Plasma Stability and Control
Topical Group

The stability of fusion plasma and its active control is one of the major research tasks on the way towards building a fusion power plant. The EFDA Plasma Stability and Control Topical Group (often abbreviated as the MHD Topical Group, whereby MHD is the acronym of Magnetohydrodynamics) is at the forefront in this challenge. Stable systems are characterised by the fact that they do not easily change. They tend to return to their original position if slightly displaced from it. Unstable equilibria are different: Even small changes can be a trigger and make them leave their original state, hence loosing their equilibrium position. They behave this way because they have free potential energy which can be transformed into other forms of energy.

Think of a ball at the top of a hill, or at the bottom of a valley (see the figure). If the ball at the top is only pushed very slightly out of this equilibrium position, gravitational forces act upon it and it will roll down the hill. Its budget of potential energy is converted into kinetic energy. In the valley, the gravitational force acts as a restoring force that pulls the ball back if it is displaced. The bottom of the valley is a stable equilibrium. It is the same with instabilities in the plasma – small changes can trigger large effects if the plasma is in an unstable equilibrium.

A thermonuclear plasma is confined by magnetic fields under high kinetic pressure conditions (i.e. high temperature and density): This equilibrium may become unstable and a number of instabilities can influence the plasma dynamics. While some of these are tolerable, and in some cases even benign (see, for example, the RFX results highlighted in this Fusion News), most of them are not. In fact, some of them will lead to unacceptable degradation of plasma performance, whereas others could even destroy the plasma and cause very severe heat loads or electromechanical forces. It is therefore vital to understand these instabilities, to learn how they evolve and how they can be avoided or mitigated.

Unstable and stable equilibria states: A small disturbance will cause the ball on top of the hill to leave its position, while the ball in the valley will return to its original location.

Magnetohydrodynamics (MHD) is a very powerful tool that can be used to study plasma equilibrium and stability in the presence of electromagnetic fields. It describes the plasma as a conducting fluid. The MHD model is based on a small set of equations: basically, conservation laws for mass, momentum and energy coupled with Maxwell equations. The theory of MHD stability of toroidal plasmas is highly developed and provides an excellent qualitative and quantitative description of plasma behaviour, also thanks to very advanced numerical simulations.

Taking into account our current knowledge of fusion science, one can predict that fusion reactors will be affected by instabilities. Hence, methods must be found to deal with them. One can avoid instabilities by running the plasma in stable equilibria. If they are unavoidable, one can suppress them or mitigate their effects. The first solution appears to be straightforward, but is not always easy, since these conservative scenarios often are not aggressive enough in terms of pushing fusion performance.

Hence, instabilities must be controlled or actively suppressed or their effects must be mitigated. To do so one must be able to detect them and this is best done in the early stage of their development. Thereafter, one can act on the plasma, either by applying appropriate magnetic fields, electromagnetic waves, or by injecting gas or pellets. The key to all these techniques is feedback control. In a feedback loop, one or more quantities, which need to be controlled, i.e. kept at a reference value determined by the user, are constantly measured and adjusted. In the case of a fusion device, one can, for instance, monitor the amplitude of the – typically unwanted – magnetic field perturbation that is produced by an instability. A sensor measures its quantity and feeds the data to a computer which continuously adjusts the control input (for example, by changing the current in active coils, which in turn produce a respective magnetic field), in order to keep the reference value.

Richard Buttery received his Ph.D. in theoretical particle physics at the University of Manchester in 1993. In his work, he used quantum chromodynamics to study photon emission from quarks as they emerge from particle collisions in an accelerator. After his Ph.D. he started working for UKAEA, where he progressed from modelling and experiments in tokamak stability, to leadership of research programmes in UKAEA and at JET as a scenario and stability expert. Until recently, he led the UKAEA Stability and Equilibrium Group and the MAST Upgrade with regards to Physics and was vice-chair of the EFDA Plasma Stability and Control Topical group. In August 2009, Richard joined General Atomics in San Diego, USA.

Types of instability

At a basic level the MHD Model classifies instabilities by their destabilising cause. Two main destabilising forces arise as a result of electrical current and pressure spatial variation (also called gradients) within the plasma chamber. The latter is associated with the curvature of the magnetic field. Since a fusion reactor is designed to confine hot plasmas in its interior, with milder conditions at the edge, spatial variations, i.e. gradients, are unavoidable, and are actually desirable. The corresponding instabilities are referred to as current and pressure driven.

Segment of the vacuum vessel of RFX-mod, Padova. The vacuum vessel is shown in orange, the mechanical supporting structure in grey. The green parts represent the coils of the feedback system.

A third main source of instabilities is a population of “fast” ions, namely ions that have a speed significantly higher than that of the bulk plasma ions. In current devices these fast ions are generated by auxiliary heating schemes such as injected beams or externally launched electromagnetic waves at ion resonance frequencies like Ion Cyclotron Resonance Heating. In the burning plasmas of fusion reactors, we will also have alpha particles, a fact that increases the importance of these instabilities in fusion science.

For all three types of these driving forces, a number of instabilities have been classified.

