Electrostatic gyrokinetic simulation of global tokamak boundary plasma and the generation of nonlinear intermittent turbulence

S. Ku, R.M. Churchill, C.S. Chang, and R. Hager, E.S. Yoon, M. Adams, E. D’Azevedo, P. H. Worley

January 26, 2017

**Introduction**

Understanding physics in the boundary region of a tokamak plasma is critically important for the fusion performance in the core plasma and for the integrity of the material surface surrounding the boundary plasma. The global plasma confinement and the divertor heatload width depends on the transport property of the edge plasma. However, understanding the boundary plasma has been difficult due to the nonlinear multiscale nature of the scaleinseparable multi-physics, magnetic separatrix, plasma interaction with material wall, and the existence of neutral particles. The scale inseparable multi-scale physics includes background profile evolution, neoclassical particle orbit dynamics, and plasma turbulence and instability. Since the boundary plasma is in a non-thermal equilibrium state with strong sources and sinks, and the particle orbital motions sampling widely different physical regions, it is not in a Maxwellian state. A fluid approximation may not produce a high fidelity boundary physics. The best way to understand the boundary physics at high fidelity at this time is to use a large-scale gyrokinetic simulation. However, the existing gyrokinetic codes developed for the core plasma have difficulty in simulating the boundary plasma due to the difficulties described above.

An improved current potential method for fast computation of stellarator coil shapes

Matt Landreman

September 15, 2016

**Abstract**

Several fast methods for computing stellarator coil shapes are compared, including the classical NESCOIL procedure [Merkel, Nucl. Fusion 27, 867 (1987)], its generalization using truncated singular value decomposition, and a Tikhonov regularization approach we call REGCOIL in which the squared current density is included in the objective function. Considering W7-X and NCSX geometries, and for any desired level of regularization, we find the REGCOIL approach simultaneously achieves lower surface-averaged and maximum values of both current density (on the coil winding surface) and normal magnetic field (on the desired plasma surface). This approach therefore can simultaneously improve the free-boundary reconstruction of the target plasma shape while substantially increasing the minimum distances between coils, preventing collisions between coils while improving access for ports and maintenance. The REGCOIL method also allows finer control over the level of regularization, and it eliminates two pathologies of NESCOIL: the resulting coil shapes become independent of the arbitrary choice of angles used to parameterize the coil surface, and the resulting coil shapes converge rather than diverge as Fourier resolution is increased. We therefore contend that REGCOIL should be used instead of NESCOIL for applications in which a fast and robust method for coil calculation is needed, such as when targeting coil complexity in fixed-boundary plasma optimization, or for scoping new stellarator geometries.

Intrinsic Turbulence Stabilization in a Stellarator

P. Xanthopoulos, G. G. Plunk, A. Zocco, and P. Helander

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

(Received 12 February 2016; published 7 June 2016)

**Abstract**

The magnetic surfaces of modern stellarators are characterized by complex, carefully optimized shaping and exhibit locally compressed regions of strong turbulence drive. Massively parallel computer simulations of plasma turbulence reveal, however, that stellarators also possess two intrinsic mechanisms to mitigate the effect of this drive. In the regime where the length scale of the turbulence is very small compared to the equilibrium scale set by the variation of the magnetic field, the strongest fluctuations form narrow bandlike structures on the magnetic surfaces. Thanks to this localization, the average transport through the surface is significantly smaller than that predicted at locations of peak turbulence. This feature results in a numerically observed upshift of the onset of turbulence on the surface towards higher ion temperature gradients as compared with the prediction from the most unstable regions. In a second regime lacking scale separation, the localization is lost and the fluctuations spread out on the magnetic surface. Nonetheless, stabilization persists through the suppression of the large eddies (relative to the equilibrium scale), leading to a reduced stiffness for the heat flux dependence on the ion temperature gradient. These fundamental differences with tokamak turbulence are exemplified for the QUASAR stellarator [G. H. Neilson et al., IEEE Trans. Plasma Sci. 42, 489 (2014)].

