J. Plasma Fusion Res. SERIES, Vol. 9 (2010)

The Study about the Relationship between Plasma Current in Open MagneticField and the Formation of Closed Flux Surface in CPD
Masaki ISHIGURO1, Kazuaki HANADA2, Hideki ZUSHI2, Kohnosuke SATO2,Kazuo NAKAMURA2, Hiroshi IDEI2, Mizuki SAKAMOTO2, Makoto HASEGAWA2,Shoji KAWASAKI2, Hisatoshi NAKASHIMA2 and Aki HIGASHIJIMA2
1

Interdisciplinary Graduate School of Engineering Sciences Kyushu University, Kasuga 816-8580, Japan2

Research Institute for Applied Mechanics, Kyushu University, Kasuga 816-8580, Japan(Received: 29 October 2009 / Accepted: 6 January 2010)

We investigate the physics of the formation of closed flux surfaces under the condition that a radio frequency(RF) wave is injected into the Compact Plasma Wall Interaction Experimental Device (CPD). From the orbits of theenergetic electrons calculated for the open magnetic flux configuration, we estimate the plasma current Ies due toenergetic electrons. We find that Ies increases with decreasing poloidal magnetic field, and observe the formation ofclosed flux surfaces in the experiments under the condition of low poloidal magnetic field (i.e., high Ies condition).
This result suggests that the condition of high Ies is suitable for forming closed flux surfaces and that Ies can be used
as an indicator to optimize the operational magnetic field condition for forming closed flux surfaces.
Keywords: spherical tokamak, plasma current start-up, RF injection, energetic electron orbit, closed flux surface

driving plasma current with energetic electrons. Current
ramp-up with energetic electrons is needed insuperconductive tokamaks because the inductive electricfield is weak. ECH assistance is also used forsuperconductive tokamaks. Therefore, knowledge of theuse of energetic electrons for plasma ramp-up in an ST isuseful for operating superconductive tokamaks such asITER.
The plasma current start-up phase is divided into threephases, A, B, and C. Phase A is before breakdown, phase B
is between breakdown and the formation of a closed flux
surface, and phase C is after the formation of a closed flux
surface. The conditions required for phases A and C havebeen studied for many devices. Estimating whether or notbreakdown occurs can be done using the Townsend
avalanche theory [6]. After establishment of a maintained
closed flux surface, the plasma behavior can be estimatedfrom the equilibrium, which can be obtained by solving theGrad Shafranov equation [7]. In phase B, the question of
how to obtain the most suitable condition for forming aclosed magnetic flux surface is still unanswered.
The main purpose of this letter is thus to find theproper conditions in phase B to initiate the plasma current
with energetic electrons and to form closed flux surfaces.
To achieve this goal, we need to establish an indicator that
determines the relative ease of current driving. In phase B,
where single particle orbits play an essential role, collisions
between energetic electrons and other electrons and ions
are infrequent [8].
In this letter, we estimate the current due to energetic

1. Introduction

Because of the possibility of high beta, sphericaltokamaks (STs) have recently gained importance in thestudy of magnetic confinement fusion reactors. STs have asmall aspect ratio (A = R0/a, where R0 is the major radius
and a is the minor radius of tokamak plasmas) and theircentral space is quite limited [1]. The capacity of supplying
magnetic flux needed to induce plasma current in STs isless than that in conventional tokamaks, where induced
toroidal electric fields are enough to drive the plasma
current, even for low temperature plasmas, because
sufficient magnetic flux can be supplied by the central
solenoid (CS) coils.
Because CS coils do not supply sufficient magnetic
flux in STs, a non-inductive method such as electron
cyclotron heating (ECH) due to radio frequency (RF) waveinjection [2] can be used to start the plasma current. Evenin ohmic heating (OH) assistance by ECH is needed (ECH+ OH) [3]. Some researchers perform experiments on
plasma current start-up in STs without CS coils [4]. Thus,
plasma start-up without the assistance of an inductive
electric field is an important issue in the operation of STs.
For RF injection, energetic electrons accelerated by
RF waves are important for plasma current initiation in theopen magnetic flux configuration [5]. Because of the low
aspect ratio, grad B is larger in STs than in conventional
tokamaks, and this condition facilitates the confinement ofenergetic electrons in the open magnetic field. Judging
from these features, the ST configuration is good forishiguro@triam.kyushu-u.ac.jp

18©2010 by The Japan Society of Plasma
Science and Nuclear Fusion Research

M. Ishiguro et al., The Study about the Relationship between Plasma Current in Open Magnetic Field and the Formation of Closed Flux Surface in CPD

Fig.1 Orbits of electrons in open magnetic flux
configuration. Solid lines show orbits projection, anddashed lines show magnetic line projection on
poloidal plane.

Fig.2 Volume in which we assume that electronsexist. In this study, ΔR = ΔZ = 0.005m and Rres =0.19m. Hence, V has a cylindrical shape which has
0.19m inner radius, 0.005m thickness and 0.005m
height.

electrons accelerated by RF waves for the various magnetic
configurations and compare the results with theexperimental results from CPD. From the results ofcomparison, the indicator which suggests the relative easeof current start-up is proposed. In Section 2, we discusselectron orbits and the method of estimating the current.
The experimental apparatus is described in Section 3, andexperimental results and analysis are given in Section 4.
We discuss the results of numerical calculations in Section
5 and present a summary and conclusion in Section 6.

