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  • 1.
    Bergkvist, Tommy
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Non-linear dynamics of Alfvén eigenmodes excited by fast ions in tokamaks2007Doctoral thesis, comprehensive summary (Other scientific)
    Abstract [en]

    The tokamak is so far the most promising magnetic configuration for achieving a net production of fusion energy. The D-T fusion reactions result in 3.5 MeV alpha-particles, which may destabilize Alfvén eigenmodes through wave-particle interaction. These instabilities redistribute the alpha-particles from the central region of the plasma towards the edge, where they are thermalized, and hence result in a reduced heating efficiency. The high-energy alpha-particles may even be thrown out of the plasma and may damage the wall.

    To investigate the destabilization of Alfvén eigenmodes by high-energy ions, ion cyclotron resonance heating (ICRH) and neutral beam injection (NBI) are often used to create a high-energy tail on the distribution function. The ICRH does not only produce high-energy anisotropic tails, it also decorrelates the wave-particle interaction with the Alfvén eigenmodes. Without decorrelation of the wave-particle interaction an ion will undergo a superadiabatic oscillation in phase space and there will be no net transfer of energy to the mode. For the thermal ions the decorrelation from collisions dominates while for the high-energy ions the decorrelation from ICRH dominates. As the unstable modes grow up, the gradients in phase space, which drive the mode, are reduced, resulting in a weaker drive. The dynamics of the system becomes non-linear due to a continuous restoration of the gradients by D-T reactions and ICRH.

    In this thesis the non-linear dynamics of toroidal Alfvén eigenmodes (TAEs) during ICRH has been investigated using the SELFO code. The SELFO code, which calculates the distribution function during ICRH self-consistently using a Monte-Carlo metod, has been upgraded to include interactions with TAEs. The fast decay of the mode amplitude as the ICRH is switched off, which is seen in experiments, as well as the oscillation of the mode amplitude as the distribution function is repetetively built up by the ICRH and flattened by the TAE has been reproduced using numerical simulations. In the presence of several unstable modes the dynamics become more complicated. The redistribution of an alpha-particle slowing down distribution function as well as the reduced heating efficiency in the presence of several modes has also been investigated.

  • 2.
    Bergkvist, Tommy
    et al.
    KTH, Superseded Departments, Electrical Systems.
    Hellsten, Torbjörn
    KTH, Superseded Departments, Electrical Systems.
    Self-consistent calculations of the distribution function and wave field during ICRF heating and global Alfvén wave excitation2004In: Proceeding of Theory of Fusions Plasmas, 2004, p. 123-132Conference paper (Refereed)
  • 3.
    Bergkvist, Tommy
    et al.
    KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Hellsten, Torbjörn A K
    KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Holmström, Kerstin
    KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Non-linear Alfvén eigenmode dynamics of a burning plasma in the presence of ion cyclotron resonance heating2006In: EPS Conf. Plasma Phys., EPS, 2006, p. 1792-1795Conference paper (Refereed)
    Abstract [en]

    Alfvén eigenmodes (AEs) excited by α particles in a burning plasma can degrade the heating efficiency by spatial redistribution of the resonant α particles. Changes of the orbit invariants in phase space by collisions and other waves, such as magnetosonic waves during ion cyclotron resonance heating (ICRH), lead to changes in the phase between the αs and AEs, causing a decorrelation of the interactions. ICRH lead to an increased decorrelation of the AE interactions and hence a stronger radial redistribution of the thermonuclear α particles by the AEs. Renewal of the distribution function by thermonuclear reactions and losses of α particles to the wall lead to a continuous drive of the AEs and a radial redistribution of the α particles. The redistribution results in a degradation of the heating efficiency.

  • 4.
    Bergkvist, Tommy
    et al.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics. KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Hellsten, Torbjörn
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics. KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Holmström, Kerstin
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics. KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Effects of ICRH on the dynamics of fast particle excited alfven eigenmodes2007In: Radio Frequency Power in Plasmas, American Institute of Physics (AIP), 2007, Vol. 933, p. 455-458Conference paper (Refereed)
    Abstract [en]

    ICRH is often used in experiments to simulate destabilization of Alfvén eigenmodes by thermonuclear α-particles. Whereas the slowing down distribution of α-particles is nearly isotropic, the ICRH creates an anisotropic distribution function with non-standard orbits. The ICRH does not only build up gradients in phase space, which destabilizes the AEs, but it also provides a strong phase decorrelation mechanism between ions and AEs. Renewal of the distribution function by thermonuclear reactions and losses of α-particles to the wall lead to a continuous drive of the AEs. Simulations of the non-linear dynamics of AEs and the impact they have on the heating profile due to particle redistribution are presented.

