- Email: [email protected]
Power matching between plasma generation and electrostatic acceleration in helicon electrostatic thruster
Accepted Manuscript Power matching between plasma generation and electrostatic acceleration in helicon electrostatic thruster D. Ichihara, Y. Nakagawa, A. Uchigashima, A. Iwakawa, A. Sasoh, T. Yamazaki PII:
S0094-5765(17)30634-3
DOI:
10.1016/j.actaastro.2017.06.032
Reference:
AA 6367
To appear in:
Acta Astronautica
Received Date: 5 May 2017 Revised Date:
27 June 2017
Accepted Date: 28 June 2017
Please cite this article as: D. Ichihara, Y. Nakagawa, A. Uchigashima, A. Iwakawa, A. Sasoh, T. Yamazaki, Power matching between plasma generation and electrostatic acceleration in helicon electrostatic thruster, Acta Astronautica (2017), doi: 10.1016/j.actaastro.2017.06.032. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
Power Matching between Plasma Generation and Electrostatic Acceleration in Helicon Electrostatic Thruster D. Ichihara,1,a) Y. Nakagawa,1) A. Uchigashima,1) A Iwakawa,1) A Sasoh,1) and T. Yamazaki2) 1
Department of Aerospace Engineering, Nagoya University, Nagoya, Aichi 464-8603, Japan
RI PT
2
Mitsubishi Heavy Industry ltd., 16-5 Konan 2-chome, Minato-ku, Tokyo 108-8215, Japan
The effects of a radio-frequency (RF) power on the ion generation and electrostatic acceleration in a helicon electrostatic thruster were investigated with a constant discharge voltage of 300 V using argon as the working gas at a flow rate either of 0.5 Aeq (Ampere equivalent) or 1.0 Aeq. A RF power that was even smaller than a direct-current (DC) discharge power
SC
enhanced the ionization of the working gas, thereby both the ion beam current and energy were increased. However, an excessively high RF power input resulted in their saturation, leading to an unfavorable increase in an ionization cost with doubly charged ion production being accompanied. From the tradeoff between the ion production by the RF power and the
optimal RF to DC discharge power ratio of 0.6 -1.0.
1
I.
Introduction
M AN U
electrostatic acceleration made by the direct current discharge power, the thrust efficiency has a maximum value at an
Electric propulsion has an advantage over chemical propulsion owing to its high specific impulse capability, and the
3
usefulness of electric propulsion has been demonstrated in orbit transfer1-3. Based on the space propulsion principle, thrust
4
and specific impulse have opposite dependences on the propellant mass flow rate with a constant power; in particular, a large
5
thrust is obtained with a high mass flow rate but low specific impulse, however, a high specific impulse is obtained with a
6
low mass flow rate but small thrust. This competing performance of specific impulse and thrust should offset each other in
7
the tradeoff between payload mass and working period4,5. Ion thrusters, in which accelerates only ions by an electrostatic
8
potential difference larger than 1.0 kV, have an important advantage of high thrust efficiency in a high specific impulse range
9
on the order of 3000 s or higher6. However, its thrust density is limited by the space charge limitation7,8. In other electric
10
thrusters, such as Hall thrusters9,10, highly efficient multistage plasma thrusters11, and magnetoplasmadynamic thrusters12,13,
11
where accelerate quasi-neutral plasma, the ionization and acceleration of the propellant are performed in a common channel;
12
therefore, the propellant ionization and thrust generation processes cannot be separated. Zharinov et al14. proposed a
13
double-stage Hall thruster, which has an intermediate electrode between the upstream anode and downstream cathode for
14
separating the propellant ionization and acceleration. A number of investigations into the operation characteristics15,16 and
15
optimal intermediate electrode locations17,18 were conducted. Silnikov et al19. proposed the utilization of nanosecond surface
16
discharge to produce positively-charged ions with a density of the order of 1019 to 1020 m-3 in the first stage of a double-stage
AC C
EP
TE D
2
a)
Author to whom correspondence should be addressed. Electronic mail: [email protected].
1
ACCEPTED MANUSCRIPT 17
electric propulsion thruster. Although this method can be useful for the impulse generation after the nanosecond discharge, it
18
is not suitable for a thruster of direct-current (DC) discharge operation. Adam et al 20 . investigated the operation
19
characteristics of a Hall thruster combined with an annular helicon plasma source and obtained a slight thrust increase.