2. Electron Orbits in Open Magnetic Flux
Configuration and the Method of Current
Estimation

Figure1 shows some examples of electron orbits inthe open magnetic flux configuration. Electron orbits areclassified into three patterns: “lost”(a), “banana”(b), and“co-moving”(c). Electrons whose orbits do not return tomid-plane but instead attain the wall are classified as lost.
Banana electrons are trapped by the magnetic mirror
because of the dependence of the toroidal field on themajor radius. Co-moving electrons are confined even in the
open magnetic flux configuration without stagnating in the
mirror trap.
The guiding center of electron orbits in the tokamak
configuration has two poloidal velocities. One is thepoloidal component of velocity along the magnetic field
line and the other is the drift velocity generated by thetoroidal field curvature and gradient. When these twovelocities have opposite directions and nearly the samevalue, electrons barely move on a poloidal cross section,
but remain confined in small areas in the open magnetic
flux configuration. The current carried by these confinedelectrons is unidirectional, so that they can contribute to
the plasma current in the open magnetic configuration.
However, “lost” electrons are believed to not remain in thevacuum vessel long enough to carry plasma current [7].

Fig.3 Side view of CPD including PF coils
The electron orbits strongly depend on their initial velocity,
pitch angle, and poloidal field shape and strength. Inparticular, the n-index of the poloidal open magnetic flux
configuration is a key to confining electrons.
The current driven by confined electrons is estimatedas follows. The current Isp carried by confined electron isI speN.
t(1)

where e is the fundamental charge of the electron, N is thenumber of rotations executed on the toroidal plane in time t,
and t is the time required to complete one closed orbit in
the poloidal plane [see Figs. 1(b) and (c)]. The entire
current Ies is estimated by19M. Ishiguro et al., The Study about the Relationship between Plasma Current in Open Magnetic Field and the Formation of Closed Flux Surface in CPD

Fig.4 Time evolution of plasma current (solid line) andHα (dashed line). RF power in sn504063 is 70kW andin sn506599 is 50kW. Bp in sn504063 is 120 Gauss andin 506599 is 40 Gauss.

I esf v

Fig.5 Energetic electron orbits in velocity space areshown. Horizontal axis shows electron velocity along
magnetic line, vpara, and vertical axis shows electronvelocity perpendicular to magnetic line, vperp. Thesetwo velocities are normalized by light speed. The
position of each symbol shows the velocity of electron
at the initial point of orbital calculation where the ECR
layer crosses the mid plane. The sort of symbol shows
the sort of orbit which the electron traces, co-moving,banana and lost. (See Fig.1) Ies is calculated without
considering the contribution of lost electrons. Theenergy shown by most outside symbols is 30 keV,which is max energy considered in the calculation ofIes.

V ³ f v I sp dv§ m ·¸© 2S kT ¹22S n cos T1  cos T 2 ¨§ mv 2 ·uv 2 exp ¨ ¸,© 2kT ¹(2)where V is the volume in which the electrons exist and θ1and θ2 indicate the range of pitch angle considered. We
assume that energetic electrons (between 1 and 30 keV)exist uniformly in the toroidal direction with density 1017
m–3. The orbit calculation is started where the electron
cyclotron resonance (ECR) layer crosses the mid plane.
The volume V for the elemental area dRdZ near the startpoint (Rres, Zmid) is shown in Fig. 2.

4. Experimental Results and Analysis

Figure 4 shows the evolution of the plasma current Ip
and the Balmer line intensity Hα. In sn504063, RF injection
starts at 4 msec and breakdown occurs soon after the startof RF injection. But the plasma current does not increase
and no closed flux surface is formed. This phase isclassified as phase B. However, in sn506599, the moment
RF injection starts at 120 msec, the Hα signal and theplasma current start to increase. At 156 msec, the plasma
current suddenly increases by 1 kA for a few milliseconds.
This rapid increase in plasma current is called the “currentjump” and closed flux surfaces are thought to be formed
via the current jump. In this shot, a closed flux surface isthought to form just after the current jump [9].
The main difference between sn504063 and3. Experimental Apparatus

Figure 3 shows a schematic of CPD, which is acompact ST (R0 ≥ 0.3 m, a ≤ 0.2 m, aspect ratio A ≥ 1.5)
with one CS coil and three sets of poloidal field (PF) coils.
The inner diameter of the vacuum chamber is 0.22 m andthe outer wall diameter and height are 1.2 m. Four toroidal
field (TF) coils produce a toroidal magnetic field Bt = 0.25
T at R = 0.3 m with a TF coil current of 90 kA. A set of 8.2
GHz klystrons of up to 200 kW are used for ECH. In thisexperiment, the ECR layer is at R = 0.19 m.

