Plasma and Fusion Research: Regular Articles

Volume 14, 3405078 (2019)

Experimental Analysis on Variation of the Amount of Particles
Passing Through Traveling Wave Direct Energy Converter∗)
Kazuhiro SHIBATA, Hiromasa TAKENO, Kazuya ICHIMURA, Satoshi NAKAMOTO
and Yousuke NAKASHIMA1)
Graduate School of Engineering, Kobe University, Kobe 657-8501, Japan
Plasma Research Center, University of Tsukuba, Tsukuba 305-8577, Japan1)(Received 27 December 2018 / Accepted 22 March 2019)
Traveling wave direct energy converter (TWDEC) was proposed as an eﬃcient energy recovery device for14.7 MeV protons produced by D-3 He fusion reaction. Protons are velocity-modulated and bunched up, theninduce traveling wave field which traps and decelerates themselves. In simulation experiments, it was found thatthe amount of particles was larger during application of modulation/deceleration field in the condition providing
high eﬃciency than other conditions. This paper treats the phenomenon and will present results of analyticalexperiments and discussion. We found that ions were scattered due to modulation, and variation of the numberof ions was corresponding to variation of deceleration eﬀect. The possible mechanism of the phenomenon isscattering of particles due to bunching and its suppression due to trapping by deceleration field. In other words,
high eﬃciency would be obtained by suppression of scattering.
c 2019 The Japan Society of Plasma Science and Nuclear Fusion ResearchKeywords: TWDEC, constant deceleration scheme, dual-frequency modulation, scattering, particle trapping
DOI: 10.1585/pfr.14.3405078

1. Introduction
In D-3 He fusion power generation, most of energy
produced by fusion reaction is carried as kinetic energy ofcharged particles such as electrons, thermal ions, and highenergy protons of 14.7 MeV. The proton energy cannot betreated by conventional electrostatic converters due to technical limitations. To overcome this problem, applicationof a traveling wave direct energy converter (TWDEC) [1]is expected. Direct energy converters (DECs), which are
made up of a cusp-type direct energy converter (CuspDEC)[2] and a TWDEC, were proposed as eﬃcient energy recovery devices for D-3 He fusion reaction in the previous
research [3].
The charged particles from a reactor are incident intoDECs, the energy of electrons and thermal ions are processed in CuspDEC and that of protons are in TWDEC.
The CuspDEC is placed in the upstream, and designed
to discriminate thermal ions and electrons from incident
plasma. These particles are gathered into collectors, andthose energy is converted into DC power. TWDEC is designed based on inverse process of a linear accelerator, andworks for energy recovery from 14.7 MeV protons. It consists of a modulator and a decelerator. Incident protons
are introduced into the modulator and bunched up in thedownstream by axial velocity modulation using RF electric field. The decelerator is located at the bunching point

and bunched protons excite an electrostatic traveling wave.
The wave is designed to be decelerated and traps protons
by its potential well so that trapped protons are decelerated. Reduced kinetic energy of the protons are converted
into the RF energy through an external transmission circuit
connected to the decelerator.
In previous research on modulation process, numerical calculation predicted a possibility of ion scattering due
to bunching [4]. Actually, a phenomenon suggesting ion
scattering was found in simulation experiments [5]. Insuch a situation, some ions go out of the system and theirenergy is lost. Thus, cause and influence on deceleration of
the phenomenon should be investigated [6]. In this work,
we performed experimental analysis on radial scattering ofions by using an array of concentric electrodes, and investigated influence on deceleration process in various deceleration experiments.
In Sec. 2, the experimental setup and evaluation methods are shown. Overview of the TWDEC simulator andexperimental procedure are explained. Measurement devices and evaluation are also explained. In Sec. 3, experimental results are shown, and discussion is also presented.
In Sec. 4, conclusion of the paper is given.

2. Experimental Step
2.1 TWDEC simulator

author’s e-mail: takeno@eedept.kobe-u.ac.jp∗) This article is based on the presentation at the 27th International Toki
Conference (ITC27) & the 13th Asia Pacific Plasma Theory Conference(APPTC2018).