20
However, the thrust–power ratio and thrust efficiency deteriorated. Harada et al21. examined the combination of a cylindrical helicon plasma source and electrostatic acceleration in a
22
helicon electrostatic thruster (HEST); a ring anode and hollow cathode in a cusped magnetic field were set in the downstream
23
region from the helicon plasma source. HEST realized DC electrostatic acceleration with maintaining a constant-rate
24
production in the helicon plasma source with a density of the order of 1019 m-3. Unlike to the ion thrusters nor the thruster
25
proposed in Ref. 19, the thrust density is not limited by the space charge limitation7, 8. By inputting 1500 W of RF power to
26
the helicon plasma source and applying 300 V of acceleration voltage, the average ion beam energy was comparable to the
27
applied voltage equivalent. Uchigashima et al22. reported anode geometry effects on the ion acceleration characteristics of
28
HEST. Nevertheless, a few open questions remain, i.e., the extent of the helicon plasma source contribution for enhancing the
29
thrust efficiency, and whether there exists an optimal RF power to acceleration power ratio. This study is aimed at
30
quantitatively investigating the power matching between RF plasma generation and electrostatic acceleration in HEST.
M AN U
SC
RI PT
21
AC C
EP
TE D
31
32 33 34 35
II.
FIG. 1 Schematic of HEST.
Experimental Apparatus and Procedure
36
Figure 1 shows a schematic of the HEST21. HEST has a radio-frequency (RF) plasma source in the upstream region and
37
electrostatic acceleration electrodes in the downstream region. The RF plasma source was comprised of a ceramic
38
(Photoveel) tube with an inner diameter of 27 mm and length of 150 mm. A Nagoya type III (m = +1) helical antenna was 2
ACCEPTED MANUSCRIPT fixed onto the axis of a water-cooled solenoid coil. The exit of the RF plasma source was located at the center of the solenoid
40
coil. The magnetic field strength was 100 mT at the coil center. A copper ring anode with an inner diameter of 27 mm and
41
thickness of 10 mm was placed 25 mm axially downstream from the coil center. In the downstream region, the magnetic field
42
was greatly modified using 16 cylindrical Nd–Fe–B permanent magnets and soft iron yokes to generate a diverging magnetic
43
field followed by a field-free region where the magnetic field strength was less than 3 mT. A commercial hollow cathode
44
(DLHC-1000, Kaufman & Robinson Inc.) was used and its orifice was placed 70 mm off-axis at 175 mm axially downstream
45
from the coil center. The RF power was supplied by an RF power source (RFK50ZH, Kyosan Electric Mfg. Co., Ltd.)
46
through an auto-matching circuit box (MBK50, Kyosan Electric Mfg. Co., Ltd.). The RF power frequency was set to 13.56
47
MHz.
SC
48
RI PT
39
To evaluate the ion beam energy Ei from an ion energy distribution function (IEDF), a retarding potential analyzer 23
49
(RPA)
50
probe24. The RPA or nude Faraday probe was fixed onto the swing system, which consists of a stepping motor and
51
250-mm-long stainless steel arm. Here, the cylindrical coordinates (r, z) for an axisymmetric configuration are defined with
52
their origin set at the axial position of the left surface of the ring anode. The swing center was at (r, z) = (0 mm, 115 mm). In
53
the horizontal plane on the center axis of the HEST, the ion current density ji as a function of azimuthal angle, θ, with respect
54
to the center axis was measured. In this paper, the definitions of Ei, Ji, and <θ> are identical to those mentioned in Ref. 22.
55
Figure 2 shows an example of Ei(θ) and ji(θ), which are normalized by Ei(0) and ji(0), respectively. Because Ei(θ) varied by
56
less than ±5% against Ei(0) in |θ| ≤ <θ>, Ei(0) is used as the representative value.
TE D
M AN U
was used. The ion beam current Ji and ion beam divergence half-angle <θ> were measured using a nude Faraday
1.2
58
AC C
Normalized ji(θ )
EP
1.0
400
ji(θ )
300
0.8
Ei(θ )
0.6
200
0.4
0.0 -150 -100
100
<θ > <θ >
0.2 -50
0
Ei(θ ) , eV
57
50
100
0 150
θ , deg.
