7 T Niobium-Titanium based Persistent-Mode Superconducting Magnet for an Electron Beam Ion Source

A high field magnet is a key element of cryogenic electron beam ion sources (EBISs), which are known for generating highly charged ions through the magnetic compression of an electron beam. Herein, we report the design, fabrication, and evaluation of a 7 T niobium-titanium (Nb-Ti) superconducting magnet capable of persistent-mode operation. The magnet was designed using finite element analysis by considering its magnetic, thermal, and mechanical properties. The designed magnet was then fabricated, assembled, and evaluated for various design parameters in a recondensing-type liquid helium cryostat. After several quench trainings, the magnet reached a target magnetic field of 7 T with an operating current of 200 A, a magnetic field uniformity of 0.24%, and an electron beam focusing length of 1.3 m inside the bore. The magnet was successfully operated in the persistent-mode for 9.5 days (228 hours) and achieved a field-decay rate of 0.42 ppm∙h-1. The magnet evaluation results confirm that our superconducting magnet system can be applied to an EBIS to carry out stable and effective electron beam compression.


I. INTRODUCTION
An electron beam ion source (EBIS) is known for producing highly charged ions (HCIs) [1]- [6]. To create a high-density electron that improves the quality of HCIs, it is essential that the electron beam focusing is present within an EBIS [1], [7], [8]. A sufficiently strong and uniform magnetic field is functionally required, therefore, for focusing the electron beam within an EBIS [3], [9]- [11]. Two types of EBIS exist: a room-temperature EBIS, in which the magnetic field is generated using permanent magnets and a cryogenic EBIS, in which the magnetic field is generated using a superconducting magnet.
In cryogenic EBISs, a niobium-titanium (Nb-Ti) based liquid helium (LHe) cooled superconducting magnet generates a strong and uniform magnetic field, which efficiently focuses the electron beam [2]. Alessi et. al. reported a 5 T superconducting magnet for an EBIS manufactured by ACCEL Instruments GmbH (now Bruker Advanced Supercon GmbH) [12]. The magnet exhibited features of a warm bore of 204 mm, a length of 2 m, and a field uniformity of ±0.5% over the trap length of 1.5 m. Kondrashev et. al. also reported a 6 T superconducting magnet for an EBIS [13]. The magnet exhibited a warm bore of 155 mm and a length of 1 m [14]. In addition, J. Zhu et. al. reported a 4.5 T superconducting magnet for an electron beam ion trap with the persistent-mode operation [15]. The magnet exhibited a warm bore of 75 mm, a length of 75 mm, and a field homogeneity of ±200 ppm over the trap length of 20 mm. In recent years, the price of LHe continuously increased, and this trend is expected to continue [16]- [18]. Therefore, to minimize the need to frequently refill the cryostat of the superconducting magnet, developing a recondensing-type LHe cryostat for an EBIS system is highly desirable [19]. Recently, a 5 T superconducting magnet was developed and installed in an LHe recondensing-type cryostat for an EBIS at Brookhaven National Laboratory [20], [21]. The magnet exhibits features of a warm bore of 215 mm, a length of 2.3 m, and a field uniformity of ±0.5% over the trap length of 1.5 m. To further improve the performance of an EBIS such as the smaller electron beam radius, however, an Nb-Ti magnet with a higher magnetic field and spatial uniformity is required [3]. Because the high inductance of the magnet for EBIS causes a long current charging time, it is necessary to improve the operation efficiency by applying the persistentmode. If an Nb-Ti magnet also adopts the persistent-mode in an LHe recondensing-type cryostat, it would considerably reduce the operational cost of the system and the heat input into the cryostat [18], [19], [22].
In the present study, we design, fabricate, and evaluate a 7 T Nb-Ti based persistent-mode superconducting magnet for an EBIS. Our magnet exhibits a warm bore of 204 mm, a length of 2 m. Also, depending on the operaitng time and beam physics, field-decay rate of less than 1 ppm ⋅ h -1 and field uniformity of below ±0.3% over a trap length of 1.3 m were required. We evaluate the performance and crosssection of the procured Nb-Ti wire. By considering the performance of the wire, the coil is designed and analyzed with a focus on magnetic field uniformity and the distribution of radial and hoop stresses within the winding pack. The switching times of persistent current switch (PCS) are estimated using finite element analysis (FEA). Following the design, both the magnet and PCS are fabricated using the wet winding method. Finally, the transport current, field uniformity, and persistent-mode capability of the fully assembled magnet are systematically evaluated.