A schematic view of the experimental simulator isshown in Fig. 1. The device consists of sections of ion
source, extraction, modulation, deceleration, and measure-3405078-1

c 2019 The Japan Society of Plasma
Science and Nuclear Fusion Research

Plasma and Fusion Research: Regular Articles

Volume 14, 3405078 (2019)
designed the decelerator based on the constant deceleration
scheme [11]. In this scheme, traveling wave with constantdeceleration traps ions in its potential well and trapped ionsare decelerated together. The axial position of electrodes
corresponding to 0.5π phase interval can be determined bydeceleration α according to Vex . For Vex = 1.6 kV and3.2 kV, we take α = 5.5 × 1011 m/s2 and 7.8 × 1011 m/s2 ,respectively, and 6 and 8 electrodes are placed, respectively. The first electrode is at the bunching position. The
structure of the electrodes are the same as that in the modulator. Each 0.5π lagging voltage can be obtained by an
RF source of Vdec of 7 MHz synchronized with Vmod1 anddelay lines.

2.2 Measurement and evaluation

Fig. 1 Experimental simulator.

ment. These sections are placed coaxially.
In the ion source section, a helium plasma is generated
by supplying an RF power of 15 MHz to an RF antenna.
The discharge is assisted by magnetic field created by twomagnetic coils shown in Fig. 1. The discharge is performedby repetitive pulse operation, and the pulse has a frequencyof 667 Hz and 67% duty ratio.
In the extraction section, extraction voltage Vex is applied to an extraction electrode at the end of the ion source.
In this paper, Vex = 1.6 kV and 3.2 kV are used. The extracted ions are bundled into a beam shape by applying Vc
to a cylindrical convergence electrode placed in the downstream of the extraction electrode.
In the modulator, we adopted the dual-frequency modulation method to improve deceleration eﬀect. The dualfrequency modulation was proposed as favourable modulation method to improve ion bunching [7, 8]. Actualstructure of the modulator has four coaxial disk electrodes
with a hole of 6 cm diameter covered by mesh. A sinusoidal wave voltage of 7 MHz (Vmod1 ) and synchronized
one of 14 MHz with leading phase diﬀerence of 0.5π rad(Vmod2 ) are applied to the second (M2 ) and the third (M3 )electrodes, respectively, and other electrodes are grounded.
The axial intervals between electrodes are the same as therunning length of the ions in quarter period of 7 MHz. The
eﬀect of dual-frequency modulation was confirmed as generation characteristics of the third harmonic component [8]and variation of energy distribution function [9] in the previous papers.
For deceleration experiment in the simulator, formation of traveling wave in the decelerator is achieved byapplication of external RF voltages (Vdec ) instead of induction due to bunched ions. This is called ‘active decelerator’ [10]. In the actual experiments, two function
generators synchronized with each other are used. Thosesignals are pulse-modulated and amplified as Vmod1 andVdec . The phase of the signals can be controlled independently, and that for Vmod1 is zero. As for Vdec , phases ofθdec = nπ/4 (n = 0, 1, ..., 7) are settled for examinationof deceleration eﬀect for each experimental condition. We

At the end of the device, a Faraday cup (FCP) is installed which consists of an ion repeller grid (IR), a secondary electron repeller grid (SER) and an ion collector
electrode (C). The entrance hole of the cup has also grid,and the size of the hole as well as those of the holes ofIR and SER are the same diameter of 6 cm with thoseof TWDEC electrodes. The ions are discriminated foreach energy by applying sweeping voltage (VIR ) to the IR.
In the experiment, collector current Ic discriminated foreach energy is obtained. The distribution function of the−1/2(dIc ) / (dVIR )|VIR =E/e ,ions f (E) is given by f (E) = VIR
where E and e mean ion energy and unit charge, respectively.
The average∞ ∞ energy of the ions are given by E =E · f (E)dE/ 0 f (E)dE. We used deceleration rate de0
fined by Rdec = (E0  − E) /E0  for evaluation of deceleration eﬀect, where E0  means the average energy ofincident ions without modulation and deceleration.
An array of concentric ring electrodes used for measurement of radial distribution of ions is installed at theend of TWDEC simulator instead of the Faraday cup. Its
structure is shown in Fig. 1. The array consists of six ring
electrodes which are P1 -P6 counting from the center. Thesize of each electrodes is shown in the figure. The electrodes are placed by removing the decelerator and the FCP,
and the electrode array is axially movable to obtain axial
variation of the radial distribution.
In the experiment, a multi-point boxcar integrator(MPB) was used to obtain time variation of energy distribution. The MPB was developed by authors [12]. The tim-Fig. 2 Timing chart of RF (Vmod1 , Vmod2 , Vdec ) applications and
MPB sampling.

