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Comparisons of the nonlinear and the quasilinear model for the bump-on-tail instability with phase decorrelation
KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.ORCID iD: 0000-0002-3262-1958
KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.ORCID iD: 0000-0002-7142-7103
2014 (English)Conference paper, Published paper (Refereed)
Abstract [en]

The dynamics of discrete global modes in a toroidal plasma interacting with an energetic particle distribution is studied, and in particular when the dynamics of the system using the nonlinear and quasilinear descriptions are macroscopically similar. The dynamics can be described with a nonlinear bump-on-tail model in a two-dimensional phase space of particles. A Monte Carlo framework is developed for this model with an included decorrelation of the wave-particle phase, which is used to model extrinsic stochastisation of the wave-particle interactions. From this description, a quasilinear version of the model is also developed, which is described by a diffusive process in energy space due to the added phase decorrelation. Due to the reduced dimensionality of phase space, the quasilinear description is typically less computationally demanding than the nonlinear description. The purpose of the studies is to find conditions when a quasilinear model sufficiently describes the same phenomena of the wave-plasma interactions as a nonlinear model does. Via numerical and theoretical parameter studies, regimes where the two models overlap macroscopically are found. These regimes exist above a given threshold of the strength of the decorrelation, where coherent phase space structures are destroyed on time scales shorter than characteristic time scales of nonlinear particle motion in phase space close to the wave-particle resonance. Specifically for the quasilinear model, a theoretical value of the time scale of quasilinear flattening is derived and numerically verified.

Place, publisher, year, edition, pages
2014. Vol. 561
Series
Journal of Physics: Conference Series, ISSN 1742-6588
Keyword [en]
Dynamics, Time measurement, Wave plasma interactions
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-159056DOI: 10.1088/1742-6596/561/1/012019ISI: 000346423600019Scopus ID: 2-s2.0-84919338077OAI: oai:DiVA.org:kth-159056DiVA: diva2:782670
Conference
Joint Varenna-Lausanne International Workshop on the Theory of Fusion Plasmas, SEP 01-05, 2014, Varenna, ITALY
Note

QC 20150122

Available from: 2015-01-22 Created: 2015-01-20 Last updated: 2017-03-24Bibliographically approved
In thesis
1. The dynamics of Alfvén eigenmodes excited by energetic ions in toroidal plasmas
Open this publication in new window or tab >>The dynamics of Alfvén eigenmodes excited by energetic ions in toroidal plasmas
2015 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Experiments for the development of fusion power that are based on magnetic confinement deal with plasmas that inevitably contain energetic (non-thermal) particles. These particles come e.g. from fusion reactions or from external heating of the plasma. Ensembles of energetic ions can excite plasma waves in the Alfvén frequency range to such an extent that the resulting wave fields redistribute the energetic ions, and potentially eject them from the plasma. The redistribution of ions may cause a substantial reduction heating efficiency, and it may damage the inner walls and other components of the vessel. Understanding the dynamics of such instabilities is necessary to optimise the operation of fusion experiments and of future fusion power plants.

A Monte Carlo model that describes the nonlinear wave-particle dynamics in a toroidal plasma has been developed to study the excitation of the abovementioned instabilities. A decorrelation of the wave-particle phase is added in order to model stochasticity of the system (e.g. due to collisions between particles). Based on the nonlinear description with added phase decorrelation, a quasilinear version of the model has been developed, where the phase decorrelation has been replaced by a quasilinear diffusion coefficient in particle energy. When the characteristic time scale for macroscopic phase decorrelation becomes similar to or shorter than the time scales of nonlinear wave-particle dynamics, the two descriptions quantitatively agree on a macroscopic level. The quasilinear model is typically less computationally demanding than the nonlinear model, since it has a lower dimensionality of phase space.