20

M. Ishiguro et al., The Study about the Relationship between Plasma Current in Open Magnetic Field and the Formation of Closed Flux Surface in CPD

Fig.6 The map of formation of closed flux surface on
Ies and injected RF power. The calculation of Ies wasdone at the various magnetic configuration with thecondition of T = 1keV, n = 1017 m-3 and Rres = 0.19m. ○shows the condition that Bpp / Bpc > 2.0, where Bpp is
the value of poloidal magnetic field made by plasma
current and Bpc is the one made by PF coil at the innerlimiter. In this condition, formation of closed flux
surface is confirmed experimentally. Δ Shows thecondition that 1.0 < Bpp / Bpc <=2.0 and ● shows thecondition that Bpp / Bpc < 1.0.
sn506599 is the condition of the poloidal magnetic field. In
sn504063, the poloidal magnetic field strength Bp is about
120 Gauss, whereas in sn506599 Bp = 40 Gauss. The
reduced Bp causes a different confinement of the energetic
electrons in the open magnetic field, as shown in Fig. 5.
The result is that the plasma current ramps up more easily.
The co-moving area in sn506599 is broader than in
sn504063, suggesting that more co-moving electrons areconfined in the open magnetic field in sn506599 than in504063. In addition, the estimated current Ies carried byconfined energetic electrons in sn506599 (where the closed
flux surface is observed) is 0.38 kA, which is larger thanthat the 0.16 kA observed in sn504063 (where no closed
flux surface is observed).
Judging from these results, we believe that thecondition where Ies takes high value can be good for theformation of closed flux surfaces. Such a relation between
the condition of high Ies and the formation of closed flux
surfaces is observed in many shots. Figure 6 shows themap of the formation of closed flux surface on Ies as afunction of the injected RF power. The open circles
indicate the operational conditions for which a closed flux
surface formed, which is only in the region of high Ies andhigh RF power. This result supports the conclusion that thecondition of high Ies can be good for the formation ofclosed flux surfaces and shows that the RF power has athreshold for the formation of closed flux surfaces. Thus,
we believe that confined energetic electrons generated byRF injection play an important role in forming closed flux
surfaces and that the RF power level seems to be related

Fig.7 Improvement of confinement condition by theplasma current. The meaning of symbols is shown inthe caption of Fig.5. Figure (a) shows the case inwhich 1kA plasma current distributes in broad areaand figure (b) shows the case of concentration plasma
current of 0.25kA.
with the generation of energetic electrons. Under theseconditions, Ies can be used as an indicator to optimize theoperational conditions to form closed flux surfaces withenergetic electrons.

5. Discussion

As mentioned in Section 4, closed flux surfaces areformed via the current jump. In this section, we discuss thecurrent jump mechanism.
In sn506599, the current jump occurs when theplasma current in the open magnetic field becomes large.
Just before current jump, the magnetic field shape ismodified by the plasma current in the open magnetic field.
Modification of the magnetic field can change theconfinement condition of the energetic electrons, which ispossibly the source of the current jump. Thus, forsn506599, Ies is calculated with the plasma current effectadded to the magnetic field generated by the PF coils.
The calculation is done assuming two distributions of
the plasma current. In one distribution, the plasma current
exists in a broad area on the poloidal projection of themagnetic line near the ECR layer. In the other distribution,
the plasma current is concentrated at one point. In the21

M. Ishiguro et al., The Study about the Relationship between Plasma Current in Open Magnetic Field and the Formation of Closed Flux Surface in CPD

Fusion Energy Conference EX/P6-9 (2008).

former case, the assumed plasma current imitates thecurrent carried by banana electrons, whereas in the lattercase it imitates co-moving current. The change in theconfinement condition and Ies is shown in Fig. 7. For thiscalculation, plasma current is set at 1 kA for the broad
distribution and 0.25 kA for the concentrated distribution.
The plasma current leads to an improvement in both theconfinement condition and Ies. In particular, theconcentrated plasma current can change the confinement
condition dramatically, even for the condition of small
plasma current. Thus, if the plasma current is concentrated,a small increase in the current can change the confinement
condition rapidly and we believe that such a rapid change
in magnetic field can contribute to the rapid increase inplasma current (i.e., the current jump). Moreover, it is easy
for confined electrons to get more energy from the RF
wave because these electrons pass through the ECR layer
many times. Thus, improving the confinement condition
can cause an increase in the temperature of the energetic
electrons, which is also a possible source of the current
jump.
Experimental verification of this model is the subjectof future work.

6. Summary and Conclusion

To investigate the physics of the plasma current
initiation phase and to establish an index for optimizationof the operational conditions that form closed flux
surfaces with energetic electrons, we calculate theelectron orbits and estimate the current. From the resultsof the ECH plasma current start-up experiment at theCPD, we believe that high Ies facilitates the formation of
the closed flux surface. Thus, we proposed using Ies as anindex for optimization of the operational conditions toform closed flux surfaces with energetic electrons.

7. Acknowledgements

This work is performed with the support and under
the auspices of the NIFS Collaboration Research Program(NIFS05KUTRO14, NIFS08KUTRO022). This work is
partially supported by a Grant-in-aid for Scientific
Research from Ministry of Education, Science andCulture of Japan.

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