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ing chart of RF applications and sampling by MPB in theactual experiment are shown in Fig. 2. The sampling timing is determined by taking period of steady state of plasma
production and sweeping energy range into account. ForVex = 1.6 kV, Vmod1/2 and Vdec are in 300 - 1000 µs fromthe start of plasma production, so every 40 µs during 320 920 µs are taken. For Vex = 3.2 kV, 320, 640, and 960 µs
are taken for 400 - 1000 µs RF application.

3. Results & Discussion
3.1

Radial behavior of ions

Ion beam currents were measured by the concentricring electrodes. In order to discuss the variation of radial
distribution due to beam modulation, the results are summarized as in Fig. 3. Note that the abscissa (L) means axial
position of the array of concentric ring electrodes basedon bunching position, and ordinate (Rc ) means ratio of themodulated beam current relative to the corresponding current without modulation.
The current measured by P1 of the most inner electrode is consistently smaller than 1. Those of P2 and P3change a little around 1 for all axial positions. That of P4
decreases in the downstream of bunching point. For P5 , allcurrents except at L = 30 mm are over 1. That of P6 of
the most outer electrode is consistently larger than 1.2, andlarger values are found around bunching point. When wesummarize roughly, internal components of the ion beam
decrease due to modulation while external ones increase,and the variation is large in the downstream of the bunching point. Thus, it can be said that ions are scattered byfield of ions bunched by modulation.

3.2

Fig. 3 Ratio of the modulated beam current relative to that without modulation for each ring electrode (P1 -P6 ).

Fig. 4 Example of energy distribution.

Time variation of the amount of particles

An example of the energy distribution of the ion beammeasured by the FCP is shown in Fig. 4. The energy distribution of the beam is originally as that by black curve,
and becomes as that by red curve due to deceleration. In
spite of the condition of Vex = 1.6 kV, the original beam
has a peak at 1.8 keV. This energy diﬀerence may be due
to potential of the plasma in the ion source. The diﬀerence of initial beam energy aﬀects deceleration process inthe designed decelerator. However, the present diﬀerence(0.2 keV) is almost the same as that by modulation voltage(190 V), so the particles can be trapped with bouncing motion in the potential well of traveling wave. From this result, we can calculate the number
 of ions by integrating theenergy distribution function:f (E)dE. Time evolutionof the energy distribution is obtained by MPB sampling in
one measurement, so time evolution of the number of ionsis also obtained.
The time variation of the number of ions of 1.6 keVion beam is shown in Fig. 5. The number of modulated particles is denoted by black squares, and those of decelerated
particles are denoted by red triangles for θdec = 5π/4 whenRdec = 39.1% and blue inverse triangles for θdec = 3π/4Fig. 5 Time variation of the number of ions of 1.6 keV ion beam.

when Rdec = −11.1%. The number of particles increases
as time elapses from 40 µs to 280 µs due to plasma production. During RF application from 300 µs to 920 µs, thenumber of ions decreases without deceleration. In the casewith deceleration of high Rdec , decrement of the number ofions is suppressed and the same level before RF applicationis recovered around 700 µs. In the case with decelerationof low Rdec , however, decrement of the number of ions isenhanced and the level is lower than without deceleration.
The time variation of the number of the ions of 3.2
keV ion beam is also examined, and is shown in Fig. 6 byusing the same symbols as those in Fig. 5 (high/low Rdec
are obtained by diﬀerent θdec ). In the three conditions, thenumber of ions is the same with each other at 300 µs. After
RF application, the number of ions without deceleration
increases a little. In the condition of high Rdec , the numberof ions is larger than without deceleration, while it is lessin the low Rdec condition.

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Fig. 6 Time variation of the number of ions of 3.2 keV ion beam.

Fig. 7 Relative number of ions (Ni ) versus deceleration rate
(Rdec ) (Vex = 1.6 kV).

By applying modulation, spatially gathered ions repel
each other, and are scattered. Thus, the number of ions inthe beam path limited by the size of the holes of TWDEC
electrodes decreases, and that introduced into the FCP withthe same hole size decreases.

