Plasma and Fusion Research: Regular Articles

Volume 14, 2405027 (2019)

Analytical Experiment of Time Evolution of Deceleration Eﬀect inTraveling Wave Direct Energy Converter Using Dual-Frequency
Modulation∗)
Kazuhiro SHIBATA, Hiroki SATO, 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 10 September 2018 / Accepted 10 December 2018)
Traveling wave direct energy converter (TWDEC) was proposed as an eﬃcient energy recovery device for
D-3 He fusion power generation. It is designed to convert the kinetic energy of 14.7 MeV protons produced byfusion reaction and is based on the inverse process of a linear accelerator. It consists of a modulator and adecelerator. In modulation process, dual-frequency modulation was proposed to improve bunching. Following
to the proposal, deceleration experiment was performed, where the conditions of conventional and proposed
methods were in a sequence. The result included other eﬀects such as time variation of modulation eﬀect, thus
the eﬀect of dual-frequency modulation to deceleration has not been clarified yet. In this work, the deceleration
experiment was performed with conventional and proposed methods independently. In addition, time variationof deceleration eﬀect was observed to exclude the time variation of the modulation eﬀect. As a result, the eﬀectof dual-frequency modulation to deceleration process was observed clearly. Higher eﬃciency was obtained withdual-frequency modulation.
c 2019 The Japan Society of Plasma Science and Nuclear Fusion ResearchKeywords: D-3 He fusion power generation, TWDEC, dual-frequency modulation, deceleration
DOI: 10.1585/pfr.14.2405027

1. Introduction
In D-3 He fusion power generation, most of produced
energy is carried as kinetic energy of charged particles.
Thus, high eﬃciency can be expected by applying directenergy converters (DECs) [1]. The DECs consist of a cusptype dirtect energy converter (CuspDEC) [2] and a traveling wave direct energy converter (TWDEC) [3]. The CuspDEC is placed in the upstream, and designed to discriminate thermal ions and electrons from plasma flowing out
from a reactor. These particles are gathered into collector, and those energy is converted into DC power. The
TWDEC is placed in the downstream, and designed to convert kinetic energy of 14.7 MeV protons. Its principle isbased on the inverse process of a linear accelerator. TheTWDEC consists of a modulator placed in the former stage
and a decelerator placed in the latter stage. The protons areincident into the modulator and bunched up in the downstream by velocity modulation. The bunched protons areintroduced into the decelerator and induce traveling wave
field by electrostatic induction on passing through deceleration electrodes. The protons are trapped and decelerated
by the traveling wave, and the reduced kinetic energy isconverted into RF power.
author’s e-mail: 179t233t@stu.kobe-u.ac.jp∗) This article is based on the presentation at the 12th International Conference on Open Magnetic Systems for Plasma Confinement (OS2018).

According to the theory of constant deceleration [4]used for design of the decelerator, high eﬃciency can be
expected for suﬃcient trapping of ions provided by betterbunching and narrower energy spread. In the modulation,
single sinusoidal wave was used conventionally, and thisscheme does not necessaarily provide complete bunching.
The use of dual-frequency for modulation was proposed toimprove bunching [5]. To achieve an ideal spatial bunching, in which all particles incident during one RF period
gather at the same spatial position at the same time, a necessary waveform of electric field was derived analytically.
This ideal waveform is similar to sawtooth waveform, andit cannot be used in practice as it needs extrenly high voltage in high frequency. An approximated scheme using
combination of two components of fundamental and second harmonic frequencies was taken, and this scheme wascalled the dual-frequency modulation. The bunching eﬀectof the proposed scheme was examined [5], and the researchof the optimization of dual-frequency modulation has beencontinuing.
On one hand, deceleration experiments with dualfrequency modulation were performed. In the experiment,compared modulation schemes performed sequentially, so
the results contained temporal variation of modulation effect [6] although better deceleration eﬃciency were shownfor dual-frequency modulation. The last experiment did

2405027-1c 2019 The Japan Society of Plasma
Science and Nuclear Fusion Research

Plasma and Fusion Research: Regular Articles

Volume 14, 2405027 (2019)not distinguish pure eﬀect only by dual-frequency modulation scheme [7]. Thus, the eﬀect of dual-frequency modulation to deceleration process has not been clarified yet.
The purpose of this research is examination of the effects of dual-frequency modulation to deceleration processexperimentally. Based on the theory of constant deceleration, we designed the decelerator for an experimental simulator with dual-frequency modulation. Then we performedexperiments and analysis on deceleration eﬀect to dualfrequency modulated particle beam with excluding time
evolution of modulation eﬀect using the simulator.
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 comparing between single sinusoidal modulation and dual-frequency modulation are shown, and discussion is also presented. In Sec. 4, conclusion of the paper
is given.

