Thermal Properties of LARP Type Nb3Sn Superconducting Magnet Coil Electrical Insulation in Pressurized Superfluid Helium

The development of new generation, high-performance devices, such as MRI scanners or high-energy accelerators, (may be attributed to the use of) Nb3Sn based superconducting (SC) magnets, which are characterized by their ability to produce much higher magnetic fields than the presently used NbTi-based magnets. Due to the wind-and-react technology of the production of Nb3Sn magnets, new methods and materials for the magnet coil electrical insulation are required. The proper design of SC magnets demands the characterization of thermal properties of the new insulation materials, inter alia, in superfluid helium conditions. This paper provides experimental data of the thermal conductivity and Kapitza resistance for S-glass fiber reinforced ceramic-epoxy (LARP type) electrical insulation, measured in pressurized (at 1 bar pressure) superfluid helium in a temperature range of 1.50-2.00 K.

heat from the magnet coil to the magnet coolant. Those requirements are fully complied by Kapton polyimide commonly used in the NbTi magnets. Nevertheless, due to the application temperature of Kapton at up to 400 • C, this material is not suitable for the Nb3Sn magnet wind-andreact production technique, which requires a heat treatment of approximately 650 • C. Therefore, for the further development of Nb3Sn-based technology, new materials and methods for magnet coil electrical insulation are required.
Within the European Coordination for Accelerator Research and Development (EuCARD) program, four potential materials for Nb3Sn magnets coil electrical insulation have been selected and thermally characterized in pressurized superfluid helium (HeIIp) conditions. The thermal conductivity and Kapitsa resistance for Sglass fiber reinforced epoxies (RAL Mix 71, RAL Mix 237), as well as for cyanate ester epoxy resin (CE epoxy) have already been published [1,2]. Here, the data for S-glass-ceramic-epoxy laminate (LARP type) are presented.

Test Method Principle
The thermal properties of the tested material have been determined by the so-called "drum method", as schematically presented in Fig. 1 In the considered case, the heat Q s is transferred between the separated volumes by Kapitza conductance from the heated volume to one surface of the sample. It then goes through the sample material via heat conduction, and then via Kapitza conductance from the second sample surface to the isothermal (constant T b ) volume. This may be expressed as follows: where h k is the Kapitza coefficient [W/m 2 K n ], and n is the dimensionless Kapitza heat transfer exponent, while kis the heat conduction coefficient of the sample material [W/mK], and T 1 and T 2 [K] are the temperatures of the sample surface from the heated volume and the isothermal volume side, respectively. For very small temperature differences between the separated volumes (T i − T b = T << T b ), the Kapitza conductance can be linearized, and (1) can be written in the following form: As T << T b , it can be considered that T i ≈ T b , and: where R s [m 2 K/W], is the total thermal resistance of the heat transfer through the tested sample. It can be found from (3) that for small T , the total thermal resistance is the sum of twice the Kapitza resistance R K and the solid conduction resistance R C .

The Sample Holder
The sample holder (see the schematic construction in  The capillary also carries 12 0.2-mm diameter instrumentation wires, four for the temperature sensor, four for the heater, and four for spear wires, which create a further limitation in area for HeIIp heat conduction.

Test and Data Fitting Procedure
In order to determine the Kapitza resistance and thermal conductivity of the tested materials, a superfluid helium cryostat from the Wroclaw University of Technology was used. Three different thicknesses of the LARP material sheet were tested: 145±7, 250±6, and 367±11 μm. The sample holders were placed inside the cryostat measurement vessel, where the HeIIp bath temperature (T b ) was controlled at a constant level. The total T b error, accounting for the electronic readout and sensor-characteristic fitting errors, is assumed as ±1.0 mK, while the T b stabilization was better than ± 0.25 mK . Materials were tested at seven different T b levels in the range of 1.5-2.0 K. At the given bath temperature, heat Q dissipated inside each holder in a range of 0-70 mW with a 2-mW ramp. The heat was generated with the use of the KEITH-LEY 2400 source meter with an accuracy better than 0.1 % of the heat value. The temperature of the inner volume T i was recorded in steady state conditions (T i stabilization better than 0.25 mK) at a given value of Q. The total error for the T value, determined as T i at Q = 0 and T i at the given Q value, can be assumed as ± 0.5 mK. The Q transferred from the sample holder inner volume to the HeIIs bath is the sum of the heat transferred through the sample material Q s , through the holder material Q hold and through the capillary Q cap . The Q hold calculations, performed with the FE method, show that it varies from 2.5 % of Q for 145-μm thick sample to 4.5 % of Q for 367 m. The capillary heat loss was calculated for each T value and accounted for in further analysis with an assumed precision of ± 20 %, as an exact capillary cross-section area for helium conductance is difficult to determine. Figure 3 presents an exemplary plot of the total thermal resistance R s values in function of T , where the R s is calculated in accordance to (4). A detailed analysis of the total error composition shows that it is dominated by T error, as well as error resulting from the linearization of the (1), which can be found from (4): The sum of the remaining errors is comparatively small and can be considered to be systematic error. As seen from Figs. 3 and 4, the R s error value is large for T < 15 mK and for T > 80 mK. In order to minimize total error, the average value of R s with the average R s error values from the range of 20 mK > T 50 mK is taken for further analysis. The next step of the analysis is the preparation of the R ssample thickness graph for the given T b level-see Fig. 5. In this graph, R s points, fitting the line slope, stand for

Results and Discussion
In Figs. 6 and 7, thermal conductivity and the Kapitza resistance value in the function of T b in comparison with data obtained for Mix 71, Mix 237, and CE-epoxy materials are presented. It can be found that the LARP material is characterized by the lowest thermal conductivity: 25-35 % lower than Mix 237 and 10-30 % lower than CE-epoxy. On the other hand, the Kapitza resistance is very similar to the value for Mix 237 but 25 % lower than for CE-epoxy.