A Description of the Full Particle Orbit Following SPIRAL Code for Simulating Fast-ion Experiments in Tokamaks
TL;DR: The SPIRAL code is a test-particle code and is a powerful numerical tool to interpret and plan fast-ion experiments in tokamaks as discussed by the authors, where the effects of high harmonic fast wave heating on the beam-ion slowing-down distribution in NSTX is also studied.
Abstract: The numerical methods used in the full particle-orbit following SPIRAL code are described and a number of physics studies performed with the code are presented to illustrate its capabilities. The SPIRAL code is a test-particle code and is a powerful numerical tool to interpret and plan fast-ion experiments in tokamaks. Gyro-orbit effects are important for fast ions in low-field machines such as NSTX and to a lesser extent in DIII-D. A number of physics studies are interlaced between the description of the code to illustrate its capabilities. Results on heat loads generated by a localized error-field on the DIII-D wall are compared with measurements. The enhanced Triton losses caused by the same localized error-field are calculated and compared with measured neutron signals. Magnetohydrodynamic (MHD) activity such as tearing modes and toroidicity-induced Alfven eigenmodes (TAEs) have a profound effect on the fast-ion content of tokamak plasmas and SPIRAL can calculate the effects of MHD activity on the confined and lost fast-ion population as illustrated for a burst of TAE activity in NSTX. The interaction between ion cyclotron range of frequency (ICRF) heating and fast ions depends solely on the gyro-motion of the fast ions and is captured exactly in the SPIRAL code. A calculation of ICRF absorption on beam ions in ITER is presented. The effects of high harmonic fast wave heating on the beam-ion slowing-down distribution in NSTX is also studied.
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TL;DR: 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 is given in this article.
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?n 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).
222 citations
TL;DR: In this article, the stability of the Alfven Eigenmodes in the ITER 15 MA baseline scenario was investigated and it was found that only in the outer half of the plasma (r/a>0.5) can the fast ions overcome the thermal ion Landau damping.
Abstract: This paper discusses the behaviour and consequences of the expected populations of energetic ions in ITER plasmas. It begins with a careful analytic and numerical consideration of the stability of Alfven Eigenmodes in the ITER 15 MA baseline scenario. The stability threshold is determined by balancing the energetic ion drive against the dominant damping mechanisms and it is found that only in the outer half of the plasma (r/a>0.5) can the fast ions overcome the thermal ion Landau damping. This is in spite of the reduced numbers of alpha-particles and beam ions in this region but means that any Alfven Eigenmode-induced redistribution is not expected to influence the fusion burn process. The influence of energetic ions upon the main global MHD phenomena expected in ITER's primary operating scenarios, including sawteeth, neoclassical tearing modes and Resistive Wall Modes, is also reviewed. Fast ion losses due to the non-axisymmetric fields arising from the finite number of toroidal field coils, the inclusio...
112 citations
TL;DR: The physics of non-axisymmetry is a far more important topic in the theory of toroidal fusion plasmas than might be expected as discussed by the authors, and even a small toroidal asymmetry in the magnetic field strength can cause an unacceptable degradation in performance.
Abstract: The physics of non-axisymmetry is a far more important topic in the theory of toroidal fusion plasmas than might be expected. (1) Even a small toroidal asymmetry in the magnetic field strength, ?????ln?B/?????10?4, can cause an unacceptable degradation in performance. (2) Nevertheless, asymmetries?even large asymmetries ????1?can give beneficial plasma control and circumvent issues, such as magnetic-configuration maintenance and plasma disruptions, that make axisymmetric fusion devices problematic. Viewed from prospectives that are adequate for designing and studying axisymmetric plasmas, the physics of non-axisymmetric plasmas appears dauntingly difficult. Remarkably, Maxwell's equations provide such strong constraints on the physics of toroidal fusion plasmas that even a black-box model of a plasma answers many important questions. Kinetic theory and non-equilibrium thermodynamics provide further, but more nuanced, constraints. This paper is organized so these constraints can be used as a basis for the innovations and for the extrapolations that are required to go from existing experiments to fusion systems. Outlines are given of a number of calculations that would be of great importance to ITER and to the overall fusion program and that could be carried out now with limited resources.
