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Transport of energetic particles in turbulent plasmas [Elektronische Ressource] / vorgelegt von Thilo Hauff

203 pages
Thilo Hau Transport of Energetic Particlesin Turbulent Plasmas2009Transport of Energetic Particlesin Turbulent PlasmasDissertation zur Erlangungdes Doktorgrades Dr. rer. nat.der Fakultat fur Naturwissenschaftender Universitat Ulmvorgelegt vonThilo Hau aus Ulm2009Dekan: Prof. Dr. Axel Gro Erstgutachter: apl. Prof. Dr. Frank JenkoZweitgutachter: Prof. Dr. Peter ReinekerDrittgutachter: Prof. Dr. Tunde Ful opTag der Promotion: 11. November 2009For we know in part, and we prophesy in part. But when that which is perfectis come, then that which is in part shall be done away.Saint Paul, 1 Cor.13, 9-10Meiner FrauCorneliagewidmetAbstractAnomalous transport in magnetically con ned fusion plasmas is induced byelectrostatic and magnetic turbulence on scales of the Larmor radii of the ionsand electrons, and is responsible for the degradation of con nemen t, stronglycomplicating the process of achieving the necessary conditions to sustain a burn-ing plasma. The quest to understand the turbulent transport of particles, mo-mentum, and energy in magnetized plasmas remains a key challenge in nuclearfusion research. A basic issue being still relatively poorly understood is theturbulent advection of energetic particles with large drift orbits and gyroradii.Especially the interaction of fast alpha particles or ‘beam ions’ with the back-ground turbulence is of great interest.
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Thilo Hau
Transport of Energetic Particles
in Turbulent Plasmas
2009Transport of Energetic Particles
in Turbulent Plasmas
Dissertation zur Erlangung
des Doktorgrades Dr. rer. nat.
der Fakultat fur Naturwissenschaften
der Universitat Ulm
vorgelegt von
Thilo Hau
aus Ulm
2009Dekan: Prof. Dr. Axel Gro
Erstgutachter: apl. Prof. Dr. Frank Jenko
Zweitgutachter: Prof. Dr. Peter Reineker
Drittgutachter: Prof. Dr. Tunde Ful op
Tag der Promotion: 11. November 2009For we know in part, and we prophesy in part. But when that which is perfect
is come, then that which is in part shall be done away.
Saint Paul, 1 Cor.13, 9-10Meiner Frau
Cornelia
gewidmetAbstract
Anomalous transport in magnetically con ned fusion plasmas is induced by
electrostatic and magnetic turbulence on scales of the Larmor radii of the ions
and electrons, and is responsible for the degradation of con nemen t, strongly
complicating the process of achieving the necessary conditions to sustain a burn-
ing plasma. The quest to understand the turbulent transport of particles, mo-
mentum, and energy in magnetized plasmas remains a key challenge in nuclear
fusion research. A basic issue being still relatively poorly understood is the
turbulent advection of energetic particles with large drift orbits and gyroradii.
Especially the interaction of fast alpha particles or ‘beam ions’ with the back-
ground turbulence is of great interest.
In this thesis, fast particles are treated as passive test particles, and the
connection between decorrelation processes (Eulerian or Lagrangian) and the
transition to a di usiv e regime is shown to be crucial in describing transport
processes. To allow for a better understanding of the dependence of the parti-
cle di usivit y on the interaction mechanisms between the particle trajectories
on one hand and the spatio-temporal structure of a certain type of turbulence
on the other hand, a three step approach is applied: Numerical studies with
arti cially created stream functions in simpli ed geometries are used alongside
analytical models, which are eventually con rmed using self-consistent gyroki-
netic simulations with the Gene code. The particle motion is initially restricted
to two dimensions and, after having studied the crucial e ects there, extended
to three dimensions, where additional e ects come into play.
In two dimensions (i.e. in the plane perpendicular to the magnetic eld),
nite gyroradius e ects are introduced using the gyroaveraging approximation
which means that the gyrating particle is replaced by a charged ring. The
Kubo number and the gyroradius are found to be crucial parameters, separating
di eren t regimes of transport scaling. Depending on these regimes
can be found where the transport is independent of the energy, or shows a more
or less steep decline. The underlying physical mechanisms of this behavior
are identi ed and an analytical approach is developed which favorably agrees
with the simulation results. The investigations are extended by introducing
anisotropic structures like streamers and zonal o ws as well as homogeneous
drift e ects, leading to quantitative modulations of the gyroradius dependence
of the di usion coe cien t. Analytic models are used to explain these various
e ects, along with numerical simulations. Furthermore, transitions from non-
di usiv e to di usiv e transport regimes are examined.
In three dimensions, the parallel motion of the particles along the magnetic
eld lines as well as perpendicular excursions due to magnetic drifts become
important, in addition to the e ects studied in two dimensions. The multi-
tude of di eren t decorrelation mechanisms is studied and a validity condition
for ‘orbit averaging’ is obtained which is shown to be crucial for the level offast particle transport and directly related to the magnetic shear. Contrary to
popular assumptions, it is shown that ‘orbit averaging’ is not valid in general,
and decorrelation, i.e., the transition to the di usiv e regime, occurs on perpen-
dicular, not parallel scales. Furthermore, resonance mechanisms between the
perpendicular particle drifts and the diamagnetic drifts of the bulk plasma are
observed, due to which the electrostatic transport may stay at signi can t levels
for particle energies up to about ten times the thermal energy of the background
plasma. For larger energies, di eren t scaling laws { depending on the plasma
parameters and the particle energies { are derived. For electrostatic transport,
1the di usion coe cien t declines withE , which is much slower than orbit av-
eraging would suggest. The turbulent magnetic transport, however, remains
constant even for very large particle energies in the case of a large pitch angle.
For smaller pitch angles, both the electrostatic and the magnetic transport are
1=2modi ed by a factor of E . The analytical studies are con rmed by means
of nonlinear gyrokinetic simulations with the Gene code. Comparing the latter
with quasilinear simulations, one nds that it is indeed the turbulent nature
of the advecting eld which is responsible for the slow decay of the particle
transport with increasing energy. The turbulent transport of energetic particles
is discussed as a candidate for explaining recent surprising experimental results
obtained by the ASDEX Upgrade experiment, nding that our models are able
to explain the observed fast broadening of the beam current.
Finally, in order to describe the transport of fast ‘runaway electrons’, the
model is extended to relativistic conditions, exhibiting strong modi cations of
the scaling laws. They are shown to be able to explain the rather low levels of
di usion found in experimental measurements of this particle species.

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