Modeling non-stationary, non-axisymmetric heat patterns in DIII-D tokamak

D. Ciro, T. E. Evans, I. L. Caldas

(Submitted on 26 May 2016)

**Abstract**

Non-axisymmetric stationary magnetic perturbations lead to the formation of homoclinic tangles near the divertor magnetic saddle in tokamak discharges. These tangles intersect the divertor plates in static helical structures that delimit the regions reached by open magnetic field lines reaching the plasma column and leading the charged particles to the strike surfaces by parallel transport. In this article we introduce a non-axisymmetric rotating magnetic perturbation to model the time development of the three-dimensional magnetic field of a single-null DIII-D tokamak discharge developing a rotating tearing mode. The stable and unstable manifolds of the asymmetric magnetic saddle are calculated through an adaptive method providing the manifold cuts at a given poloidal plane and the strike surfaces. For the modeled shot, the experimental heat pattern and its time development are well described by the rotating unstable manifold, indicating the emergence of homoclinic lobes in a rotating frame due to the plasma instabilities. In the model it is assumed that the magnetic field is created by a stationary axisymmetric plasma current and a set of rotating internal helical filamentary currents. The currents in the filaments are adjusted to match the waveforms of the magnetic probes at the mid-plane and the rotating magnetic field is introduced as a perturbation to the axisymmetric field obtained from a Grad-Shafranov equilibrium reconstruction code.

The quest for fusion power

Steven C. Cowley

Nature Physics **12**, 384–386 (2016) doi:10.1038/nphys3719

Published online 03 May 2016

**Abstract**

Fusion power is one of a very few sustainable options to replace fossil fuels as the world’s primary energy source. Although the conditions for fusion have been reached, much remains to be done to turn scientific success into commercial electrical power.

A novel flexible field-aligned coordinate system for tokamak edge plasma simulation

J.Leddy, B.Dudson, M.Romanelli, B.Shanahan, N.Walkden

20 Apr 2016

**Abstract**

Tokamak plasmas are confined by a magnetic field that limits the particle and heat transport perpendicular to the field. Parallel to the field the ionised particles can move freely, so to obtain confinement the field lines are “closed” (ie. form closed surfaces of constant poloidal flux) in the core of a tokamak. Towards, the edge, however, the field lines begin to intersect physical surfaces, leading to interaction between neutral and ionised particles, and the potential melting of the material surface. Simulation of this interaction is important for predicting the performance and lifetime of future tokamak devices such as ITER. Field-aligned coordinates are commonly used in the simulation of tokamak plasmas due to the geometry and magnetic topology of the system. However, these coordinates are limited in the geometry they allow in the poloidal plane due to orthogonality requirements. A novel 3D coordinate system is proposed herein that relaxes this constraint so that any arbitrary, smoothly varying geometry can be matched in the poloidal plane while maintaining a field-aligned coordinate. This system is implemented in BOUT++ and tested for accuracy using the method of manufactured solutions. A MAST edge cross-section is simulated using a fluid plasma model and the results show expected behaviour for density, temperature, and velocity. Finally, simulations of an isolated divertor leg are conducted with and without neutrals to demonstrate the ion-neutral interaction near the divertor plate and the corresponding beneficial decrease in plasma temperature.

Isotope effects of trapped electron modes in the presence of impurities in tokamak plasmas

Yong Shen, J Q Dong, A P Sun, H P Qu, G M Lu, Z X He, H D He and L F Wang

Published 11 March 2016, IOP

**Abstract**

The trapped electron modes (TEMs) are numerically investigated in toroidal magnetized hydrogen, deuterium and tritium plasmas, taking into account the effects of impurity ions such as carbon, oxygen, helium, tungsten and others with positive and negative density gradients with the rigorous integral eigenmode equation. The effects of impurity ions on TEMs are investigated in detail. It is shown that impurity ions have substantially-destabilizing (stabilizing) effects on TEMs in isotope plasmas for L_{ez} ≡ L_{ne} ∕ L_{nz} >0(<0), opposite to the case of ion temperature gradient (ITG) driven modes. Detailed analyses of the isotope mass dependence for TEM turbulences in hydrogenic isotope plasmas with and without impurities are performed. The relations between the maximum growth rate of the TEMs with respect to the poloidal wave number and the ion mass number are given in the presence of the impurity ions. The results demonstrate that the maximum growth rates scale as γ_{max} ∝ M_{i}^{-0.5} in pure hydrogenic plasmas. The scale depends on the sign of its density gradient and charge number when there is a second species of (impurity) ions. When impurity ions have density profiles peaking inwardly (i.e. L_{ez} ≡ L_{ne} ∕ L_{nz}>0), the scaling also depends on ITG parameter η_{i}. The maximum growth rates scale as ν_{max}∝ M_{eff}^{-0.5} for the case without ITG (η_{i}=0) or the ITG parameter is positive (η_{i}>0) but the impurity ion charge number is low (Ζ≤ 5.0). However, when (ν> 0) and the impurity ion charge number is moderate (Ζ = 6.0-8.0), the scaling law is found as γ_{max} ≡ M_{eff}^{-1.0}. Here, Z is impurity ion charge number, and the effective mass number, M_{eff} = (1-f_{z})M_{i}+f_{z}M_{z}, with M_{i} and M_{z} being the mass numbers of the hydrogenic and impurity ions, respectively, and f_{z} = Z_{n0} ∕ n_{0e} being the charge concentration of impurity ions. In addition, with regard to the case of L_{ez} < 0, the maximum growth rate scaling is γ_{max} ≡ M_{i}^{-0.5}. The possible relations of the results with experimental observations are discussed.

