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Научно-образовательный Центр ИКИ РАН проводит цикл лекций "Процессы
переноса вещества и излучения".
Вторая и третья лекции цикла состоятся 9 и 11 июня 2004 г. в 15:00 в
Центре отображения ИКИ РАН.

Докладчик - профессор Д. Расмуссен (Дания) (Professor Jens Juul Rasmussen,
Risoe National Laboratory, Optics and Plasma Research Department, Denmark)

9 июня 2004 г. -
"Turbulent Equipartition and Anomalous Transport in Electrostatic Plasma
Turbulence"
Abstract.
Turbulent Equipartition and Anomalous Transport in Electrostatic Plasma
Turbulence


Jens Juul Rasmussen


Optics and Plasma Research Department
Risoe National Laboratory
DK-4000 Roskilde, Denmark
e-mail: jens.juul.rasmussen@risoe.dk

Turbulent transport driven by low frequency electrostatic fluctuations is
recognized to be of significant importance and may account for the major
part of the cross-field transport in magnetized plasmas. Whereas classical
collisional transport is generally down the gradients (of temperature and
density) and tend to bring the plasma towards thermal equilibrium,
turbulent transport may be directed up-gradient. This type of transport,
which in magnetically confined plasmas, is directed inward from the edge of
the plasma to the centre, leads to peaking of the density and temperature
profiles and is referred to as the "pinch flux". This behaviour may
conveniently be explained by the concept of Turbulent EquiPartition (TEP)
[1-2]. TEP is based on the existence of Lagrangian invariants in the
presence of the turbulence. The system relaxes towards equipartition of
these quantities (the TEP-state) in the accessible phase space by turbulent
mixing of the Lagrangian invariants. The TEP-state determines the mean
global behaviour of the system if the invariants are sufficiently robust,
that is they "survive" for times much longer than the turbulent mixing
time. The average profiles of density and temperature in the TEP state are
close to the linear stability threshold. Note, however, that any turbulent
mixing will arrange that these marginally stable profiles be reached, even
from below and in the absence of sources.
In this presentation, I discuss the concept of turbulent equipartition and
illustrate it by various examples ranging from large-scale zonal flow
generation in rotating fluids to the evolution of pressure driven
electrostatic flute modes in a plasma in an inhomogeneous magnetic field.
For the case of pressure driven flute mode turbulence [3-5] we have derived
a two-dimensional model coupling the evolution of density, temperature and
potential. The equations are solved numerically on a domain bounded in the
direction of the gradient of the magnetic field, and periodic in the other
direction. In all the cases investigated the saturated profiles tend to
approach the profiles predicted from TEP. Depending on how the system is
driven, we observe a clear pinch flux in either density or temperature or
both. The pinch flux is connected with the tendency for the system to
approach the TEP profiles, which coincide with the marginal stable
profiles. The evolution of "poloidal" zonal flows acting as transport
barriers and the interplay between the flows and the turbulent flux are
also discussed.

[1] Yankov, V.V., JETP Lett. 60, 171 (1994).
[2] Yankov V.V. and Nycander, J. Phys. Plasmas 4, 2907, (1997)
[3] Naulin, V., Nycander J. and Rasmussen, J. Juul, Phys. Rev. Lett. 81,
4148 (1998)
[4]Naulin, V., Rasmussen, J. Juul and Nycander, J., Physics of Plasmas 10,
1075-1082, (2003); Erratum: ibid 3804.
[5] Garcia, O.E., Naulin, V., Nielsen, A.H., and Rasmussen, J. Juul, Phys.
Rev. Lett. 92, 165003, (2004).

11 июня 2004 г. -
"Particle diffusion and density flux in low frequency, electrostatic plasma
turbulence"
Abstract.

Particle diffusion and density flux in low frequency, electrostatic plasma
turbulence



Jens Juul Rasmussen


Optics and Plasma Research Department
Risoe National Laboratory
DK-4000 Roskilde, Denmark
e-mail: jens.juul.rasmussen@risoe.dk

A characteristic feature of turbulent flows is the ability to disperse and
mix particles and heat. This process is very complex even under idealized
conditions of homogeneous and isotropic turbulence and is still far from
being understood in general. Covering a variety of important areas from the
diffusion of pollutants in environmental flows to the particle and heat
diffusion in magnetized plasmas in fusion devices this topic connects basic
research with applications.
In this talk I shall report on our recent investigations on test particle
diffusion and transport in anisotropic two-dimensional turbulence [1-3]. We
have considered electrostatic drift-wave turbulence in magnetized plasma,
described by the so-called Hasegawa-Wakatani equations, which produce a 2D
turbulent flow-field with a self-consistent instability drive. However, our
results are also relevant for particle dispersion in geophysical beta-plane
turbulence, due to the similarity between drift waves in plasmas and Rossby
waves on the beta-plane.
In general, we observe that the particle dispersion is strongly
anisotropic, with the diffusion in the zonal direction much larger than the
diffusion in the direction parallel to the background density gradient -
the radial direction (meridional direction for the beta-plane analogy). Non-
linear couplings lead to the formation of transient coherent vortical
structures, and they have a dominating influence on the particle
dispersion. We demonstrate, that the trapping of particles in and
subsequent displacement with the vortex structures leads to an anomalous
diffusion with super diffusive behaviour in the zonal direction and sub
diffusive behaviour in the radial direction.
Furthermore, we have investigated the turbulent flux originating from the
drift wave fluctuations. This flux is intermittent with large bursts and
has a strongly non-Gaussian probability distribution function. However, it
is still found that that the mean flux is well described by the flux
obtained by using the diffusion coefficient obtained from the dispersion of
ideal particles and Fick's law.
Finally, preliminary investigations of the dispersion of weakly inertial
particles will be discussed. Here a tendency for increased super diffusive
behaviour is observed

[1] Naulin, V., Nielsen, A.H., and Rasmussen, J. Juul, Diffusion of ideal
particles in a 2d-model of electrostatic turbulence. Phys. Plasmas (1999)
6, 4575 - 4585.
[2] Basu, R Naulin, V., and Rasmussen, J. Juul, Particle dispersion in
anisotropic turbulence, Com. Nonlinear Science and Numerical Simulations,
(2003), 8, 477- 492.
[3] Basu, R , Jessen, T., Naulin, V., and Rasmussen, J. Juul, Turbulent
flux and the diffusion of passive tracers in electrostatic turbulence,
Physics of Plasmas, (2003), 10, 2696 - 2703.


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