  • 5.
    Bergkvist, Tommy
    et al.
    KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Hellsten, Torbjörn
    KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Holmström, Kerstin
    KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Non-linear Alfvén Eigenmode Dynamic of Burning Plasma in the Presence of Ion Cyclotron Resonance Heating2006In: 33rd EPS Plasma Physics Conference, 2006Conference paper (Other academic)
    Abstract [en]

    Alfvén eigenmodes (AEs) excited by a particles in a burning plasma can degrade theheating efficiency by spatial redistribution of the resonant a particles. Changes of the orbitinvariants in phase space by collisions and other waves, such as magnetosonic waves duringion cyclotron resonance heating (ICRH), lead to changes in the phase between the as andAEs, causing a decorrelation of the interactions. ICRH lead to an increased decorrelation ofthe AE interactions and hence a stronger radial redistribution of the thermonuclear a particlesby the AEs. Renewal of the distribution function by thermonuclear reactions and lossesof a particles to the wall lead to a continuous drive of the AEs and a radial redistributionof the a particles. The redistribution results in a degradation of the heating efficiency.

  • 6.
    Bergkvist, Tommy
    et al.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Hellsten, Torbjörn
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Holmström, Kerstin
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Non-linear dynamics of Alfvén eigenmodes excited by thermonulcear alpha particles in the presence of ion cyclotron resonance heating2007In: Nuclear Fusion, ISSN 0029-5515, E-ISSN 1741-4326, Vol. 47, no 9, p. 1131-1141Article in journal (Refereed)
    Abstract [en]

    Alfvén eigenmodes (AEs) excited by thermonuclear α-particles can degrade the heating efficiency by spatial redistribution of the resonant α-particles. Changes of the orbit invariants in phase space by collisions and interactions with other waves, such as magnetosonic waves during ion cyclotron resonance heating (ICRH), lead to changes in the phase between the α-particles and AEs, causing a decorrelation of the interactions and stronger redistribution of the α-particles. Cyclotron interactions increase the decorrelation of the AE interactions with the high-energy ions and hence a stronger radial redistribution of the high-energy α-particles by the AEs. Renewal of the distribution function by thermonuclear reactions and losses of α-particles to the wall lead to a continuous drive of the AEs and a radial redistribution of the α-particles. The condition for excitation of AEs is shown to depend on the heating scenario where heating at the low field side creates a significant population of high-energy non-standard orbits which drive the modes. The redistribution results in a reduction in the averaged α-particle energy and a degradation of the heating efficiency. The effect on the distribution function in the presence of several unstable modes is not additive and the particle redistribution is found to saturate with an increasing number of modes.

  • 7.
    Bergkvist, Tommy
    et al.
    KTH, Superseded Departments, Alfvén Laboratory.
    Hellsten, Torbjörn
    KTH, Superseded Departments, Alfvén Laboratory.
    Johnson, T
    Laxåback, Martin
    KTH, Superseded Departments, Alfvén Laboratory.
    Nonlinear interaction between RF-heated high-energy ions and MHD-modes2003In: RADIO FREQUENCY POWER IN PLASMAS / [ed] Forest C.B., 2003, Vol. 694, p. 459-462Conference paper (Refereed)
    Abstract [en]

    Excitation of global Alfven eigenmodes by fast ions during ICRH is frequently observed in tokamaks. The importance of the phasing of the ICRH antennae for the excitation of these modes have been seen in experiments. The Alfven eigenmodes will drive the distribution function of the fast ions towards a state where the gradient in phase space is reduced. In general, the fast ions are displaced outwards, which can have a significant effect on the ICRH power deposition and lead to reduced heating efficiency. To calculate the effect on the heating profiles by the excitation of Alfven eigenmodes and the, effect on the resonating ions the Monte Carlo code FIDO, used for ICRH, has been upgraded to include particle interactions with MHD-waves. This allows self-consistent calculations of the mode amplitude and the distribution function during RF heating.

