23P040-P
Transport Analysis Study of Oscillation Phenomena for the Electric Fieldin Helical Plasmas
ヘリカルプラズマでの電場振動現象に関する輸送解析研究	 
Shinichiro Toda, Kimitaka Itoh登田慎一郎, 伊藤公孝
National Institute for Fusion Science, 322-6 Oroshi, Toki, Gifu, 509-5292, Japan
核融合科学研究所	  〒509-5292	  土岐市下石町322-6
A model for the experimental results of the periodic oscillation of the electric field, so-called the electricfield pulsation, observed in helical plasmas is presented. A self-generated oscillation of the radial electricfield is shown as the simulation result in helical plasmas. Two different time scales are found in theself-generated oscillation, which are the transport time scale and the fast time scale at the transition of theradial electric field. This oscillation because of the hysteresis characteristic is attributed to the electric field
pulsation observed in helical plasmas. The parameter region of the condition for the self-generated
oscillation is derived.

1. Introduction
The turbulence-driven transport and theformation mechanism of transport barriers are
critical issues to realize improved confinement
modes in toroidal plasmas. One possible
mechanism to explain the transport barriers is thestructural transition in the profile of the radial
electric field Er and the suppression of turbulenceby its shear. In tokamaks, the model of L/Htransition and the edge localized modes (ELMs)
which is based on the bifurcation of the radial
electric field was presented [1]. A self-generated
oscillation of the edge density and temperaturetakes place. In helical plasmas, the neoclassicalhelical-ripple transport plays a dominant role in
the process of forming the profile of Er. The
bifurcation of Er in helical plasmas takes place
and the resultant strong shear of Er was predicted
to induce the transport barrier. At the state of thepositive Er in the core region, the electron internaltransport barrier (e-ITB) is observed when theElectron Cyclotron Resonance Heating (ECRH) isapplied which is localized around the plasma
center. The temporal evolution equation for theradial electric field is solved in helical plasmas.
The cyclic phenomena in the temporal evolutionof the radial electric field, namely the electricfield pulsations, have been observed in the coreregion of Compact Helical System (CHS) [2] andLarge Helical Device (LHD) [3]. The periodic
oscillation of the electric potential which includes
the intermittency characteristic is shown in LHD.
In our previous work for the analysis of thetemporal evolutions of the radial electric field,
the stationary solutions of the radial electric field
were obtained. The temporally oscillating

solutions of Er in the core region have not beenshown yet.	 
2. Transport Analysis Results
The temporal evolution in the time interval 0.66≤t≤0.70s of Er in Fig. 1, Te, Ti and n is studied. The
solid line, the dotted-dashed line, the dotted line
and the dashed line show the temporal evolutions of
the physical quantities at ρ= 0.1, ρ = 0.3, ρ = 0.5
and ρ=1.0, respectively. The state A at t=0.6721sindicates the one at ρ = 0.3 just before the transition
from the negative Er to the positive Er. Just after thetransition from the state A, the state changes to theone 	  B at t=0.6734s. From the state B, theplasma profile changes with t->he transport timescale and reaches the state C at t= 0.6793s. Justafter the state C, the transition from the positive Er
to the negative Er takes place at ρ = 0.3 and thestate changes to the one D at t = 0.6801s. From thestate D, the plasma state changes to the state A at t=0. 6833s with the transport time scale. At the time
t= 0.6833s, plasma parameters come back to thevalues at the state A, and the transition occurs again
from the negative Er to the positive Er. The
temporal evolutions in the core region (at ρ = 0.1, ρ= 0.3 and ρ = 0.5) clearly show the characteristic of
the limit cycle. In the core region at ρ = 0.3, thetransitions occur from the negative Er to the positive
Er at t= 0.6721s and from the positive Er to thenegative Er at t= 0.6801s. The time period of thelimit cycle is about 10ms, which is determined by
the typical transport time scale. The self-generated
oscillation of the radial electric field is shown tohave two time scales: a slow time scale of thetransport time scale (about 10ms) and a fast timeand n ! 1"1019 m #3 . In the enclosed region outside
the shaded region, the stationary profile of theradial electric field is obtained even if there are
multiple solutions of the ambipolar Er at someradial locations. When the value of the density
increases further: n ! 2 "1019 m #3 , all radialstationary electric fields changes to the ion root in
the parameter region labeled ‘i root’. The parameterregion of the two patterns for the temporal
evolutions: the stationary state and theself-generated oscillation are examined on theTe / Ti ! n plane. The physical mechanism to realize$#5+* ,-./01

scale at the transition (about 1ms). The temporalchange of the Er profile causes the temporal changeof the radial profile of the neoclassical andanomalous diffusivities. Owing to the influence of
Er on transport coefficients, the temporal evolutionof the radial Te, Ti and n profiles takes place as thelimit cycle in the core region.
We study the conditions in the parameter space,
where the self-generated oscillation occurs. Whenthe intensity of source is varied, the mean values of
the temperatures and the density change, and thetemporal evolution of calculations reaches either
the stationary state or the self-generated oscillation.
Furthermore, the profile of the stationary electricfield takes different types of roots. At first,
stationary electric fields in the entire radial region
become the electron root (Er>0) in the region
labeled ‘e-root’ in Fig. 2 on the Te / Ti ! n plane. Intheregimeofthelowdensity
18"3and the high electronn ! (1 " 3) #10 m
temperature Te / Ti > 3 , the positive and stationary
solutions of Er are found. Secondly, if the density
gets larger, the electric field in the core plasma
takes the electron root, and the electric field in theouter plasma takes the ion root (Er < 0) in the region
labeled ’e-i root’. In the region labeled ‘e-i root’,
the type of the transition is classified to the hard or
soft one. The multiple solutions of Er are shown in
the enclosed region inside the ‘e-i region’:1 < Te / Ti < 2 and n ! (0.2 "1.4) #1019 m "3 . In thisregion, the so-called ’hard’ transition occurs
between the multiple ambipolar Er and thereduction of the anomalous heat diffusivity isshown due to the strong shear of the radial electricfield. In the region labeled ‘e-i region’ outside thisenclosed region, the slow (and namely, the soft)transition takes place spatially and temporally since
there are no multiple solutions of the ambipolar Er.
In the enclosed region, the shaded region is shownfor the self-generated oscillation: 1 < Te / Ti < 2"!=0.3

6!=0.1#
4!=0.547!"#%&& #%&' #%&( #%&) #%'#
2,31
Fig.1 Temporal evolution of the radial electric field

Fig.2 Parameter
oscillation

spacefortheself-generated

a self-generated oscillation is also studied,concerning the flux-gradient relation which
includes the hysteresis characteristic [4].	 
Acknowledgments
This work is partly supported by the Grant- in-Aid for
Scientific Research of JSPS (19360148, 21224014 and23561002) and by the NIFS Collaborative Research
Program (NIFS10KNXN180 and NIFS11KNST023).
References[1] S. -I. Itoh, K. Itoh and A. Fukuyama, Nucl. Fusion 33(1993) 1445.
[2] A. Fujisawa et al., Phys. Rev. Lett. 81 (1998) 2256.
[3] A. Shimizu et al., Plasma Fusion Research 5 (2010)
S1015.
[4] S. Toda and K. Itoh, Plasma Phys. Contr. Fusion 53(2011) 115011.