Experimental and numerical study of error fields in the CNT stellarator

K C Hammond, A Anichowski, P W Brenner, T S Pedersen, S Raftopoulos, P Traverso, F A Volpe

Feb. 16, 2016

**Abstract**

Sources of error fields were indirectly inferred in a stellarator by reconciling computed and numerical flux surfaces. Sources considered so far include the displacements and tilts (but not the deformations, yet) of the four circular coils featured in the simple CNT stellarator. The flux surfaces were measured by means of an electron beam and phosphor rod, and were computed by means of a Biot-Savart field-line tracing code. If the ideal coil locations and orientations are used in the computation, agreement with measurements is poor. Discrepancies are ascribed to errors in the positioning and orientation of the invessel interlocked coils. To that end, an iterative numerical method was developed. A Newton-Raphson algorithm searches for the coils’ displacements and tilts that minimize the discrepancy between the measured and computed flux surfaces. This method was verified by misplacing and tilting the coils in a numerical model of CNT, calculating the flux surfaces that they generated, and testing the algorithm’s ability to deduce the coils’ displacements and tilts. Subsequently, the numerical method was applied to the experimental data, arriving at a set of coil displacements whose resulting field errors exhibited significantly improved quantitative and qualitative agreement with experimental results.

Nuclear Fusion-A Colossal Energy Source

Snehashis Das; Shamik Chattaraj; Anjana Sengupta; Kaustav Mallick;

Jan. 31, 2016

**Abstract**

With the fast depletion of all other conventional forms of energy resources, it became very much essential to opt for alternative that will be abundant enough to last for quite an effective period of time. Lately, a lot of experimentation and projects are being undertaken to implement nuclear fusion to serve the above purpose. We are familiar with the term nuclear fission i.e. heavier elements breaking down into smaller particles releasing energy; whereas Nuclear Fusion is a phenomenon reverse of fission i.e. lighter elements unites to form heavier elements with release of energy of much greater magnitude compared to fission. In the process of fusion, the Coulomb’s Forces are much lesser compared to the binding energy of the resulting nuclei. The very first baby step towards research on fusion began in the year 1929. Building upon the nuclear transmutation experiments by Ernest Rutherford, carried out several years earlier, the laboratory fusion of hydrogen isotopes was first accomplished by Mark Oliphant in 1932. Later on, during Manhattan Project (1940), the concept of fusion was thought for the first time for military purpose, and many other followed after. Research for civil purpose began only in 1950s through thermonuclear fusion. Two projects, the National Ignition Facility and ITER were proposed for the purpose. Designs such as ICF & TOKAMAK are the mega sized reactors upon which world are looking forward to. Although a German (Correction: American) company named Lockheed Martin has begun investigating a highly classified reactor of about 100MW (much smaller in size compared to TOKAMAK), its result are yet to be seen. What we need to make a summary about is how well this method (Nuclear fusion) can be used to explore the enormous amount of energy it can produce& what are the measures taken for this purpose.

Generic configuration stellarator based on several concentric Fourier windings

Vicente Queral

(Submitted on 12 Jan 2016)

**Abstract**

Stellarators commonly comprise different sets of coils to produce diverse magnetic configurations. However, the diversity of possible configurations in a single device is usually rather limited. The achievement of a broad variety of magnetic configurations might be valuable for some purposes, for example, to assay the effect of the magnetic configuration on turbulent transport. Thus, a method is created to systematically define sets of modular coils located on concentric toroidal winding surfaces. The method is based on the expression of a Last Closed Flux Surface (LCFS) by Fourier coefficients in cylindrical coordinates and consists in the definition of successive windings located on equidistant concentric winding surfaces, each winding such that produces a magnetic field which, when added to the magnetic field generated by a sole base winding that generates a base magnetic configuration, produces a magnetic configuration whose LCFS is defined by the Fourier coefficients of the base magnetic configuration plus only one new Fourier coefficient. The utilization of a diversity of currents in the different windings would give a linear combination of magnetic fields that reproduce the LCFS defined mathematically by the respective Fourier coefficients. The deviation between a particular modelled LCFS and the obtained LCFS from the windings depends on: the order and value of each Fourier coefficient, the selected shape of concentric winding surfaces, and the possible intersection of the LCFS with the internal winding surface. The method to generate the windings is reported and the application to one case study is described. Each modelled LCFS is compared with the respective Poincar\’e plot obtained from the linear combination of magnetic fields from the windings.

