24A08
Study of Symmetry Breaking and Momentum Transport in Tokamaks
J.M. Kwon1, S-M. Yi1, T. Rhee1, P.H. Diamond1,2
1

WCI Fusion Theory Center, National Fusion Research Institute, Korea
2CMTFO and CASS, UCSD, USA

We present gyrokinetic simulation studies of symmetry breaking in electrostatic turbulence andintrinsic rotation generation in tokamak plasmas. By analyzing fluctuation spectrums obtained
from ITG and TEM turbulence simulations, we investigate the spatio-temporal patterns offluctuation energy transport and zonal flow generation. Due to the drift velocity appearing in
the relation for zonal flow generation, it is shown that ITG and TEM have different global
zonal flow shearing profiles, which results in the intrinsic torque reversal at the TEM → ITG
transition.

1. Introduction
The observation of spontaneous toroidal plasma
rotation reversals in recent experiments [1,2] poses
an interesting challenge to the theory of intrinsic
rotation generation by plasma turbulence. Theabrupt sign change occurs during the plasma
density ramp-up experiments. The density values at
the reversal show linear correlation with the criticaldensity at the linear Ohmic (LOC) to saturated
Ohmic (SOC) confinement transition, whichsuggests the connection of the reversal phenomena
to the TEM → ITG transition.
In this work, we critically examine the theory ofresidual stress generation by fluctuation symmetry
breaking as a key mechanism for the intrinsic
torque [3] and the torque reversal at the TEM →ITG transition. The global δf gyrokinetic code
gKPSP is used for the study, which employs abounced averaged kinetic model for efficientsimulation of the relevant non-adiabatic electron
responses [4].
2. Fluctuation Symmetry Breaking
We analysed the fluctuation spectrums of ITG andTEM turbulence in  and  space to study theradial propagation of fluctuation energy. It was
found that the propagation shows similar pattern inboth cases, i.e. the same direction of the radialgroup velocity of the fluctuations in the same radial
region. However, due to the drift velocity ∗
appearing in the relation for the non-linear
correlator 〈  〉 and the radial propagation of thefluctuation energy, which can be readily seen bytaking the  derivative of the simple drift wave
dispersion relation,=−∗     ,we found that opposite trends of fluctuation
asymmetry appear in  and  space for ITG
and TEM turbulence spectrum as can be seen in
Fig.1.

Fig. 1. Fluctuation spectrum in  and  forTEM (upper) and ITG (lower) turbulence. Different
asymmetry appears due to the opposite drift
velocity ∗.

In Fig.1, we can see that the TEM case shows
spectrum peaks at higher | | compared to theITG because of the higher mode numbers. It is
important to note that the spectrum peaks are
shifted toward   > 0 for the TEM and  < 0 for the ITG case, respectively.
The relation for zonal flow 〈 〉 generation by
turbulence driven Reynolds stress can be written as

Indeed, we found that the intrinsic torque androtation from TEM and ITG show roughly opposite
radial profiles as shown in Fig.2.

 〈 〉 = − 〈  〉 =   | | 

Here, we note that the key non-linear correlation offluctuating potential  for zonal flow generation
is 〈  〉 , which suggests different zonal flow
shearing profiles from TEM and ITG turbulence.
From the simulations, we found that global zonal
flow shearing profiles show roughly opposite
pattern for the TEM and ITG case.
This is significant because the ExB shearing by
zonal flow is one of the well-known mechanisms
for the || fluctuation symmetry breaking [5],which is necessary for the residual stress generation[3]. We confirmed the opposite || symmetry
breaking trend by evaluating fluctuation weightedwave vector 〈|| 〉 defined as〈|| 〉 ≡ ∑,( −  ),  ,where m, n denote poloidal and toroidal mode
number, respectively.
3. Intrinsic Torque Reversal at TEM → ITG
Transition
The residual stress formula is given by [3],
Π||=  −, || 〈 〉 + ,   || 〈 〉


〈 〉
 

The first and second term in the right hand side
represent the symmetry breaking effect byfluctuation intensity gradient and ExB shearing,
respectively. Since there are no sign flip in || and  , the results in the previous section imply
the sign reversals in both the intensity gradient andExB shearing term, which can result in the sign
reversal of the residual stress and therefore theintrinsic torque.

Fig. 2. Intrinsic rotation profiles generated byTEM(red) and ITG(green dotted) turbulence. Theyshow spatially opposite structure.
The radial profiles show the so called zonal
pattern i.e. dipolar structure. We note that the net
sign of toroidal momentum inside plasma will beultimately determined by the action of boundary
condition, which is a subject of on-going study.
Acknowledgements
This work is supported by the Ministry ofEducation, Science and Technology of Korea via
WCI project 2009-0001, by the DOE Contract No.
DE-FC02-08ER54959.
References[1] A. Bortolon, B.P. Duval, A. Pochelon, and A.
Scarabosio, Phys. Rev. Lett. 97, 235003 (2006)[2] J.E. Rice, et. al., US-EU TTF 2011[3] P.H. Diamond, C.J. McDevitt, O.D. Gurcan, T.S.
Hahm, and V. Naulin, Phys. Plasmas 15, 012303(2008)[4] B.H. Fong and T.S. Hahm, Phys. Plasmas 6, 188(1999).
[5] O.D. Gurcan, P.H. Diamond, T.S. Hahm, R. Singh,Phys. Plasmas 14, 042306 (2007)