Three-dimensional analysis of tokamaks and stellarators

Precise stellarator quasi-symmetry can be achieved with electromagnetic coils

Magnetic fields with quasi-symmetry are known to provide good confinement of charged particles and plasmas, but the extent to which quasi-symmetry can be achieved in practice has remained an open question. Recent work [M. Landreman and E. Paul, Phys. Rev. Lett. 128, 035001, 2022] reports the discovery of toroidal magnetic fields that are quasi-symmetric to orders-of-magnitude higher precision than previously known fields. We show that these fields can be accurately produced using electromagnetic coils of only moderate engineering complexity, that is, coils that have low curvature and that are sufficiently separated from each other. Our results demonstrate that these new quasi-symmetric fields are relevant for applications requiring the confinement of energetic charged particles for long time scales, such as nuclear fusion. The coils' length plays an important role for how well the quasi-symmetric fields can be approximated. For the longest coil set considered and a mean field strength of 1 T, the departure from quasi-symmetry is of the order of Earth's magnetic field. Additionally, we find that magnetic surfaces extend far outside the plasma boundary used by Landreman and Paul, providing confinement far from the core. Simulations confirm that the magnetic fields generated by the new coils confine particles with high kinetic energy substantially longer than previously known coil configurations. In particular, when scaled to a reactor, the best found configuration loses only 0.04% of energetic particles born at midradius when following guiding center trajectories for 200 ms.

Magnetic Fields with Precise Quasisymmetry for Plasma Confinement

Quasisymmetry is an unusual symmetry that can be present in toroidal magnetic fields, enabling the confinement of charged particles and plasma. Here it is shown that both quasiaxisymmetry and quasihelical symmetry can be achieved to a much higher precision than previously thought over a significant volume, resulting in exceptional confinement. For a 1 Tesla mean field far from axisymmetry (vacuum rotational transform >0.4), symmetry-breaking mode amplitudes throughout a volume of aspect ratio 6 can be made as small as the typical ∼50  μT geomagnetic field.

Design of the DEMO Fusion Reactor Following ITER

Runs of the NSTAB nonlinear stability code show there are many three-dimensional (3D) solutions of the advanced tokamak problem subject to axially symmetric boundary conditions. These numerical simulations based on mathematical equations in conservation form predict that the ITER international tokamak project will encounter persistent disruptions and edge localized mode (ELMS) crashes. Test particle runs of the TRAN transport code suggest that for quasineutrality to prevail in tokamaks a certain minimum level of 3D asymmetry of the magnetic spectrum is required which is comparable to that found in quasiaxially symmetric (QAS) stellarators. The computational theory suggests that a QAS stellarator with two field periods and proportions like those of ITER is a good candidate for a fusion reactor. For a demonstration reactor (DEMO) we seek an experiment that combines the best features of ITER, with a system of QAS coils providing external rotational transform, which is a measure of the poloidal field. We have discovered a configuration with unusually good quasisymmetry that is ideal for this task.