| 1. |
- Eriksson, Frida, 1986, et al.
(författare)
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Kinetic theory of phase space plateaux in a non-thermal energetic particle distribution
- 2015
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Ingår i: Physics of Plasmas. - : AIP Publishing. - 1089-7674 .- 1070-664X. ; 22:9, s. art.no. 092126-
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Tidskriftsartikel (refereegranskat)abstract
- The transformation of kinetically unstable plasma eigenmodes into hole-clump pairs with temporally evolving carrier frequencies was recently attributed to the emergence of an intermediate stage in the mode evolution cycle, that of an unmodulated plateau in the phase space distribution of fast particles. The role of the plateau as the hole-clump breeding ground is further substantiated in this article via consideration of its linear and nonlinear stability in the presence of fast particle collisions and sources, which are known to affect the production rates and subsequent frequency sweeping of holes and clumps. In particular, collisional relaxation, as mediated by e.g. velocity space diffusion or even simple Krook-type collisions, is found to inhibit hole-clump generation and detachment from the plateau, as it should. On the other hand, slowing down of the fast particles turns out to have an asymmetrically destabilizing/stabilizing effect, which explains the well-known result that collisional drag enhances holes and their sweeping rates but suppresses clumps. It is further demonstrated that relaxation of the plateau edge gradients has only a minor quantitative effect and does not change the plateau stability qualitatively, unless the edge region extends far into the plateau shelf and the corresponding Landau pole needs to be taken into account.
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| 2. |
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| 3. |
- Håkansson, Frida, 1986, et al.
(författare)
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Directivity of frequency sweeping kinetic instabilities
- 2013
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Ingår i: 40th EPS Conference on Plasma Physics, EPS 2013; Espoo; Finland; 1 July 2013 through 5 July 2013. - 9781632663108 ; 1, s. 421-424
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Konferensbidrag (refereegranskat)
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| 4. |
- Lilley, Matthew, 1983, et al.
(författare)
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Collective fast ion effects in tokamaks
- 2010
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Ingår i: Meeting of the Swedish Research Unit, RUSA, November 10-11 2010, Stockholm.
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)
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| 5. |
- Lilley, Matthew, 1983, et al.
(författare)
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Drag induced energetic particle modes
- 2011
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Ingår i: International Sherwood Fusion Theory Conference, Austin, Texas, May 2 – 4, 2011.
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Konferensbidrag (refereegranskat)
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| 6. |
- Nyqvist, Robert, 1983, et al.
(författare)
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Adiabatic Description of Long Range Frequency Sweeping
- 2012
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Ingår i: Nuclear Fusion. - : IOP Publishing. - 1741-4326 .- 0029-5515. ; 52:9
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Tidskriftsartikel (refereegranskat)abstract
- A theoretical framework is developed to describe long range frequency sweeping events in the 1D electrostatic bump-on-tail model with fast particle sources and collisions. The model includes three collision operators (Krook, drag (dynamical friction) and velocity space diffusion), and allows for a general shape of the fast particle distribution function. The behaviour of phase space holes and clumps is analysed in the absence of diffusion, and the effect of particle trapping due to separatrix expansion is discussed. With a fast particle distribution function whose slope decays above the resonant phase velocity, hooked frequency sweeping is found for holes in the presence of drag collisions alone.
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| 7. |
- Nyqvist, Robert, 1983, et al.
(författare)
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Collisional Nonlinear Energetic Particle Modes
- 2010
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Ingår i: Meeting of the Swedish Research Unit, RUSA 2010, November 10 – 11 2010, Stockholm, Sweden.
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)
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| 8. |
- Nyqvist, Robert, 1983, et al.
(författare)
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Modeling of Long-Range Sweeping Phenomena
- 2011
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Ingår i: Joint US-EU TTF Workshop, San Diego, California, April 6 – 9, 2011 (oral presentation).
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Konferensbidrag (refereegranskat)
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| 9. |
- Nyqvist, Robert, 1983, et al.
