Present magnetic confinement concepts require the generation of magnetic fields of order 1 T to 10 T (Tesla) in the plasma. Two different technologies are considered here: low-temperature superconductors and actively cooled copper. The development of high-temperature superconductors is promising, especially using MgB2, but still at a very preliminary stage to allow predicting the parameters of a fusion-relevant system (see [Casali and Bruno, 2005, 2008]). A cryoplant must keep all wiring in its superconductive state.
Superconductor technology. The development of low-temperature superconductors for the International Tokamak Experimental Reactor (ITER) to be built in France has currently produced Nb3Sn cables that can carry a current density in the range 50MA/m2 at a magnetic field of 12.5 T [Huguet, 2003]. The current density that can be achieved in the cable depends on strand performance (in the case of ITER 650 A/mm2) but also on other parameters such as the Cu/non-Cu ratio, the void fraction, and the amount of space needed for the cooling channel, jacket, and insulator, all typically reducing the strand performance by an order of magnitude. Note, however, that Nb3Sn strands with a critical current density of 2,000 A/mm2 have been already produced, and that strands with a critical current density in the range of 3,000 A/mm2, about a factor of 3 larger than ITER requirements, are expected in the near future. Note also that the number above refers to a maximum magnetic field in the conductor of 12.5 T: higher values of the critical current can be achieved at lower magnetic fields. Thus, values up to 250 MA/m2, envisaged in some studies, can be considered already realistic. The cable specific weight assumed here is 6 t/m3 using current (conservative and ground-based) tokamak magnetic practice and technology. A cylindrical solenoid with a radial width of 0.2 m can therefore
produce a 12.5 T magnetic field. If rm and V are the radius of the solenoid and the internal volume, the mass of the magnet (neglecting the supporting structure) is approximately given by
Actively-cooled copper magnet. The use of copper magnet technologies allows the achievement of larger magnetic fields, which, as we will see, lead to higher values of fusion power density. An upper bound to the magnet mass is given by the virial theorem
with cstress « 1 GPa. Taking pmag = 2.5 t/m3 the above estimate yields about 6001 for an ITER-size magnet.
The magnet mass is proportional to the volume of the solenoid. Since within the present model the plasma volume Vp is a factor (rp/rm)2 smaller than the magnet volume, and since the plasma volume is related to fusion power by Pfus = PspecVp, with Pspec being the fusion power density in the reaction chamber, we can write
Comparison between superconducting and copper magnets for fusion application shows that the use of superconductors always gives advantages in terms of the magnet mass over copper magnets, unless very high-magnetic field values are required.
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