59 60 61
FIG. 2 Dependence of the normalized ion current density ji (curve) and Ei (circle) on rotation angle θ. Ĵ1 = 1.0 Aeq, Ĵ2 = 0.36 Aeq, Vd = 300 V, Ps = 300 W.
62
In order to measure the beam currents of singly and doubly charged ions, an E × B probe25 was used. Figure 3 shows a
63
schematic of the E × B probe, which consists of a metal mesh (0.28 mm × 0.28 mm square, solidity of 56 %), entrance orifice, 3
ACCEPTED MANUSCRIPT E × B deflection section, exit orifice, and ion collector. The entrance orifice, which has an inner diameter of 4.2 mm and
65
thickness of 6 mm, was connected to the E × B deflection section entrance. Inside the E × B deflection section, a uniform
66
magnetic field was applied. The magnetic field strength was set to 110 mT using Nd–Fe–B permanent magnetic plates and
67
soft iron yokes. An electric field, perpendicular to both the magnetic field and exhaust direction, was applied between the pair
68
of stainless steel electrode plates. The electrode plate has a length of 100 mm and width of 10 mm. The inter-electrode
69
distance was set to 10 mm. The exit orifice, which has an inner diameter of 2.0 mm and length of 7 mm, was placed at the E
70
× B deflection section exit. The ion collector has an effective collection diameter of 5 mm and was located 8 mm axially
71
downstream from the exit orifice. The electrode plates were connected to a function generator (SG-4322, IWATSU Electric
72
Co., Ltd.) through a power amplifier (NF Corporation) to supply a voltage difference VE×B, which varied from 0 to 100 V at
73
0.02 Hz. The ion collector was grounded through a serially connected resistor (15 kΩ ± 1.0%) to measure the collected ion
74
current JE×B. In order to increase the signal-to-noise ratio, a low-pass filter with a cutoff frequency of 33 Hz was used. Figure
75
4 shows an example of the measured JE×B, which is normalized by the maximum value. The E × B probe was fixed at the
76
same position as the RPA, i.e., (r, z) = (0 mm, 350 mm). The normalized JE×B was smoothly fit to superimposed Lorentzian
77
functions using the least squares method. The ion current fraction of each charge state was estimated from each Lorentzian
78
function peak height26. The secondary electron emission coefficients, i.e., 0.1 and 0.4 for singly and doubly charged ions,
79
respectively27, were used to correct the current fraction estimation. In the case shown in Fig. 4, the current fraction of singly
80
charged ions (red dashed line) and doubly charged ions (blue dashed line) was 76 and 24%, respectively. The effective
81
acceleration voltage of each charge-state ion was estimated from the VE×B value at the peak28 of the corresponding
82
Lorentzian function.
SC
M AN U
TE D
EP AC C
83
RI PT
64
84 85 86
FIG. 3 Schematic of E × B probe. 4
ACCEPTED MANUSCRIPT
Normalized JE×B
1.2 Normalized JE×B Fit Fitting curves
1.0 0.8 0.6 0.4
0.0 0
20
40
60
80
VE×B , V
87
RI PT
0.2 100
FIG. 4 Dependence of the normalized-corrected ion current JE×B on the swing voltage VE×B of the E × B probe measurement. Ĵ1 = 1.0 Aeq, Ĵ2 = 0.36 Aeq, Vd = 300 V, Ps = 600 W.
92
tip was made of tungsten wire with a diameter of 0.3 mm and effective length of 3.0 mm. The measured probe current (I) –
93
voltage (V) curve was fitted by a theoretical formula29.
SC
88 89 90 91
M AN U
The electron number density, ne, and electron temperature, Te, were measured using a double probe. The double probe
V + c1V + c 2 . I = I sat ⋅ tanh 2 kTe e
(1)
Here, Isat is ion saturation current, k is Boltzmann constant, and e is elementally charge. The coefficient c1 corresponds to
95
sheath expansion in the ion saturation region and c2 reflects any offset currents owing to stray capacitance30. Te and Isat were
96
determined as a fitting parameters. Electron number density was calculated from Eq.(2).
