A Conduction-Cooled Superconducting Magnet System-Design , Fabrication and Thermal Tests

A conduction-cooled superconducting magnet system with an operating current of 105.5 A was designed, fabricated and tested for material processing applications. The magnet consists of two coaxial NbTi solenoid coils with an identical vertical height of 300 mm and is installed in a high-vacuumed cryostat. A two-stage GM cryocooler with a cooling power of 1.5 W at 4.2 K in the second stage is used to cool the system from room temperature to 4.2 K. In this paper, the detailed design, fabrication, thermal analysis and tests of the system are presented.


Introduction
Many research areas have benefited from the application of high field superconducting magnets.Particularly, magnetic field effects have recently been observed for material, chemical, and biological systems [1], [2].A high field magnet system with a wide warm bore is convenient for researchers to carry out material processing experiments, because it provides enough space to install samples, as well as the cooling, heating and monitoring systems [3].Conduction-cooled superconducting magnets have become increasingly popular in research and industry due to their ease and simplicity of operation as compared to traditional superconducting magnets immersed in liquid helium (LHe) [4], [5].
In 1983, Hoenig.M. first demonstrated a thermal design of the conduction-cooled superconducting magnet combined with GM cryocoolers [6].However, due to the heat leakage through copper current leads, only Nb 3 Sn superconductors could be used, and the magnet could only carry a current of 40 A. The development of high-temperature superconductors, along with the progress of cryocoolers, has enabled large-scale applications of conduction-cooled superconducting magnets [7].It is expected that the conduction-cooled solution may replace the conventional solution utilizing liquid helium in the near future.
A conduction-cooled superconducting magnet system was designed, fabricated and tested for material processing applications in the Applied Superconductivity Laboratory, Institute of Electrical Engineering, Chinese Academy of Sciences (IEE, CAS).The magnet has a warm bore of Ø 250 mm and a maximum central field of 4.5 T. This paper presents the detailed design, fabrication, thermal analysis and tests.In addition, the AC losses generated during charging are estimated.The 3D cross-sectional view of the superconducting magnet system is illustrated in Fig. 1.Two NbTi solenoid coils are wound coaxially with an identical vertical height of 300 mm.The two coils are electrically connected in series, and a single power supply is used to provide the operating current of 105.5 A. Fig. 2 shows the flux density distribution along the central axis.The maximum central field is 4.5 T, with 1.5 T contributed by the inner coil and 3 T by the outer coil.Detailed parameters are listed in Table 1.

Fabrication and assembly
Wet-winding technology is adopted to fabricate the superconducting coils.The coils are wound onto a brass former, which not only has a robust mechanical strength but a relatively high thermal conductivity at 4.2 K [3].The former has a 2 mm wide slot along the axial direction in order to reduce the eddy current loss during charging.A 1 mm thick polyimide insulation layer is coated on the outside surface of the brass former.The first layer of the inner coil is directly wound on the insulation layer but not bonded to it.
During the winding, the DW-3 epoxy resin is used to impregnate the coils and fill the space between superconducting wires.To improve the thermal conductivity, aluminium nitride (AlN) powder is added into the epoxy resin with a weight ratio of 1:2 [8]. 10 mm thick fiberglass saturated with epoxy resin is wound onto the outer surface of the inner coil, and the outer coil is then wound directly onto the fiberglass and bonded to it.
After the outer coil is finished, Ø 1 mm stainless steel wire is applied as an overbinding layer to support the electromagnetic force in the coils [4].The coils are then moved to a furnace for curing.After 8 hours at 60℃, the epoxy is cured and the coils are ready to be assembled and installed in the cryostat.
The configuration of the system is schematically shown in Fig. 3.The magnet is covered by a radiation shield and wrapped with multi-layer insulation (MLI) to minimize thermal radiation.An off-the-shelf two-stage GM cryocooler RDK-415D with 50 W at 50 K in the first stage and 1.5 W at 4.2 K in the second stage is used to cool the system.The first stage of the cold head is rigidly attached to the radiation shield, whereas the second stage is connected to the magnet through a flexible copper braid.This arrangement ensures the highest possible heat removal rate in the first stage where both temperatures and heat loads are greater, while still permitting different thermal contraction between components as the apparatus cools from room temperature [9].During the assembly, 0.1 mm thick indium foils are placed between the contact surfaces to reduce the thermal contact resistance.The binary current lead, a combination of a copper conductor in the high-temperature section and an HTS conductor in the low-temperature section, is employed to reduce the heat load in the second stage [7].The apparatus is installed in a vacuum vessel and suspended by G-10 supporting rods.

Thermal analysis
To ensure the operating temperature, heat loads of the system must be limited.There are four different heat loads: thermal conduction through the supporting rods, thermal radiation, conduction heat leakage from residual gas, and heat transferred from current leads [10].

