To send this article to your account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about sending content to .
To send this article to your Kindle, first ensure firstname.lastname@example.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.
Find out more about sending to your Kindle.
Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Invited contributions from the 17th European Fusion Theory Conference
As a follow-up to the 17th edition of the European Fusion Theory Conference, a collection of papers will be published in the Journal of Plasma Physics (JPP). This collection is intended as a Special Issue of a regular journal. Thus, papers are expected to be of high quality and will undergo a standard review. The invited papers in this special collection address the wide range of topics represented in this conference, from basic plasma physics theory to turbulent and neoclassical transport, fast particles, heating and current drive, computational modeling. We encourage all invited speakers and poster presenters to the conference to submit contributions. There will be no publication charge.
The problem of pressure driven infernal type perturbations near the plasma edge is addressed analytically for a circular limited tokamak configuration which presents an edge flattened safety factor. The plasma is separated from a metallic wall, either ideally conducting or resistive, by a vacuum region. The dispersion relation for such types of instabilities is derived and discussed for two classes of equilibrium profiles for pressure and mass density.
Pedestal modelling is crucial to predict the performance of future fusion devices. Current modelling efforts suffer either from a lack of kinetic physics, or an excess of computational complexity. To ameliorate these problems, we take a first-principles multiscale approach to the pedestal. We will present three separate sets of equations, covering the dynamics of edge localised modes (ELMs), the inter-ELM pedestal and pedestal turbulence, respectively. Precisely how these equations should be coupled to each other is covered in detail. This framework is completely self-consistent; it is derived from first principles by means of an asymptotic expansion of the fundamental Vlasov–Landau–Maxwell system in appropriate small parameters. The derivation exploits the narrowness of the pedestal region, the smallness of the thermal gyroradius and the low plasma
(the ratio of thermal to magnetic pressures) typical of current pedestal operation to achieve its simplifications. The relationship between this framework and gyrokinetics is analysed, and possibilities to directly match our systems of equations onto multiscale gyrokinetics are explored. A detailed comparison between our model and other models in the literature is performed. Finally, the potential for matching this framework onto an open-field-line region is briefly discussed.
Hamiltonian extended magnetohydrodynamics (XMHD) is restricted to respect helical symmetry by reducing the Poisson bracket for the three-dimensional dynamics to a helically symmetric one, as an extension of the previous study for translationally symmetric XMHD (Kaltsas et al., Phys. Plasmas, vol. 24, 2017, 092504). Four families of Casimir invariants are obtained directly from the symmetric Poisson bracket and they are used to construct Energy–Casimir variational principles for deriving generalized XMHD equilibrium equations with arbitrary macroscopic flows. The system is then cast into the form of Grad–Shafranov–Bernoulli equilibrium equations. The axisymmetric and the translationally symmetric formulations can be retrieved as geometric reductions of the helically symmetric one. As special cases, the derivation of the corresponding equilibrium equations for incompressible plasmas is discussed and the helically symmetric equilibrium equations for the Hall MHD system are obtained upon neglecting electron inertia. An example of an incompressible double-Beltrami equilibrium is presented in connection with a magnetic configuration having non-planar helical magnetic axis.
This paper addresses one aspect of the problem of the suppression of tearing mode magnetic islands by electron cyclotron current drive (ECCD) injection, formulating the problem as the converse of a forced reconnection problem. New physical conditions are discussed which should be considered in the technical approach towards a robust control strategy. Limits on the ECCD deposition are determined to avoid driving the system into regimes where secondary instabilities develop. Numerical simulations confirming the theory are also presented.
Kinetic ballooning modes in magnetically confined toroidal plasmas are investigated putting emphasis on specific stellarator features. In particular, we propose a Mercier criterion which is purposely designed to allow for direct comparison with local flux-tube gyrokinetics simulations. We investigate the influence on the marginal frequency of the mode of a magnetic curvature which is inhomogeneous on the magnetic flux surface due to the fieldline-label dependence. This is a typical (surface) global effect present in non-axisymmetry. Finally, we propose an artificial equilibrium model that explicitly retains the fieldline-label dependence in the magnetic drift, and analyse the stability of the system by introducing a representation of the perturbations similar to the flux-bundle model of Sugama et al. (Plasma Fusion Res., vol. 7, 2012, 2403094). The coupling of flux bundles is shown to have a stabilising effect on the most unstable local flux-tube mode.
There has been a growing interest, over the past few years, on understanding the effect on radio frequency waves due to turbulence in the scrape-off layer of tokamak plasmas. While the far scrape-off layer density width is of the order of centimetres in contemporary tokamaks, in ITER (International Thermonuclear Experimental Reactor), and in future fusion reactors, the corresponding width will be of the order of tens of centimetres. As such, this could impact the spectral properties of the waves and, consequently, the transport of wave energy and momentum to the core plasma. The turbulence in the scrape-off layer spans a broad range of spatial scales and includes blobs and filaments that are elongated along the magnetic field lines. The propagation of radio frequency waves through this tenuous plasma is given by Maxwell’s equations. The characteristic properties of the plasma appear as a permittivity tensor in the expression for the current in Ampere’s equation. This paper develops a formalism for expressing the permittivity of a turbulent plasma using the homogenization technique. This technique has been extensively used to express the dielectric properties of composite materials that are spatially inhomogeneous, for example, due to the presence of micro-structures. In a similar vein, the turbulent plasma in the scrape-off layer is spatially inhomogeneous and can be considered as a composite material in which the micro-structures are filaments and blobs. The classical homogenization technique is not appropriate for the magnetized plasma in the scrape-off layer, as the radio frequency waves span a broad range of wavelengths and frequencies – from tens of megahertz to hundreds of gigahertz. The formalism in this paper makes use of the Fourier space components of the electric and magnetic fields of the radio frequency waves for the scattered fields and fields inside the filaments and blobs. These are the eigenvectors of the dispersion matrix which, using the Green’s function approach, lead to a homogenized dielectric tensor.
In a reactor plasma like demonstration power station (DEMO), when using the radio frequency (RF) for heating or current drive in the lower hybrid (LH) frequency range (Franke et al., Fusion Engng Des., vol. 96–97, 2015, p. 46; Cardinali et al., Plasma Phys. Control. Fusion, vol. 59, 2017, 074002), a large fraction of the ion population (the continuously born
-particle, and/or the neutral beam injection (NBI) injected ions) is characterized by a non-thermal distribution function. The interaction (propagation and absorption) of the LH wave must be reformulated by considering the quasi-linear approach for each species separately. The collisional slowing down of such an ion population in a background of an electron and ion plasma is balanced by a quasi-linear diffusion in velocity space due to the propagating electromagnetic wave. In this paper, both propagations are considered by including the ion distribution function, solution of the Fokker–Planck equation, which describes the collisional dynamics of the
-particles including the effects of frictional slowing down, energy diffusion and pitch-angle scattering. Analytical solutions of the Fokker–Planck equation for the distribution function of
-particles with a background of ions and electrons at steady state are included in the calculation of the dielectric tensor. In the LH frequency domain, ray tracing (including quasi-linear damping), can be analytically solved by iterating with the Fokker–Planck solution, and the interaction of the LH wave with
-particles, thermal ions and electrons can be accounted self-consistently and the current drive efficiency can be evaluated in this more general scenario.
The effect of electrostatic microturbulence on fast particles rapidly decreases at high energy, but can be significant at moderate energy. Previous studies found that, in addition to changes in the energetic particle density, this results in non-trivial changes to the equilibrium velocity distribution. These effects have implications for plasma heating and the stability of Alfvén eigenmodes, but make multiscale simulations much more difficult without further approximations. Here, several related analytic model distribution functions are derived from first principles. A single dimensionless parameter characterizes the relative strength of turbulence relative to collisions, and this parameter appears as an exponent in the model distribution functions. Even the most simple of these models reproduces key features of the numerical phase-space transport solution and provides a useful a priori heuristic for determining how strong the effect of turbulence is on the redistribution of energetic particles in toroidal plasmas.