J. Plasma Fusion Res. SERIES, Vol. 9 (2010)

Characteristics of hydrogen supersonic cluster beam generated by a Laval nozzle
Akiyoshi MURAKAMI, Junichi MIYAZAWA1), Hayato TSUCHIYA1), Takanori MURASE1),
Naoko ASHIKAWA1), Tomohiro MORISAKI1), Ryuichi SAKAMOTO1) and Hiroshi YAMADA1)The Graduate University for Advanced Studies, 322-6 Oroshi-cho,Toki, 509-5292, Japan1)

National Institute for Fusion Science, 322-6 Oroshi-cho,Toki, 509-5292, Japan(Received: 20 November 2009 / Accepted: 23 February 2010)

Formation of a hydrogen cluster jet using a Laval nozzle has been investigated in the temperature range from120 K to 300 K. Time-resolved 2-D images of Rayleigh scattering due to clusters have been measured by a fast
charge coupled device camera. The scattering signal from hydrogen clusters is detected when the temperature is
below 178 K, as expected from a calculation result of the condition to produce clusters. The scattering signal
intensity is inversely proportional to the fifth power of the gas temperature and cubic dependence on the backing
pressure as expected from an available cluster model.
Keywords: hydrogen cluster, Laval nozzle, fueling method, solenoid valve, Rayleigh scattering, Hagena parameter
temperature range from 120 K to 300 K. Time-resolved
2-D images of Rayleigh scattering due to clusters havebeen measured by a fast charge coupled device (CCD)
camera. Characteristics of cluster jet ejected from the Laval
nozzle are discussed with regard to dependence on pressure
and temperature.

1. Introduction

Physics of cluster formation by gas jet has been studied
since 1956 [1]. A cluster beam for fusion research wasstudied firstly as the source of plasma heating in the 1970s[2]. Cluster jet injection (CJI) comes to the front again inrecent study of fueling [3]. Fueling methods of gas puffing
and pellet injection have been studied for a long time. Gas
puffing has been used since early fusion plasma
experiments. Especially in large plasmas, most of theparticles supplied by gas puffing are ionized outside of theplasma confinement region. As a result, the fuelingefficiency is as low as ~10 % [4]. On the other hand, pellet
injection is able to supply fuel particles to the plasma coreregion [5]. However, a pellet injection device itself iscomplicated compared with a gas puff device and still has
demanding technological issues for a fusion reactor. A newfueling method of supersonic cluster beam (SSCB)
injection is being developed in the National Institute forFusion Science. SSCB is an improved version of CJI
developed for HL-2A, where liquid nitrogen of 77 K is
used for gas cooling [3] and, the supersonic gas injector(SGI) developed for NSTX, where a Laval nozzle is usedto generate supersonic gas jet [6]. Recently, the results ofsupersonic molecular beam injection (SMBI) on HL-2A
are reported, where a conic nozzle is installed on the valveof CJI [7]. In SSCB, high-pressure hydrogen gas can becooled to less than 100 K by a GM refrigerator and will beejected through a fast solenoid valve with a Laval nozzle.
Deeper penetration of the fuel particles injected by SSCB
than ordinary gas puffing is expected to be beneficial forhigh fueling efficiency in large plasmas.
In this study, formation of the H2 cluster jet using aLaval nozzle for SSCB has been investigated in the2. Cluster Theory2.1 Hagena Parameter

The condition to produce clusters can be describedby an empirical scaling parameter �* that is proportional
to a so-called “Hagena parameter”, k [8, 9]

Γ* = k(d tan α )0.85 P ,T02.290(1)where d is the nozzle diameter in �m, � is the expansion
half angle (� = 45° for the sonic case, � < 45° for thesupersonic case), P0 is the backing plenum pressure in
10-4 MPa, and T0 is the pre-expansion temperature in
Kelvin. Massive condensation, where the cluster size
exceeds 100 atoms/cluster, is generally observed for �* >1000[8, 9]. Figure 1 shows the parameter �* as a functionof the gas temperature, where d = 300 �m, � = 12°, P0 = 4
MPa are assumed, respectively. The nozzle diameter of d= 300 �m and � = 12° are equal to those of the Laval
nozzle used in this experimental study. The curve line inthe Laval nozzle hole has one inflection point. The angleof � = 12° corresponds to the slope angle of the tangent at
the inflection point. It means that the angle of � = 12° is
the maximum expansion half angle on the Laval curveline. In this calculation, species-dependent k of 184, 3.85,2360, 528, 185, and 1650 are used for H2, He, CH4, N2,Ne, and Ar, respectively. Previous study showed thatclear scattering signals are observed at high valve

author’s e-mail:murakami.akiyoshi@LHD.nifs.ac.jp79©2010 by The Japan Society of Plasma
Science and Nuclear Fusion Research��

A. Murakami et al., Characteristics of Hydrogen Supersonic Cluster Beam Generated by a Laval Nozzle

106105104H

21000

CHNeAr4N

2100

He101Fig. 1

050 100 150 200 250 300 350
T (K)Fig. 2

Calculated results of the scaling parameter �*,

Schematic of the experimental setup. A solenoidvalve installed in the vacuum chamber is cooled bywhere d = 300 �m, � = 12°, P0 = 4 MPa. The
parameter of hydrogen at the temperature region of

the GM refrigerator through copper plates.