The Ignition Design Space of Magnetized Target Fusion

Irvin Lindemuth Ph.D.

Dec. 28, 2015

**Abstract**

The simple magnetized target implosion model of Lindemuth and Kirkpatrick (Nucl. Fusion 23, 263, 1983) has been extended to survey the potential parameter space in which three types of magnetized targets—cylindrical with axial magnetic field, cylindrical with azimuthal magnetic field, and spherical with azimuthal magnetic field—might achieve ignition and produce large gain at achievable radial convergence ratios. The model has been used to compute the dynamic, time-‐dependent behavior of many initial parameter sets that have been based upon projected ignition conditions using the quasi-‐ adiabatic and quasi-‐flux-‐conserving properties of magnetized target implosions. The time-‐dependent calculations have shown energy gains greater than 30 can potentially be achieved for each type of target. By example, it is shown that high gain may be obtained at extremely low convergence ratios, e.g., less than 15, for appropriate initial conditions. It is also shown that reaching the ignition condition, i.e., when fusion deposition rates equal total loss rates, does not necessarily lead to high gain and high fuel burn-‐up. At the lower densities whereby fusion temperatures can be reached in magnetized targets, the fusion burn rate may be only comparable to the hydrodynamic heating/cooling rates. On the other hand, when the fusion burn rates significantly exceed the hydrodynamic rates, the calculations show a characteristic rapid increase in temperature due to alpha particle deposition with a subsequent increased burn rate and high gain. A major result of this paper is that each type of target operates in a different initial density-‐energy-‐velocity range. The results of this paper provide initial target plasma parameters and driver parameters that can be used to guide plasma formation and driver development for magnetized targets. The results indicate that plasmas for spherical, cylindrical with azimuthal field, and cylindrical with axial field targets must have an initial density greater than approximately 10^{17}/cm^{3}, 10^{18}/cm^{3}, and 10^{20}/cm^{3}, respectively, implying constraints on target plasma formation research.

An Improved Neoclassical Drift-Magnetohydrodynamical Fluid Model of Helical Magnetic Island Equilibria in Tokamak Plasmas Richard Fitzpatrick, Institute for Fusion Studies, Department of Physics, University of Texas at Austin

19 Nov 2015

**Abstract**

The effect of the perturbed ion polarization current on the stability of neoclassical tearing modes is calculated using an improved, neoclassical, four-field, drift-MHD model. The calculation involves the self-consistent determination of the pressure and scalar electric potential profiles in the vicinity of the associated magnetic island chain, which allows the chain’s propagation velocity to be fixed. Two regimes are considered. First, a regime in which neoclassical ion poloidal flow damping is not strong enough to enhance the magnitude of the polarization current (relative to that found in slab geometry). Second, a regime in which neoclassical ion poloidal flow damping is strong enough to significantly enhance the magnitude of the polarization current. In both regimes, two types of solution are considered. First, a freely rotating solution (i.e., an island chain that is not interacting with a static, resonant, magnetic perturbation). Second, a locked solution (i.e., an island chain that has been brought to rest in the laboratory frame via interaction with a static, resonant, magnetic perturbation). In all cases, the polarization current is found to be either always stabilizing, or stabilizing provided that ηi ≡ d ln Ti/d ln ne does not exceed some threshold value. In certain ranges of ηi, the polarization current is found to have have a stabilizing effect on a freely rotating island, but a destabilizing effect on a corresponding locked island.