II. NIOBIUM-TITANIUM SUPERCONDUCTING WIRE FOR AN ELECTRON BEAM ION SOURCE
A rectangular multifilament Nb-Ti/Cu (copper) wire for winding the magnet was procured from Luvata [23]. The rectangular wire was selectively chosen to improve the filling factor of the winding pack. First, the transverse cross-section of the wire was observed using an optical microscope, as shown in Fig. 1(a). The formvar insulated wire measured 1.4  0.95 mm. The wire exhibited 78 inner filaments (each 80 µm in diameter), a 2.4:1 ratio of copper (Cu) to superconductor, and a Young's modulus of ~100 GPa (<100 K). To observe the selected area of the wire more closely, the detailed scanning electron microscope (SEM) was also carried out. The SEM image of the selected area of the wire is shown in Fig. 1(b), along with the corresponding electron dispersive X-ray spectroscopy (EDS) element maps and line spectrums of one of the filaments. As can be seen in Fig.  1(b), the filaments were composed of Nb-Ti/Cu, and the matrix material was pure Cu. Next, the critical current (Ic) of the Nb-Ti/Cu wire was measured in different magnetic fields at 4.2 K with an electric field criterion of 0.1 µV ⋅ cm -1 , as shown in Fig. 1(c). Based on the Ic values, the corresponding critical current density (Jc) was also calculated. The Ic of the wire in the 7 T at 4.2 K was estimated to be 425 A, whereas, in 8 T, it was 312 A. The magnet was designed based on the wire performance.

A. NIOBIUM-TITANIUM MAGNET DESIGN
The superconducting magnet design aimed to meet the required electron beam focusing length of 1.3 m with a 7 T field and a field uniformity of <0.3% in the length along the central axis of the magnet. In this design, some design parameters were predetermined to assemble other pre-built accelerator components and beamline. Hence, the inner diameter (ID) and length of the magnet were fixed at 276 mm and 2 m, respectively. The thickness of the magnet bobbin was designed to be 8 mm to sufficiently withstand the mechanical stresses generated under the cryogenic and high magnetic field environments. The operating current was limited below 250 A. By considering these constraints, we designed the Nb-Ti superconducting magnet for an EBIS, as shown in Fig. 2. To adhere to the magnet's required design parameters, our design included a main coil and a set of correction coils, and the detailed design parameters are shown in Table I.
The magnetic field and structural stability of the designed superconducting magnet were evaluated by finite element analysis based on Table I. The thermal stability can be evaluated with the temperature margin, which is estimated by the operating point on the straight line for the critical temperature and critical current [24]. In our designed magnet, the temperature margin was ~2 K. The surface plot of the magnetic flux density norm of the magnet is shown in Fig.  3(a). As can be seen in the figure, the peak field in the magnet was calculated to be 7.1 T. Fig. 3(b) shows magnetic field density versus axial distance (z-axis) plots of the designed and deformed (thermal and magnetic stresses combined) model. As can be seen Fig. 3(b), the magnetic   field was maintained without field distortion due to deformation. The magnetic field uniformity was calculated by (Bmax-Bmin)/(Bmax+Bmin)×100%. The field uniformity along the beam focusing length was estimated to 0.24%, which is still within the required field uniformity of ±0.3% over a trap length of 1.3 m. A superconducting magnet is known to suffer from magnetic stress (called the Lorentz force) and, in cryogenic environments, thermal stress [24]- [26]. To ensure the mechanical stability of the solenoid, estimating the total combined stress (thermal and magnetic) was thus necessary.
In the designed solenoid model, stainless steel (SS) tension wire was banded to the outside of the solenoid to improve mechanical stability. The mechanical stress and stability in the solenoid magnet depending on the tension wire were estimated using magnetic-thermal-structural FEM analysis. Fig. 4 shows the radial and hoop stress distributions for the raxis direction at the center and at 350 and 750 mm along the z-axis in the solenoid. Also, these results were compared with and without SS tension wire. In Fig. 4(a), it can be seen that the radial stress distribution was compressive and applying the tension wire acts to contract more in the radial direction. Moreover, a solenoid magnet swells under the magnetic field due to the Lorenz force (hoop stress). Fig. 4(b) shows the hoop stress that acts on the circumferential direction of the winding with and without tension wire. The hoop stress was reduced with the tension wire, and its values were significantly lower than the yield strength of the Nb-Ti, which is ~310 MPa at 4.2 K [27]. This estimation indicates that the solenoids were mechanically more stable with SS tension wire.