70 citations
TL;DR: The National Spherical Torus Experiment (NSTX-U) as mentioned in this paper has been used to test physics theories for next-step tokamak operation, including ITER.
Abstract: Research on the National Spherical Torus Experiment, NSTX, targets physics understanding needed for extrapolation to a steady-state ST Fusion Nuclear Science Facility, pilot plant, or DEMO. The unique ST operational space is leveraged to test physics theories for next-step tokamak operation, including ITER. Present research also examines implications for the coming device upgrade, NSTX-U. An energy confinement time, ?E, scaling unified for varied wall conditions exhibits a strong improvement of BT?E with decreased electron collisionality, accentuated by lithium (Li) wall conditioning. This result is consistent with nonlinear microtearing simulations that match the experimental electron diffusivity quantitatively and predict reduced electron heat transport at lower collisionality. Beam-emission spectroscopy measurements in the steep gradient region of the pedestal indicate the poloidal correlation length of turbulence of about ten ion gyroradii increases at higher electron density gradient and lower Ti gradient, consistent with turbulence caused by trapped electron instabilities. Density fluctuations in the pedestal top region indicate ion-scale microturbulence compatible with ion temperature gradient and/or kinetic ballooning mode instabilities. Plasma characteristics change nearly continuously with increasing Li evaporation and edge localized modes (ELMs) stabilize due to edge density gradient alteration. Global mode stability studies show stabilizing resonant kinetic effects are enhanced at lower collisionality, but in stark contrast have almost no dependence on collisionality when the plasma is off-resonance. Combined resistive wall mode radial and poloidal field sensor feedback was used to control n?=?1 perturbations and improve stability. The disruption probability due to unstable resistive wall modes (RWMs) was surprisingly reduced at very high ?N/li?>?10 consistent with low frequency magnetohydrodynamic spectroscopy measurements of mode stability. Greater instability seen at intermediate ?N is consistent with decreased kinetic RWM stabilization. A model-based RWM state-space controller produced long-pulse discharges exceeding ?N?=?6.4 and ?N/li?=?13. Precursor analysis shows 96.3% of disruptions can be predicted with 10?ms warning and a false positive rate of only 2.8%. Disruption halo currents rotate toroidally and can have significant toroidal asymmetry. Global kinks cause measured fast ion redistribution, with full-orbit calculations showing redistribution from the core outward and towards V?/V?=?1 where destabilizing compressional Alfv?n eigenmode resonances are expected. Applied 3D fields altered global Alfv?n eigenmode characteristics. High-harmonic fast-wave (HHFW) power couples to field lines across the entire width of the scrape-off layer, showing the importance of the inclusion of this phenomenon in designing future RF systems. The snowflake divertor configuration enhanced by radiative detachment showed large reductions in both steady-state and ELM heat fluxes (ELMing peak values down from 19?MW?m?2 to less than 1.5?MW?m?2). Toroidal asymmetry of heat deposition was observed during ELMs or by 3D fields. The heating power required for accessing H-mode decreased by 30% as the triangularity was decreased by moving the X-point to larger radius, consistent with calculations of the dependence of E???B shear in the edge region on ion heat flux and X-point radius. Co-axial helicity injection reduced the inductive start-up flux, with plasmas ramped to 1?MA requiring 35% less inductive flux. Non-inductive current fraction (NICF) up to 65% is reached experimentally with neutral beam injection at plasma current Ip?=?0.7?MA and between 70?100% with HHFW application at Ip?=?0.3?MA. NSTX-U scenario development calculations project 100% NICF for a large range of 0.6?
59 citations
Journal Article•
TL;DR: A detailed knowledge of the interplay between MHD instabilities and energetic particles has been gained from direct measurements of fast-ion losses (FILs) using a scintillator based FIL detector as mentioned in this paper.
