Plasma and Fusion Research: Regular Articles

Volume 11, 2405013 (2016)

Studies on the Axial Position of the Decelerator
in Traveling Wave Direct Energy Converter∗)
Tomohiro KATSURA, Takahiro WAKAIZUMI, Hiromasa TAKENO,Kazuya ICHIMURA1) and Yousuke NAKASHIMA1)
Department of Electrical and Electronic Engineering, Kobe University,
1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan1)
Plasma Research Center, University of Tsukuba, 1-1-1 Tennodai-cho, Tsukuba 305-8572, Japan(Received 30 November 2015 / Accepted 19 January 2016)
In D-3 He fusion, most of fusion energy is carried by created protons as kinetic energy, so direct energy
conversion can be applied. A traveling wave direct energy converter was proposed as an energy recovering system
for these protons, which was composed of a modulator and a decelerator. The axial position of the decelerator is
one of the important device parameters for both energy conversion eﬃciency and device size. The best position
for conversion eﬃciency was considered to be the bunching position at which proton density is the highest, but
it was not examined well. In this study, we investigated the dependence of deceleration eﬃciency on the axial
position of the decelerator by using simulation experiments and numerical calculations. The results show that thebunching position is not necessarily the optimum one for conversion eﬃciency.
c 2016 The Japan Society of Plasma Science and Nuclear Fusion ResearchKeywords: advanced fusion, direct energy conversion, TWDEC
DOI: 10.1585/pfr.11.2405013

1. Introduction
In D-3 He fusion, neutrons are hardly created, andmost of fusion energy is carried by created protons as kinetic energy, so direct energy conversion can be applied.
However, energy of these protons is 14.7 MeV and corresponding voltage necessary for a conventional electrostaticconverter exceeds an engineering limit. For this issue, atraveling wave direct energy converter (TWDEC) was proposed as an energy recovering system for these protons [1].
A TWDEC is composed of a modulator and a decelerator. Incident proton beam is velocity-modulated by radio
frequency (RF) field in the modulator and bunched in thedownstream. The beam is guided to the decelerator which
consists of a lot of electrodes aligned in the direction of
the beam and an external circuit to which the electrodes
are connected. When the bunched beam passes throughthese electrodes, the induced current in the circuit excites a
traveling wave, the field of which decelerates the protons.
The decreased kinetic energy of protons is converted into
electricity in the external circuit.
The axial position of the decelerator is one of the important device parameters for both energy conversion efficiency and device size. When the decelerator is settled
near the modulator, the device can be compact, but theeﬃciency cannot be high. The best position for conversion eﬃciency is considered to be the bunching position at
author’s e-mail: takeno@eedept.kobe-u.ac.jp∗) This article is based on the presentation at the 25th International Toki
Conference (ITC25).

which proton density is the highest. In the previous study,
the authors conducted simulation experiments and numerical calculations by setting a decelerator at the bunchingposition [2]. The highest experimental record of the eﬃciency was obtained, however, the optimum axial position
was not examined.
In this study, we investigate the dependence of deceleration eﬃciency on the axial position of the decelerator.
By using simulation experiments and numerical calculations, we examine the eﬃciency by changing the distance
between the modulator and the decelerator, and discuss theoptimum position of the decelerator based on the results.
In Sec. 2, the experimental device is explained. InSec. 3, not only experimental and numerical results, butalso discussion on the axial position of the decelerator isshown. In Sec. 4, conclusion of the paper is given.

2. Experimental Device
In Fig. 1, a schematic view of the device used in theexperiment is given. It consists of an ion source, a modulator, a decelerator, and a measurement section.
To use helium ions instead of protons, helium plasma
is produced by an application of a static magnetic field andan RF power of 15 MHz in the ion source of a glass tube.
The RF power is supplied with amplitude modulation bycontinuous rectangular pulse of 1 kHz and a duty of 50%.
By applying high voltage (Vex ) to an extraction electrode,helium ions are extracted to the metal chamber. In thisstudy, Vex is usually set to be 3.2 kV. A convergence elec-2405013-1

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

Plasma and Fusion Research: Regular Articles

Volume 11, 2405013 (2016)

Fig. 1 Schematic view of the experimental device.