TE D
94
ne =
I sat κAeff
mi . kTe
(2)
Here, κ (= 0.61), and Aeff are density decrement inside pre-sheath, and effective current correction area, respectively. In order
98
to take the sheath thickness into account, an iterative process31 was used to estimate Aeff. To measure the space potential Vs
99
with respect to the cathode potential, a floating emissive probe32 was used. The emissive probe tip was made of a
100
1%-thoriated tungsten wire with a diameter of 0.185 mm. The emissive probe tip was semicircular shape with a diameter of
101
2.0 mm. To emit a sufficient amount of thermionic electrons, the emissive probe tip was Joule heated by supplying a heater
102
current of 5.5 A. Because of the space charge limitation7, 8, the floating voltage Vf of the emissive probe was corrected by a
103
factor of ψckTe/e33 to calculate Vs.
AC C
EP
97
Vs = V f + Ψc kTe e
5
(3)
ACCEPTED MANUSCRIPT 104
The correction factor ψc varied from 0 to 1.5 for argon gas. The double probe or emissive probe was mounted on a stepping
105
motor, and the probe sweep time at each point was shorter than 0.3 s. The probe axis was oriented to the center axis of the
106
thruster.
107
III. Results and Discussion
108
A.
RI PT
Operating conditions
All experiments were conducted in a 3.2-m-long, 1.2-m-diameter, stainless steel vacuum chamber. The chamber was
110
evacuated by a cryogenic pump with an exhaust speed of 8400 l/s, which was backed by a dry pump with an exhaust speed of
111
120 l/s. The ambient pressure in the vacuum chamber, measured by an ionization gauge, was maintained lower than 10 mPa
112
with a total working gas flow rate of 1.36 Aeq. The working gas flow rate supplied to the plasma source Ĵ1 was set to 0.5 or
113
1.0 Aeq, and the RF power to the plasma source Ps was increased every 20 W from 0 to 300 W and every 100 W from 300 to
114
1500 W. The discharge voltage Vd was set to 300 V in the Ei(0), Ji, and discharge current Jd measurements, and 200 V in the
115
probe measurements. The hollow cathode was operated with a working gas flow rate, Ĵ2, of 0.36 Aeq, and the keeper current
116
Jk was set to 2.0 A. Each operation condition for measuring Ei(0), Ji, <θ>, Jd, and keeper voltage Vk was repeated at least
117
twice. In the following figures, the circles represent the average value. The error bars in Ei(0) correspond to the standard
118
deviation defined in Ref. 22, whereas those in Ji, Jd, and <θ> correspond to the standard deviation (±σ) obtained from the
119
number of trials. The uncertainty of Te was estimated based on the standard deviation of the theoretical-curve (Eq. (1)) fitting
120
and that of ne and Vs were estimated by applying the low of propagation of error in Eqs. (2) and (3), respectively. The
121
working gas supplied through both the plasma source and hollow cathode was argon (purity 99.9999%). The operation time
122
was at least 3.5 s at each operating condition.
123
B.
TE D
M AN U
SC
109
EP
Ion current and energy characteristics in Ĵ1 = 0.5 Aeq operation Figure 5(a) shows the variation of Ji with Ps for the Ĵ1 = 0.5 Aeq and Vd = 300 V operation. Ji increased with Ps. In
125
particular, Ji increased from 0.07 to 0.36 A as Ps increased from 0 to 40 W. When Ps > 40 W, Ji increased more gradually. At
126
Ps = 1500 W, Ji was equal to 0.80 A, which is 93% of the total supplied flow rate Ĵ1 + Ĵ2. Figure 5(b) shows the variation of
127
Ei(0) with Ps with Ĵ1 = 0.5 Aeq and Vd = 300 V operation. Ei(0) decreased from 133 to 107 eV as Ps increased from 0 to 40
128
W. Conversely, while Ps increased from 40 to 80 W, Ei(0) increased rapidly from 107 to 188 eV. At Ps = 1500 W, Ei(0)
129
reached 265 eV, which is 88% of Vd. In Ref. 20, by combing the annular helicon plasma source with a Hall thruster, the ion
130
beam current increased up to 50% of Ĵ1 + Ĵ2 with the increase in helicon plasma source input power. However, the ion beam
131
energy decreased to 80% of Vd. In this experiment, Ji and Ei(0) increased by a factor of 11 and 2, respectively, as Ps increased
AC C
124
6
ACCEPTED MANUSCRIPT 132
from 0 to 1500 W. Therefore, in the Ĵ1 = 0.5 Aeq operation case, the RF plasma source contributed to both the ion generation
133
and electrostatic acceleration.
