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Beyond 100 Tesla ...

Magnetic fields in excess of 100 T can only be generated at the expense of a drastic reduction in pulse duration. Invariably, they also lead to the destruction of the coil which, however, doesn’t prevent the use of Megagauss magnetic fields (1 Megagauss = 100 Tesla) for scientific experiments.

The LNCMI Megagauss generator is one out of three platforms worldwide that are making use of capacitor-driven single-turn coils (STC) to produce fields in the 150 to 250 T range for scientific applications. Although still higher fields can be obtained with flux compression techniques, STCs have the advantage that the coil destruction does not affect the experimentally useful volume: Samples, cryostats and other equipment generally survive and experiments can therefore be performed reproducibly.

Magnetic forces and how to deal with them

Magnets are generating a force field that acts not only on magnetic objects in their vicinity, but also on themselves: In a simple solenoid, for example, the so-called magnetic pressure tends to radially expand and axially compress the windings. As a consequence, the maximum field that can be obtained in an electromagnet without destroying it is limited by the mechanical strength of its components, that is, conductors and reinforcing materials.

To reach a field of, say, 100 T, a magnet would have to sustain a pressure of 4 GPa, which corresponds to a weight of 40 tons resting on a surface of 1 cm². So far this pressure level has prevented any successful attempt to build a magnet that can generate fields approaching 100 T without exploding. This does not mean, however, that fields above this threshold cannot be generated at all. One just has to resort to so-called destructive techniques.

The destructive generation of magnetic fields in the Megagauss range is based on a simple principle: Since the mechanical strength of the coil is no longer capable of containing the magnetic pressure statically, one makes use of the inertia of the conductor material to contain it dynamically. In the simplest case, this is done by very rapidly injecting a current into a coil. Whereas both the force and the magnetic field build up simultaneously with the current, the expansion of the coil is momentarily delayed by its inertia. It is within this delay that a high magnetic field can be generated.

Single turn coils — the not-so-destructive generation of Megagauss fields

STCs are based on the simple principle described above. In a diameter of, say, 10 mm, a STC driven by a state-of-the-art capacitor bank can provide pulses of roughly 6 μs duration peaking well above 200 T. Even higher fields have been obtained by electromagnetic or explosive flux compression, a technique that makes use of an imploding metal cylinder to compress a magnetic flux captured within. However, STCs have an undeniable advantage for scientific experiments: the inevitable explosion of the coil does not affect the bore volume as the prevailing forces are directed radially away from the field axis. Small cryostats and sample holders can therefore be placed in the bore without risk of damage.

Another convenient feature of STCs is that the breaking of the coil does not create a discontinuity in the magnetic field. This can be understood by considering the hypothetical case of a magnetic field being cut-off instantaneously. Such cut-off, if it could be realized, would induce an intense electric field that would in turn give rise to an electric arc. In other words, a current would start to flow that would simply reestablish the magnetic field. In an exploding coil this mechanism can be thought of as being responsible for the creation of plasma discharges bridging the gaps between broken conductor fragments. The discharge thus continues smoothly despite the violent explosion of the coil. This doesn’t mean, of course, that the explosion has no effect at all on the magnetic field. Obviously, any increase of the bore area diminishes the field strength which is why one still has to make sure that the rise time of the current is faster than the coil expansion.

A simple principle, but the devil’s in the detail

Unlike non-destructive pulsed magnets, STCs as such are extremely simple: They consist of a metal strip bent into a loop that is attached to triangular feed flanges serving as current contacts. The difficulty in using STCs rather lies in the design of a suitable generator capable of injecting the necessary energy with sufficient speed into the coil. To produce 200 T in 10 mm diameter requires the conversion of roughly 50 kJ from capacitive to inductive energy in less than 2 μs, that is, with a power of 25 GW. In order to accomplish this, capacitor banks must be tailored to the needs of STCs. They must feature extremely low inductances of typically 10 nH while being able to sustain at least twice the operating voltage of 50 to 60 kV.

On closer inspection, the design of a suitable generator doesn’t remain the only challenge related to STCs. Any in-depth characterization of physical mechanisms governing STCs that goes beyond the simple principles discussed above, must take into account a complex non-linear interdependence of mechanical, thermal and electromagnetic phenomena. Shock-wave dynamics, non-linear magnetic diffusion, inhomogeneous heating, sublimation and plasma formation are only a few keywords to be addressed in this connection.