Fig. 3. Rutherford cable Von Mises stress distribution: (a) non-cored cable, (b) cored cable [34]
The feasibility of fabricating Rutherford cables with internal austenitic steel strips was demonstrated for the rapid-cycling synchrotron project at GSI [36, 60]. Austenitic steel strips provide structural reinforcement, as seen above in Figure 3, and reduces electrical losses from interstrand coupling currents. By placing a 25 micrometer thick, 8 millimeter wide austenitic steel core inside the Rutherford cables for GSI’s fast-pulsed synchrotron SIS300, the cross-resistance in the cable was increased tenfold with respect to the Relativistic Heavy Ion Collider cable [59]. The ramp-rate dependence of the RHIC cable’s field quality and the losses were measured at BNL [33].
Coil’s designed with thinner wiring and more turns perform better analytically [52] but this results in the need for a higher voltage power supply [47]. It is more practical to use multicoil’s where a number of coaxial coils are energised independently. Multicoil design is now generally accepted as the requirement for generating 80 to 100 T fields in non-destructive pulsed magnets [7, 29, 35, 56, 62] where lifetimes are in the 10,000 to 200,000 pulse range depending on configuration, field and repetition rate etc. [8]. A number of techniques can be applied to design and optimise a magnet for the intended use case, for example genetic algorithms were used to find the ideal coil configurations of the dipole magnet for the SIS300 accelerator project [41, 42].
Despite the variety of development & optimisation techniques, each design must be constructed as a finite element mesh [55] for numerical modelling. A strong coupling of field calculations, thermal simulations and analysis is presented in [2] for solenoids & in [28, 34, 58] for Rutherford windings. The thermal, electromagnetic and stress problems are solved on the same FE mesh for each step, however fine grain meshing and synergetic behaviours [25] make this approach computationally expensive [51]. The simplification of FE geometries can deliver some benefit however as the same calculations will be replicated in each satellite, an array representative of the swarm can remove detailed analysis of each element to enable reasonable run time.
With the advance of modelling tools and research, it was determined that the performance of pulsed magnets is governed by the ability of the coil materials to cope with the Lorentz forces & internal heating. The maximum field strength is limited by the power distribution busbars mechanical strength [8] while the pulse duration is limited by the power supply and heat capacity of the coil [47]. This requires a rapidly discharged power source and refrigeration system to reduce the heat generated by the intense electrical input required for each pulse. [21]. To address the thermal constraint that limits pulse duration, the use of liquid helium coolant baths is industry standard [37, 39, 31, 51]. During a pulse, coils heat up due to the large amount of electrical energy coursing through the material lattice. To cool them down again to be ready for the next pulse requires direct liquid cooling [22].
Liquid Helium is preferred for it’s almost zero viscosity [57] and high specific heat capacity as a Phase II liquid when beneath 2.17K [8, 31, 51]. Beneath the phase transition surface, liquid Helium acts as a solid with almost perfect conduction. The lack of viscosity allows the liquid to fill in micrometre gaps to give complete surface coverage of the coil cabling. The removal of ‘air gaps’ in the cable or it’s wrapped reinforcement ensures that no sites form thermal stress points for coolant boil-off and resulting quench propagation. The heat absorption capacity of the coolant bath is defined by the volume and flow rate [31] which must be balanced against the input energy joule heating of the coil [12] in line with its selected safety systems ie quench heaters. Cooling of a superconductive solenoid can thus be reduced to an energy cost based on the refrigeration & fluid control components optimised at the point of peak current in the coil, just beneath the material’s quench surface.
As the optimisation of any multicoil design is strongly related to the available energy supplies for the sub-coils [48, 49] the power storage system is the final component for inspection. Given the proposed context, the highest current density will be selected before follow-on requirements are optimised. In Nb3Sn superconductors this is approximately 3000A/mm2 thus cable wire count is defined by the maximum power supply within the available volume minus operational requirements such as cooling.
Satellite power systems have progressively shifted from nickel metal hydroxide (NiMH) to lithium-ion (Li-ion) since the early 2000s [11] and this trend is mirrored in pulsed magnetic researchers increased use of capacitor power supplied for multicoil HEPS systems as seen in [17, 18, 54, 62, 63]. A number of chemistry [6, 9, 45] and electrode options [32] are being investigated to improve existing capabilities as no transformationally new technology has commercialised successfully since Li-ion. The proposed solenoid’s power system will thus be based on NiMH or Li-ion capacitors [10] as the industry standard with improvements sought from low temperature capacitor chemistries [30, 64], high current transformer input designs [3, 16] and the growing body of electric vehicle research [5].
The proposed context requires maximising mutual inductance and the peak current density, while there are many similarities to the presented accelerator electromagnet research, there are components such as the pulse transformers that will require tailored design solutions to produce an optimised pulsewave profile. The design & limits defined by this literature review are now presented in a sample coil for inspection. For the proposed coil design, resulting inductances are found and force between objects computed to determine if propulsion is viable. Analysis of this novel propulsion method uses ideal conditions that remove many of the considerations of reality, such as electrical losses or material failure modes. These initial simplifications are necessary to demonstrate the multifaceted concept is theoretically sound and analytically functional before further research and Simulink modelling can examine and document the effect of these factors in detail.