(författare)
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Non-monotonic frequency sweeping of fast particle driven instabilities
- 2012
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Ingår i: 39th EPS Conference on Plasma Physics 2012, EPS 2012 and the 16th International Congress on Plasma Physics; Stockholm; Sweden; 2 July 2012 through 6 July 2012. - 9781622769810 ; 1, s. 619-622
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Konferensbidrag (refereegranskat)
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| 10. |
- Sharapov, S.E., et al.
(författare)
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Energetic particle instabilities in fusion plasmas
- 2013
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Ingår i: Nuclear Fusion. - : IOP Publishing. - 1741-4326 .- 0029-5515. ; 53:10, s. 104022-
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Tidskriftsartikel (refereegranskat)abstract
- Remarkable progress has been made in diagnosing energetic particle instabilities on present-day machines and in establishing a theoretical framework for describing them. This overview describes the much improved diagnostics of Alfvén instabilities and modelling tools developed world-wide, and discusses progress in interpreting the observed phenomena. A multi-machine comparison is presented giving information on the performance of both diagnostics and modelling tools for different plasma conditions outlining expectations for ITER based on our present knowledge.
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| 11. |
- Anderson, Dan, 1943, et al.
(författare)
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The least uncomfortable journey from A to B
- 2016
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Ingår i: American Journal of Physics. - : American Association of Physics Teachers (AAPT). - 0002-9505 .- 1943-2909. ; 84:9, s. 690-695
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Tidskriftsartikel (refereegranskat)abstract
- A short introduction is given about direct variational methods and their relation to Galerkin and moment methods, all flexible and powerful approaches for finding approximate solutions to difficult physicalequations. An application of these methods is given in the form of the variational problem of minimizing the discomfort experienced during different journeys, between two fixed horizontal points while keeping the travel time constant. The analysis is shown to provide simple, yet accurate, approximate solutions of the problem and illustrates the usefulness and the power of direct variational and moment methods. It also demonstrates the problem of a priori assessing the accuracy of the approximate solutions and illustrates that the variational solution does not necessarily provide a more accurate solution than that obtained by moment methods.
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| 12. |
- Eriksson, Frida, 1986, et al.
(författare)
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Kinetic theory of phase space plateaux
- 2015
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Ingår i: 42nd European Physical Society Conference on Plasma Physics, EPS 2015.
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Konferensbidrag (refereegranskat)
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| 13. |
- Lilley, M. K., et al.
(författare)
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Formation of Phase Space Holes and Clumps
- 2014
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Ingår i: Physical Review Letters. - 1079-7114 .- 0031-9007. ; 112:15
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Tidskriftsartikel (refereegranskat)abstract
- It is shown that the formation of phase space holes and clumps in kinetically driven, dissipative systems is not restricted to the near threshold regime, as previously reported and widely believed. Specifically, we observe hole-clump generation from the edges of an unmodulated phase space plateau, created via excitation, phase mixing and subsequent dissipative decay of a linearly unstable bulk plasma mode in the electrostatic bump-on-tail model. This has now allowed us to elucidate the underlying physics of the hole-clump formation process for the first time. Holes and clumps develop from negative energy waves that arise due to the sharp gradients at the interface between the plateau and the nearly unperturbed, ambient distribution and destabilize in the presence of dissipation in the bulk plasma. We confirm this picture by demonstrating that the formation of such nonlinear structures in general does not rely on a "seed" wave, only on the ability of the system to generate a plateau. In addition, we observe repetitive cycles of plateau generation and erosion, the latter due to hole-clump formation and detachment, which appear to be insensitive to initial conditions and can persist for a long time. We present an intuitive discussion of why this continual regeneration occurs.
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| 14. |
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| 15. |
- Nyqvist, Robert, 1983, et al.
(författare)
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Alfvén Waves in Tokamaks
- 2010
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Ingår i: Meeting of the Swedish Research Unit, RUSA 2010, November 10 – 11 2010, Stockholm, Sweden.
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)
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| 16. |
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| 17. |
- Nyqvist, Robert, 1983, et al.
