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.