Plasma and Fusion Research: Regular Articles

Volume 11, 2401014 (2016)

Evaluation of Dark Current Profile for Prediction of Voltage
Holding Capability on Multi-Aperture Multi-GridAccelerator for ITER∗)
Ryo NISHIKIORI, Atsushi KOJIMA, Masaya HANADA, Mieko KASHIWAGI,
Kazuhiro WATANABE, Naotaka UMEDA, Hiroyuki TOBARI, Masafumi YOSHIDA,
Masahiro ICHIKAWA, Junichi HIRATSUKA, Yasushi YAMANO1) , Tetsuya OKURA1)
and NB Heating Technology Group
1)

Japan Atomic Energy Agency, 801-1 Mukoyama, Naka 311-0193, Japan
Saitama University, 255 Shimo-Okubo, Sakura-ku, Saitama 338-8570, Japan(Received 30 November 2015 / Accepted 18 January 2016)

Dark current analysis to estimate the current density of the field-emitted electrons have been developed
for the prediction of the yoltage holding capability of multi-aperture multi-grid accelerators used in JT-60SA andITER neutral beam injectors. From the experimental measurement of the field-emitted electrons in multi-aperture
multi-grid accelerators, βEBD , which represent the critical current density to trigger the breakdown, were foundto be constant with around 6 × 103 kV/mm regardless of the electric field profiles and the surface conditions inan accelerator with a surface area of 0.1 m2 . In addition, the dark current was measured in the region with theelectric field above ∼60% of the electric field at the breakdown, which leads to the determination of the emission
region in the analytical estimation of the dark current. Furthermore, from the measurement of βEBD on electrodes
with various surface area, βEBD was found to decreases with an increase of the surface area S (βEBD = 4 ×
103 S −0.3 ). From these results, the dark current profile at the critical current density can be estimated from theelectric field analysis, which leads to the development of the breakdown model and the prediction of the voltage
holding capability on the multi-aperture multi-grid accelerators.
c 2016 The Japan Society of Plasma Science and Nuclear Fusion ResearchKeywords: ITER, MAMuG, neutral beam injector, voltage holding capability, breakdown, field-emitted electron,
field enhancement factor, eﬀective electric field, dark current
DOI: 10.1585/pfr.11.2401014

1. Introduction
A neutral beam injector (NBI) with negative ion
source and high-energy high-current electrostatic accelerator with multi-aperture multi-grid (MAMuG) concept [1] isindispensable for fusion plasma heating and current drivein future fusion reactors. For JT-60SA and ITER NBI systems, 22 - 40 A negative ion beams are required to be accelerated up to 0.5 - 1 MeV [2, 3]. To achieve such highenergy high-current beams, one of the critical issues is thehigh voltage holding which is dominated by breakdown inaccelerators.
Previously, the voltage holding capability of the MAMuG accelerators has been empirically investigated interms of the geometric characteristics such as the area,
the multi-aperture and the multi-grid eﬀects [4, 5] because
there is no reliable physics-based-model for the predictionof the voltage holding capability. In the past results, it
was suggested that breakdown was triggered by dark current and the voltage holding capability followed Clump-theory [6].
Therefore, an estimation of the dark current due tofield-emitted electrons [7] is one of key techniques forthe prediction of the voltage holding capability. However,there is no available technique to estimate the dark current
profile in accelerators having large-area grid and a lot ofaperture with locally-strong electric field.
This time, toward the development of the dark current
analysis, the behavior of the dark current depending on theelectric field and surface area was investigated by using
accelerators having various electric field profiles.

2. Evaluating Field-emitted Electrons
In a vacuum condition, electrons are emitted frommetal surface by applying high voltage according toFowler-Nordheim (F-N) theory [8, 9]. In this F-N theory,
current density j of field-emitted electrons are given by,author’s e-mail: nishikiori.ryo@jaea.go.jp∗) This article is based on the presentation at the 25th International Toki
Conference (ITC25).

