Plasma and Fusion Research: Regular Articles

Volume 11, 2405045 (2016)

Study of the Axial Ion Confinement Time for High Particle FluxOperations of GAMMA 10/PDX∗)
Kazuya ICHIMURA, Yousuke NAKASHIMA, Md. Maidul ISLAM, Md. Shahinul ISLAM,
Keita SHIMIZU, Kazuma FUKUI, Masato OHUCHI, Mafumi HIRATA, Ryuya IKEZOE,Shuhei SUMIDA, Masayuki YOSHIKAWA, Naomichi EZUMI, Mizuki SAKAMOTO,
Makoto ICHIMURA and Tsuyoshi IMAI
Plasma Research center, University of Tsukuba, 1-1-1 Tennoudai, Tsukuba, Ibaraki 305-8577, Japan(Received 30 November 2015 / Accepted 18 February 2016)
Characteristics of axial plasma confinement in recent high-density mode of GAMMA 10/PDX tandem mirror
is reported in this paper. The parameter of the end-loss ion flux is an important issue in the divertor simulation
studies in GAMMA 10/PDX. With an ICRF heating in the anchor-cells of the machine, large increase in theelectron line-density in the central-cell (NLCC) and the end-loss particle flux were observed. The behavior of theelectron line density, plasma temperature and the amount of end-loss ion flux during the experiments suggested
that the mechanism of the axial ion loss was changed due to the increase of ion collision frequency. In contrast
with the standard operations of GAMMA 10/PDX, plasma parameters in recent high-density operations stays
in the range of high collision frequency. In such collisional plasma, the end-loss ion particle flux show linear
dependence on the plasma density instead of the parabolic dependence expected in plasmas of low collisionfrequency. In the high collision frequency plasma, it is notable that plasma potential φ largely changes thedependence of the particle flux on the plasma density.
c 2016 The Japan Society of Plasma Science and Nuclear Fusion ResearchKeywords: tandem mirror, GAMMA 10/PDX, mirror confinement, divertor simulation, particle flux
DOI: 10.1585/pfr.11.2405045

1. Introduction
Linear machines for plasma experiments are convenient for divertor studies because of their simple structure and operation easiness. The aim of this research is tomake it feasible to conduct experiments of divertor plasma
physics and plasma wall interaction (PWI) in the range ofhigh plasma temperature relevant to SOL plasma in upcoming ITER or DEMO reactor by using a linear machine.
Many linear machines have been contributing to the designof divertor system in fusion experimental machine such as
ITER. However, plasma temperature in most linear machines is low because most linear machines do not confine
a plasma long enough to store high amount of energy in theplasma. Ion temperature in a typical linear device is lessthan a few eV, which is much less than that of SOL plasmain fusion reactors, a few hundreds of eV. Therefore, experimental research of linear divertor simulator with hightemperature range is required.
A large tandem mirror device, GAMMA 10/PDX is a
powerful tool to perform such experimental research since
the machine is able to produce the end-loss particle flux
which has high temperature [1–3]. In previous research,
the energy distribution and the current density of the endauthor’s e-mail: ichimara_kazuya@prc.tsukuba.ac.jp∗) This article is based on the presentation at the 25th International Toki
Conference (ITC25).

loss ion were measured by the end-loss ion energy analyzer(ELIEA) and the particle flux estimated from measured ion
current density is 5 × 1022 particles/m2 sec.
In order to increase the amount of particle flux to thevalue expected in ITER or other fusion device; 1023 ∼1024
particles/m2 sec, new antennas of ICRF have been installed
and in recent experiments, large increase of plasma density and end-loss particle flux due to the new ICRF heating
method were observed [4]. In this article, results of thehigh-density experiments with new ICRF antenna configurations are reported and discussions on the characteristicsof mirror confinement in the newly achieved high-density
operations of the tandem mirror are made.

2. Experimental Setup
As a feature of the device, GAMMA10/PDX has 27meter machine length and plasma radius larger than 10 cm.
As shown in Fig. 1, the machine consists of seven cells:
the central cell, anchor cells, plug/barrier cells and endcells. Also, high power (300 kW) ICRF heating systems
are equipped and used for plasma production and heating.
In a standard operation, H2 plasma is initiated by the ignition of MPD arcjet plasma gun, and heated up to ion
temperature of several keV by ICRF wave from type III(Nagoya type III) and type II (double half turn) antennas.
Double arc type (DAT) antennas for ICRF are installed in2405045-1c 2016 The Japan Society of Plasma
Science and Nuclear Fusion ResearchPlasma and Fusion Research: Regular Articles

Volume 11, 2405045 (2016)

Fig. 1 (a) Vacuum vessels of GAMMA 10/PDX with resonancepositions of ICRF heating wave from three antennas(ICRF type III, type II, and anchor DAT) and the positionof the end-loss ion energy analyzer. (b) Plot of magnetic
field strength along z-axis.