134 350 300 Ei (0) , eV
Ji , A
1.5 Ji = J$ 1 + J$2
1.0
250 200 150 100
0.5
50
(a) 0.0
(b)
0 500
1000
1500
0
500
1000
1500
SC
0
Ps , W Ps , W FIG. 5. Ps dependence with Ĵ1 = 0.5 Aeq, Ĵ2 = 0.36 Aeq, and Vd = 300 V. (a) Ji vs. Ps, (b) Ei(0) vs. Ps. Uncertainty in Ji was better than ± 2% of the averaged value.
M AN U
135 136 137
Ei (0) = Vd
RI PT
2.0
Figure 6 shows the distribution of ne, Te, and Vs on the center axis for the Ps = 0 and 300 W, and Vd = 200 V operation.
139
Owing to a low signal-to-noise ratio, the ne and Te values at z > 150 mm were not obtained except for the center axis. In the
140
Ps = 0 W operation, ne was equal to 2.0 × 1017 m−3 at z = 0 mm and decreased toward the downstream region. However, it had
141
a local minima of 6.3 × 1016 m−3 at z = 85 mm and a local maxima of 1.5 × 1017 m−3 at z = 125 mm. Meanwhile, in the Ps =
142
300 W operation, at z = 0 mm, ne = 3.0 × 1018 m−3. This is more than 10 times higher than that of the operation at Ps = 0 W. ne
143
then decreased monotonically toward the downstream direction. Shoji et al34. measured the variations in electron number
144
density with the change in RF power. By using a Nagoya type III antenna (m = + 1), a steep density increase was observed at
145
approximately 400 W of RF power in the argon gas operation. They also reported that the required RF power to produce a
146
steep density increase was smaller when the RF power frequency was close to the lower hybrid frequency ωLH, which can be
147
calculated as in Eq. (4).
AC C
EP
TE D
138
ωLH ≡ ωci ⋅ ωce
(4)
148
Here, ωci and ωce are the ion cyclotron frequency and electron frequency, respectively. For a singly charged argon ion,
149
ωLH = 10.3 MHz at B = 100 mT. This is close to the RF power frequency (13.56 MHz). Therefore, the HEST also exhibited a
150
density jump in the same RF power range to that reported in Ref. 34; as a result, Ji increased from 0.07 A at Ps = 0 W to 0.61
151
A at Ps = 300 W (see Fig. 5(a)).
152
In the Ps = 0 W operation, Te had a peak value of 20 eV at z = 85 mm. Conversely, in the Ps = 300 W operation, Te had a
153
local peak of 16 eV at z = 85 mm and a maximum of 27 eV at z = 125 mm. The electron temperature distribution relates to
154
the space potential distribution. In the Ps = 0 W operation, Vs at z = 0 mm was 99 V and started to decrease from z = 85 mm, 7
ACCEPTED MANUSCRIPT which is the same location to where Te had the peak value. At z = 350 mm, Vs was 26 V. Through this potential drop, the
156
thermionic electrons diffused from the hollow cathode gained kinetic energy and then lost it by ionization collision with the
157
injected working gas. These energy gain and loss mechanisms affect the electron peak temperature and distribution31. In the
158
Ps = 300 W operation, Vs at z = 0 mm was 198 V, which is almost identical to the discharge voltage (200 V). At z = 85 mm,
159
Vs started to monotonically decrease toward the downstream direction and reached 38 V at z = 350 mm. The measured Vs
160
values at z = 0 and 350 mm were consistent with the IEDF, i.e., in the Ps = 300 W operation, the ion beam potential and space
161
potential were 184 and 41 V, respectively. The above results indicate that the ions were electrostatically accelerated from
162
near the anode potential and obtained an average energy of Ei(0), as shown in Fig. 5(b).
