The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc.

Numerical Simulation of Neoclassical Currents, Parallel Viscosity, and Radial Current Balance in Tokamak Plasmas

Timo Kiviniemi

Dissertation for the degree of Doctor of Science in Technology to be presented with due permission for public examination and debate in Auditorium F1 at Helsinki University of Technology (Espoo, Finland) on the 10th of August, 2001, at 12 o'clock noon.

Overview in PDF format (ISBN 951-22-5538-3)   [958 KB]
Dissertation is also available in print (ISBN 951-22-5537-5)


One of the principal problems en route to a fusion reactor is that of insufficient plasma confinement, which has lead to both theoretical and experimental research into transport processes in the parameter range relevant for fusion energy production. The neoclassical theory of tokamak transport is well-established unlike the theory of turbulence driven anomalous transport in which extensive progress has been made during last few years. So far, anomalous transport has been dominant in experiments, but transport may be reduced to the neoclassical level in advanced tokamak scenarios.

This thesis reports a numerical study of neoclassical fluxes, parallel viscosity, and neoclassical radial current balance in tokamaks. Neoclassical parallel viscosity and particle fluxes are simulated over a wide range of collisionalities, using the fully kinetic five-dimensional neoclassical orbit-following Monte Carlo code ASCOT. The qualitative behavior of parallel viscosity derived in earlier analytic models is shown to be incorrect for high poloidal Mach numbers. This is because the poloidal dependence of density was neglected. However, in high Mach number regime, it is the convection and compression terms, rather than the parallel viscosity term, that are shown to dominate the momentum balance. For fluxes, a reasonable agreement between numerical and analytical results is found in the collisional parameter regime. Neoclassical particle fluxes are additionally studied in the banana regime using the three-dimensional Fokker-Planck code DEPORA, which solves the drift-kinetic equation with finite differencing. Limitations of the small inverse aspect ratio approximation adopted in the analytic theory are addressed.

Assuming that the anomalous transport is ambipolar, the radial electric field and its shear at the tokamak plasma edge can be solved from the neoclassical radial current balance. This is performed both for JET and ASDEX Upgrade tokamaks using the ASCOT code. It is shown that shear high enough for turbulence suppression can be driven at the Low (L) to High (H) transition conditions without taking into account anomalous processes. In agreement with experiments, simulations indicate a higher threshold temperature for the L–H transition in JET than in ASDEX Upgrade. The parametric dependence of the shear on temperature, density, and magnetic field, however, is similar for both devices. In agreement with some theoretical models and experimental observations, the results also suggest that the critical shear for strong turbulence suppression in JET should be lower than in ASDEX Upgrade.

This thesis consists of an overview and of the following 7 publications:

  1. T.P. Kiviniemi and J.A. Heikkinen, Choice of constants of motion coordinates in numerical solving of the three-dimensional Fokker-Planck equation for tokamaks, Computer Physics Communications 107 (1997) pp. 149-154. © 1997 Elsevier Science. By permission.
  2. T.P. Kiviniemi, J.A. Heikkinen, A.G. Peeters, Test particle simulation of nonambipolar ion diffusion in tokamaks, Nuclear Fusion 40 (2000) pp. 1587-1596. © 2000 IAEA. By permission.
  3. T.P. Kiviniemi, J.A. Heikkinen, A.G. Peeters, Effect of poloidal density variation on parallel viscosity for large Mach numbers, Physics of Plasmas 7 (2000) pp. 5255-5258. © 2000 American Institute of Physics. By permission.
  4. J.A. Heikkinen, T.P. Kiviniemi, A.G. Peeters, T. Kurki-Suonio, S.K. Sipilä, W. Herrmann, W. Suttrop, H. Zohm, Ion orbit loss current in ASDEX Upgrade, Plasma Physics and Controlled Fusion 40 (1998) pp. 693-696. © 1998 Institute of Physics Publishing. By permission.
  5. J.A. Heikkinen, T.P. Kiviniemi, A.G. Peeters, Neoclassical radial current balance in tokamaks and transition to the H-mode, Physical Review Letters 84 (2000) pp. 487-490. © 2000 American Physical Society. By permission.
  6. T.P. Kiviniemi, J.A. Heikkinen, A.G. Peeters, S.K. Sipilä, Monte Carlo guiding-centre simulations of ExB flow shear in edge transport barrier, accepted for publication in Plasma Physics and Controlled Fusion. © 2001 Institute of Physics Publishing. By permission.
  7. T.P. Kiviniemi, T. Kurki-Suonio, S.K. Sipilä, J.A. Heikkinen, A.G. Peeters, L-H transport barrier formation: self-consistent simulation and comparison with ASDEX Upgrade experiments, Czechoslovak Journal of Physics 49, No. 12, Supplement S3, (1999) pp. 81-92. © 1999 Czechoslovak Journal of Physics. By permission.

Keywords: fusion, plasma, tokamak, neoclassical transport, Monte Carlo, L-H transition, Mach

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© 2001 Helsinki University of Technology

Last update 2011-05-26