~180K corresponds to that of nitrogen at the room
temperature.

backing pressure of more than 3-4 MPa at the room
temperature in the case of CH4, N2, and Ar. Meanwhile,in the case of H2, He, and Ne, no scattering signal has
been detected up to 8.0 MPa at the room temperature [10].
This calculation result shows the parameter �* of H2 atthe temperature region of ~180 K corresponds to that ofN2 at the room temperature. In other words, it implies thatH2 will form clusters when the gas temperature is ~180 K
from the room temperature.

2.2 Rayleigh Scattering

Fig.3

The total Rayleigh scattering signal SRS is
proportional to the product of the scattering cross section
� and the number density of clusters nc. The cross section
� is proportional to the square of the averaged cluster size
Nc defined by the averaged number of atoms per a cluster.
nc is approximately given by the monomer density before
becoming cluster, n0, divided by Nc, i.e., nc � n0/Nc. The
scattering signal SRS is proportional to P0Nc since themonomer density is proportional to the backing plenum
pressure P0. Farges et al. showed that Nc ∝ P01.8-2.1,
assuming a multilayer icosahedral model [11, 12]. Thismeans that the scattered light signal SRS should vary asbelow,(2)S RS ∝ P02.8 −3.1 .

Laval nozzle with 300 �m throat diameter. Thenozzle was connected by the end of solenoid valve.

3. Experimental Setup

Fig. 4The experimental setup is shown in Fig. 2. A solenoid
valve of Parker-Hannifin Pulse Valve Series 99B07 is used.
The available backing pressure is up to 8 MPa. This valve
is equipped with the Laval nozzle of 300 �m throatdiameter. The valve is installed in the vacuum chamber andcooled by a GM refrigerator via connection with copper

Typical CCD image in the case of H2 at 125 K andthe cross section of the Laval nozzle. The backing
pressure is 8.0 MPa, and the exposure time is 10ms. The laser beam direction (y) is perpendicular tothe gas flow (x). The broken lines denote extensionof the exit hole with a diameter of Laval nozzle(5.8 mm)80

A. Murakami et al., Characteristics of Hydrogen Supersonic Cluster Beam Generated by a Laval Nozzle

plate and shafts. The temperature of copper valve jacket ismeasured by a thermocouple. The picture of the Laval
nozzle is shown in Fig. 3. A semiconductor laser ofNEOARK LDP2-6535A with 650 nm standard wavelengthand 35 mW power is guided in the chamber toperpendicularly intersect the gas flow. A beam dump is set
at the opposite side of the laser inlet and the Laval nozzle
is rolled by black tape in such a way that the stray light islowered. The distance between the nozzle exit and the laser
chord is 17 mm. A fast CCD camera of 1280 × 1024 pixels
is arranged in the direction perpendicular to both the gas
flow (x-direction) and the laser beam (y-direction). A
typical CCD image of 8.0 MPa H2 cluster jet at 125 K andthe cross section of the Laval nozzle are shown in Fig. 4. A
straight emission line that is scattered by clusters isobserved along the laser beam.

Fig.5

The image of scattering signal emission line in thecase of H2 at 178K. The backing pressure is 5.0
MPa, and the exposure time is 10 ms.

0.012

5.8 mm

4. Results and Discussion

119 K
120 K

4.1 Temperature dependence of scattering signal

0.008

The scattering signals are detected when thetemperature is below ~180 K as expected from thecalculation. The image of scattering signal emission lineof H2 at 178 K is shown in Fig. 5. The empirical scaling
parameter �*of H2 at ~180 K nearly corresponds to thatof N2 at the room temperature. Figure 6 shows scattering
signal profiles along the laser light direction (y), where
the temperature is varied from 119 K to 143 K. The
exposure time of the CCD camera is fixed to 10 ms andthe backing pressure is fixed to 5 MPa for this scan. The
width of 5.8 mm in Fig. 6 denotes the exit hole diameterof the Laval nozzle. These profiles are axisymmetric. The
full-width of half-maximum (FWHM) is 6.2 ± 0.2 mm.
The FWHM does not depend on temperature. Two peaks
observed in the profiles indicate that the center of cluster
flow has hole. Similar hollow profile was observed in thestudy on plasma produced by laser pulses irradiating acluster target generated by a Laval nozzle [13]. The points
on three y-coordinate (y = 2.9 for �, 0.7 for �, 0 mm for �)of the scattering profile are plotted in Fig. 7. The signal
points of y = 2.9 mm is the radial of nozzle exit holediameter (5.8 mm). The signal points of y = 0.7 mm
indicate the peak signals in the profiles. The signal pointsof y = 0 mm show the center of hollow profiles. Thepoints on three y-coordinate of scattering signal increase
with ~T0-5. This result is similar to the results in Ref. [8].

