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Published by Fusion Energy Division, Oak Ridge National Laboratory
Building CR 5600 P.O. Box 2008 Oak Ridge, TN 37831-6169, USA
Editor: James A. Rome Issue 136 April 2012
E-Mail: [email protected] Phone (865) 482-5643
On the Web at http://www.ornl.gov/sci/fed/stelnews
Dynamical coupling between
gradients and transport in
tokamaks and stellarators
Understanding the relation between free energy sources
and transport in systems far from thermal equilibrium is a
fundamental issue that has been debated for years. Instabilities
governed by a gradient will typically produce
transport events at all scales, thus connecting different
regions of plasma. In the case of a critical gradient mechanism,
the functional dependence between the transport
flux and the gradient is expected to show a sharp increase
as the system crosses the instability threshold and finite
background transport below the threshold, implying a nonlinear
relation between gradients and turbulent transport
[1].
Edge turbulent transport is strongly bursty and a significant
part is caused by a few large transport events within a
small fraction of time [2]; this possibly reflects the fact
that systems out of thermal equilibrium are dynamically
exploring different accessible states, i.e., regimes with different
plasma gradients and correspondingly different
transport levels. Then, the physics of transport and plasma
gradients should be discussed and characterized in terms
of probability distribution functions instead of just average
values. The dynamical coupling between gradients and
transport has been investigated in the plasma boundary of
different tokamak (JET, ISTTOK) and stellarator (TJ-II)
devices, revealing that the size of turbulent events is minimum
near the most probable gradient [3]. These experimental
results are compared with results from two simple
and very different models of plasma turbulence and transport.
Experiments were carried out in the TJ-II stellarator
(PECRH  600 kW, BT = 1 T, R = 1.5 m, a  0.22 m) [4],
the ISTTOK tokamak (R = 0.46 m, a = 0.085 m, Ip = 5–7
kA, B = 0.5 T), and the JET tokamak [5]. Edge fluctuations
have been characterized using multiple Langmuir
probes arrays. We measured the ion saturation current
(Isat) as a proxy for the edge plasma density (n), the
plasma floating potential, and the turbulent radial EB turbulent
transport E×B ignoring temperature fluctuations.
The coupling of the probability density function (PDF) of
the turbulent transport with the PDF of the density gradient
is studied by computing the conditional expected value
of the E×B turbulent flux for a given density radial gradient.
The investigation of the dynamical interplay between
edge fluctuations in density gradients and EB turbulent
transport has shown that these parameters are strongly
coupled in tokamak and stellarator plasmas. Observations
suggest that fluctuations are self-regulated in such a way
that the most probable density gradient minimizes the size
of the radial turbulent transport events; thus, as the density
gradient deviates from the most probable gradient, the
EB turbulent driven transport increases, and the system
performs a relaxation that tends to drive the plasma back
to the marginally stable situation that minimizes the size of
transport events (Figs. 1 and 2). The local system relaxes
to the most probable state in a time comparable to the
autocorrelation time of turbulence.
Experimental results were found to be consistent with
results from two very different models [6, 7] of plasma
turbulence and transport, where nonlocal effects play an
important role. These nonlocal effects result from a series
In this issue . . .
dynamical coupling between gradients and
transport in tokamaks and stellarators
The dynamical coupling between density gradients
and particle transport has been investigated using
similar experimental tools in the plasma boundary of
tokamak (JET, ISTTOK) and stellarator (TJ-II) devices,
showing that the size of turbulent events is minimum in
the proximity of the most probable density gradient.
Experimental results were found to be consistent with
results from two very different models of plasma turbulence
and transport. The present findings, common to
several plasma devices, suggest the importance of
self-regulation mechanisms between plasma transport
and gradients in fusion devices. .............................. 1
Stellarator News -2- April 2012
of feedback mechanisms at different radial locations
where at a given point in the plasma the local gradients
drive the turbulence and turbulence controls the transport.
These observations [3] provide a guideline for further
developments in plasma diagnostics, transport modeling,
and data processing to characterize transport and gradients
in terms of joint PDFs. In particular, the influence of
plasma conditions in the sharpness of the flux-gradient
dynamical relation when the plasma deviates from its
average value above the most probable gradient should be
investigated systematically.
References
[1] F. Ryter, F. Leuterer, G. Pereverzev, et al., Phys. Rev.
Lett. 86 (2001) 2325
[2] M. Endler, H. Niedermeyer, L. Giannone, et al., Nucl.
Fusion 35 (1995) 1307.
[3] C. Hidalgo, C. Silva, B. A. Carreras, et al., Phys. Rev.
Lett. 108 (2012) 065001.
[4] J. Sánchez et al., Nucl. Fusion 49 (2009) 104018.
[5] C. Hidalgo, B. Gonçalves, M.A. Pedrosa, et al., J. Nucl.
Mater. 313 (2003) 863.
[6] L. Garcia, B. A. Carreras, and D. E. Newman, Phys.
Plasmas 9 (2002) 841.
[7] L. Garcia, B. A. Carreras, V.E. Lynch, et al., Phys. Plasmas
8 (2001) 4111.
C. Hidalgo,1 C. Silva,2 B.A. Carreras,3 B. van Milligen,1 H.
Figueiredo,2 L. García,4 M. A. Pedrosa,1 B. Gonçalves,2 A.
Alonso1
1) EURATOM-CIEMAT, Madrid, Spain
2) EURATOM-IST, Lisbon, Portugal
3) University of Alaska, Fairbanks, AK USA
4) Universidad Carlos III, Madrid, Spain
E-mail: [email protected]
Fig. 1. Probability density function (PDF) of fluctuations in
radial Isat gradients and expected value of turbulent flux for
a given value of fluctuating density gradient as a function of
(rIsat rIsat)/, where  is the rIsat standard deviation,
in the plasma edge in the JET tokamak.
Fig. 2. Flux-gradient relation in the TJ-II stellarator.
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