(författare)
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Asymmetric radiative damping of low shear toroidal Alfven eigenmodes
- 2012
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Ingår i: Physics of Plasmas. - : AIP Publishing. - 1089-7674 .- 1070-664X. ; 19:8, s. Art. Nr. 082517-
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Tidskriftsartikel (refereegranskat)abstract
- Radiative damping of toroidicity-induced Alfven eigenmodes (TAEs) in tokamaks, caused by coupling to the kinetic Alfven wave (KAW), is investigated analytically in the limit of low magnetic shear. A significant asymmetry is found between the radiative damping of the odd TAE, whose frequency lies above the central TAE gap frequency omega(0), and that of the even TAE, with frequency omega
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| 18. |
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| 19. |
- Nyqvist, Robert, 1983, et al.
(författare)
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Fast Ion Driven Alfvén Eigenmodes within the q=1 Radius
- 2009
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Ingår i: 36th European Physical Society Conference on Plasma Physics 2009, EPS 2009; Sofia; Bulgaria; 29 June 2009 through 3 July 2009. - 9781622763368 ; 33 E2, s. 1527-1530
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Konferensbidrag (refereegranskat)
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| 20. |
- Nyqvist, Robert, 1983
(författare)
-
Fast Particle Driven Instabilities in Tokamak Plasmas
- 2013
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The burning plasmas of the next generation tokamak fusion experiment ITERwill contain signicant populations of highly energetic ions. Both fusion gener-ated alpha particles and fast ions accelerated by auxiliary heating schemes arecapable of exciting instabilities in the Alfven frequency range, which may inturn cause redistribution of energetic particles and lead to deleterious eventssuch as e.g. monster sawtooth crashes. On present day machines, many aspectsof fast ion collective eects are observed and well understood, including e.g. ex-citation of toroidal Alfven eigenmodes (TAEs) and frequency sweeping Alfvencascades. However, a currently hot topic is the role of kinetic and nonlinearAlfvenic instabilities, including explanations for rapid frequency sweeping andunambiguous identication of energetic particle modes.This thesis presents theoretical research carried out on the linear and non-linear dynamics of fast particle driven instabilities, with a major focus on suchevents in tokamaks. In the linear regime, we investigate particle behavior inthe presence of a given electromagnetic perturbation. In particular, we formu-late a condition on the prescribed wave amplitude to cause stochastic particlemotion and we calculate the rate coecients for the associated diusive ran-dom walks. We also derive analytic expressions for the damping rate of evenand odd TAEs, which arises as a result of non-ideal coupling to radially prop-agating waves. The damping is found to be weak for the odd mode, whichraises concern for the connement of energetic particles on ITER, where an-tiballooning instabilities are likely to be resonantly driven by passing, fusionborn alpha particles.Nonlinearly, we develop a simple one-dimensional model to investigate theimpact of signicant frequency shifts on the dynamics of frequency sweeping,weakly driven modes. We include a number of previously neglected long rangeeects that are all capable of signicantly altering the temporal frequencysweeping patterns. In the case when the fast particle collision operator con-tains both a drag-like slowing-down term, due to binary, small-angle Coulombcollisions, and velocity space diusion, the model predicts transiently hookedand steady state frequency sweeping patterns. The latter scenario turns outto be analytically tractable.
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| 21. |
- Nyqvist, Robert, 1983, et al.
(författare)
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Modeling of long range frequency sweeping for energetic particle modes
- 2013
-
Ingår i: Physics of Plasmas. - : AIP Publishing. - 1089-7674 .- 1070-664X. ; 20:4
-
Tidskriftsartikel (refereegranskat)abstract
- Long range frequency sweeping events are simulated numerically within a one-dimensional, electrostatic bump-on-tail model with fast particle sources and collisions. The numerical solution accounts for fast particle trapping and detrapping in an evolving wave field with a fixed wavelength, and it includes three distinct collisions operators: Drag (dynamical friction on the background electrons), Krook-type collisions, and velocity space diffusion. The effects of particle trapping and diffusion on the evolution of holes and clumps are investigated, and the occurrence of non-monotonic (hooked) frequency sweeping and asymptotically steady holes is discussed. The presented solution constitutes a step towards predictive modeling of frequency sweeping events in more realistic geometries.
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| 22. |
- Nyqvist, Robert, 1983, et al.