RI PT
155
SC
163 1019 Ps=300W
M AN U
ne , m
-3
1018 1017
0W
1016 15 1040
Hollow cathode position
Te . eV
30 20
0 250 200
Vs = Vd
150 100
50
EP
Vs from cathode , V
TE D
10
0
0
100
200
300
400
168
Figure 7 shows the color contours of ne, Te, and Vs for the Ps = 300 W and Vd = 200 V operation. The ne distribution is
169
affected by the diverging magnetic field. As shown in Fig. 7(a), ne was confined within r ≤ 20 mm. From z = 70 mm, the end
170
of the diverging magnetic field, the low electron number density region spread within r ≤ 20 mm. As shown in Fig. 7(b), in
171
the r ≥ 20 mm region, Te maintained a constant value along the magnetic lines of force because electrons have a considerably
172
larger mobility in the direction parallel to the magnetic lines of force than that in the perpendicular direction35. Conversely, in
173
the r ≤ 20 mm region, Te varied along the magnetic lines of force. From Fig. 7(c), Vs decreases toward the downstream
AC C
164 165 166 167
z , mm FIG. 6 ne, Te, and Vs distribution on axis. Ĵ1 = 0.5 Aeq, Ĵ2 = 0.36 Aeq, Vd = 200 V. Uncertainty in ne, Te, and Vs were better than +15%/-23%, ± 8.7%, and ± 4% of the averaged value, respectively.
8
ACCEPTED MANUSCRIPT 174
direction and the axial electric field was generated. Oudini et al36. reported that if the electron temperature and/or plasma
175
density gradients are large, the magnetic lines of force will no longer be equipotential. As shown in Figs. 7(a) and (b), ne and
176
Te varied along the magnetic lines of force, particularly, within z ≤ 20 mm and r ≤ 20 mm. Therefore, the space potential also
177
varied along the magnetic lines of force and decreased in the axial direction.
TE D
M AN U
SC
RI PT
178
FIG. 7. Distribution of (a) ne, (b) Te, and (c) Vs. Ĵ1 = 0.5 Aeq, Ĵ2 = 0.36 Aeq, Vd = 200 V, Ps = 300 W. Uncertainties in ne, Te, and Vs were no more than +14%/-22%, ± 10%, and ± 5% of the averaged value, respectively. Linear interpolation was applied among probe measurement points.
184
C.
EP
179 180 181 182 183
AC C
Ion current and energy characteristics in Ĵ1 = 1.0 Aeq operation
185
Figure 8(a) shows the variations of Ji with Ps in the Ĵ1 = 1.0 Aeq and Vd = 300 V operation. In the Ps = 0 W operation, Ji
186
was equal to 1.0 A, which is 77% of Ĵ1 + Ĵ2. In general, Ji increased with Ps. However, Ji had a local minimum at Ps = 40 W.
187
When Ps > 40 W, Ji increased with Ps. At Ps = 400 W, Ji was equal to the value of Ĵ1 + Ĵ2, and, at Ps = 1500 W, Ji was 1.2
188
times larger than Ĵ1 + Ĵ2. According to the current fraction of each charge-state ion measured by the E × B probe, the doubly
189
charged argon ion current had 22% of Ji at Ps = 500 W and increased to 27% at Ps = 700 W.
190
Figure 8(b) shows the variations of Ei(0) with Ps for the Ĵ1 = 1.0 Aeq and Vd = 300 V operation. When Ps ≤ 200 W, Ei(0)
191
maintained approximately 60 eV and then increased from Ps = 200 W. However, Ei(0) was gradually saturated at
192
approximately 220 eV, which is 73% of Vd. From the E × B probe measurement in the Ps = 600 W operation (see Fig. 4), the 9
ACCEPTED MANUSCRIPT effective acceleration voltage of a singly charged and doubly charged argon ion were 186 V and 143 V, respectively. Kim et
194
al37. measured the effective acceleration voltage on the axis of a Hall thruster. The effective acceleration voltage of a doubly
195
charged ion was 10–30 V lower than that of a singly charged ion. From simulations by Katz et al38., the doubly charged ions
196
were generated at a lower space potential region than that of the singly charged ions. Youbong et al39. measured the effective
197
acceleration voltage of each charge-state ion in a cylindrical Hall thruster and reported an up to 30 V lower acceleration
198
voltage of doubly and triply charged ions than that of singly charged ions. In our experiments, the doubly charged ions had a
199
43 V lower effective acceleration voltage than that of the singly charged ions. As shown in Fig. 6, the space potential of the
200
HEST decreased monotonically from the upstream anode potential toward the downstream direction. Therefore, as described
201
in Ref. 38, doubly charged ions were generated in a low space potential region, and, as a result, the effective acceleration
202
voltage was also lower than that of singly charged ions. These results indicate that, in this Ĵ1 = 1.0 Aeq operation, the
203
contribution of Ps to the increase of Ei(0) was limited because of the generation of low-energy doubly charged ions.