123 K
126 K
128 K
130 K
133 K
138 K
143 K

0.004

0-0.6 -0.4 -0.2
Fig. 600.2
y (cm)

0.4

0.6

Scatter signal profiles normalized by the exposure
time (�s), where the temperature is varied from
119K to 143K.

4.2 Pressure dependence of scattering signal

Figure 8 shows scattering signal profiles along thelaser light direction (y), where the backing pressure isincreased from 3.0 to 8.0 MPa at ~125 K. The FWHM ofthese profiles is 5.83 ± 0.3 mm and roughly corresponds
to the exit hole diameter of the Laval nozzle. The points
on three y-coordinate (y = 2.9 for �, 0.7 for �, 0 mm for�) scattering profiles in Fig. 8 as a function of thebacking pressure are plotted in Fig. 9. The peak scattering

Fig.7 The points on three y-coordinate (y = 2.9 for �, 0.7for �, 0 mm for �) of the scattering profiles in fig.5
are plotted.

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A. Murakami et al., Characteristics of Hydrogen Supersonic Cluster Beam Generated by a Laval Nozzle

5.8 mm

0.04

8 MPa

0.03

7 MPa
6 MPa
5 MPa

0.02

4 MPa
3 MPa

0.01
0-0.6 -0.4 -0.2
Fig.8

00.2
y (cm)

0.4

0.6Scatter signal profiles normalized by the exposure
time (�s), where the backing pressure is varied
from 3.0 MPa to 8.0MPa

signal (y = 0.7 mm) increases with ~P03. The result isFig.10

The images of cluster scattering signals in thecase of H2 at ~130 K without the Laval nozzle (a)and with Laval nozzle (b). The backing pressure is
5.0 MPa, and the exposure time is 10 ms. A shadow
graph image of the particle flow in the case of CH4at 180 K with the Laval nozzle (c). The backing
pressure is 7.0 MPa, and the exposure time is 1 ms.

particle flow is visible by eye and it is possible to take theimage of shadow graph by the CCD camera. Figure 10 (c)shows a shadow graph image of the particle flow in thecase of CH4 at 180 K with the Laval nozzle. The backing
pressure is 7.0 MPa, and the exposure time is 1 ms. Fig. 10(b) and (c) imply that the width of clusters during 17 mm issimilar to the exit hole diameter and the width of the liquid
particle flow is slightly broader than that of clusters.
Previous study shows the expansion half angle of thesolenoid valve without a Laval nozzle is 22.5°[10]. The
divergence of cluster jet has been decreased after
installation of the Laval nozzle.

Fig.9 The points on three y-coordinate (y = 2.9 for �, 0.7for �, 0 mm for �) of the scattering profiles in fig.7
are plotted.

similar to the expectation of Eq. (2) and the results in Ref.
[8, 10]. Farges et al. estimated this relation assuming a
multilayer model for Ar cluster. This suggests that thestructure of hydrogen cluster also has the multilayer
model for Ar cluster. The other signal points of y = 2.9 and0 mm are smaller than the cubic dependence on thebacking pressure.
Figure 10 shows the images of cluster scattering
signals in the case of H2 at ~130 K without the Laval
nozzle (a) and with the Laval nozzle (b). In the case of N2,Ar and CH4, a rapid increase of the signal intensity has
been observed and similar results are also shown in Ref.
[8]. The scattering signals of this region are much stronger
than that of clusters. This might presumably be due to thephase transition to the liquid state. In this regime, the5. Summary

Clustering condition for hydrogen has been
investigated in the temperature range from 120 K to 300 K.
The Rayleigh scattering signal is detected by the CCDcamera when the hydrogen gas temperature is below 178 K
as expected from available model. The scattering signals

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A. Murakami et al., Characteristics of Hydrogen Supersonic Cluster Beam Generated by a Laval Nozzle

increases with ~T0-5 and ~P03 as expected from a clustermodel. The divergence of cluster jet has been decreased
after installation of the Laval nozzle. Based on theknowledge obtained here, a supersonic cluster beam(SSCB) injection is planned as a new fueling scheme inLHD.

Acknowledgments
This work has been financially supported by NIFS09ULPP517.

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