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j=1.54 × 10−6 (βE)2φt2 (y)−6.83 × 109 φ3/2 v(y)
× exp
,
βE(1)

c 2016 The Japan Society of Plasma
Science and Nuclear Fusion Research

Plasma and Fusion Research: Regular Articles

Volume 11, 2401014 (2016)

where β is the field enhancement factor, E is the electricfield, φ is the work function, and t(y) and v(y) are the correction factors. Here, E can be expressed as average electric field Eave in actual electrodes where Eave is the quotientof applied voltage V and gap length d.
Eq. (1) is deformed as follows to evolve β fromexperimentally-measured values: I 
2.84 × 109 φ3/2 d 1
ln 2 = −βVV



10.4
β2 A+ ln 1.54 × 10−6exp, (2)φd2
φ1/2
where A is the emission area in F-N theory. If the dark current is originated in field-emitted electrons, then the plotof 1/V vs ln(I/V 2 ) become linear. As noticed from eq. (2),this plot called F-N plot gives β with the gradient M by,
2.84 × 109 φ3/2 d.
(3)
MTherefore βEave , so-called eﬀective electric field
which is a key parameter to estimate the current density of
the field-emitted electrons, has been determined from experiments. If βEave can be evaluated without experiment,
the dark current density can be analyzed.
By using miniaturized parallel electrodes, whose surface area is 1/6000 of that for JT-60SA, βEave is reported
to be constant regardless of breakdown voltage [10]. However, the field distribution is complicated in actual MAMuG accelerator. Electric field is higher around the apertures in the grid with small surface area, and lower in theregion of support where gap and surface area is larger thanthose of the grid as shown in Fig. 1. Therefore, it is necessary to investigate the influence of field distribution on
βEave .
In addition, in order to understand the dark current
profile, lower limit of electric field for the field emissionis also important. In the experiments, dark current can bemeasured only in the region with relatively strong electricfield. This indicates that there is a certain limit of the electric field for the field emission and breakdown does not occur in the region where electric field is below the limit. By
applying this lower limit, dark current analysis based onβEave can be realized as shown in Fig. 1 where electrons
are emitted from anywhere.
Toward the analytical estimation of the field-emitted
electrons, these two issues were investigated.

Fig. 1 Calculation result of electric field analysis in the MeV accelerator. Filled contour shows the electric field strength,
and the line shows trajectory of electrons emitted from
cathode surface.

β=−

3. Experimental Setup
Dedicated experiment for high voltage holding was
carried out by using an acceleration of a 5-stage MAMuG
accelerator for cathode and anode electrodes. Both electrodes are composed of copper grid, aluminum flange, andstainless steel support. Same grids with surface dimensionof 204 mm × 234 mm and 49 apertures were used in bothelectrodes. Diameter of flange and support was 796 mmfor cathode and 430 mm for anode.

Fig. 2 (a) Schematic of experimental setup. High voltage wasapplied to cathode. (b) Photo of anode which is divided
into 3 parts insulating from each other.

In this experiment, the anode was divided into 3 regions by insulating from each other to measure the darkcurrent separately as shown in Fig. 2. These regions havediﬀerent electric field profile and average electric field
Eave . Although Eave were same in grid and flange regionswith gap length of 20 mm, grid has about 3 times higher
electric field around the apertures. Gap length in support
region is 183 mm, thus Eave is lower compared to grid andflange regions.
Negatively charged high voltage is applied to the cathode by a power supply with capability of −300 kV and
10 mA in a vacuum pressure below 4 × 10−3 Pa. Applied
voltage was increased by 1 kV/1 sec until breakdown occurs in a shot.
This shot is repeated until VBD is saturated after thespark conditioning is fully satisfied. Dark currents in eachregion and applied voltage were measured in each shotand parameters of VBD , VFE , IBD , and β were estimatedas shown in Fig. 3. Here, VBD is the voltage where breakdown occurs. VFE is the lower limit of the voltage wheredark current is firstly measured. IBD is the dark current justbefore the breakdown occurs. β is the field enhancement
factor which is derived from eq. (3) with the gradient of FN plot as shown in Fig. 3 (b) and assuming work function

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Volume 11, 2401014 (2016)

Fig. 3 (a) Typical voltage and current acquired from the experiment. (b) F-N plots made from acquired data for eachregion. Range of the plots depend on the range of theapplied voltage where dark currents were observed.