Fig. 2 Results of DAT antenna heating in both east and west anchor cells; (a) electron line densities in each cells, (b) ion
particle flux density measured by west-ELIEA and (c) ion
temperature of the end-loss ion flux.

both east and west anchor regions and used to heat theplasma in anchor cells. In a series of GAMMA 10/PDX experiments, it was found that adding a plasma heating wave
by DAT antenna into an anchor region shows the remarkable eﬀect of increasing the end-loss ion flux [2–4]. Then,in this series, simultaneous heating by both east and west
anchor DAT antennas has been performed. As a main diagnostic tool for the end-loss ion flux, end-loss ion energy
analyzer (ELIEA) is installed on the inner wall of the end
cells in order to observe the energy distribution and thecurrent density of the end-loss ion flux incident to the end
region [5].

3. Results and Discussions
Figure 2 shows the result of ICRF heating into botheast and west anchor cells (EA+WA) [6]. In this case,
NLEA, NLWA and NLCC were increased largely and thedegree of line density increase during ICRF is almost samein EA and WA. Therefore, symmetry of plasma parametersin east side and west side of the machine can be assumed.
On the other hand, ion temperature measured by ELEIA
is slightly lowered by ICRF anchor DAT. Degradation ofwave heating eﬃciency due to increase of plasma density
is considered to be the cause of lowered ion temperature.
In addition, it is notable that the amount of ion particle flux
become maximum in the time range from t = 200 ms to t
= 210 ms, where ECRH and NBI is applied to the centralcell. In Fig. 3, the radial profile of the end-loss ion particle
flux in the high density experiment is plotted. It seems
that the radial profile or plasma radius was enlarged during
the additional plasma heating by both east and west anchor DAT antennas. Superimposing of plasma heating by
ECRH and NBI for the high density plasma results in anincrease and peaking of particle flux.
Ion particle flux measured by west ELIEA plottedFig. 3 The ion particle flux measured at the west end-cell plottedagainst the x-axis.

against the electron line density in the central cell (NLCC)
in various cases of experiments are shown in Fig. 4 Experiments using ICRF antennas type III and type II, which isa standard experimental situation of GAMMA 10/PDX isrepresented by solid circles. In the standard condition, theamount of particle flux was relatively small, however, theion temperature is relatively high in the condition [2, 3].
Experiments that superimposed the ICRF wave in either
east or west anchor regions are plotted as open squares andopen circles respectively. In the current experiments, ICRF
heating by using west anchor DAT appears slightly more
eﬀective compared with east anchor DAT It is consideredthat the slight asymmetry of the machine in anchor regions
is a cause of the diﬀerence; however, further investigationis needed. The high-density operations achieved by using both east and west anchor DAT antennas are shown as

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plasma potential works as an enhancement factor of axialion loss. In equation, the eﬀect of the plasma potential isexplained as a degradation of mirror ratio
R,Reﬀ = qφ1+T i //(3)where φ is plasma potential. The eﬀective mirror ratio Reﬀ
represents the actual mirror confinement performance inexperiments.
With considering plasma potential, the dependence ofion particle flux on the plasma density becomes as follows;Γi ∝Fig. 4 Ion particle flux measured by ELIEA plotted against theelectron line density in the central cell.

solid triangles. In the high density operations, the amountof particle flux is largely enhanced and the value 1.7 × 1023
particles/m2 sec was achieved. Ion temperature in the operations is relatively low since the strong ion heating fromtype II antenna is absent in the operation.
Overall, in Fig. 4, there is a co-relationship between
the ion particle flux and the electron line density in thecentral cell. The behavior is natural because the amountof end-loss particle flux is given by the equation Γi =Ntotal /τion where Γi is an ion particle flux, τion is the axial ion confinement time and Ntotal is the total number ofions existing in CC, EA and WA mirror fields. It can be assumed that the addition of plasma heating by anchor DATantenna increases the amount of particle flux by increasing Ntotal . On the other hand, as seen in Fig. 2, addition ofECRH and NBI increases the particle flux without changing the plasma density. Therefore the eﬀect of ECRH andNBI on the high density plasma can be considered as thechange of ion confinement time. The confinement time ofGAMMA 10/PDX experiments without confinement potential cases are usually explained by simple-mirror theory [7] written as
τion = 1.8 × τii × log(R),(1)

where R is the mirror ratio and τii is the collision time ofion-ion collisions written as
3

τii =

6.6 × 10−3 × T i2//
N × (10−20 ) × Zi4 × ln Δ.