Tokamak Plasma Boundary Reconstruction Using Toroidal Harmonics and an Optimal Control Method

Blaise Faugeras, CASTOR Team-Project, INRIA and Laboratoire J.A. Dieudonné CNRS UMR 7351

Nov. 17, 2015

**Abstract**

This paper proposes a new fast and stable algorithm for the reconstruction of the plasma boundary from discrete magnetic measurements taken at several locations surrounding the vacuum vessel. The resolution of this inverse problem takes two steps. In the first one we transform the set of measurements into Cauchy conditions on a fixed contour ΓO close to the measurement points. This is done by least square fitting a truncated series of toroidal harmonic functions to the measurements. The second step consists in solving a Cauchy problem for the elliptic equation satisfied by the flux in the vacuum and for the overdetermined boundary conditions on ΓO previously obtained with the help of toroidal harmonics. It is reformulated as an optimal control problem on a fixed annular domain of external boundary ΓO and fictitious inner boundary ΓI . A regularized Kohn-Vogelius cost function depending on the value of the flux on ΓI and measuring the discrepency between the solution to the equation satisfied by the flux obtained using Dirichlet conditions on ΓO and the one obtained using Neumann conditions is minimized. The method presented here has led to the development of a software, called VacTH-KV, which enables plasma boundary reconstruction in any Tokamak.

GPEC, A Real-Time Capable Tokamak Equilibrium Code

M. Rampp, R. Preuss, R. Fischer and the ASDEX Upgrade Team

November 16, 2015

**Abstract**

A new parallel equilibrium reconstruction code for tokamak plasmas is presented. GPEC allows to compute equilibrium flux distributions sufficiently accurate to derive parameters for plasma control within 1 ms of runtime which enables real-time applications at the ASDEX Upgrade experiment (AUG) and other machines with a control cycle of at least this size. The underlying algorithms are based on the wellestablished offline-analysis code CLISTE, following the classical concept of iteratively solving the Grad-Shafranov equation and feeding in diagnostic signals from the experiment. The new code adopts a hybrid parallelization scheme for computing the equilibrium flux distribution and extends the fast, shared-memory-parallel Poisson solver which we have described previously by a distributed computation of the individual Poisson problems corresponding to different basis functions. The code is based entirely on open-source software components and runs on standard server hardware and software environments. The real-time capability of GPEC is demonstrated by performing an offline-computation of a sequence of 1000 flux distributions which are taken from one second of operation of a typical AUG discharge and deriving the relevant control parameters with a time resolution of a millisecond. On current server hardware the new code allows employing a grid size of 32 × 64 zones for the spatial discretization and up to 15 basis functions. It takes into account about 90 diagnostic signals while using up to 4 equilibrium iterations and computing more than 20 plasma-control parameters, including the computationally expensive safety-factor *q* on at least 4 different levels of the normalized flux.

Turbulence spreading as a non-local mechanism of global confinement degradation and ion temperature profile stiffness

S. Yi, J.M. Kwon, P.H. Diamond and T.S. Hahm

Published 11 August 2015

**Abstract**

A new non-local mechanism of the global confinement degradation and ion temperature profile stiffness is proposed based on the results of global gyrokinetic simulations. We find that turbulence spreading into a marginally stable zone can increase turbulent transport to a level exceeding the predictions of the local theories. Also, we present the first quantification of the parametric dependence of turbulence spreading and resulting confinement degradation on toroidal rotation shear and magnetic shear: turbulence spreading is significant for high magnetic shears s > 0.2, while it is slowed for low magnetic shears. The suppression of turbulence spreading by toroidal rotation shear is only effective for the low magnetic shears, which is in a good agreement with the experimental trends of core confinement improvement. Our findings suggest that the non-local mechanism is indispensable for accurate transport modeling in tokamak plasmas.

Thermo-fluid dynamics and corrosion analysis of a self cooled lead lithium blanket for the HiPER reactor

R. Juárez, C. Zanzi, J. Hernández and J. Sanz

Published 30 July 2015

**Abstract**

The HiPER reactor is the HiPER project phase devoted to power production. To reach a preliminary reactor design, tritium breeding schemes need to be adapted to the HiPER project technologies selection: direct drive ignition, 150 MJ/shot × 10 Hz of power released through fusion reactions, and the dry first wall scheme. In this paper we address the main challenge of the HiPER EUROFER-based self cooled lead lithium blanket, which is related to the corrosive behavior of Pb–15.7Li in contact with EUROFER. We evaluate the cooling and corrosion behavior of the so-called separated first wall blanket (SFWB) configuration by performing thermo-fluid dynamics simulations using a large eddy simulation approach. Despite the expected improvement over the integrated first wall blanket, we still find an unsatisfactory cooling performance, expressed as a low outlet Pb–15.7Li temperature plus too high corrosion rates derived from local Pb–15.7Li high temperature and velocity, which can mainly be attributed to the geometry of the channels. Nevertheless, the analysis allowed us to devise future modifications of the SFWB to overcome the limitations found with the present design.