Today, deeply studied instabilities are disruptions, Edge Localised Modes (ELM), Neoclassical Tearing Modes (NTM) and Tearing Modes, sawteeth and Resistive Wall Modes (RWM), all of which are current or pressure driven, or both. Fast-particle driven modes, like Toroidal Alfvén Eigenmodes (TAE), fishbones and energetic particle modes (EPM) are also investigated.

More detailed information on the nature of these instabilities can be found in a longer version of this article available on the EFDA website.

How to cope with instabilities

ELMs, NTMs and RWMs can efficiently be suppressed by active external means. Recently, dedicated magnetic fields, which perturb the plasma edge magnetic field, have been found to mitigate ELMs (see article on the stochasticity workshop in the May 2009 edition of Fusion News). In fact due to these findings, such perturbation coils have been implemented into the ITER design during the last design review.

Launching focused microwaves in a plasma is an efficient way to stabilise NTMs (see article on the “seek and destroy” system in this Fusion News), while disruptions can be mitigated by injecting hydrogen or deuterium pellets into the plasma, or releasing large amounts of noble gases into the plasma.

Active coils are used to stabilise MHD instabilities such as Resistive Wall Modes. An electrical current is fed into these coils which then produce a magnetic field that exactly cancels the perturbation produced by the instability.

Fusion devices have very demanding requirements for MHD feedback control systems and Europe is at the forefront of this research. At RFX-Mod in Padova, for instance, 192 active coils are simultaneously and independently feedback controlled. At ASDEX upgrade in Garching the position of special mirrors can be feedback controlled to focus microwaves on moving target instabilities. ITER will also have a number of feedback systems to control MHD stability.

Piero Martin is a professor at the Physics Department of the University of Padova, Italy, and head of the European experiment RFX, the Reversed Field Pinch device which is based in Padova. He is chair of the EFDA Topical Group on “Plasma Stability and Control”, and leads the EU delegation in the ITPA MHD Topical Group. For the period 2005-07, he served as Task Force Leader of the “MHD instabilities and their active control” Task Force in the ASDEX Upgrade experiment at the Max-Planck Institut für Plasmaphysik in Garching. He is a member of the “International Liaison Committee” of the “Center for Magnetic Self-Organization”, which is a frontier physics centre founded by the US National Science Foundation. From 1997 to 2007 he was group leader for one of the five physics research groups of the Consorzio RFX. He is currently serving as a member of the panel in the US ReNeW process, the aim of which is to support the US DoE in planning the fusion research during the ITER era. His expertise in fusion covers several areas both in science and management. He has contributed to both RFP and Tokamak physics. He is the author of more than 90 papers in refereed journals, and has been invited to give talks at the main international conferences, in many universities and research centres. He has been promoting and managing several international collaborations and projects. He is active in outreach and promotion of fusion science and has been supervisor of many undergraduate and Ph.D. theses. In 2006, one of his students was awarded one of the EPS prizes for the best Ph.D. thesis in plasma physics.

Work programme of the MHD Topical

The work programme of the MHD Topical Group is based on five main areas, namely: Fast Particles Physics, Disruptions, Sawteeth and Tearing Modes (NTMs), Edge Localised Modes (ELMs) and Stability at high Beta (RWMs). An approach is proposed for the future that focuses on key areas and gaps where European coordination is needed, setting the programme within a strategic overview of the longer term needs and development of the field.

In the short term, the programme will focus on disruptions which is the most urgent and serious issue for ITER. Further key elements are also flagged in the four other fields of plasma stability, in particular, in order to predict control requirements for ITER and development of the practical control approaches for these instabilities.

A longer-term roadmap is based on four new crosscutting initiatives: “3D and non-linear effects”, “Supra-thermal particle physics”, “Control and mitigation” and “Diagnostics”. The aim is to foster common approaches and share knowledge and work between the different fields or disciplines. One example is the field of disruptions, where a broader view might help to exploit the efforts made on 3D field in other MHD areas, such as on non-linear issues, multi- mode coupling and interaction with external perturbation, transport of thermal and fast particles in 3D magnetic fields, feedback control, etc.

One main goal of the MHD Topical Group is to support scientific communication amongst the European research groups by providing a forum which will enable the exchange of information on research programs, tools and results. This is done in a yearly general meeting, additional topical meetings and by exploiting the web and remote communication tools. A successful example is the working session on disruptions, which was jointly organised in February by the Integrated Tokamak Modelling and Plasma Wall Interaction Task Forces and by the MHD Topical Group. This work-shop has been extremely useful to assess the state of the art in this field and to coordinate the European effort.

The topical group also promotes the excellence of EU MHD work within the international fusion community. Internationally, Europe holds a leading position in all areas of MHD and it is extremely important that, within the global ITER community, this position is maintained and reinforced.

Last, but certainly not least, among the duties of the MHD Topical Group there is the task of providing advice to the EFDA leadership on training and educational needs. MHD has considerable potential in this field, since a lively and open fusion oriented MHD program has the built-in capabilities of communicating with other scientific fields. This may help to attract new resources to the field and increase public awareness of our efforts and our results.
A BIG thank you to Piero Martin, who continuously supported our work on this article

A longer article, which explains the various instabilities in more detail, can be found at the EFDA website: