## Kinetic and fluid modelling of the SOL

D. Tskhakaya1, I. Borodkina1, O. Shyshkin1

1Institute of Plasma Physics of the CAS, Za Slovankou 3, 182 00 Prague 8, Czech Republic

Plasma transport modelling in the Scrape-Off Layer (SOL) represents one of the most complex numerical studies used in magnetic confinement fusion. These models require...

Impurity seeding studies were performed for the first time in the slot divertor at DIII-D, showing that with suitable use of radiators, full detachment is possible without degradation of core confinement [1]. First ever multi species SOLPS-ITER simulations including full cross-field drifts and neutral-neutral collisions activated in DIII-D demonstrate the importance of target shaping and...

The interaction between the plasma and the solid wall at the divertor/limiter target in tokamak devices affects turbulence in the plasma edge, thus impacting the overall confinement [1,2]. While the gyrokinetic framework allows one to describe turbulence and transport in the core of tokamak plasmas, most of present gyrokinetic codes still lack an adequate description of plasma-wall interaction...

Turbulent transport has long been understood to be the dominant transport mechanism in tokamaks. Stellarators, such as W7X, that have been optimised to reduce collisional (neoclassical) transport are also expected to be limited by turbulent transport [1]. Combined theoretical, computational, and experimental progress has advanced our understanding of turbulence properties and the resultant...

JOREK [1] is one the most advanced non-linear simulation codes for studying MHD instabilities that can occur in magnetically confined fusion plasmas as well as their control. It leverages extensive parallel programming to obtain accurate results regarding the dynamics of the high-energy magnetically confined plasma inside the vacuum vessel of a tokamak or stellarator. In addition, a...

Inertial Fusion Energy production using lasers represents a key approach to nuclear fusion energy on earth. The concept of laser-driven Inertial Confinement thermonuclear Fusion (ICF) was proposed in 1972 in seminal papers by American and Russian scientists [Basov1972, Nuckolls1972], which initiated a worldwide effort to demonstrate inertial fusion in the laboratory. After five decades of...

Global energy confinement studies based on empirical scaling expressions represent an important instrument for benchmarking experiments in tokamaks and stellarators, for specification of boundary conditions in modeling activities, for guiding the development of theoretical models of heat transport and for extrapolating plasma performance to new machines, such as ITER.

In this contribution,...

We present a new model to describe neoclassical transport in strong gradient regions in tokamaks such as internal transport barriers and the pedestal [1]. Previous work on neoclassical transport across transport barriers assumed large density and potential gradients but a small temperature gradient [2], or neglected the gradient of the mean parallel flow [3]. Using a large aspect ratio and low...

Making use of a large experimental database of pedestals of H-mode ELMy JET-ILW pulses [1], we propose several approaches to systematic prediction of the height of the electron-temperature pedestal and of the electron temperature at the top of the density pedestal, with the engineering parameters and the density profiles as inputs. Simulations of ETG turbulence in steep-gradient regions of the...

The presentation will introduce the principles of suppressing edge localized modes (ELMs) by external magnetic perturbations (RMPs). It will explain models that allow the description of the processes and highlight recent developments. Direct comparisons between simulations and experiments will be shown, and an outlook to the application for future machines like ITER will be given.

The...

An accumulation of heavy impurities in the tokamak core is detrimental for its performance and can lead to disruption of the plasma. In smaller to medium size tokamaks the effective neoclassical transport in the pedestal is radially inwards [3]. In larger tokamaks---e.g. ITER--- where the temperature gradient is higher, the neoclassical transport is predicted to be outwards. The models are...

A possible triggering mechanism of Alfvén waves (AWs) in tokamak plasmas, based on localized perturbations induced by magnetic reconnection events, is discussed in the framework of nonlinear viscoresistive 3D MHD modeling.

Nicolas Lopez

University of Oxford

A wave near an isolated turning point is typically assumed to have an Airy function profile with respect to the separation distance. This description is incomplete, however, and is insufficient to describe the behavior of more realistic wavefields that are not simple plane waves [1]. Asymptotic matching to a prescribed incoming wavefield generically...

One of the most well-established codes for modeling non-linear Magnetohydrodynamics (MHD) for tokamak reactors is JOREK, which solves these equations with a Bézier surface based finite element method. This code produces a highly sparse but also very large linear system. The main solver behind the code uses either GMRES or Bi-CGSTAB with a physics-based preconditioner, but even with the...

Tungsten divertors in tokamaks are designed to withstand and evacuate the excess heat coming from the hot plasma. Some of the tungsten divertor can melt, enter the plasma, and itself become a high-Z impurity plasma. If it enters the core, it can emit enough radiation to cause a loss of thermal plasma energy and degrade or terminate tokamak operation [1]. Thus, it is crucial to develop a...

Evolving a two-fluid model based on the drift-reduced Braginskii equations [1], GBS [2] is a three-dimensional flux-driven turbulence code designed for simulating plasma turbulence and kinetic neutral dynamics in the tokamak boundary. The GBS simulation domain covers the entire tokamak volume, avoiding the need for an artificial boundary between the core and edge regions, thus preserving the...

To enhance the computational efficiency of particle codes in performing multi-n nonlinear simulations, piecewise finite elements have been developed in tokamak plasma, along with previous work [1,2,3]. Clebsch coordinates are constructed depending on the toroidal domain, which is consistent with the finite difference scheme [1]. In this work, the cubic spline finite element is adopted [3]. The...

This work deals with the relation/interaction between plasma flow and magnetic field during the process of reversed-field pinch (RFP) quasi-helical self-organization [1, 2], featuring improved confinement in the RFX-mod RFP [3].

Experimental [3] and modelling [4] evidence shows that helical self-organization is characterized by quasi-periodical relaxation-reconnection events: partial...

ICRH is an attractive auxiliary heating system for future fusion reactors as it enables direct power deposition to the ions and does not suffer from high density cutoffs. However, ICRH launcher structure needs to be positioned close to the edge plasma to efficiently couple the launched power. This gives rise to enhanced plasma wall interactions near and far from the launching structure. One of...

The gyromoment (GM) approach was developed by B. J. Frei et al. [1] to address the challenges associated with the gyrokinetic (GK) modeling of turbulent dynamics in the boundary region of fusion devices. Based on expanding distribution functions onto a Hermite-Laguerre polynomial basis and evolving in space and time the expansion coefficients, the GM approach has the potential to efficiently...

Ion cyclotron resonance heating (ICRH) is known to create a population of fast ions in fusion plasmas. The non-Maxwellian distribution functions are obtained by solving the Fokker-Planck equation and are needed to describe the radio-frequency wave power deposition and transport phenomena.

This work uses wave fields and power deposition predicted by FEMIC [1], a finite element model for ICRH....

We apply the Physics-informed Neural Networks (PINNs) to the magnetohydrodynamic (MHD) simulations. We build a neural network to find a solution of the MHD equations. We use the coordinate of space-time as model inputs and the outputs of the model are the magnetic field, the plasma bulk velocity, the plasma mass density, and the plasma thermal pressure. The MHD equations are combined into the...

Neoclassical tearing modes (NTM) are metastable magnetic islands in tokamaks; however, they appear frequently in experiments without any noticeable triggering event. In order to understand this, it has been numerically shown that turbulence can create a seed island by mode coupling [1,2,3], even remotely [4] ; such a seed island has been shown in 2D models to further grow from the NTM...

Confinement quality in fusion plasma is significantly influenced by the presence of heavy impurities, e.g. Tungsten, which can lead to radiative heat loss and reduced confinement. This study explores impurity transport modeled by inertial particles in edge plasma, a previously unexamined aspect in plasma physics, using high-resolution direct numerical simulations of the Hasegawa-Wakatani...

The dependence of L-H transition power threshold on plasma density is well documented and captured by the “ITPA 2008 scaling” [1] for high density D plasmas. In view of ITER operations, several studies with different H isotopes resulted in a 1/A mass dependence of the threshold [2]. Of particular interest for ITER H-mode access at low auxiliary power is the existence of a minimum L-H power...

Parametric decay instabilities might play a significant role in various plasma physics phenomena and have garnered considerable interest in recent years [1]. In this study, we compare a model of parametric decay instabilities against the data observed during experiments conducted in the AUG (ASDEX Upgrade) fusion device while performing Electron Cyclotron Wall Conditioning (ECWC)[2].

During...

Integrated modelling for magnetically confined tokamak plasmas is an indispensable tool in interpreting and in guiding the tokamak experiments. To evolve the plasma profiles (current, densities, temperatures), integrated modelling schemes solve a system of stiff diffusion-advection transport equations, constructed using a set of physical models for equilibrium, transport and sources. It is...

P. Costello1

, G. G. Plunk1

, and P. Helander1

1 Max-Planck-Institut für Plasmaphysik, Wendelsteinstraße 1, 17491 Greifswald, Germany

Since the development of gyrokinetic theory, a myriad of instabilities, which lead to

unwanted turbulent transport in tokamaks and stellarators, have been discovered. A recent

series of publications [1, 2, 3] have introduced a novel approach to computing...

The EC launcher conceptual design is moving towards an engineering design that will satisfy all physics requirements under the various system constraints, including maximum flexibility in case of further refinements of plasma scenarios and tasks [1]. In the current DEMO reference scenario, for the specific magnetic field and plasma density/temperature adopted, the gyrotron frequencies...

Università degli Studi Padova - Consorzio RFX

The strong uncertainty related to the estimate of the viscosity coefficient represents an important challenge in the application of magneto-hydrodynamics (MHD) simulation results to laboratory plasmas [1]. This is particularly relevant in the contest of the reversed-field pinch (RFP) configuration, where the viscosity together with the resistivity...

Max Planck Institute for Plasma Physics

Energetic particles will play a central role in future burning plasma experiments, and their

confinement is an important aspect for a fusion reactor. Understanding the effects of energetic

particles (EPs) is essential, as they can strongly interact with the main plasma and drive

magnetohydrodynamic (MHD) instabilities. One notable example is the...

University of Oxford

We investigate the saturation of turbulence in a three-field, fluid model of a magnetised plasma in a Z-pinch magnetic geometry. The model is derived by taking a long-wavelength limit of gyrokinetics and subsequently ordering the electron-temperature-gradient (ETG) to be much larger than all other equilibrium gradients, while still retaining the curvature and...

The particle-in-cell code PICLS is a full-f finite element tool intended to simulate turbulence in the tokamak scrape-off layer using gyrokinetic ions and drift-kinetic electrons. Up until now however, PICLS has been a purely electrostatic code with a prescribed background magnetic field. This approach is not perfectly suited to represent unstable regimes occurring in the scrape-off layer,...

The Divertor Tokamak Test (DTT) [1],[2] is a superconducting device under construction in Frascati, Italy. DTT was proposed to assess the performance of a conventional ITER divertor and address the power exhaust issue that will affect future fusion devices as DEMO. DTT will be equipped with three auxiliary heating systems, including a Neutral Beam Injection (NBI) system. DTT NBI is a...

A linear theory of non local transport in relativistic unmagnetized plasmas is presented. The relativistic effects are due to high electron thermal energy. The relativistic Fokker-Planck equation is analytically solved for perturbed plasmas with respect to the global thermal equilibrium defined by the Maxwell–Boltzmann–Jüttner electron distribution function (EDF). The perturbed EDF is...

The presence of non-axisymmetric perturbations of an axisymmetric toroidal magnetic field results in the chaoticity of the magnetic field lines and strongly affects the charged particle motion and therefore the particle, energy and momentum transport in toroidal plasmas [1-2]. Particle chaoticity is determined by resonance conditions relating the unperturbed Orbital Frequencies of the...

A relatively simple way to evaluate bootstrap current in stellarators involves the use of the long mean free path asymptotic formula by Shaing and Callen [1]. This formula contains all the information about device geometry in a geometrical factor, independent of plasma parameters. This method is particularly suited for stellarator optimization, where multiple quick estimates of bootstrap...

Recent advances in stellarator optimization have led to unprecedented improvement in neoclassical transport in Wendelstein 7-X [1] such that anomalous transport is contributing a significant portion of the transport, especially in the Scrape-Off-Layer (SOL) [2]. Here, we present isothermal fluid turbulence simulations using the BOUT++ framework [3,4] in the edge and scrape-off-layer (SOL) of...

Recent experiments using the 3-ion ICRH heating scheme [Kazakov NF 2015] have been successful at generating substantial populations of MeV range fast ions in the deep core of JET, mimicking the effect of fusion-born alpha particles in future burning plasmas. We analyze an ICRH heated L-mode in which fast ions destabilized a wide range of Alfvén eigenmodes (AEs) as observed using magnetics,...

The geodesic-acoustic-mode (GAM) is a plasma oscillation observed in fusion reactors with toroidal geometry (such as the Tokamak or Stellarator) and are recognized to be the non-stationary branch of the zonal flows (ZFs). Similarly to the ZFs, GAMs are understood to regulate cross-field turbulence and thus enhance energy confinement [1]. Still, their direct effect on turbulence is not yet...

SOLPS-ITER modelling of plasma rotation with co-rotating atoms in the Magnum-PSI beam.

H.J. de Blank1 , J. Verstappen1, J. Gonzalez2, I. Classen1, E. Westerhof1

1 DIFFER - Dutch Institute for Fundamental Energy Research. De Zaale 20, 5612AJ, Eindhoven, The Netherlands

2 ARCNL, P.O.Box 93019, 1090BA Amsterdam, The Netherlands

In the ITER divertor heat loads of 10 MWm-2 are expected in...

A numerical tool modelling the excitation and evolution of electron avalanche ionization in the breakdown phase of start-up in tokamaks is presented. We estimate the energization efficiency of the nonlinear interaction between spatially localized Gaussian EC-fields propagating in vacuum with an ensemble of seed electrons. This process is coupled with the acceleration of electrons due to the...

The stellarator is a device designed to achieve controlled fusion by magnetic confinement.

Despite several advantages over tokamaks, its lack of axisymmetry creates some difficulties to confine the plasma: in an unoptimised stellarator reactor, both thermal ions and the fast ions produced by DT fusion would be lost faster than in a tokamak. On the other hand, stellarators are characterised by...

In order to be candidates to fusion power plants, stellarators must be optimized, i.e. the magnetic field needs to be tailored to have sufficiently good confinement properties. When the optimization process is performed to minimize neoclassical losses, the goal is to obtain a magnetic field that is close to omnigeneity. A magnetic field is omnigenous [1] if the radial drift of collisionless...

Quasi-isodynamic (QI) stellarators are a uniquely attractive fusion reactor candidate due to their low neoclassical transport, excellent confinement of fusion-borne alpha particles, and vanishingly small bootstrap currents [1]. Due to the complexity of their geometries, QI stellarators must generally be designed through numerical optimization, which requires an objective metric that quantifies...

In the last experimental campaign of Wendelstein 7-X (W7-X) the new ICRH antenna [1] was brought into operation. With only one of the two antenna straps being operable in the last campaign, the available phasing options as well as the amount of power that could be coupled into the core plasma were limited. Nevertheless, the antenna is expected to be fully functional for the next operational...

Concentrated exhaust power deposition must be avoided in a fusion power plant. A strategy to prevent this is to seed heavy impurities in the divertor, which radiate strongly at the local plasma temperature. This can help to maintain a uniform power deposition over the divertor structure. However, if the impurity migrates upstream, it can produce a number of detrimental effects, including fuel...

The neutral atoms in the plasma edge of nuclear fusion devices are typically modeled using a kinetic approach and more specifically the Monte Carlo (MC) code EIRENE [1]. Although EIRENE has been proved very reliable and effective, there are some drawbacks such as the statistical noise introduced by the MC techniques and the computational cost, which is significantly increased in high...

To accurately model the plasma dielectric properties in presence of rotational transform, most of the theoretical models and full-wave codes addressing radiofrequency wave propagation and absorption in tokamaks are based on toroidal and poloidal Fourier expansions of the RF fields (see for instance [1-4]). A significant drawback of this field representation is its lack of flexibility, in that...

To understand plasma behaviour in the scrape-off layer (SOL), we need to know the boundary conditions for the plasma and electromagnetic fields near a divertor. At the plasma-wall boundary, in the direction perpendicular to the wall, there are four length scales of interest. These are the Debye length $\lambda_D$, the ion gyroradius $\rho_i$, the projection of the collisional mean free path in...

Decades of research has demonstrated the necessity of using kinetic plasma models to accurately model the flux of heat and particles through the closed-field line region of tokamaks. In the much colder open-field-line region beyond the last closed flux surface (LCFS), fluid models are typically used to model the flux of heat and particles to the divertor. Recently, kinetic plasma models have...

Modelling the large amplitude fluctuations of the plasma edge, particularly across the separatrix into the hot scrape-off layers of future reactors, can require costly full-f kinetic simulations, with heavily restricted time-step due to uninteresting fast waves [1]. Here we demonstrate the first steps in the implementation of a method allowing consistent evolution of the system up to the...

Stellarator magnetic configurations need to be optimized in order to meet all the required properties of a fusion reactor. The stellarator Wendelstein-X (W7-X) was optimized to be approximately quasi-isodynamic (QI). In an exactly QI field, trapped particles orbit, on average, in the poloidal direction, and therefore remain confined [1]. Neoclassical transport is thus expected to be low....

This work is based on the variational principle for magnetic field lines introduced in 1983 by Cary and Littlejohn [1]. The action principles for magnetic field lines and for Hamiltonian mechanics are recalled to be analogous. It is shown that the first one can be rigorously proved from first principles without analytical calculations. Not only the action principles are analogous, but also a...

Since the early 90ties, 3D nonlinear MHD studies have been developing a fundamental framework for the understanding of the Reversed Field Pinch (RFP) self-organization. The simple visco-resistive MHD approximation clearly shows that 3D reconnection processes strongly characterize the dynamics in an ample range of the dimensionless Lundquist/Hartmann numbers, as well as in experimental...

Importance of Parallel Dispersion in ICRF Modelling of Travelling Wave Antenna Concept in DEMO-Like Plasmas in 2D Axisymmetry

B. Zaar$^1$, T. Johnson$^1$, L. Bähner$^1$, R. Bilato$^2$, R. Ragona$^3$, and P. Vallejos$^4$

$^1$KTH Royal Institute of Technology, Stockholm, SE-114 28, Sweden

$^2$Max-Planck-Institut für Plasmaphysik, Garching, D-85748, Germany

$^3$Department of Physics,...

M. F. F. Nave1, A. Mauriya1, M. Barnes2, E. Delabie3, J. Ferreira1, J. Garcia4 , A. Kirjasuo5, F.I. Parra6, M. Romanelli7 and JET Contributors*

EUROfusion Consortium, JET, Culham Science Centre, Abingdon, OX14 3DB, UK

1Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, P1049-001 Lisboa, Portugal

2Rudolf Peierls Centre for Theoretical Physics, Oxford University, UK

3Oak...

The dynamics of magnetic islands and the role they play in fusion plasmas are usually approached and predicted using extensions of the original theory by Rutherford [1, 2], on which estimates for their impact on the operation of present and future magnetic confinement devices are based. Likewise, diagnostics to detect their presence [3] and techniques to limit their impact are operated on the...

Implementation of an analytical Jacobian in the MEQ free-boundary tokamak equilibrium code suite

See attached PDF.

Recently, a general theoretical framework for the transport of Phase Space Zonal Structures (PSZS) has been developed \cite{zonca2015,falessi2019}. PSZS are the long-lived toroidal symmetric ($n=0$) structures that define the nonlinear equilibrium in the presence of fluctuations such as Alfv\'enic instabilities. In order to include sources and sinks and collisional slowing down processes, a...

Nonlinear inverse bremsstrahlung absorption (NLIBA) of intense electromagnetic waves in homogeneous plasmas may have significant impact on many physical phenomena through modifications of the electron distribution function (EDF). These modifications depend on the relevant parameter $ \alpha=\frac{v_0^2}{v_t^2\ } $, where $v_0 $ is the quiver velocity and $v_t $ is the electron thermal...

The performance of magnetic-confinement-fusion devices is often limited by the presence of turbulent fluctuations that lead to enhanced transport and energy losses. Both experimental and numerical investigations have shown that the turbulent fluctuations, and thus the transport properties of magnetised plasma, are influenced by the presence of sheared flows [1, 2, 3, 4]. Such flows can be...

The ST40 tokamak [1], built and operated by Tokamak Energy, is a high field spherical tokamak (ST), B=2.2T at R0=0.4 – 0.5m, A=1.6 – 1.9 with a mission to extend the ST reactor physics basis [2]. Overall energy confinement in STs is largely determined by turbulent electron heat transport, with ion thermal conductivity close to neoclassical levels in higher collisionality H-modes. Electron...

Until recently, theoretical studies in support of the commercial realization of fusion energy mostly focused on research in support of ITER and on the analysis of plasmas in existing tokamaks and stellarators, far from ignition conditions. Recent appearance of privately funded research has advanced alternative concepts, in particular the development of high-beta spherical configuration and...

A two-species (one main ion and electrons) fluid model for describing ion temperature gradient (ITG) turbulence in a Z-pinch magnetic geometry has been derived from gyrokinetics. Firstly, we carry out a mass ratio expansion ($\sqrt{m_e/m_i} \ll 1$) similar to the procedure introduced in \cite{Schekochihin_2009}. It is then followed by small $k_{\perp}\rho_i$ expansion, where $k_{\perp}$ is the...

Transport phenomena in fusion plasma devices can be categorized into turbulent and neoclassical parts. Although the primary contribution to particle and heat losses in both tokamaks and optimized stellarators is originates from turbulence, the significance of neoclassical transport theory should not be overlooked. Its applications, for example the prediction of the bootstrap current, are of...