M AN U
SC
RI PT
193
204
350
2.0
Ji = J$1 + J$2 1.0 0.5
TE D
Ji , A
Ei (0) , eV
300
1.5
(a)
0.0 0
1000
1500
250 200 150 100
50
(b)
0 0
500
1000
1500
Ps , W Ps , W FIG. 8. Ps dependence with Ĵ1 = 1.0 Aeq, Ĵ2 = 0.36 Aeq, and Vd = 300 V. (a) Ji vs. Ps, (b) Ei(0) vs. Ps. Uncertainty in Ji was better than ± 1% of the averaged value.
EP
205 206 207
500
Ei (0) = Vd
Figure 9 shows the color contours of ne, Te, and Vs for the Ĵ1 = 1.0 Aeq, Ps = 300 W, and Vd = 200 V operation. By
209
increasing Ĵ1, the maximum value of ne increased to 6.9 × 1018 m−3 at (r, z) = (0 mm, 0 mm). As shown in Fig. 9(a), the
210
electrons were confined by the diverging magnetic field as well as the Ĵ1 = 0.5 Aeq operation (see Fig. 7(a)). However, in the
211
Ĵ1 = 1.0 Aeq operation, the local peak of electron temperature vanished and the maximum electron temperature decreased to
212
16 eV at (r, z) = (20 mm, 5 mm). This ne increase and Te decrease with increasing working gas flow rate have also been
213
observed in Hall thrusters40. As shown in Fig. 9(c), in the r ≥ 5 mm region, Vs maintained a constant value along the magnetic
214
lines of force. In the r ≤ 5 mm region, Vs varied along the magnetic lines of force because of the large ne and Te gradient36;
215
this also occurs in the Ĵ1 = 0.5 Aeq operation (see Fig. 7(c)). In general, Vs decreased from the upstream to downstream
216
regions, and an axial electric field was generated. At (r, z) = (0 mm, 0 mm) and (0 mm, 350 mm), Vs was equal to 159 and 35
AC C
208
10
ACCEPTED MANUSCRIPT 217
V, respectively. In the Ĵ1 = 0.5 Aeq operation, ions were accelerated from the anode potential (see Fig. 6). However, by
218
increasing Ĵ1, the working potential difference decreased and, as a result, the acceleration performance deteriorated, as shown
219
in Fig. 8(b).
TE D
M AN U
SC
RI PT
220
221
FIG. 9 Distribution of (a) ne, (b) Te, and (c) Vs. Ĵ1 = 1.0 Aeq, Ĵ2 = 0.36 Aeq, Vd = 200 V, Ps = 300 W. Uncertainties in ne, Te, and Vs were better than +14%/-23%, ± 3.7%, and ± 1.8% of the averaged value, respectively. Linear interpolation was applied among probe measurement points.
226
IV. Thruster Performance
227
A.
AC C
EP
222 223 224 225
Current characteristics
228
Figure 10 shows the dependence of Ji on Jd and Ĵ1 for the Ps = 0 – 1500 W and Vd = 300 V operation. Being independent
229
of Ĵ1 and Ps, Ji was almost a linear function of Jd. Ji/Jd was adequately fit to a gradient of 0.4–0.6, which indicates that the
230
discharge current was composed of 40 - 60% of the ion beam current from the plasma source, and the rest was the electron
231
backflow from the hollow cathode.
232
11
ACCEPTED MANUSCRIPT 2.0 1.5
0.6
0.4
1.0
Ji /Jd = 0.2
0.5 0.0 0.0
1.0
2.0
3.0
RI PT
Ji , A
1.0 0.8
J$1 , Aeq 0.5 1.0
4.0
233 234 235
Jd , A FIG. 10. Ji vs. Jd. Ĵ2 = 0.36 Aeq, Vd = 300 V, Ps = 0 – 1500 W. Uncertainty in Jd was better than ± 3% of the averaged value.
