| 1. |
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| 2. |
- Stahl, Adam, 1985, et al.
(författare)
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Kinetic modelling of runaway-electron dynamics
- 2015
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Ingår i: Proceedings of the 14th IAEA Technical Meeting on Energetic Particles in Magnetic Confinement Systems.
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Improved understanding of runaway-electron formation and decayprocesses are of prime interest for the safe operation of large tokamaks, and theirdynamics during dynamical scenarios such as disruptions are of particular concern. Inthis contribution, we present kinetic modelling of scenarios with time-dependent plasmaparameters – in particular, we investigate hot-tail runaway generation during a rapiddrop in plasma temperature. With the goal of studying runaway-electron generationwith a self-consistent electric field-evolution, we also discuss the implementation ofa conservative collision operator and demonstrate its properties. An operator foravalanche runaway-electron generation which includes the proper energy dependenceof the runaway distribution, is investigated, and the avalanche growth rate is shownto be significantly affected in some parameter regimes. These developments all pavethe way for an improved modelling of runaway-electron dynamics during disruptionsor other dynamic events.
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| 3. |
- Decker, Joan, 1977, et al.
(författare)
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Numerical characterization of bump formation in the runaway electron tail
- 2016
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Ingår i: Plasma Physics and Controlled Fusion. - : IOP Publishing. - 1361-6587 .- 0741-3335. ; 58:2, s. 025016-
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Tidskriftsartikel (refereegranskat)abstract
- Runaway electrons are generated in a magnetized plasma when the parallel electric field exceeds a critical value. For such electrons with energies typically reaching tens of MeV, the Abraham–Lorentz–Dirac (ALD) radiation force, in reaction to the synchrotron emission, is significant and can be the dominant process limiting electron acceleration. The effect of the ALD force on runaway electron dynamics in a homogeneous plasma is investigated using the relativistic finite-difference Fokker–Planck codes LUKE (Decker and Peysson 2004 Report EUR-CEA-FC-1736, Euratom-CEA), and CODE (Landreman et al 2014 Comput. Phys. Commun. 185 847). The time evolution of the distribution function is analyzed as a function of the relevant parameters: parallel electric field, background magnetic field, and effective charge. Under the action of the ALD force, we find that runaway electrons are subject to an energy limit, and that the electron distribution evolves towards a steady-state. In addition, a bump is formed in the tail of the electron distribution function if the electric field is sufficiently strong. The mechanisms leading to the bump formation and energy limit involve both the parallel and perpendicular momentum dynamics; they are described in detail. An estimate for the bump location in momentum space is derived. We observe that the energy of runaway electrons in the bump increases with the electric field amplitude, while the population increases with the bulk electron temperature. The presence of the bump divides the electron distribution into a runaway beam and a bulk population. This mechanism may give rise to beam-plasma types of instabilities that could, in turn, pump energy from runaway electrons and alter their confinement.
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| 4. |
- Embréus, Ola, 1991, et al.
(författare)
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Numerical calculation of ion runaway distributions
- 2015
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Ingår i: 42nd European Physical Society Conference on Plasma Physics, EPS 2015.
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Konferensbidrag (refereegranskat)abstract
- Numerical solver of the 2D ion Fokker-Planck equation has been presented, and its usefulness demonstrated in investigating the conditions required for ion runaway in cold and hot tokamak plasmas. It is shown that Alfvénic activity observed in disruption experiments are unlikely to be explained by the runaway mechanism alone.
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| 5. |
- Embréus, Ola, 1991, et al.
(författare)
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Numerical calculation of ion runaway distributions
- 2015
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Ingår i: Physics of Plasmas. - : AIP Publishing. - 1089-7674 .- 1070-664X. ; 22:5, s. 052122-
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Tidskriftsartikel (refereegranskat)abstract
- Ions accelerated by electric fields (so-called runaway ions) in plasmas may explain observations in solar flares and fusion experiments; however, limitations of previous analytic work have prevented definite conclusions. In this work, we describe a numerical solver of the 2D non-relativistic linearized Fokker-Planck equation for ions. It solves the initial value problem in velocity space with a spectral-Eulerian discretization scheme, allowing arbitrary plasma composition and time-varying electric fields and background plasma parameters. The numerical ion distribution function is then used to consider the conditions for runaway ion acceleration in solar flares and tokamak plasmas. Typical time scales and electric fields required for ion acceleration are determined for various plasma compositions, ion species, and temperatures, and the potential for excitation of toroidal Alfvén eigenmodes during tokamak disruptions is considered.
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| 6. |
- Hirvijoki, Eero, 1985, et al.
(författare)
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Radiation reaction induced non-monotonic features in runaway electron distributions
- 2015
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Ingår i: Journal of Plasma Physics. - 0022-3778 .- 1469-7807. ; 81:5, s. 475810502-
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Tidskriftsartikel (refereegranskat)abstract
- Runaway electrons, which are generated in a plasma where the induced electric field exceeds acertain critical value, can reach very high energies in the MeV range. For such energetic electrons,radiative losses will contribute significantly to the momentum space dynamics. Under certainconditions, due to radiative momentum losses, a non-monotonic feature – a “bump” – can formin the runaway electron tail, creating a potential for bump-on-tail-type instabilities to arise. Herewe study the conditions for the existence of the bump. We derive an analytical threshold conditionfor bump appearance and give an approximate expression for the minimum energy at which thebump can appear. Numerical calculations are performed to support the analytical derivations.