N2.
log (Reﬀ )(4)

Here it can be noted that the particle flux depends on thesquare of plasma density N. However, in Fig. 4, parabolic
dependence of the particle flux on the plasma density cannot be seen clearly. Especially in high density operation
data indicates that the dependence is linear. This is because the collision frequency in mirror confined plasma
became too high and the mechanism of particle loss has
been changed. In standard operation of GAMMA 10/PDX,
ion-ion collision time is 100 times longer than the averagetransit time of the ion, vion /L where L is the half lengthof mirror magnetic field. Therefore, few collisions are expected during a transport of end-loss particle to the endregion. On the other hand, collision time is only 1.6 timesof the transit time in high density operations and therefore
the eﬀect of collision in the loss cone need to be taken intoaccount. This shift of plasma confinement time is theoretically predicted by Monte-carlo simulations [8] and in highcollision regime, plasma confinement time can be writtenas;√π × Reﬀ × L.
(5)
τion =
T i //In this case, the amount of particle flux becomesqφ
N × T i // × 1 +T i //.
Γi ∝R×L(6)

In high collision plasma, the confinement time is not determined by collision time, but an axial transit time of theions. Therefore, in high density operations, particle flux islikely to depend linearly on the plasma density.

(2)

4. The Use of Plasma Potential

In addition, when considering an actual mirror confined plasma, eﬀect of the plasma potential must be included. The mass of electrons are much smaller than hydrogen ions and therefore electrons in GAMMA 10/PDX
escapes from the mirror much faster than ions. As a result,positive electrostatic potential between the mirror confinedplasma and the wall of machine is formed. This positive

According to the theorem of mirror confinementin high collision frequency regime, the particle flux in
GAMMA 10/PDX in current high density operations or
higher density operations will follow the linear dependence instead of parabolic dependence shown in Fig. 5.
That means extremely large power of ICRF heating will
be required to achieve particle flux larger than 1024

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Plasma and Fusion Research: Regular Articles

Volume 11, 2405045 (2016)

Fig. 5 Ion particle flux measured by ELIEA plotted against theelectron line density in the central cell with linear andparabolic fitting curves.

time of ions in high density operation depend directly on
the mirror ratio Reﬀ instead of the logarithm of Reﬀ . Therefore the change of mirror ratio due to the plasma potential
becomes more eﬀective in high density experiments.
Experimental result of particle flux enhancement byusing ECRH is plotted in Figs. 6 (a) and (b). ECRH is anelectron heating device and therefore plasma potential israised by the application of ECRH. Here, in standard collisionless plasma, increase of plasma potential by 200 V
results the increase in particle flux by 0.5 ∼ 1.0 × 1022
particles/m2 sec. On the other hand, the increase in plasma
density by about 50 V results the enhancement of particle
flux by 3.0 ∼ 5.0 × 1022 particles/m2 sec in high density operation.

5. Summary
For the divertor simulation study that is recently focused in GAMMA 10/PDX, the method to enhance theamount of ion particle flux was studied. Plasma heating by
new ICRF antennas has eﬀectively enhanced the buildupof plasma density and particle flux. It was observed thatthe high plasma density and low plasma temperature in thehigh density operations resulted in the enhancement of ionion collision and changes mirror confinement characteristics. The observation suggested that it will be helpful to
use the eﬀect of plasma potential as a support strategy forthe future upgrade of the particle flux.

Acknowledgements
This study was supported by the NIFS as bidirectional collaborative research (NIFS12KUGM066).
The author thanks the members of the GAMMA 10 research group for their collaboration on the experiments andfor helpful discussions.

Fig. 6 Time behaviors of ion particle flux and plasma potentialin (a) standard operation and (b) high density operation.

particles/m2 sec. Thus, the use of a plasma potential canbe helpful to reduce an eﬀort required to enhance the particle flux. As in equation (1) and (5), mirror confinement[1] Y. Nakashima et al., J. Nucl. Mater. 438, S738 (2013).
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[7] D. V. Sivukhin, Review of Plasma Physics 4, 202 (1966).
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