trode is set in the downstream of the extraction electrodeto suppress diﬀusion of the extracted ion beam by an application of convergence voltage (Vc ).
The modulator consists of four grid electrodes. The
modulation voltage (Vmod ) of 7 MHz is applied to the electrode M2 , and other electrodes (M1 , M3 , M4 ) are grounded.
In this condition, standing wave field (SWF) is created in
the region between M1 and M2 and that between M2 andM3 . The extracted helium ions are velocity modulated bythese electric fields. The intervals between the electrodes
are 14 mm which is equivalent to a quarter of the wavelength of the traveling wave for the beam extracted with
Vex = 3.2 kV.
The decelerator consists of ten grid electrodes. The
first electrode of D1 and the tenth electrode D10 aregrounded, and the deceleration voltage (Vdec ) is applied toother electrodes (D2 –D9 ). In an actual TWDEC, Vdec isinduced by incident bunched beam. In the simulation experiments, however, Vdec is applied externally because thebeam is too weak to induce strong field enough to beam
deceleration. This scheme is called active decelerator [3].
Vdec is supplied by an RF source synchronized with Vmod
via coaxial delay lines which have terminals to connect
the electrodes at every π/2 phase positions. The electrodeDi and Di+4 (i = 2,3,4,5) are connected, respectively, andvoltages of the same amplitude are applied although they
have some errors to the ideal values, and the details arepresented in the previous paper [2]. The decelerator is designed based on the constant deceleration scheme, the details of which are also presented in Ref. 2. In this study, a
new function is introduced that this set of decelerator electrodes is movable in the axial direction. We can change thedistance between the modulator and the decelerator fromthe outside of the metal chamber by using a guiding rod.
We define L as a distance between M3 and D2 .
In the measurement section, a Faraday cup is installedat the end of the device. It consists of an ion repeller grid(IR), a secondary electron repeller grid, and a collector
plate (C). The current of C (IC ) is averaged by a boxcar
integrator synchronized by plasma production RF pulses.

By sweeping the voltage of IR (VIR ), IC –VIR characteristic
is obtained. An energy distribution f (E) can be derived
from the following equation:
dIC 
1,(1)f (E) ∝ √VIR dVIR VIR = Ee
where E is ion energy and e is unit charge.
The average energy of the ions can be obtained by∞E f (E)dE.
(2)
E = 0 ∞f (E)dE
0Deceleration eﬃciency can be defined byηdec =E0  − E,
E0 

(3)

where E0  means the average energy of incident beam.
We examined ηdec for eight kinds of phase diﬀerence
between Vmod and Vdec for one case, and the largest ηdec
was taken for evaluation.

3. Results and Discussion
3.1 Experimental results
The measurement conditions are Vex = 3.2 kV, Vc =520 V, Vmod = 200 V0p (V0p : zero-to-peak voltage), andVdec = 150 V0p , where the value of the deceleration voltage
amplitude is that on D5 and D9 . We examined energy distribution by changing L. In the present experimental conditions, L corresponding to the bunching length is about
24 cm which is confirmed by numerical calculation shownin Sec. 3.3.
Figure 2 shows examples of measured f (E) by solidcurves. Here, (a) and (b) are for L = 16 cm and 36 cm, respectively. In the figure, f (E) of the incident beam, that is,
Vmod = Vdec = 0 V0p is also indicated by dashed curves,
showing that E0  is found around extracting energy ofeVex = 3.2 keV. Note that the ordinate value for the incident beam is scaled by 1/3.
According to Fig. 2, there are both decelerated (lowerthan 3.2 keV) and accelerated (higher than 3.2 keV) ions2405013-2

Plasma and Fusion Research: Regular Articles

Volume 11, 2405013 (2016)

Fig. 2 Measured energy distribution functions.

Fig. 3 Calculated energy distribution functions.

when Vmod and Vdec are applied. The decelerated ions are
more than accelerated ions, thus the average energy decreases due to operation of TWDEC. Comparing (a) and(b) in Fig. 2, f (E ∼ 2 keV) for (b) is larger than that for(a), and f (E ∼ 4 keV) for (b) is smaller than that for (a).
This means that deceleration eﬀect varies according to theaxial position of the decelerator and that for L = 36 cm issuperior to that for L = 16 cm.

ous research [5], this phenomenon depends on time andinsuﬃcient modulation reduces with the lapse of Vmod application time. In the present experiment, we extended thepulse width for Vmod , so the remained component was significantly reduced.