Fig. 4 Experimental result of (a) VBD and VFE , (b) IBD in eachregion, and (c) β in each region in each shot.

of 4.6 eV for copper [11], 4.3 eV for aluminum [12], andfor stainless steel [13] respectively.

4. Experimental Result
Figure 4 shows the history of the measured parametersin each shot.
VBD increases up to ∼120 kV in maximum as the spark
conditioning progresses and VFE varies along with VBD .
Note that low VFE due to the unstable condition after thebreakdown is excluded.
IBD for grid and flange were constant throughout theexperiment with around 1 mA. It seems that breakdown occurs in some probability when dark current is beyond thecritical value which is independent of applied voltage. IBD
for support varies by the shot which have little involvementin breakdowns.
β decreases in opposition to the increase of VBD whichis consistent with previous result [10]. It is thought to bethat β indicates the degree of progress of spark conditioning.

4.1

Influence of electric field on βEave
geid

Figure 5 (a) shows βEave in each region. When Eave =fiange
Eave = EBD was defined because all the breakdowns occurred in either the grid or the flange which two has same
gap lengths, then βEBD were found to be same in both region with around 6 × 103 kV/mm which indicates that influence of the electric field around the apertures of the gridsupportwas smaller than theis included in β. Measured βEave
support2
wasothers with around 9 × 10 kV/mm because βEave

Fig. 5 Experimental result of (a) βEave in each region and (b)VFE /VBD .

smaller than EBD , namely no breakdown was observed inthe support region.
In addition, βEBD were kept constant throughout theexperiment which means that βEBD is independent of theVBD . This result can be explained if the breakdown occurs in some probability when current density of the fieldemitted electrons is beyond the critical value which is independent of VBD .

4.2 Lower limit of the field emission
From the measurement of VFE , lower limit of the applied voltage for the field emission was found to be ∼60%of the VBD regardless of VBD as shown in Fig. 5 (b). Thissuggests that lower limit of the field emission depends onthe condition of the accelerator and field-emitted electrons

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Plasma and Fusion Research: Regular Articles

Volume 11, 2401014 (2016)
in empirical surface area eﬀect. Therefore it is expectedthat βEBD can be extrapolated from surface area leading to
the estimation of field-emitted electrons in various electricfield profile.

5. SummaryFig. 6 Relation between surface area and measured βEBD in various electrodes. Open circle is the result from miniaturized parallel electrodes [10].

which triggers the breakdown are produced in the region
where surface electric field is higher than 0.6 EBD . Thisis consistent with no breakdown observed in the support
region where Eave is less than 0.6 EBD .

4.3

Surface area eﬀect of current density

From two results above, it can be concluded that
βEBD , which is constant regardless of the breakdown voltage, shows the critical dark current density to trigger thebreakdown and the region of > 0.6 EBD is related to bebreakdown induced by the dark current. Therefore, criticalcurrent density of the field-emitted electrons to trigger thebreakdown are expected to be estimated in the electric field
analysis by using βEBD within the region of > 0.6 EBD .
By applying this assumption, surface area having influence on breakdown can be determined. Figure 6 shows
the relation between surface area of various electrodes andmeasured βEBD in each electrode. βEBD decreases as surface area S increases with βEBD = 4 × 103 S −0.3 , whichindicate that the critical dark current density for breakdown is reduced by increasing the surface area. This result
agrees with the reduction of the voltage holding capability

Analytical technique to estimate the current density of
the field-emitted electrons have been developed for multiaperture multi-grid accelerators such as JT-60SA and ITER
NBI. This time, dark currents were measured in variationof the electric fields to investigate βEave and emission region of the electrons in actual MAMuG accelerators.
As the results, βEBD that represents the critical darkcurrent density were found to be around 6 × 103 kV/mm
regardless of the regions and the conditions in an accelerator. Furthermore, βEBD have dependence only on the surface area of the emission region with βEBD = 4 × 103 S −0.3
where electric field is above 60% of EBD .
The developed analytical estimation of dark current
will lead to the development of the model of the breakdown process in accelerators which is necessary for theprediction of the voltage holding capability.
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