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.

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.

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