  • 8.
    Bergkvist, Tommy
    et al.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Hellsten, Torbjörn
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Johnson, T.
    Laxåback, Martin
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Non-linear study of fast particle excitation of global Alfvén eigenmodes during ICRH2005In: Nuclear Fusion, ISSN 0029-5515, E-ISSN 1741-4326, Vol. 45, p. 485-493Article in journal (Refereed)
    Abstract [en]

    High-power ion–cyclotron resonance heating (ICRH) can produce centrally peaked fast ion distributions with wide non-standard drift orbits exciting Alfvén eigenmodes (AEs). The dynamics of the AE excitation depends not only on the anisotropy and the peaking of the fast ion distribution but also on the decorrelation of the AE interactions and the renewal of the fast ions resonant with the AE by ion–cyclotron interactions. A method of self-consistently including the evolution of the distribution function of fast ions during excitation of AEs and ICRH has been developed and implemented in the SELFO code. Numerical simulations of the AE dynamics and ICRH give a variation of the AE amplitude consistent with the experimentally observed splitting of the mode frequency. The experimentally observed fast damping of the mode as the ICRH is switched off is also evident in the simulations.

  • 9.
    Bergkvist, Tommy
    et al.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Hellsten, Torbjörn
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Johnson, Thomas
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Self-consistent study of fast particle redistribution by Alfvén eigenmodes during Ion cyclotron resonance heating2005In: Proceedings of the 9th IAEA Technical Meeting on Energetic Particles in Magnetic Confinement Systems, 2005, p. 14-20Conference paper (Refereed)
  • 10.
    Hellsten, Torbjörn A. K.
    et al.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Holmström, Kerstin
    KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Johnson, Thomas J.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Bergkvist, Tommy
    KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Laxåback, Martin
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    On ion cyclotron emission in toroidal plasmas2006In: Nuclear Fusion, ISSN 0029-5515, E-ISSN 1741-4326, Vol. 46, no 7, p. S442-S454Article in journal (Refereed)
    Abstract [en]

    A detailed study of ion cyclotron interactions in a toroidal plasma has been carried out in order to elucidate the role of toroidal effects on ion cyclotron emission. It is well known that non-relaxed distribution functions can give rise to excitation of magnetosonic waves by ion cyclotron interactions when the distribution function increases with respect to the perpendicular velocity. We have extended and clarified the conditions under which even collisionally relaxed distribution function can destabilize magnetosonic eigenmodes. In a toroidal plasma, cyclotron interactions at the plasma boundary with ions having barely co-current passing orbits and marginally trapped orbits can cause destabilisation by the strong inversion of the distribution function along the characteristics of cyclotron interaction by neo-classical effects. The unstable interactions can further be enhanced by tangential interactions, which can also prevent the interactions from reaching the stable part of the characteristics, where they interact with trapped orbits. Conditions on the localization of the magnetosonic eigenmodes for unstable excitation are analysed by studying the anti-Hermitian part of the susceptibility tensor of thermonuclear alpha-particles. The pattern of positive and negative regions of the anti-Hermitian part of the susceptibility tensor of thermonuclear alpha-particles is, in general, consistent with the excitation of edge localized magnetosonic eigenmodes, even though the eigenmodes are usually not localized in the major radius and for distribution functions that have relaxed to steady state.

  • 11.
    Hellsten, Torbjörn
    et al.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Bergkvist, Tommy
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Johnson, Thomas
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Laxåback, Martin
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Effects of Finite Orbit Width and RF-Induced Spatial Diffusion on Ion Cyclotron Emission2005In: Radio Frequency Power in Plasmas: 16th Topical Conference on Radio Frequency Power in Plasmas / [ed] S. J. Wukitch and P. T. Bonoli, Melville, New York: AIP Conference Proceedings , 2005, p. 50-53Conference paper (Refereed)
    Abstract [en]

    The theory of ion cyclotron emission, ICE, in tokamak plasmas has been revised by including the effects of finite orbit width and RF-induced spatial transport in the wave-particle interactions. Two mechanisms for excitation of edge localised magnetosonic modes are discussed. An inverted distribution function of suprathermal ions near the plasma edge is driving the modes. Counter current propagating waves can be excited by interacting with barely co passing ions. Co current propagating waves interacting at the inner leg only can drive the modes unstable by throwing the fast ions out of the plasma.

