnet during the rapid current discharge for a quench, the protection heaters were activated only in some windings, in order to obtain the measure of the resistive and inductive voltages separately. The analysis of the results confirms a very low value of the dynamic inductance at the beginning of the discharge, which later approaches the nominal value. Indications of dynamic inductance variation were already found from the analysis of current decay during quenches in the previous magnets HQ02a and HQ02a2; however, with this dedicated test of HQ02b, a quantitative measurement and assessment has been possible. An analytical model using interfilament coupling current influence for the inductance lowering has been implemented in the quench calculation code QLASA, and the comparison with experimental data is given. The agreement of the model with the experimental results is very good and allows predicting more accurately the critical parameters in quench analysis (MIITs, hot spot temperature) for the MQXF Nb$_{3}$Sn quadrupoles, which will be installed in the High Luminosity LHC

Axial-Field Magnetic Quench Antenna for the Superconducting Accelerator Magnets

We have developed and tested a novel magnetic inductive antenna for detecting and localizing quenches and flux jumps in superconducting accelerator magnets during ramping and steady-state operations. The antenna principle is based upon sensing temporal variation of the axial field gradient in the magnet bore that is specific to propagating quench. Two antenna configurations were developed and built, optimized respectively for sensing disturbances of the off-axis (for the dipole magnet) and axial (for the quadrupole magnet) gradient of the axial field. The antennas were qualified during tests of LBNL's high-field dipole, HD3b, and LARP's Nb$_{3}$Sn quadrupole HQ02b. A reliable and accurate localization of quenches and flux jumps was demonstrated. Upon ramping up the magnet current, we observed peculiar dynamics of the magnetic disturbances travelling along the cable at velocities of ~800 m/s. Also, details of slow quench propagation in the HQ02 quadrupole at a small fraction of operational current were detected and recorded

Testing of a Single 11 T Nb3SnNb_3Sn Dipole Coil Using a Dipole Mirror Structure

FNAL and CERN are developing an 11 T Nb$_{3}$Sn dipole suitable for installation in the LHC. To optimize coil design parameters and fabrication process and study coil performance, a series of 1 m long dipole coils is being fabricated. One of the short coils has been tested using a dipole mirror structure. This paper describes the dipole mirror magnetic and mechanical designs, and reports coil parameters and test results

Analysis of Field Errors for LARP Nb3_3 Sn HQ03 Quadrupole Magnet

The U.S. large hadron collider (LHC) Accelerator Research Program, in close collaboration with The European Organization for Nuclear Research (CERN), has developed three generations of high-gradient quadrupole (HQ) Nb3Sn model magnets, to support the development of the 150 mm aperture Nb3Sn quadrupole magnets for the high-luminosity LHC. The latest generation, HQ03, featured coils with better uniformity of coil dimensions and properties than the earlier generations. The HQ03 magnet was tested at fermi national accelerator laboratory (FNAL), including the field quality study. The profiles of low-order harmonics along the magnet aperture observed at 15 kA, 1.9 K can be traced back to the assembled coil pack before the magnet assembly. Based on the measured harmonics in the magnet center region, the coil block positioning tolerance was analyzed and compared with earlier HQ01 and HQ02 magnets to correlate with coil and magnet fabrication. To study the capability of correcting the low-order nonallowed field errors, magnetic shims were installed in HQ03. The expected shim contribution agreed well with the calculation. For the persistent-current effect, the measured a4 can be related to 4% higher in the strand magnetization of one coil with respect to the other three coils. Finally, we compare the field errors due to the interstrand coupling currents between HQ03 and HQ02