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| 7. |
- Newton, Sarah, 1981, et al.
(författare)
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Numerical calculation of ion runaway distributions
- 2015
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Ingår i: 57th Annual Meeting of the APS Division of Plasma Physics. ; 60:19, s. CP12.00118-
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Ion acceleration by electric fields is of interest in many plasma scenarios. Limitations of analytic descriptions prevent their general use in following the evolution of such ``runaway ion'' populations. Therefore we have implemented an initial value solver, CODION, for the linearized ion drift kinetic equation, with a non-relativistic Fokker-Planck collision operator. A spectral-Eulerian discretization scheme is used for 2D velocity space. The background plasma is taken to be homogeneous and static, with arbitrary composition. We demonstrate the use of the numerical distribution function to study ion acceleration in solar flares and tokamak plasmas. The variation of the strength and duration of the electric field required to produce a significant fast ion population is illustrated. Low frequency magnetic activity, indicative of toroidal Alfv\'{e}n eigenmode excitation, has been observed during tokamak disruptions. Taking typical disruption parameters, we show that accelerated bulk ions are unlikely to reach a sufficient velocity to provide the resonant drive.
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| 8. |
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| 9. |
- Stahl, Adam, 1985, et al.
(författare)
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Effective Critical Electric Field for Runaway-Electron Generation
- 2015
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Ingår i: Physical Review Letters. - 1079-7114 .- 0031-9007. ; 114:11, s. 115002-
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Tidskriftsartikel (refereegranskat)abstract
- In this Letter we investigate factors that influence the effective critical electric field for runaway-electrongeneration in plasmas. We present numerical solutions of the kinetic equation and discuss the implications forthe threshold electric field. We show that the effective electric field necessary for significant runaway-electronformation often is higher than previously calculated due to both (1) extremely strong dependence of primarygeneration on temperature, and (2) synchrotron radiation losses. We also address the effective critical field inthe context of a transition from runaway growth to decay. We find agreement with recent experiments, but showthat the observation of an elevated effective critical field can mainly be attributed to changes in the momentum-space distribution of runaways, and only to a lesser extent to a de facto change in the critical field.
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| 10. |
- Stahl, Adam, 1985, et al.
(författare)
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Reaction of runaway electron distributions to radiative processes
- 2015
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Ingår i: 57th Annual Meeting of the APS Division of Plasma Physics. ; 60:19, s. PP12.00103 -
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- The emission of electromagnetic radiation by a charged particle in accelerated motion is associated with a reduction in its energy, accounted for by the inclusion of a radiation reaction force in the kinetic equation. For runaway electrons in plasmas, the dominant radiative processes are the emission of bremsstrahlung and synchrotron radiation. In this contribution, we investigate the impact of the associated radiation reaction forces on the runaway electron distribution, using both analytical and numerical studies, and discuss the corresponding change to the runaway electron growth rate, which can be substantial. We also report on the formation of non-monotonic features in the runaway electron tail as a consequence of the more complicated momentum-space dynamics in the presence of radiation reaction.
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| 11. |
- Hirvijoki, Eero, 1985, et al.
(författare)
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Gaussian radial basis functions for plasma physics: Numerical aspects
- 2015
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Ingår i: 42nd European Physical Society Conference on Plasma Physics, EPS 2015, Lisbon, Portugal, 22-26 June 2015.
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Konferensbidrag (refereegranskat)abstract
- A magnetized plasma is described by the Vlasov equation and the non-linear Fokker-Planck collision operator [1]. The Vlasov part describes phase-space advection and the collision operator adds dissipation due to collisional energy and momentum exchange. Numerical discretization of the collision operator, however, is far from trivial. Recently, we have developed a new approach [2] to address this issue. The new approach is based on an expansion in Gaussian Radial Basis Functions (RBFs), a method widely used in neural network calculations [3]. In this paper, we discusss useful details regarding the numerical implementation of the RBF method.
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| 12. |
- Hirvijoki, Eero, 1985, et al.
(författare)
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Guiding-center transformation of the radiation-reaction force in a nonuniform magnetic field
- 2015
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Ingår i: Journal of Plasma Physics. - 0022-3778 .- 1469-7807. ; 81:5, s. 475810504-
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we present the guiding-center transformation of the radiation-reaction force of a classical point charge traveling in a nonuniform magnetic field. The transformation is valid as long as the gyroradius of the charged particles is much smaller than the magnetic field nonuniformity length scale, so that the guiding-center Lie-transform method is applicable. Elimination of the gyromotion time scale from the radiation-reaction force is obtained with the Poisson bracket formalism originally introduced by [A. J. Brizard, Phys. Plasmas 11 4429 (2004)], where it was used to eliminate the fast gyromotion from the Fokker-Planck collision operator. The formalism presented here is applicable to the motion of charged particles in planetary magnetic fields as well as in magnetic confinement fusion plasmas, where the corresponding so-called synchrotron radiation can be detected. Applications of the guiding-center radiation-reaction force include tracing of charged particle orbits in complex magnetic fields as well as kinetic description of plasma when the loss of energy and momentum due to radiation plays an important role, e.g., for runaway electron dynamics in tokamaks.