(författare)
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On wave-particle interaction in axisymmetric toroidal systems
- 2011
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Ingår i: Physica Scripta. - : IOP Publishing. - 1402-4896 .- 0031-8949. ; 84:1, s. 015503-
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Tidskriftsartikel (refereegranskat)abstract
- A general formalism is developed to describe the interaction of charged particles with electromagnetic waves in terms of coupled finite difference mapping equations that incorporate tokamak topology. The approach is based on considering non-adiabatic changes in the constants of particle motion and it covers a range of wave-particle resonance frequencies, from the precessional to cyclotron frequencies of both passing and trapped ions. The concept of overlapping resonances is used to estimate the threshold for a single plane wave to cause stochastic particle motion. In the stochastic regime, the process is Markovian, and particle diffusion in three-dimensional phase space takes place. Estimations of diffusion coefficients are carried out in the two cases of waves interacting with passing and trapped ions by means of the cyclotron and bounce resonances, respectively, and previously known results are recovered in the proper limits.
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| 23. |
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| 24. |
- Nyqvist, Robert, 1983, et al.
(författare)
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Radiative Damping of Low Shear Toroidal Alfvén Eigenmodes
- 2010
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Ingår i: 37th EPS Conference on Plasma Physics, June 21 – 25 2010, Dublin, Ireland.
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Konferensbidrag (refereegranskat)abstract
- An important issue for alpha-particle transport due to Alfvén instabilities in burningITER plasmas [1] is the number of unstable Alfvén eigenmodes (AEs) and their properties at high plasma pressure. Multiple low shear toroidal Alfv´en eigenmodes (LSTAEs) [2, 3, 4] are of major concern for ITER scenarios, where extended regions of low magnetic shear may exist in e.g. sawtoothing plasmas or hybrid regimes [1, 5]. In contrast to the conventional TAE, which has a single eigenfrequency per TAE gap, the number of LSTAEs per gap is given by l ~= Є/S [4], and can be quite large in a low-shear region.Moreover, LSTAEs are less affected by high plasma pressure than TAEs: in fact, the very discovery of LSTAEs was galvanised by DT experiments on TFTR, where unstable AEs were detected at very high plasma pressure [2]. More recently, LSTAEs were recognized as important features of sawtoothing tokamak plasmas. On JET, core localized ”tornado” modes (LSTAEs inside the q = 1 radius) were found to precede monster sawtooth crashes [6], and on Alcator C-Mod, frequency chirping AEs associated with very low shear were observed during the sawtooth cycle [7].In this contribution, we develop a theory of LSTAEs by incorporating non-ideal effects associated with finite ion Larmor gyroradius into the MHD model [4]. The radiativedamping for LSTAEs at the top and bottom of the TAE gap is calculated in the limit of high mode number and first order gyroradius, using the characteristic LSTAE ordering d/dr > m/r. We also estimate the LSTAE drive due to ICRH-accelerated fast ions [8] and obtain the mode excitation threshold for ICRH-driven TAEs.
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| 25. |
- Nyqvist, Robert, 1983, et al.
(författare)
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Spreading of collimated particle beams within a generalized Fokker-Planck diffusion equation
- 2009
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Ingår i: Nuclear Science and Engineering. - 0029-5639 .- 1943-748X. ; 163:1, s. 85-90
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Tidskriftsartikel (refereegranskat)abstract
- Recently, an expansion of the Boltzmann scattering operator describing the angular spreading of particle beams was given that included the effects of large angle scattering processes, thus generalizing the classical Fokker-Planck equation, valid in the limit of small angle scattering. The present work aims at making an analytical comparison between predictions based on the classical Fokker-Planck equation and those based on a generalized one, which includes a first-order correction term in the expansion of the Boltzmann scattering operator. The analysis is carried out for thin slabs where backscattering effects can be neglected and makes use of a moment approach, which leads to an infinite system of recursively coupled ordinary differential equations. The system is truncated in a consistent manner, and the effects of large angle scattering on the evolution of the moments are determined in explicit analytical form. An approximate similarity solution of the generalized Fokker-Planck equation is also found, and the results of both approaches provide a clear picture of the increased diffusive beam spreading due to large angle scattering. A comparison with previously published Monte Carlo simulation results shows good agreement.
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| 26. |
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| 27. |
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