  • 12.
    Hellsten, Torbjörn
    et al.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Bergkvist, Tommy
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Johnson, Thomas
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Laxåback, Martin
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Integrated Modelling of ICRH and AE Dynamics2005In: IEA Burning Plasma Workshop, 2005Conference paper (Other academic)
  • 13.
    Hellsten, Torbjörn
    et al.
    KTH, Superseded Departments, Alfvén Laboratory.
    Bergkvist, Tommy
    KTH, Superseded Departments, Alfvén Laboratory.
    Johnson, Thomas
    KTH, Superseded Departments, Alfvén Laboratory.
    Laxåback, Martin
    KTH, Superseded Departments, Alfvén Laboratory.
    Non-linear study of fast particle excitation of global Alfvén eigenmodes during ICRH2004In: Proceedings 20th IAEA Fusion Energy Conference, 2004Conference paper (Refereed)
  • 14.
    Hellsten, Torbjörn
    et al.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Holmström, Kerstin
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Johnson, Tomas
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Bergkvist, Tommy
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Laxåback, Martin
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    ICE in toroidal plasmas2005In: IAEA Technical Meeting on Fast Particles, 2005Conference paper (Other academic)
  • 15.
    Hellsten, Torbjörn
    et al.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Laxåback, Martin
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Bergkvist, Tommy
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Johnson, Thomas
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Zastrow, K.-D.
    et, al
    Fast Wave Current Drive and Direct Electron Heating in JET ITB Plasmas2006In: Proc 21st IAEA Fusion Energy Conference, 2006Conference paper (Refereed)
    Abstract [en]

    Experiments with Fast Wave Current Drive, FWCD, and heating have been carried out in JET Internal Transport Barrier (ITB) discharges with strongly reversed magnetic shear. In order to maximize the current drive efficiency and increase the electron damping, and at the same time modifying the current profile in the transport barrier, hot low density ITB plasmas with strongly reversed magnetic shear, close to current hole, were created with Lower Hybrid Current Drive. It was difficult to strongly modify the central plasma current, even though the calculated current drive efficiency in terms of ampere per watts absorbed by the electrons was fairly high, 0.07A/W, because of: the strongly inductive nature of the plasma current due to the high electric conductivity; the interplay between the fast wave driven current and the bootstrap current, which, due to the dependence of the bootstrap current on the poloidal magnetic field, decreases the bootstrap current as the driven current increases; and parasitic absorption of the waves that decreased the power absorbed by the electrons. The power absorbed by the electrons was measured with a power modulation technique and the associated fast wave current drive calculated. Current diffusion simulations using the JETTO transport code, assuming neoclassical resistivity, were then carried out to calculate what changes to the plasma current profile could be expected from the current drive. The simulations showed a much slower response to the current drive compared to the measured central current densities suggesting a faster current penetration in the experiments than expected from neoclassical theory. Whereas the direct electron heating by fast magnetosonic waves using dipole spectra has proven to be an effective method to heat electrons in high-temperature ITB plasmas, even for a single pass damping of only a few percent, the heating in FWCD experiments with + 90o and - 90o antenna phasings were, for similar single pass damping as for the dipole, strongly degraded by parasitic losses, and with a heating efficiency of about half that of the dipole. Observations supporting that the losses are primarily caused by the presence of rectified RF-sheath potentials come from the large differences in performance and in Beryllium-II and Carbon-IV line radiation intensities between the dipole and ±90o phasings.

  • 16.
    Holmström, Kerstin
    et al.
    KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Bergkvist, Tommy
    KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Hellsten, Torbjörn
    KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    On the dynamics of Alfvén eigenmode excitation2006In: EPS Conference on Plasma Physics 2006, EPS 2006, 2006, p. 1796-1799Conference paper (Refereed)
    Abstract [en]

    Alfvén eigenmodes (AEs) excited by fast ions can cause losses of fast ions in thermonuclear experiments. To describe the dynamics of the AE excitation, it is necessary to include the decorrelation of the AE interactions and the renewal of the distribution function in the unstable regions on time scales that are short compared to the decorrelation time. For simulation of AE excitation for finite decorrelation times, a Monte Carlo operator describing the phase decorrelation between ions and AEs has been developed for implementation in the SELFO code.

  • 17. Testa, D.
    et al.
    Bergkvist, Tommy
    KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Borba, D.
    Boswell, C.
    Fasoli, A.
    Hellsten, Torbjörn
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Sharapov, S.
    Measurement of the instability threshold for toroidal alfvén eigenmodes in jet tokamak plasmas2005In: 32nd EPS Conference on Plasma Physics 2005, EPS 2005, Held with the 8th International Workshop on Fast Ignition of Fusion Targets: Europhysics Conference Abstracts, 2005, p. 2122-2125Conference paper (Refereed)
1 - 17 of 17
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  • ieee
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