Helical equilibrium configurations in RFP plasmas

An important advancement in the study of plasmas confined in RFP configuration ia the observation of their tendency to perform a transition, as plasma current is increased, from a state called Multiple Helicity (MH) to another one called Quasi Single Helicity (QSH). In the MH state there are several non-axisymmetric perturbations of the plasma column, which are MHD modes in saturation regime. These modes are intrinsic to the configuration, since they are responsible of the "dynamo" mechanisms, which sustains it in time, opposing the resistive diffusion of the magnetic field profiles.  In the QSH state, instead, a single mode, called dominant mode, prevails, while the others, called secondary, have reduced amplitudes. Furthermore, as plasma current is increased, the secondary mode amplitude decreases, and the plasma tends to the ideal Single Helicity (SH) state, where a single mode is responsible for the dynamo.

This transition is extremely relevant for the fusion perspectives of the RFP configuration. In fact, in the MH state the superposition of the magnetic islands generated by the different modes gives rise to magnetic chaos, in analogy to what happens in a hamiltonian system with several resonant perturbations, and the rsulting confinement properties of the plasma are poor. On the contrary, the ideal SH state is chaos-free, and is expected to feature conserved magnetic surfaces and tokamak-like confinement.

A special flavour of QSH state is given by the so-called Single Helical Axis (SHAx) state, which arises when the magnetic field topology is modified due to the annihiliation of the O-point corresponding to the magnetic axis of the plasma column and the X-point of the dominant mode island. This results in a transition to a configuration with a single helical magnetic axis, which is reminiscent of the plasmas produced in stellarator devices.

My main contribution to the paper on this important topic which was published in 2009 on Nature Physics has been the development of an equilibrium reconstruction for the SHAx states, that is the determination of a function of spatial coordinates which is constant on the magnetic surfaces, neglecting the effect of secondary modes. This has allowed to show that density and electron temperature are indeed constant on such surfaces, implicitly demonstrating their at least partial existence, that is the spontaneous emergence of order from chaos.

Presently I am working on the improvement of this reconstruction and on the computation of averages of different quantities on the helical magnetic surfaces. A more ambitious goal is the computation of an ohmic equilibrium, that is one which takes into account also Ohm's law, usually neglected in tokamak equilibrium calculations. Finding such a solution would imply the theoretical demonstration of the possibility of realizing a pure SH state, and would allow to investigate the effect of the boundary condition imposed on the magnetic field using external coils.

Essential bibliography

R. Lorenzini, E. Martines, P. Piovesan, D. Terranova, P. Zanca, M. Zuin, et al., Self-organized helical equilibria as a new paradigm for ohmically heated fusion plasmas, Nature Physics 5, 570 (2009).

R. Lorenzini, D. Terranova, A. Alfier, P. Innocente, E. Martines, R. Pasqualotto, P. Zanca, Single-helical-axis states in reversed-field-pinch plasmas, Physical Review Letters 101, 025005 (2008).

D. F. Escande, P. Martin, S. Ortolani, A. Buffa, P. Franz, L. Marrelli, E. Martines, G. Spizzo, S. Cappello, A. Murari, R. Pasqualotto, P. Zanca, Quasi-single-helicity reversed-field-pinch plasmas, Physical Review Letters 85, 1662 (2000). [pdf]