B. PERSISTENT CURRENT SWITCH DESIGN AND FABRICATION
Due to the high inductance of the magnet, its operation efficiency is low with slow current ramping rate. To overcome this issue, the persistent-mode operation was applied to our magnet. By considering operating period in EBIS system, the field-decay rate in persistent-mode limited ppm ⋅ h -1 (1µT decay per hour). For this operation, we designed PCS to make closed-loop with Nb-Ti magnet. The operation of designed magnet was predicted with a current ramping rate of 0.02 A ⋅ s -1 and a power supply with a compliance voltage of 2.5 V. By considering these parameters, the PCS was designed with a 7.44 Ω resistance at 20 K to restrict the maximum leakage current to 0.17%. Nb-Ti/Cu-Ni (copper-nickel) wire has higher electrical resistance in a normal state than Nb-Ti/Cu wire [28], [29]. This means that Nb-Ti/Cu-Ni provides a smaller PCS coil and effectively limits the leakage current to the PCS. Thus, the Nb-Ti/Cu-Ni wire was used to design and fabricate the PCS. The PCS wire exhibited a diameter of 0.57 mm including an insulation of 0.07 mm, a resistivity of 1.24 Ω ⋅ m -1 at 20 K, and an Ic of 300 A in 3 T at 4.2 K. The PCS was installed away from the high field region to minimize the influence of the magnetic field. The total required conductor for the PCS was approximately 6 m in length. The designed PCS demonstrated an ID, outer diameter (OD), and height of 30, 33, and 18 mm, respectively. To make the PCS resistivity to charge the main magnet, a nichrome wire heater was wound inside the PCS coil. The heater wire exhibited a diameter of 0.203 mm and an electrical resistivity of 33.2 Ω ⋅ m -1 . To generate 1.48 W of heating power with a 110 mA heater current, the required length of the heater was ~3.67 m, and the total resistance was 121.89 Ω. Fig. 5 shows the rationally designed PCS and its schematic diagram. As can be seen in Fig. 5(a), Nb-Ti/Cu-Ni and nichrome wires were wound around the G10 structure.
For thermal insulation, Teflon was used on the outside of the Nb-Ti/Cu-Ni winding. An aluminum cover was designed to house the PCS for the rapid switching operation. The PCS temperature behavior was predicted by FEA, as shown in Fig. 5(b). As can be seen in the figure, we estimated that it would take 75 sec for the PCS to reach 20 K from 4.2 K after the heater was turned on; we estimated that it would take 125 sec for the PCS to cool down to 4.2 K after the PCS heater was turned off.

C. MAGNET MANUFACTURING
Based on our magnet design, we manufactured an Nb-Ti superconducting magnet for an EBIS, as shown in Fig. 6(a). The center part was composed of the main coil for the 7 T center field, and the end parts were composed of correction coils. For the coil winding, a wet winding method was used with Stycast insulation between wires. The Lorentz force in a solenoid coil causes an expanding strain. To reinforce this issue, the SS tension wire was wound on the outside of the coil, as shown in Fig. 6(b). Fig. 6(c) shows electrical components such as PCS (for persistent-mode operation), diodes (for coil protection), and Nb-Ti superconducting joints, as well as the corresponding electrical circuit diagram of the entire magnet system. For quench protection, as a passive method, adiabatic using the copper matrix of Nb-Ti wire, and cold diodes of 3.5 V were connected in parallel with both ends and the center tap of the coil. Specifically, five superconducting joints were applied to connect the magnet coils, and two joints were utilized to make a closed circuit between the PCS and the magnet. Our superconducting joint technology has been reported in a previous study [22].