other electrodes are grounded. The intervals of the electrodes are the same as the quarter wavelength corresponding to 7 MHz.
The decelerator was designed based on the theory ofconstant deceleration [4]. According to the theory, potential well of traveling wave with constant deceleration
traps bunched ions. When trapped ions increase by betterbunching eﬀect, the eﬃciency of TWDEC is expected to behigher. In the actual structure of the decelerator which consists of six disk electrodes with a hole covered by mesh, thetraveling wave are excited by applying deceleration voltages of 7 MHz (Vdec ) synchronized with that of modulator
to 6 electrodes (D1 -D6 ). By using terminal voltage of delay lines, the phase of each electrode voltage is lagging
with 0.5π against that of the former one. Axial distance ofelectrodes installed in the decelerator from bunching position is shown in Table 1. In this structure, deceleration ofappplied traveling wave is taken to be 5.5 × 1011 m/s2 .

2.2 Measurement and evaluation

2. Experimental Setup
2.1

TWDEC experimental device

A schematic view of the experimental simulator isshown in Fig. 1. The device consists of sections of ion
source, extraction, modulation, deceleration, and measurement. 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 amplitude of the power is modulated by 667 Hz
repetitive pulse with 67% duty ratio.
In the extraction section, extraction voltage denoted
by Vex is applied to an extraction electrode placed at theend of the ion source section. The helium ions are extracted and have an energy corresponding to Vex . The extracted ions are bundled into a beam shape by appling Vc toa cylindrical focusing electrode placed in the downstreamof the extraction electrode.
The modulator consists of four disk electrodes witha hole covered by mesh. A sinusoidal wave voltage of
7 MHz (Vmod1 ) and synchronized one of 14 MHz with leading phase diﬀerence of 0.57π rad (Vmod2 ) are applied to thesecond (M2 ) and third (M3 ) electrodes, respectively, andAt the end of the device, a Faraday cup is installed
which consists of an ion repeller grid (IR), a secondary
electron repeller grid (SER) and an ion collector electrode(C). The ions are discriminated for each energy by applying sweeping voltage (VIR ) to the IR. In the experiment,collector current Ic discriminated for each energy is obtained.
The distribution function of the ions f (E) is given−1/2(dIc ) / (dVIR )|VIR =E/e . E and e meansby f (E) = VIR
ion energy and unit charge, respectively. The aver∞age energy of the ions are given by E = 0 E ·∞f (E)dE/ 0 f (E)dE. We used deceleration rate definedby ηdec = (E0  − E) /E0  for evaluation of decelerationeﬀect. E0  means the average energy of incident ions.
In the experiment, a multi-point boxcar integrator(MPB) was used to obtain time variation of energy distribution. The MPB was developed by authors [6]. The
timing chart of RF applications and sampling by MPB in
the actual experiment is shown in Fig. 2. When we take
Table 1 Axial distance of deceleration electrodes from bunchingposition.

Electrodes
Position [mm]Fig. 1 Experimental simulator.

D10D29D318D426D534

D641Fig. 2 Timing chart of RF applications and MPB sampling.

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Plasma and Fusion Research: Regular Articles

Volume 14, 2405027 (2019)the origin of time at the start of the plasma production,
both the modulation and the deceleration start at 300 µs
and continue for 700 µs. During plasma production, theMPB sampling is performed every 40 µs until 920 µs.

3. Experimental Results & Discussion
3.1

Energy distribution function

Energy distributions of the ions in modulation process
and that in deceleration process are shown in 3.1.1 and3.1.2, respectively. For all measurements, Vex = 1.6 kV
and Vc = 300 V. Energy distribution functions of the ions
was derived from I-V characteristics at 920 µs when thetime variation of the signal stopped suﬃciently.
3.1.1

Modulation process

The energy distributions of the single sinusoidallymodulated particle beam and the dual-frequency modulated one are shown in Fig. 3 and Fig. 4, respectively. In
these figures, the energy distribution function of the incident ion beam is denoted by dashed curve. Note that ordinate is scaled by 1/4. The ions distributed around 1.8 keV

Fig. 3 Energy distribution of modulated ions by single sinusoidal wave. Conditions of RF voltages are Vm1 =190 V0p , Vm2 = 0 V0p , Vdec = 0 V0p . (V0p : zero-to-peakvoltage)

Fig. 4 Energy distribution of modulated ions by dual-frequencywave.
Conditions of RF voltages are Vm1 =190 V0p , Vm2 = 100 V0p , Vdec = 0 V0p .