In the presented studies, several effects on the macroscopic wave-particle dynamics by the presence of phase decorrelation have been theoretically and numerically analysed, e.g. effects on the growth and saturation of the wave amplitude, and on the so called frequency chirping events with associated hole-clump pair formation in particle phase space. Several effects coming from structures of the energy distribution of particles around the wave-particle resonance has also been studied.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2015. xiv, 71 p.
Series
TRITA-EE, ISSN 1653-5146 ; 2015:014
Keyword
Fusion plasma physics, tokamak, wave-particle interactions, toroidal Alfvén eigenmodes, bump-on-tail instabilities, magnetohydrodynamics, nonlinear dynamics, quasilinear dynamics, Hamiltonian mechanics, Monte Carlo method
National Category
Fusion, Plasma and Space Physics
Research subject
Electrical Engineering
Identifiers
urn:nbn:se:kth:diva-163127 (URN)978-91-7595-499-8 (ISBN)
Presentation
2015-05-22, Seminar Room, 3rd floor, Teknikringen 31, Stockholm, 13:15 (English)
Opponent
Supervisors
Funder
Swedish Research Council, 621-2011-5387
Note

QC 20150330

Available from: 2015-03-30 Created: 2015-03-27 Last updated: 2015-03-30Bibliographically approved
2. The dynamics of Alfvén eigenmodes excited by energetic ions in toroidal plasmas
Open this publication in new window or tab >>The dynamics of Alfvén eigenmodes excited by energetic ions in toroidal plasmas
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The future fusion power plants that are based on magnetic confinement will deal with plasmas that inevitably contain energetic (non-thermal) particles. These particles come, for instance, from fusion reactions or from external heating of the plasma. Ensembles of energetic ions can excite eigenmodes in the Alfvén frequency range to such an extent that the resulting wave fields redistribute the energetic ions, and potentially eject them from the plasma. The redistribution of ions may cause a substantial reduction of heating efficiency. Understanding the dynamics of such instabilities is necessary to optimise the operation of fusion experiments and of future fusion power plants.

Two models have been developed to simulate the interaction between energetic ions and Alfvén eigenmodes. One is a bump-on-tail model, of which two versions have been developed: one fully nonlinear and one quasilinear. The quasilinear version has a lower dimensionality of particle phase space than the nonlinear one. Unlike previous similar studies, the bump-on-tail model contains a decorrelation of the wave-particle phase in order to model stochasticity of the system. When the characteristic time scale for macroscopic phase decorrelation is similar to or shorter than the time scale of nonlinear wave-particle dynamics, the nonlinear and the quasilinear descriptions quantitatively agree. A finite phase decorrelation changes the growth rate and the saturation amplitude of the wave mode in systems with an inverted energy distribution around the wave-particle resonance. Analytical expressions for the correction of the growth rate and the saturation amplitude have been derived, which agree well with numerical simulations. A relatively weak phase decorrelation also diminishes frequency chirping events of the eigenmode.

The second model is called FOXTAIL, and it has a wider regime of validity than the bump-on-tail model. FOXTAIL is able to simulate systems with multiple eigenmodes, and it includes effects of different individual particle orbits relative to the wave fields. Simulations with FOXTAIL and the nonlinear bump-on-tail model have been compared in order to determine the regimes of validity of the bump-on-tail model quantitatively. Studies of two-mode scenarios confirmed the expected consequences of a fulfillment of the Chirikov criterion for resonance overlap. The influence of ICRH on the eigenmode-energetic ion system has also been studied, showing qualitatively similar effects as seen by the presence of phase decorrelation.

Another model, describing the efficiency of fast wave current drive, has been developed in order to study the influence of passive components close to the antenna, in which currents can be induced by the antenna generated wave field. It was found that the directivity of the launched wave, averaged over model parameters, was lowered by the presence of passive components in general, except for low values of the single pass damping of the wave, where the directivity was slightly increased, but reversed in the toroidal direction.

Abstract [sv]

De framtida fusionskraftverken baserade på magnetisk inneslutning kommer att hantera plasmor som oundvikligen innehåller energetiska (icke-termiska) partiklar. Dessa partiklar kommer exempelvis från fusionsreaktioner eller från externa uppvärmningsmekanismer av plasmat. Ensembler av energetiska joner kan excitera egenmoder i Alfvén-frekvensområdet i en sådan utsträckning att de resulterande vågfälten omfördelar de energetiska jonerna i rummet, och potentiellt slungar ut jonerna ur plasmat. Omfördelningen av joner kan orsaka en väsentligen minskad uppvärmningseffekt. Det är nödvändigt att förstå dynamiken hos denna typ av instabilitet för att kunna optimera verkningsgraden hos experiment och hos framtida fusionskraftverk.