IV. OPERATION TEST OF 7 T NIOBIUM-TITANIUM SUPERCONDUCTING MAGNET
To evaluate the performance of the assembled magnet, a recondensing-type LHe cryostat was designed as shown in Fig. 7(a). It mainly consists of a vacuum chamber, a thermal shield, and a helium vessel. The LHe capacity of the cryostat was designed to be 400 L for cooling the superconducting magnet. To prevent any heat transfer, the thermal shield and helium vessel were floated by using Kevlar on the support link. In addition, Multilayer insulation was wrapped around the exterior of the thermal shield and the helium vessel. We reported our recondensing-type LHe cryostat design and thermal analysis previously [19]. From the reported results, the heat loads by conduction, radiation, and Joule heat were 46 W and 0.614 W, respectively, in the thermal shield and the helium vessel. For these, a couple of two-stage Gifford-McMahon cryocoolers with a cooling margin of 1.5 W at 4.2 K and 45 W at 50 K were installed in the cryostat. Resultantly, the stable operation of the cryostat is expected with cooling margins of 48.9% and 79.5%. Fig. 7(b) shows manufactured recondensing-type LHe cryostat. As can be seen in the figure, high temperature superconductor (HTS) current leads, LHe ports, and recondensing units (including two Gifford-McMahon cryocoolers) were located at the upper center part. Once the magnet was cooled by the cryogen injected through the LHe port, the current was applied through the HTS current leads. During magnet operation, the heat loads were directly generated by conduction, radiation, and Joule heat, resulting in LHe vaporization. This vaporized LHe was then recondensed to minimize losses and improve cooling cost efficiency for practical operation. For the operation test of the superconducting system, a total of 12 temperature sensors were placed at the top and bottom of the coil, cold heads of cryocoolers, HTS current leads, helium vessel inner wall, and thermal shield inner wall. In addition, two LHe level sensors were installed on the edge of the inner wall of the helium vessel.
A low-temperature superconducting magnet designed for very high currents requires extensive quench training to enable the magnet to function at its full targeted currents [30]. Fig. 8(a) shows coil current and magnetic field versus quench training number plots for the assembled magnet. As can be seen in the figure, after five times intended "quench training", an operating current of 200 A and magnetic field of 7 T were reached in our magnet. Once the assembled magnet reached the target operation condition, it was stably operated without the quench. After that, the magnet was further evaluated for its magnetic field distribution and uniformity. This test was one of the important milestones of the successful design and fabrication of our magnet system because, as mentioned earlier, field strength and uniformity in an EBIS are important for effective electron beam compression. To evaluate these parameters (field strength and uniformity), the assembled magnet was tested at 4.2 K. In this test, the temperature and the magnetic field were acquired by using cryogenic temperature and hall sensors, respectively. A real-time data was recorded by using LabVIEW software. For field uniformity, magnet field distribution was acquired along the z-axis with intervals of 50 mm by mounting a hall sensor on the x-y-z position stage. Fig. 8(b) shows measured magnetic field distribution along the z-axis. The inset figure in Fig. 8(b) shows the field distribution in the electron beam compression region. The  measured field uniformity was 0.24% at a 7 T magnetic field.
The persistent current is circulated in the closed circuit between the magnet and the PCS. For field-decay measurement, a hall-sensor, which is located at center of the magnet, detected the magnetic field generated by the persistent current. Fig. 8(c) shows the result of the persistentmode operation. The magnet was operated in the persistentmode without the externally applied current for approximately 228 hours (9.5 days), excluding the current charging time. The magnet remained stable at the 7 T field, with a field-decay rate of approximately 0.42 ppm ⋅ h-1 (61 nT decay per hour). The field decay caused by the n-value factor was negligible, since the charging current of 200 A was only 47% of the coil's critical current at 7 T [31]. As a result, we confirmed that our system can offer stable, longterm operation without any external current source.

V. CONCLUSION
A 7 T Nb-Ti based superconducting magnet capable of persistent-mode operation was successfully designed, manufactured, and evaluated for EBIS application. In the design phase, various numerical analyses were carried out to evaluate the magnetic, thermal, and mechanical stabilities in terms of magnet operation. The magnet was designed so that it met the required materials strength and magnetic field uniformity even after structural deformation. Based on the design, the magnet coils, PCS, and superconducting joints were separately manufactured and assembled. Finally, the magnet was installed into a recondensing-type LHe cryostat. The magnet attained a target field of 7 T at a current of 200 A with a field uniformity of 0.24%. Next, the magnet was consistently operated in the persistent-mode at the 7 T field for 9.5 days. During persistent-mode operation, the magnet achieved a magnetic field decay rate of 0.42 ppm ⋅ h -1 , which is reliable performance for practical application. Based on the results, our magnet is capable of providing stable, long-term operation for generating HCIs in EBISs.