Abstract: A detailed knowledge of the interplay between MHD instabilities and energetic particles has been gained from direct measurements of fast-ion losses (FILs). Time-resolved energy and pitch angle measurements of FIL caused by neoclassical tearing modes (NTMs) and toroidicity-induced Alfven eigenmodes (TAEs) have been obtained using a scintillator based FIL detector. The study of FIL due to TAEs has revealed the existence of a new core-localized MHD fluctuation, the Sierpes mode. The Sierpes mode is a non-pure Alfvenic fluctuation which appears in the acoustic branch, dominating the transport of fast-ions in ICRF heated discharges. The internal structure of both TAEs and Sierpes mode has been reconstructed by means of highly resolved multichord soft x-ray measurements. A spatial overlapping of their eigenfunctions leads to a FIL coupling, showing the strong influence that a core-localized fast-ion driven MHD instability may have on the fast-ion transport. We have identified the FIL mechanisms due to NTMs as well as due to TAEs. Drift islands formed by fast-ions in particle phase space are responsible for the loss of NBI fast-ions due to NTMs. In ICRF heated plasmas, a resonance condition fulfilled by the characteristic trapped fast-ion orbit frequencies leads to a phase matching between fast-ion orbit and NTM or TAE magnetic fluctuation. The banana tips of a resonant trapped fast-ion bounce radially due to an E × B drift in the TAE case. The NTM radial bounce of the fast-ion banana tips is caused by the radial component of the perturbed magnetic field lines.
46 citations
References
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Abstract: This book offers a thoroughly updated guide to the MPI (Message-Passing Interface) standard library for writing programs for parallel computers Since the publication of the previous edition of Using MPI, parallel computing has become mainstream Today, applications run on computers with millions of processors; multiple processors sharing memory and multicore processors with multiple hardware threads per core are common The MPI-3 Forum recently brought the MPI standard up to date with respect to developments in hardware capabilities, core language evolution, the needs of applications, and experience gained over the years by vendors, implementers, and users This third edition of Using MPI reflects these changes in both text and example code The book takes an informal, tutorial approach, introducing each concept through easy-to-understand examples, including actual code in C and Fortran Topics include using MPI in simple programs, virtual topologies, MPI datatypes, parallel libraries, and a comparison of MPI with sockets For the third edition, example code has been brought up to date; applications have been updated; and references reflect the recent attention MPI has received in the literature A companion volume, Using Advanced MPI, covers more advanced topics, including hybrid programming and coping with large data
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Book•
01 Aug 19911,230 citations
"A Description of the Full Particle ..." refers methods in this paper
...The SPIRAL code is written in the C language [10] and it makes use of the Numerical Algorithms Group (NAG) library routine: nag ode ivp adams gen (d02cjc) [11] which is a highly accurate, variable order, variable step size modified Adams method for solving the differential equations....
[...]
01 Dec 2004
TL;DR: The NRL Plasma Formulary originated over twenty five years ago and has been revised several times during this period, including the most recent revision in 2015.
Abstract: : The NRL Plasma Formulary originated over twenty five years ago and has been revised several times during this period
736 citations
TL;DR: In this article, an elementary but rigorous derivation for a variational principle for guiding center motion is given, and the application of variational principles in the derivation and solution of gyrokinetic equations is discussed.
Abstract: An elementary but rigorous derivation is given for a variational principle for guiding centre motion. The equations of motion resulting from the variational principle (the drift equations) possess exact conservation laws for phase volume, energy (for time-independent systems), and angular momentum (for azimuthally symmetric systems). The results of carrying the variational principle to higher order in the adiabatic parameter are displayed. The behaviour of guiding centre motion in azimuthally symmetric fields is discussed, and the role of angular momentum is clarified. The application of variational principles in the derivation and solution of gyrokinetic equations is discussed.
647 citations
TL;DR: The NUBEAM module as mentioned in this paper is a comprehensive computational model for Neutral Beam Injection (NBI) in tokamaks, which is used to compute power deposition, driven current, momentum transfer, fueling, and other profiles.
636 citations