Heat loads calculation
Thermal conduction can be easily determined by Fourier's Law expressed below: ( ) where Q c is the thermal conduction; T H and T C are the temperatures in the high and low-temperature terminal, respectively; A and L are the cross section area and the length of the component; ( ) T λ is the temperaturedependent thermal conductivity.The thermal conductivity of different materials can be found in [11].
The radiation shield in the system operates at an intermediate temperature and 16 layers of MLI are wrapped around the shield.The radiation heat load can be calculated by: where Q r is the radiation heat load; ε is the emissivity of the material, the typical value of which is 0.05 [12]; σ is the Stefan-Boltzmann constant which equals 5.67 × 10 -8 W• m -2 • K -4 ; S denotes the area of the cold body and n is the number of layers of MLI; T 1 and T 2 represent the high and low temperatures, respectively.T 1 is 300 K and T 2 is around 50 K for calculating the heat load of the first stage, while T 1 is 50 K and T 2 is 4.2 K for calculating the heat load of the second stage.The heat leakage of residual gas Q g can be approximately given by: where the constant c 0 is 1.2 for the air and the accommodation coefficient α is 0.5 [13].P is pressure in the vacuum vessel, and ∆T = T 1 ̶ T 2 is the temperature difference.
The heat transferred from the copper current leads Q CL is the sum of conduction heat and the Joule heat.It can be determined by: where L 0 is Lorenz constant and it equals 2.445 × 10 -8 W • Ω / K 2 ; I is the transporting current.T H and T C are 300 K and 50 K, respectively.The HTS current leads are CSL12/80.3,supplied by CAN Superconductors, s.r.o.The heat leakage from 64 K to 4 K is 0.12 W per pair.
Through ( 1) to ( 4) and based on the specifications of the system, the heat loads of the first and second stages are determined to be 15.2 W and 0.3 W, respectively.The heat loads of each stage match the cooling capacity of the GM cryocooler with sufficient margin.A finite element (FE) thermal model is built based on ANSYS software.SOLID90, a 3-D, 2nd-order, 20-node element is employed in the model [14].Fig. 4 and Fig. 5 are the simulated temperature distributions in the shield and the coils, respectively.

Thermal simulation
It can be seen that the temperature distribution in the shield is inhomogeneous and the temperature difference is 2.5 K. Fig. 5 shows that the temperature difference in the superconducting coils is less than 0.1 K, and the temperature of the inner coil is slightly higher than that of the outer coil, which is due to the fiberglass layers between the two coils.
The temperature difference between the second stage and the top end plate of the magnet is simulated as 0.2 K, resulting from the thermal resistance of the copper braid as well as the thermal contact resistance in the interfaces.

AC losses during charging
It is complex to accurately calculate AC losses in real situations.In this paper, we make a ballpark estimate based on some widely-accepted empirical formulas in [15], [16].Because of the tiny slot in the brass former, the eddy current loss is very small and is ignored during charging [17].The AC losses considered here include hysteresis loss and coupling loss.Each loss contribution is calculated separately, and the total AC losses are treated as the sum of these contributions.
The hysteresis loss P hy (W/m 3 ) is estimated by: where r f is the filament radius of the superconducting wires; dB/dt is the changing rate of flux density; J op and J c are the operating and critical current densities, respectively.J c is a function of temperature and flux density, which is described in Fig. 6.where µ 0 is the air permeability and t is the time The system is equipped with six temperature sensors.The locations of these sensors are indicated in Fig. 8.The cryocooler started working when the cryostat was pumped down to the range of 10 -4 mbar.It took approximately 80 hours to cool the magnet from room temperature to the 4 K level.
Fig. 9 shows the cooling process of the system.After the system was stabilized, the temperatures T5 at the top end plate and T6 at bottom end plate reached 6.4 K and 4.8 K, respectively.The temperatures T1 in the first stage and T2 in the second stages were 52.1 K and 3.5 K, respectively.T5 was 1.8 K higher than T6, which was also observed in other repeated tests.It was speculated that the temperature sensor at the top end plate of the magnet was not installed or calibrated properly.

Charging
The current was increased by 0.02 A/s up to 80 A, and then by 0.015 A/s to 105.5 A. The temperatures of the second stage and the magnet versus time during charging are shown in Fig. 10.It can be seen that the AC losses result in a temperature increase of 0.7 K in the magnet.The big difference between T5 and T6 could be due to improper installation or calibration of the temperature sensor.

Conclusions
A conduction-cooled superconducting magnet system with a Ø 250 mm warm bore was successfully fabricated.The superconducting magnet could steadily transport a current of 105.5 A and generate a maximum central field of 4.5 T. The heat loads of the first and second stages were 15.2 W and 0.3 W, respectively.The AC losses during charging resulted in a temperature increase of 0.7 K in the magnet.The performance of the system was proved to be satisfying.

Fig. 4 -
Fig. 4 -Temperature distribution in the shield.The left and right holes are the warm bore and the position of 1st stage of the cold head, respectively.

Fig. 6 -
Fig. 6 -Critical current density of NbTi superconductor with respect to the flux density under different temperatures The coupling loss P cp (W/m 3 ) is calculated based on:2

Fig. 9 -
Fig. 9 -Cooling process of the system

Fig. 10 -
Fig. 10 -The temperature increase during charging.T2, T5, T6 are the temperatures in the second stage, top end plate and bottom end plate, respectively.

Table 1 -
Parameters of the superconducting magnet