T. Hein

Rechenzentrum Garching (RZG) of the Max Planck Society and the IPP, Arching, Bavaria, Germany

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Publications (9)18.67 Total impact

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    ABSTRACT: Toroidal momentum transport mechanisms are reviewed and put in a broader perspective. The generation of a finite momentum flux is closely related to the breaking of symmetry (parity) along the field. The symmetry argument allows for the systematic identification of possible transport mechanisms. Those that appear to lowest order in the normalized Larmor radius (the diagonal part, Coriolis pinch, E × B shearing, particle flux, and up–down asymmetric equilibria) are reasonably well understood. At higher order, expected to be of importance in the plasma edge, the theory is still under development.
    Full-text · Article · Aug 2011 · Nuclear Fusion
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    ABSTRACT: The effect of a finite βe = 8πneTe/B2 on the turbulent transport of toroidal momentum in tokamak plasmas is discussed. From an analytical gyrokinetic model as well as local linear gyrokinetic simulations, it is shown that the modification of the parallel mode structure due to the nonadiabatic response of passing electrons, which changes the parallel wave vector k∥ with increasing βe, leads to a decrease in size of both the diagonal momentum transport as well as the Coriolis pinch under ion temperature gradient turbulence conditions, while for trapped electron modes, practically no modification is found. The decrease is particularly strong close to the onset of the kinetic ballooning modes. There, the Coriolis pinch even reverses its direction.
    No preview · Article · Jul 2011 · Physics of Plasmas
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    ABSTRACT: A detailed analysis of experimental data from the ASDEX Upgrade tokamak is carried out to shed light on the properties of confinement and transport in the current ramp-up and ramp-down phases of the plasma discharge. The experimental database is used to identify the relevant ranges of parameters explored during the ramp-up and the ramp-down. The energy confinement time observed in the two ramps displays interesting evolution, in many cases attaining different values at the same current level between ramp-up and ramp-down. The possible reasons for this behaviour are investigated. Interpretative transport simulations are used as a tool to clarify the interplay between different parameters, which are coupled in a non-linear way. In addition, a theory-based transport model is used to understand the behaviour of confinement as observed in the experiment, evidencing the role of both turbulent and neoclassical transport. Linear gyrokinetic calculations are performed to identify the relevant turbulence regime, showing that a broad range of frequencies, in the trapped electron modes (TEMs) and in the ion temperature gradient modes (ITGs) regimes, is explored during both the ramp-up and ramp-down. In the same framework, a quasi-linear model is applied to calculate the value of the local logarithmic density gradient and compare it with the experimental value. Finally, first non-linear simulations of heat transport during the current ramps are presented.
    No preview · Article · Apr 2011 · Nuclear Fusion
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    T. Hein · C. Angioni · E. Fable · J. Candy
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    ABSTRACT: Electromagnetic effects on the radial transport of electrons in the core of tokamak plasmas are studied by means of linear and nonlinear gyrokinetic simulations with the code GYRO[J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] and by an analytical derivation. The impact of a finite {beta}, that is, a finite ratio of the plasma pressure to the magnetic pressure, is considered on the fluctuations of the magnetic field through Ampere's law, as well as on the geometrical modification of the vertical drift produced by the Shafranov shift in the magnetic equilibrium, which, for realistic descriptions, has to be included in both electrostatic and electromagnetic modeling. The condition of turbulent particle flux at the null, which allows the determination of stationary logarithmic density gradients when neoclassical transport and particle sources are negligible, is investigated for increasing values of {beta}, in regimes of ion temperature gradient and trapped electron mode turbulence. The loss of adiabaticity of passing electrons produced by fluctuations in the magnetic vector potential produces an outward convection. When the magnetic equilibrium geometry is kept fixed, this induces a strong reduction of the stationary logarithmic density gradient with increasing {beta}. This effect is partly compensated by the geometrical effect on the vertical drift. This compensation effect, however, is significantly weaker in nonlinear simulations as compared to quasilinear calculations. A detailed comparison between quasilinear and nonlinear results reveals that the predicted value of the logarithmic density gradient is highly sensitive on the assumptions on the wave number spectrum applied in the quasilinear model. The qualitative consistency of the theoretical predictions with the experimental results obtained so far on the dependence of density peaking on {beta} is discussed by considering the additional impact, with increasing {beta}, of a particle source delivered by neutral beam injection heating. (Some figures in this article are in color only in the electronic version.)