3.2

Results of numerical calculation

We also examined deceleration eﬀects by using numerical calculations which was one-dimensional particle
orbit calculation. In the calculation model, particles are affected only by electric field due to electrode voltages, andspace charge eﬀect is not taken into account. The details
are explained in Ref. 4. The conditions of Vex , Vmod , andVdec are the same as those in the simulation experiment.
Figure 3 shows calculated energy distribution functions for the cases of (a) L = 16 cm and (b) L = 36 cm.
Comparing (a) and (b) in Fig. 3, the energy distribution in
E < 2.5 keV for (b) is more than that for (a), and vice-versa
in 3.5 keV < E < 4 keV. These results are well corresponding to the experimental results in Fig. 2 while ions around3.2 keV are quite few in Fig. 3. This diﬀerence around extracting energy comes from the phenomenon that the insuﬃcient modulation results in the remained component of
the incident beam in the experiment, and it was observedin the previous experiments [2]. According to the previ-

3.3 Evaluation by deceleration eﬃciency
and discussion
Deceleration eﬃciency was evaluated according toEq. (3). Figure 4 shows deceleration eﬃciency versus L forexperimental result. The values are averaged ones for fivetimes measurement and the error bars represent the standard deviation. The maximum ηdec of 26.4% is obtained at
L = 32 cm, which is much higher than about 24% aroundbunching length.
We also examined by numerical calculation. In Fig. 5,
deceleration eﬃciency and axial ion distributions as functions of L are shown, where L means both distance between
the modulator and the decelerator, and axial position fromthe modulator electrode M3 . As for the axial ion distributions, those just by modulation field application for eightdiﬀerent RF phases are shown, and they mean snap shotswith an interval of 1/8 of RF period. The highest ion density is obtained for π/2 phasing at L = 23.8 cm. As thecalculation employs randomness in the energy distributionof incident ions, the bunching position has ambiguity andis estimated to be 23.8 - 24.5 cm. As for deceleration eﬃciency, ηdec was calculated by using Eq. (3) where numer-2405013-3

Plasma and Fusion Research: Regular Articles

Volume 11, 2405013 (2016)

Fig. 4 Deceleration eﬃciency versus distance between the modulator and the decelerator for experiment.

Fig. 6 Bunching and maximum eﬃciency positions for someconditions of Vmod and Vdec .

celerate ions in a trapping region of the phase space [6].
According to Fig. 5, dully bunched peaks are in the downstream. Ions in those peaks can be decelerated if the trapping region is wide. Total number of those ions is morethan those in the peak at the bunching position. Thus,
the maximum eﬃciency position of the decelerator may
be far from the bunching position. The quantitative analysis should be a future work because it is diﬃcult to obtain
final energy of ions as the bouncing motion is interrupted
at the end of the decelerator with a short length.

4. Conclusion
Fig. 5 Deceleration eﬃciency and ion distribution as functionsof L for numerical calculation.

ically calculated average energy of ions is used. The tendency of variation is quite similar to that for experiment inFig. 4. The maximum value is at L = 32 cm which is thesame as that for the experiment. However, ηdec is higher
than that for the experiment by approximately 8%. This isdue to above-mentioned remained component of incident
beam observed in the experiment. These results show thatthe bunching position is not necessarily the optimum one
for eﬃciency and the optimum L is 32 cm in the conditionof Vmod = 200 V0p and Vdec = 150 V0p .
The optimum positions for other conditions were also
examined by numerical calculation. The results for thesimilar structure as the experiment are summarized inFig. 6. The bunching length is determined by Vmod (abscissa) and its ambiguity is expressed by an error bar. The
position of the decelerator giving the maximum eﬃciency
depends on Vmod and Vdec , and it is diﬀerent from thebunching position for both cases of Vdec = 150 V0p and230 V0p . Thus, the bunching position is not necessarily theoptimum one for eﬃciency. This is completely diﬀerent
from conventional expectation.
This may be because that the decelerator is designed
based on the constant deceleration scheme, which can de-In this study, we investigated the dependence of deceleration eﬃciency on the axial position of the decelerator byusing simulation experiments and numerical calculations.
In the experiment, the maximum deceleration eﬃciency is
obtained at a diﬀerent position from the bunching position.
This is confirmed by numerical calculation including different working parameters cases. Thus, the bunching position is not necessarily the optimum one for eﬃciency andthis is diﬀerent from conventional expectation. The detailed analysis on the constant deceleration scheme is necessary in future.

Acknowledgment
The authors acknowledge valuable discussions withDrs. J. Miyazawa and T. Goto. This work was supported inpart by the bilateral coordinated research between Plasma
Research Center, Univ. Tsukuba, National Institute for Fusion Science, and Kobe Univ. (NIFS13KUGM082).
[1] H. Momota, LA-11808-C, Los Alamos Natl. Lab. 8 (1990).
[2] Y. Togo et al., Plasma Fusion Res. 10, 3405013 (2015).
[3] H. Takeno et al., Fusion Eng. Des. 83, 1696 (2008).
[4] H. Takeno et al., Jpn. J. Appl. Phys. 39, 5287 (2000).
[5] H. Takeno et al., The 10th Joint Conference on Fusion Energy, 20-130 (2014) (in Japanese).
[6] H. Katayama and K. Sato, J. Plasma Fusion Res. 77, 698(2001) (in Japanese).

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