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| 13. |
- Hirvijoki, Eero, 1985, et al.
(författare)
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Monte Carlo method and High Performance Computing for solving Fokker–Planck equation of minority plasma particles
- 2015
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Ingår i: Journal of Plasma Physics. - 0022-3778 .- 1469-7807. ; 81:3, s. Art. no. 435810301 -
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Tidskriftsartikel (refereegranskat)abstract
- This paper explains how to obtain the distribution function of minority ions in tokamak plasmas using the Monte Carlo method. Since the emphasis is on energetic ions, the guiding-center transformation is outlined, including also the transformation of the collision operator. Even within the guiding-center formalism, the fast particle simulations can still be very CPU intensive and, therefore, we introduce the reader also to the world of high-performance computing. The paper is concluded with a few examples where the presented method has been applied.
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| 14. |
- Hirvijoki, Eero, 1985, et al.
(författare)
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The Gaussian Radial Basis Function Method for Plasma Kinetic Theory
- 2015
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Ingår i: Physics Letters, Section A: General, Atomic and Solid State Physics. - : Elsevier BV. - 0375-9601. ; 379:42, s. 2735-2739
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Tidskriftsartikel (refereegranskat)abstract
- Description of a magnetized plasma involves the Vlasov equation supplemented with the non-linear Fokker–Planck collision operator. For non-Maxwellian distributions, the collision operator, however, is difficult to compute. In this Letter, we introduce Gaussian Radial Basis Functions (RBFs) to discretize the velocity space of the entire kinetic system, and give the corresponding analytical expressions for the Vlasov and collision operator. Outlining the general theory, we also highlight the connection to plasma fluid theories, and give 2D and 3D numerical solutions of the non-linear Fokker–Planck equation. Applications are anticipated in both astrophysical and laboratory plasmas.
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| 15. |
- Varje, J., et al.
(författare)
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Effect of plasma response on the fast ion losses due to ELM control coils in ITER
- 2016
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Ingår i: Nuclear Fusion. - : IOP Publishing. - 1741-4326 .- 0029-5515. ; 56:4
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Tidskriftsartikel (refereegranskat)abstract
- Mitigating edge localized modes (ELMs) with resonant magnetic perturbations (RMPs) can increase energetic particle losses and resulting wall loads, which have previously been studied in the vacuum approximation. This paper presents recent results of fusion alpha and NBI ion losses in the ITER baseline scenario modelled with the Monte Carlo orbit following code ASCOT in a realistic magnetic field including the effect of the plasma response. The response was found to reduce alpha particle losses but increase NBI losses, with up to 4.2% of the injected power being lost. Additionally, some of the load in the divertor was found to be shifted away from the target plates toward the divertor dome.
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| 16. |
- Äkäslompolo, S, et al.
(författare)
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Calculating the 3D magnetic field of ITER for European TBM studies
- 2015
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Ingår i: Fusion Engineering and Design. - 0920-3796.
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Tidskriftsartikel (refereegranskat)abstract
- The magnetic perturbation due to the ferromagnetic test blanket modules (TBMs) may deteriorate fast ion confinement in ITER. This effect must be quantified by numerical studies in 3D. We have implemented a combined finite element method (FEM) – Biot-Savart law integrator method (BSLIM) to calculate the ITER 3D magnetic field and vector potential in detail. Unavoidable geometry simplifications changed the mass of the TBMs and ferritic inserts (FIs) up to 26%. This has been compensated for by modifying the nonlinear ferromagnetic material properties accordingly. Despite the simplifications, the computation geometry and the calculated fields are highly detailed. The combination of careful FEM mesh design and using BSLIM enables the use of the fields unsmoothed for particle orbit-following simulations. The magnetic field was found to agree with earlier calculations and revealed finer details. The vector potential is intended to serve as input for plasma shielding calculations.
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| 17. |
- Äkäslompolo, S, et al.
(författare)
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ITER fast ion confinement in the presence of the European test blanket module
- 2015
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Ingår i: Nuclear Fusion. - 1741-4326 .- 0029-5515. ; 55:9, s. 093010-
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Tidskriftsartikel (refereegranskat)abstract
- This paper addresses the confinement of thermonuclear alpha particles and neutral beam injected deuterons in the 15 MA Q = 10 inductive scenario in the presence of the magnetic perturbation caused by the helium cooled pebble bed test blanket module using the vacuum approximation. Both the flat top phase and plasma ramp-up are studied. The transport of fast ions is calculated using the Monte Carlo guiding center orbit-following code ASCOT. A detailed three-dimensional wall, derived from the ITER blanket module CAD data, is used for evaluating the fast ion wall loads. The effect of the test blanket module is studied for both overall confinement and possible hot spots. The study indicates that the test blanket modules do not significantly deteriorate the fast ion confinement.
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