Real-time capable first principle based modelling of tokamak turbulent transport

J. Citrin, S. Breton, F. Felici, F. Imbeaux, T. Aniel, J.F. Artaud, B. Baiocchi, C. Bourdelle, Y. Camenen and J. Garcia

Published 30 July 2015

**Abstract**

A real-time capable core turbulence tokamak transport model is developed. This model is constructed from the regularized nonlinear regression of quasilinear gyrokinetic transport code output. The regression is performed with a multilayer perceptron neural network. The transport code input for the neural network training set consists of five dimensions, and is limited to adiabatic electrons. The neural network model successfully reproduces transport fluxes predicted by the original quasilinear model, while gaining five orders of magnitude in computation time. The model is implemented in a real-time capable tokamak simulator, and simulates a 300 s ITER discharge in 10 s. This proof-of-principle for regression based transport models anticipates a significant widening of input space dimensionality and physics realism for future training sets. This aims to provide unprecedented computational speed coupled with first-principle based physics for real-time control and integrated modelling applications.

Experimental observation of response to resonant magnetic perturbation and its hysteresis in LHD

Y. Narushima, S. Sakakibara, S. Ohdachi, Y. Suzuki,K.Y. Watanabe, S. Nishimura, S. Satake, B. Huang, M. Furukawa, Y. Takemura, K. Ida, M. Yoshinuma, I. Yamada and The LHD Experiment Group

Published 5 June 2015

**Abstract**

The magnetic island in the large helical device (LHD) shows the dynamic behaviour of the healing/growth transition with the hysteretic behaviour. The thresholds of plasma beta and poloidal flow for island healing are larger than that for growth. The threshold of resonant magnetic perturbation (RMP) for healing is smaller than that for growth. Furthermore, thresholds of the amplitude of RMP depend on the magnetic axis position Rax in the LHD. The RMP threshold increases as the magnetic axis position Rax increases. The poloidal viscosity may be considered as a candidate to explain the experimental observation from the viewpoint of the relationship between the electromagnetic torque and the viscous torque.

WEST Physics Basis

C. Bourdelle, J.F. Artaud, V. Basiuk, M. B´ecoulet, S. Bremond, J. Bucalossi, H. Bufferand, G. Ciraolo, L. Colas, Y. Corre, X. Courtois, J. Decker, L. Delpech, P. Devynck, G. Dif-Pradalier, R.P. Doerner, D. Douai, R. Dumont, A. Ekedahl, N. Fedorczak, C. Fenzi, M. Firdaouss, J. Garcia, P. Ghendrih, C. Gil, G. Giruzzi, M. Goniche, C. Grisolia, A. Grosman, D. Guilhem, R. Guirlet, J. Gunn, P. Hennequin, J. Hillairet, T. Hoang, F. Imbeaux, I. Ivanova-Stanik, E. Joffrin, A. Kallenbach, J. Linke, T. Loarer, P. Lotte, P. Maget, Y. Marandet, M.L. Mayoral, O. Meyer, M. Missirlian, P. Mollard, P. Monier-Garbet, P. Moreau, E. Nardon, B. Pegourie, Y. Peysson, R. Sabot, F. Saint-Laurent, M. Schneider, J.M. Travere1, E. Tsitrone, S. Vartanian, L. Vermare, M. Yoshida, R. Zagorski and JET Contributors

Published 6 May 2015

**Abstract**

With WEST (Tungsten Environment in Steady State Tokamak) (Bucalossi et al 2014 Fusion Eng. Des. 89 907–12), the Tore Supra facility and team expertise (Dumont et al 2014 Plasma Phys. Control. Fusion 56 075020) is used to pave the way towards ITER divertor procurement and operation. It consists in implementing a divertor configuration and installing ITER-like actively cooled tungsten monoblocks in the Tore Supra tokamak, taking full benefit of its unique long-pulse capability. WEST is a user facility platform, open to all ITER partners. This paper describes the physics basis of WEST: the estimated heat flux on the divertor target, the planned heating schemes, the expected behaviour of the L–H threshold and of the pedestal and the potential W sources. A series of operating scenarios has been modelled, showing that ITER-relevant heat fluxes on the divertor can be achieved in WEST long pulse H-mode plasmas.