3.3

Relation between the number of ions anddeceleration eﬀect

We examined relation between variation of the number of ions and deceleration rate in the conditions of Vdec
= 150, 180, 220 V0p (V0p means zero-to-peak voltage).
When we vary θdec , Rdec changes even in the same Vdec
condition. The results of Vex = 1.6 kV are summarizedin Fig. 7. Note that the ordinate of Fig. 7 means the number of ions on 920 µs relative to that on 280 µs in the samemeasurement. According to Fig. 7, a positive correlation
is found between the number of ions and the deceleration
rate in each Vdec condition. The number of ions is large
when the deceleration rate is high, and vice-versa.
We also examined relation between the deceleration
rate and the number of ions for Vex = 3.2 kV, and the results are shown in Fig. 8. Figures 8 (a) and (b) show increase rate of the number of ions and the deceleration rateversus initial phase of traveling wave θdec , respectively.
Note that the ordinate in Fig. 8 (a) shows increase rate ofnumber of ions from 320 µs to 960 µs. The chained line
shows the level without RF application which means thepure incident beam. In the modulation indicated by theblue solid line, the increase rate is smaller than the incident beam, which is considered to be due to ion scattering. The red squares are those of deceleration, and theyroughly vary sinusoidally to θdec . The deceleration rate inFig. 8 (b) changes from −17% to 53% in accordance withthe increase rate. The result in Fig. 8 also shows variationof the increase rate is corresponding to variation of the deceleration rate.
From those results, we can conclude there is a strong
correlation between the number of ions and the deceleration rate. As for the mechanism of this correlation, we canconsider as follows.
In the constant deceleration scheme, the decelerator isdesigned so that an electrostatic wave travels and is decel-Fig. 8 Dependences on initial phase of traveling wave (θdec ) of(a) increase rate of the number of ions from 320 µs to960 µs (Ri ) and (b) deceleration rate (Rdec ) for 3.2 keVion beam.

erated axially. Ions are trapped by the potential well of thetraveling wave so that the trapped ions are decelerated. Fordeceleration, required trapping is in the axial direction, but
the eﬀect also restricts radial ion motion. The modulated
ion beam is scattered by the field created by bunched ions,however, restriction by the trapping corrects ion orbits inthe axial direction. So the number of ions in the beam column could be changed by application of deceleration field.
As TWDEC works based on the inverse process of alinear accelerator, the deceleration eﬀect depends on theinitial phase of the traveling wave θdec . In the phase of
better eﬀect, the number of trapped ions are more, which
results in higher deceleration rate. On one hand, the trapping also aﬀects radially, so the number of ions in the beamcolumn increases. That’s why the number of ions and thedeceleration rate correlates.
As for scattering phenomenon, the existence of thephenomenon was just confirmed experimentally [5], and3405078-4

Plasma and Fusion Research: Regular Articles

Volume 14, 3405078 (2019)its detailed examination has not been done. Further simulation experiments, such as measurement at a larger radius
are required. At the same time, the scattering phenomenon
itself is possible to become an obstacle in the experiments
without a decelerator. As an operation only with a modulator is nothing but a simulation experiment, influence of thescattering phenomenon can be relatively reduced by employing a thick ion beam.

4. Conclusion
We carried out experimental analysis on ion scattering in a TWDEC simulator. As a result, we found that ionsmoved outward due to bunching by modulation. Subsequently, deceleration experiments were performed, and it
was found that number of ions changes having a correlation with deceleration eﬀect. The number of ions increases
in the preferred deceleration conditions while it decreases
in the other conditions. Thus, it can be said that the ion
scattering is restricted by the trapping eﬀect by the potential well of traveling wave.

Acknowledgment

ordinated research between PRC, Univ. Tsukuba, NIFS,and Kobe Univ. (NIFS13KUGM082), and was also supported in part by a Grant-in-Aid for Scientific Research(B) (16H04317) from JSPS.
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[6] K. Shibata et al., Plasma Conference 2017, 24P-90 (2017).
[7] H. Sato et al., Joint meeting of 26th International Toki Conference and 11th Asia Plasma and Fusion Association Conference, P1-99 (2017).
[8] H. Takeno et al., Plasma Fusion Res. 14, 2405014 (2019).
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This work was supported in part by the bilateral co-3405078-5