To date, the most advanced concepts for fusion confinement are the tokamak and the stellarator. The stellarator is exemplified by the Wendelstein 7-X (W7-X) stellarator, which is undergoing preparations to begin operation in Greifswald, Germany. The tokamak scheme is currently the leading variant for plasma confinement and is therefore being used for the ITER design and is planned for the DEMO reactor. However, reliably achieving and maintaining the stability of fusion plasmas remains an important fundamental issue that needs to be resolved.

In both tokamaks and stellarators, stochastic magnetic fields can arise and influence the interplay between three-dimensional (3D) magnetic topology and plasma confinement. Stellarator devices represent an inherent three-dimensional challenge. They make use of the island divertor concept, and stochasticity and magnetic topology therefore play a fundamental role in their operation. With the extended operational regimes pioneered on the Large Helical Device (LHD) and with W7-X, attention has been directed towards the challenge of 3D plasma equlibria, transport and plasma–surface interactions.

In the tokamak line, non-axisymmetric magnetic perturbations, which change the magnetic topology, are applied on the majority of large-scale tokamaks nowadays to control plasma edge stability and transport. Recent research has highlighted the significance of the role that stochasticity and 3D magnetic topology also play in this fundamentally 2D concept. Their influence can be seen in transport and energy confinement, in the nature of disruption events and in the control of various magnetohydrodynamic (MHD) instabilities, most notably edge-localized modes (ELMs), which expel considerable amounts of energy from the plasma and pose a risk of damaging plasma–facing components in ITER and other next-generation fusion devices.

The existence of these stochastic and 3D effects brings tokamak and stellarator physics closer together, and a holistic approach to studying them provides the most promising path to making good progress. Understanding these effects is essential for the success of future fusion devices, and they represent a hot topic in current fusion research. In addition, reversed field pinches offer access to these topics with unique features such as the bifurcation into self-generated 3D equilibria and multi-mode unstable plasma conditions with a high degree of magnetic field stochasticity. Joint discussions of these aspects across the three communities will foster progress on basic as well as applied understanding in these complex branches of high-temperature plasma physics. Therefore, it will be of great interest and scientific importance to share the most up-to-date theories and techniques and to provide a platform for discussion between leading experts in the field.

The 597^th WEH Seminar is an attempt to discuss issues relating to stochastic fields in fusion plasmas from all sides, bringing together experts from different devices (tokamaks, stellarators and reversed-field pinches) and from different fields (equilibrium and confinement, turbulence, MHD instabilities, transport and plasma–wall interactions). It will build upon the success of the 480^th WEH Seminar entitled Active Control of MHD Stability held in June 2011 and the 531^st WEH Seminar entitled 3D versus 2D in Hot Plasmas held April–May 2013, during which it became clear that stochastic effects play a complex and crucial role in fusion plasmas. However, this seminar will differ from the previous ones, which focused on integrating experimental methods of controlling MHD instabilities and comparing the relative merits of 2D and 3D conceptualizations of hot plasmas. Instead, the focus here will be on the underlying physics of stochastic effects on a wide range of fields.

The success of these two previous WEH Seminars is exemplified by the publication of two associated special issues of the journal Nuclear Fusion and the planned publication of an associated book, which is currently in the process of being compiled. This proposed WEH Seminar is set to surpass the previous two in terms of the number of participants since it will absorb the International Workshop on Stochasticity in Fusion Plasmas, which ran successfully for over a decade and established itself as the foremost international workshop in this field.

Discussing together and summarizing recent approaches will improve the physics understanding of various effects of stochastic fields in magnetically confined plasmas. In addition, analysing the influence of stochasticity and magnetic topology in fusion plasmas will be beneficial and will guide the design of future fusion devices. A further major goal of this seminar is to give young scientists the opportunity to enter an active and growing field of research by interacting with world-leading experts.