corresponding to Vex . The energy distribution function of
the modulated ion beam is denoted by solid curve. For
the single sinusoidal modulation of Fig. 3, the ions around
1.8 keV decrease and those in the range of 1.5 - 2.1 keVappear. The components around 1.6 keV and 2.0 keV are
more than that around 1.8 keV, so FWHM of the distribution is over 0.4 keV. For the dual-frequency modulationof Fig. 4, the component of 1.8 keV is more than those inother energy range, and FWHM is less than 0.2 keV.
These results are considered qualitatively as follows.
Figure 5 shows a sinusoidal waveform (blue) and an approximated dual-frequency one (red). If time passing
through the modulation field region is short, variation ofparticle energy depends on intensity of the electric field onincident timing. We roughly discuss by dividing the energy
range into two: high and low ranges as shown in the figure,where the boundary is taken to be +/−0.5 as an example.
As for high energy range, the corresponding periodof the dual-frequency waveform (red solid arrows) is narrower than that of the sinusoidal waveform (blue solid arrows). The number of incident particles is proportional totime period, so particles whose energy are greatly changed
under the dual-frequency modulation are fewer than thoseunder the sinusoidal modulation. As for low energy range,
wider period of the dual-frequency waveform (red dottedarrows) than that of the sinusoidal waveform (blue dottedarrows) results in more particles with small change in energy.
This consideration agrees with the diﬀerence of energy distribution shown in Figs. 3 and 4. The period ofhigh energy range in the dual-frequency modulation is affected by the short period of second harmonic frequency,
while the long period of the fundamental frequency determines that in the single sinusoidal modulation.
From those results, it can be said that averaged energy
spread of ions decreases when dual-frequency modulation
is applied.

Fig. 5 Energy ranges and corresponding periods for sinusoidal
waveform (blue) and approximated dual-frequency one(red).

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Volume 14, 2405027 (2019)

Fig. 6 Energy distribution of decelerated ions with single sinusoidal modulation. Conditions of RF voltages are Vm1 =190 V0p , Vm2 = 0 V0p , Vdec = 220 V0p .

Fig. 7 Energy distribution of decelerated ions with dualfrequency modulation. Conditions of RF voltages are
Vm1 = 190 V0p , Vm2 = 100 V0p , Vdec = 220 V0p .

3.1.2

Fig. 8 Time variation of deceleration rate.

3.2 Time variation of deceleration eﬀect
We evaluated time evolution of deceleration eﬀect byusing deceleration rate. Time variation of the deceleration rate is shown in Fig. 8. The deceleration rate increases
as time epalses for both single sinusoidal modulation anddual-frequency modulation. This variation is considered tobe due to time variation of modulation eﬀect.
As for the comparison of absolute deceleration rates
between single sinusoidal modulation and dual-frequency
modulation, the latter one is superior to the former one forall the time of 360 - 920 µs. For the single sinusoidally
modulated beam, the deceleration rate increases up to 30%.
On one hand, the deceleration rate with dual-frequency
modulation increases up to 39%. From this result, we clarified that the deceleration eﬀect with dual-frequency modulation is better than that with single sinusoidal modulation.

4. Conclusion

Deceleration process

The energy distribution functions of decelerated
ion beam with single sinusoidal modulation and dualfrequency modulation are shown in Fig. 6 and Fig. 7, respectively. Dashed curves are the same as those in Figs. 3and 4, and solid ones mean ions with modulation and deceleration.
According to Fig. 6, the particles around 1.8 keV significantly decrease, while those in the range of 0.2 1.2 keV appear when single sinusoidal modulation is applied. For dual-frequency modulation of Fig. 7, however,the low energy components, especially those in the rangeof 0.2 - 0.8 keV are more than those in Fig. 6. This means
larger deceleration eﬀect appears on dual-frequency modulation.
The better bunching is expected in the dual-frequency
modulation, and energy spread is narrower as shown inFigs. 3 and 4, thus, dual-frequency modulated ions are wellconcentrated in phase space of the theory of the constantdeceleration. In this situation, better deceleration eﬀect
can be expected. The results shown in Figs. 6 and 7 areconsistent with this consideration.

We carried out deceleration experiments and analysis on time evolution of deceleration eﬀect with dualfrequency modulation compared with single sinusoidalmodulation. Energy distribution of the ions and the deceleration rate were used for these evaluations. As aresult, we found that averaged energy spread of modulated particles with dual-frequency modulation was narrower than that with single sinusoidal modulation, which
was favorable for better deceleration by constant deceleration scheme. As for deceleration eﬀect, the consistentresults with modulation eﬀect was obtained that deceleration of dual-frequency modulated beam was also betterthan that of sinusoidally modulated beam. The eﬀectiveness of dual-frequency modulation to deceleration eﬀect
was confirmed.

Acknowledgments
This work was supported in part by the bilateral coordinated 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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Plasma and Fusion Research: Regular Articles

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