Advances in the physics basis for the European DEMO design

R. Wenninger, F. Arbeiter, J. Aubert, L. Aho-Mantila, R. Albanese, R. Ambrosino, C. Angioni, J.-F. Artaud, M. Bernert, E. Fable, A. Fasoli, G. Federici, J. Garcia, G. Giruzzi, F. Jenko, P. Maget, M. Mattei, F. Maviglia, E. Poli, G. Ramogida1, C. Reux, M. Schneider, B. Sieglin, F. Villone, M. Wischmeier and H. Zohm

Published 30 April 2015

**Abstract**

In the European fusion roadmap, ITER is followed by a demonstration fusion power reactor (DEMO), for which a conceptual design is under development. This paper reports the first results of a coherent effort to develop the relevant physics knowledge for that (DEMO Physics Basis), carried out by European experts. The program currently includes investigations in the areas of scenario modeling, transport, MHD, heating & current drive, fast particles, plasma wall interaction and disruptions.

Nuclear Fusion: Bringing a Star Down to Earth

A. Kirk, CCFE, Culham Science Centre, Abingdon, UK.

Published 29 Apr 2015

**Abstract**

Nuclear fusion offers the potential for being a near limitless energy source by fusing together deuterium and tritium nuclei to form helium inside a plasma burning at 100 million K. However, scientific and engineering challenges remain. This paper describes how such a plasma can be confined on Earth, and discusses the similarities and differences with fusion in stars. It focuses on the magnetic confinement technique and, in particular, the method used in a tokamak. The confinement achieved in the equilibrium state is reviewed and it is shown how the confinement can be too good, leading to explosive instabilities at the plasma edge called edge localised modes (ELMs). It is shown how the impact of ELMs can be minimised by the application of magnetic perturbations and discusses the physics behind the penetration of these perturbations into what is ideally a perfect conducting plasma.

On the power and size of tokamak fusion pilot plants and reactors

A.E. Costley, J. Hugill and P.F. Buxton

Published 28 January 2015

**Abstract**

It is generally accepted that the route to fusion power involves large devices of ITER scale or larger. However, we show,contrary to expectations, that for steady state tokamaks operating at fixed fractions of the density and beta limits, the fusion gain, Qfus, depends mainly on the absolute level of the fusion power and the energy confinement, and only weakly on the device size. Our investigations are carried out using a system code and also by analytical means. Further, we show that for the two qualitatively different global scalings that have been developed to fit the data contained in the ITER ELMy H-mode database, i.e. the normally used beta-dependent IPB98y2 scaling and the alternative beta-independent scalings, the power needed for high fusion performance differs substantially, typically by factors of three to four. Taken together, these two findings imply that lower power, smaller, and hence potentially lower cost, pilot plants and reactors than currently envisaged may be possible. The main parameters of a candidate low power (∼180 MW), high Qfus (∼5), relatively small (∼1.35m major radius) device are given.

Energetic particle physics in fusion research in preparation for burning plasma experiments

N.N. Gorelenkov, S.D. Pinches and K. Toi

Published 26 November 2014

**Abstract**

The area of energetic particle (EP) physics in fusion research has been actively and extensively researched in recent decades. The progress achieved in advancing and understanding EP physics has been substantial since the last comprehensive review on this topic by Heidbrink and Sadler (1994 Nucl. Fusion 34 535). That review coincided with the start of deuterium–tritium (DT) experiments on the Tokamak Fusion Test Reactor (TFTR) and full scale fusion alphas physics studies. Fusion research in recent years has been influenced by EP physics in many ways including the limitations imposed by the ‘sea’ of Alfv´en eigenmodes (AEs), in particular by the toroidicity-induced AE (TAE) modes and reversed shear AEs (RSAEs). In the present paper we attempt a broad review of the progress that has been made in EP physics in tokamaks and spherical tori since the first DT experiments on TFTR and JET (Joint European Torus), including stellarator/helical devices. Introductory discussions on the basic ingredients of EP physics, i.e., particle orbits in STs, fundamental diagnostic techniques of EPs and instabilities, wave particle resonances and others, are given to help understanding of the advanced topics of EP physics. At the end we cover important and interesting physics issues related to the burning plasma experiments such as ITER (International Thermonuclear Experimental Reactor).

Dynamics of L–H transition and I-phase in EAST

G.S. Xu, H.Q. Wang, M. Xu, B.N. Wan, H.Y. Guo, P.H. Diamond, G.R. Tynan, R. Chen, N. Yan, D.F. Kong, H.L. Zhao, A.D. Liu, T. Lan, V. Naulin, A.H. Nielsen, J. Juul Rasmussen, K. Miki, P. Manz, W. Zhang, L. Wang, L.M. Shao, S.C. Liu, L. Chen, S.Y. Ding, N. Zhao, Y.L. Li, Y.L. Liu, G.H. Hu, X.Q. Wu and X.Z. Gong