    Preview · Article · Oct 2010 · Physics of Plasmas
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    ABSTRACT: Pedestal and core confinement of hybrid discharges in ASDEX Upgrade (AUG) and DIII-D are studied in dedicated power scan experiments. The H98(y,2) confinement factor increases with total ?N in both tokamaks and it is higher in DIII-D with higher ? plasma shape at a given ?N. The pedestal beta, , increases linearly with total beta in AUG hybrid discharges, while it is roughly constant with ?N at fixed shape in the DIII-D power scans. The confinement enhancement with power observed with respect to the IPB98(y,2) scaling is due to an increase in pedestal confinement in AUG hybrid discharges and to an increase in core confinement in the DIII-D hybrid power scans. The increase in pedestal pressure with power in AUG hybrid discharges is primarily due to an increase in the width of the edge transport barrier at constant pressure gradient. In the DIII-D discharges the widths of the Te and ne pedestals, and , are consistent with a scaling. In the AUG hybrid power scans a dependence of on ?pol,PED cannot be excluded, while shows no dependence on ?pol,PED In both machines increases with ?. The maximum pedestal pressure achieved in the experiment prior to the onset of type I ELMs is consistent with predictions from ideal MHD; however, a physics model explaining the increase in the pedestal width with ? is still missing. The increase in with ? in the core of DIII-D is consistent with predictions by linear gyrokinetic simulations. In the plasma core, E × B shearing rate stabilization of the ITG modes is significant in both machines as beta is increased. Inclusion of electromagnetic effects in the gyrokinetic calculations provides additional stabilization at ?N values achieved in the experiment. In AUG, proximity to the kinetic ballooning threshold and/or a stronger reduction in normalized ion heat flux with increasing input power are possible explanations for the constancy of at mid-radius as beta is increased.
    No preview · Article · Jan 2010 · Nuclear Fusion
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    T. Hein · C. Angioni
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    ABSTRACT: The impact of electromagnetic effects on the transport of light and heavy impurities in tokamak plasmas is investigated by means of an extensive set of linear gyrokinetic numerical calculations with the code GYRO[J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] and of analytical derivations with a fluid model. The impurity transport is studied by appropriately separating diffusive and convective contributions, and conditions of background microturbulence dominated by both ion temperature gradient (ITG) and trapped electron modes (TEMs) are analyzed. The dominant contribution from magnetic flutter transport turns out to be of pure convective type. However it remains small, below 10% with respect to the ExB transport. A significant impact on the impurity transport due to an increase in the plasma normalized pressure parameter beta is observed in the case of ITG modes, while for TEM the overall effect remains weak. In realistic conditions of high beta plasmas in the high confinement (H-) mode with dominant ITG turbulence, the impurity diffusivity is found to decrease with increasing beta in qualitative agreement with recent observations in tokamaks. In contrast, in these conditions, the ratio of the total off-diagonal convective velocity to the diagonal diffusivity is not strongly affected by an increase in beta, particularly at low impurity charge, due to a compensation between the different off-diagonal contributions.
    Preview · Article · Jan 2010 · Physics of Plasmas
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    ABSTRACT: The transport of light and heavy impurities, as well as of energetic α particles, produced by the background electrostatic plasma turbulence is investigated by means of linear and nonlinear simulations with three gyrokinetic codes, GS2, GYRO and the recently developed GKW. The basic transport mechanisms of impurities and energetic α particles are elucidated, in combination with a simple analytical derivation. The relevance of these theoretical results in the transport modelling of the ITER standard scenario is assessed by means of ASTRA simulations, in which the transport of minority species like α particles and He ash is described by means of formulae which fit the gyrokinetic results.
    Full-text · Article · May 2009 · Nuclear Fusion

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Publication Stats

143 Citations
18.67 Total Impact Points

Top Journals


  • 2011
    • Rechenzentrum Garching (RZG) of the Max Planck Society and the IPP
      Arching, Bavaria, Germany
  • 2009-2011
    • Max Planck Institute for Plasma Physics
      • Max Planck Institute for Plasma Physics, Greifswald
      Garching bei München, Bavaria, Germany