Två modeller har utvecklats för att simulera interaktionen mellan energetiska joner och Alfvén-egenmoder. Den första är en bump-on-tail-modell, av vilken två versioner har utvecklats: en fullt icke-linjär och en kvasi-linjär. I den kvasi-linjära versionen har partiklarnas fasrum en lägre dimensionalitet än i den icke-linjära versionen. Till skillnad från tidigare liknande studier innehåller denna bump-on-tail-modell en dekorrelation av våg-partikelfasen för att modellera stokasticitet hos systemet. När den karakteristiska tidsskalan för makroskopisk fasdekorrelation är ungefär samma som eller kortare än tidsskalan för icke-linjär våg-partikeldynamik så stämmer den icke-linjära och den kvasi-linjära beskrivningen överens kvantitativt. En ändlig fasdekorrelation förändrar vågmodens tillväxthastighet och satureringsamplitud i system med en inverterad energifördelning omkring våg-partikelresonansen. Analytiska uttryck för korrektionen av tillväxthastigheten och satureringsamplituden har härletts, vilka stämmer väl överens med numeriska simuleringar. En relativt svag fasdekorrelation försvagar även "frequency chirping events" (snabba frekvensskiftningar i korttids-Fourier-transformen av egenmodens amplitudutveckling) hos egenmoden.

Den andra modellen, kallad FOXTAIL, har ett mycket bredare giltighetsområde än bump-on-tail-modellen. FOXTAIL kan simulera system med flera egenmoder, och den inkluderar effekter av olika enskilda partikelbanor relativt vågfälten. Simuleringar med FOXTAIL och med bump-on-tail-modellen har jämförts för att kvantitativt bestämma bump-on-tail-modellens giltighetsområde. Studier av scenarier med två egenmoder bekräftar de förväntade effekterna av när Chirikov-kriteriet för resonansöverlapp uppfylls. Även inflytandet av ICRH på dynamiken mellan egenmoder och energetiska joner har studerats, vilket har visat kvalitativt liknande effekter som har observerats i närvaron av fasdekorrelation.

En annan modell, vilken beskriver effektiviteten hos "fast wave current drive" (strömdrivning med snabba magnetosoniska vågor), har utvecklats för att studera inflytandet av passiva komponenter nära antennen, i vilka strömmar kan induceras av vågfälten som genereras av antennen. Det visades att den utskickade vågens direktivitet, medelvärdesbildat över modellparametrar, generellt sett minskade vid närvaron av passiva komponenter, förutom vid låg "sinlge pass damping" (dämpning av vågen vid propagering genom hela plasmat), då direktiviteten istället ökade något, men bytte tecken i toroidal riktning.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2016. 106 p.
Series
TRITA-EE, ISSN 1653-5146 ; 2016:141
Keyword
Fusion plasma physics, Tokamak, Wave–particle interactions, Toroidal Alfvén eigenmodes, Bump-on-tail instabilities, Magnetohydrodynamics, Nonlinear dynamics, Quasilinear dynamics, Hamiltonian mechanics, Monte Carlo method, ICRH, FWCD
National Category
Fusion, Plasma and Space Physics
Research subject
Electrical Engineering
Identifiers
urn:nbn:se:kth:diva-193029 (URN)978-91-7729-122-0 (ISBN)
Public defence
2016-10-28, D2, Lindstedtsvägen 5, Stockholm, 09:15 (English)
Opponent
Supervisors
Funder
Swedish Research Council, 621-2011-5387
Note

QC 20160927

Available from: 2016-09-27 Created: 2016-09-26 Last updated: 2017-06-08Bibliographically approved

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Tholerus, SimonJohnson, Thomas J.

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