Published 16 September 2014

**Abstract**

The turbulence and flows at the plasma edge during the L–I–H, L–I–L and single-step L–H transitions have been measured directly using two reciprocating Langmuir probe systems at the outer midplane with several newly designed probe arrays in the EAST superconducting tokamak. The E × B velocity, turbulence level and turbulent Reynolds stress at ∼1 cm inside the separatrix ramp-up in the last ∼20 ms preceding the single-step L–H transition, but remain nearly constant near the separatrix, indicating an increase in the radial gradients at the plasma edge. The kinetic energy transfer rate from the edge turbulence to the E × B flows is significantly enhanced only in the last ∼10 ms and peaks just prior to the L–H transition. The E × B velocity measured inside the separatrix, which is typically in the electron diamagnetic drift direction in the L-mode, decays towards the ion diamagnetic drift direction in response to fluctuation suppression at the onset of the single-step L–H, L–I–L as well as L–I–H transitions. One important distinction between the L–I–H and the L–I–L transitions has been observed, with respect to the evolution of the edge pressure gradient and mean E×B flow during the I-phase. Both of them ramp up gradually during the L–I–H transition, but change little during the L–I–L transition, which may indicate that a gradual buildup of the edge pedestal and mean E×B flow during the I-phase leads to the final transition into the H-mode. In addition, the transition data in EAST strongly suggest that the divertor pumping capability is an important ingredient in determining the transition behaviour and power threshold.

Double-Pionic Fusion of Nuclear Systems and the ABC Effect — Approaching a Puzzle by Kinematically Complete Measurements

M. Bashkanov, C. Bargholtz, M. Berlowski, D. Bogoslawsky, H. Calén, H. Clement, L. Demiroers, E. Doroshkevich, D. Duniec, C. Ekström, K. Fransson, L. Geren, L. Gustafsson, B. Höistad, G. Ivanov, M. Jacewicz, E. Jiganov, T. Johansson, O. Khakimova, S. Keleta, I. Koch, F. Kren, S. Kullander, A. Kupsc, K. Lindberg, P. Marciniewski, R. Meier, B. Morosov, C. Pauly, H. Pettersson, Y. Petukhov, A. Povtorejko, A. Pricking, R.J.M.Y. Ruber, K. Schönning, W. Scobel, B. Shwartz, T. Skorodko, V. Sopov, J. Stepaniak, P.E. Tegner, P. Thörngren-Engblom, V. Tikhomirov, A. Turowiecki, G.J. Wagner, M. Wolke, J. Zabierowski, I. Zartova, J. Zlomanczuk

(CELSIUS/WASA Collaboration)

(Dated: January 21, 2014)

**Abstract**

The ABC effect — a puzzling low-mass enhancement in the *ππ* invariant mass spectrum — is well-known from inclusive measurements of two-pion production in nuclear fusion reactions. Here we report on first exclusive and kinematically complete measurements of the most basic double pionic fusion reaction *pn → dπ ^{0} π^{0}* at beam energies of 1.03 and 1.35 GeV. The measurements, which have been carried out at CELSIUS-WASA, reveal the ABC effect to be a

*(ππ)*channel phenomenon associated with both a resonance-like energy dependence in the integral cross section and the formation of a

_{I=L=0}*∆∆*system in the intermediate state. A corresponding simple

*s*-channel resonance ansatz provides a surprisingly good description of the data.

Dynamics of L–H transition and I-phase in EAST

R.J. Goldston, Princeton Plasma Physics Laboratory

8 November 2011

**Abstract**

A heuristic model for the plasma scrape-off width in low-gas-puff tokamak H-mode plasmas is introduced. Grad B and curv B drifts into the scrape-off layer (SOL) are balanced against near-sonic parallel flows out of the SOL, to the divertor plates. The overall particle flow pattern posited is a modification for open field lines of Pfirsch–Schluter flows to include order-unity sinks to the divertors. These assumptions result in an estimated SOL width of ∼2aρp/R. They also result in a first-principles calculation of the particle confinement time of H-mode plasmas, qualitatively consistent with experimental observations. It is next assumed that anomalous perpendicular electron thermal diffusivity is the dominant source of heat flux across the separatrix, investing the SOL width, derived above, with heat from the main plasma. The separatrix temperature is calculated based on a two-point model balancing power input to the SOL with Spitzer–Harm parallel thermal conduction losses to the divertor. This results in a heuristic closed-form prediction for the power scrape-off width that is in reasonable quantitative agreement both in absolute magnitude and in scaling with recent experimental data. Further work should include full numerical calculations, including all magnetic and electric drifts, as well as more thorough comparison with experimental data.