236
B.
SC
238
In this section, the thruster performance such as thrust F, specific impulse Isp, and thrust efficiency η are estimated. From the energy conservation law, the average Z-charged ion velocity ui,Z can be calculated as
M AN U
237
Input power dependence of thruster performance
1 mi u i,2Z = eZηa,Z Vd 2
(5)
239
Here, mi, e, and ηa,ZVd are the ion mass, elementary charge, and effective acceleration voltage of Z-charged ions, respectively.
240
By combining the law of the conservation of momentum, F can be calculated as
TE D
J J i, Z F ≈ ∑ m i i u i, Z eZ Ji Z
cos θ
(6)
Here, Ji,Z/Ji is the current fraction of Z-charged ions. The ηa,ZVd and Ji,Z/Ji values are obtained by the E × B probe
242
measurement. In reality, the Ji,Z/Ji value is a function of θ37, but, in this paper, it is represented by a center axis value. The
243
cos<θ> value is also assumed to have no dependence on Z. The definition of Isp and η can be expressed as follows22:
244
AC C
EP
241
η=
I sp =
F F = ˆ m& g mi J e ⋅ g
F2
2 m i Jˆ e ⋅ (Ps + J dVd + J k V k )
(7) (8)
Here, ṁ and g are the mass flow rate and gravitational acceleration, respectively.
245
Figure 11 shows the variation of Isp calculated using Eq. (7) from the probe measurement data with the variation in Ĵ1 and
246
input energy of each working gas particle (Ps+JdVd+JkVk)/(Ĵ1+Ĵ2). In the Ĵ1 = 0.5 Aeq case, Z ≤ 1 is assumed, i.e., the exhaust
247
plume consists of only singly charged ions. Isp increased with (Ps+JdVd+JkVk)/(Ĵ1+Ĵ2) and started to saturate at about 2400 s
248
because Ji and Ei(0) reached the saturation point with the increase in Ps (see Fig. 5). In Fig. 11, the slope from the origin
249
corresponds to the thrust–power ratio and the slope started to decrease at (Ps+JdVd+JkVk)/(Ĵ1+Ĵ2) ≈ 800 W/Aeq. As shown in
250
Fig. 6, in the Ps = 300 W operation, ne at the anode inlet increased by 10 times that of the Ps = 0 W operation, and the 12
ACCEPTED MANUSCRIPT generated ions were electrostatically accelerated from near the anode potential. Therefore, when (Ps+JdVd+JkVk)/(Ĵ1+Ĵ2) < 800
252
W/Aeq, the plasma source contributes to the ion acceleration. However, when (Ps+JdVd+JkVk)/(Ĵ1+Ĵ2) > 800 W/Aeq, the
253
increasing Ps has a limited contribution to the enhancement of the ion acceleration, and the thrust–power ratio decreases.
254
Assuming that Z ≤ 1, the Ĵ1 = 1.0 Aeq case behaves identically to the Ĵ1 = 0.5 Aeq case. The Isp value reached 3100 s at Ps =
255
1500 W and the slope started to decrease at (Ps+JdVd+JkVk)/(Ĵ1+Ĵ2) ≈ 1000 W/Aeq. Considering doubly charged ions (Z ≤ 2)
256
in the Ĵ1 = 1.0 Aeq case, the Isp value decreases at most by 10% from that of the Z ≤ 1 assumption because ηa,2Vd is lower than
257
ηa,1Vd.
RI PT
251
258
SC
3500 3000 2000
M AN U
Isp , sec
2500 1500
J$1 , Aeq 0.5 (Z ≤ 1) 1.0 (Ζ ≤ 1) 1.0 (Ζ ≤ 2)
1000 500 0
259 260 261 262
500 1000 1500 2000 2500 3000 (Ps+JdVd+JkVk) / (J$1+J$2) , W/Aeq FIG. 11. Specific impulse Isp vs. specific input power (Ps+JdVd+JkVk)/(Ĵ1+Ĵ2). Ĵ2 = 0.36 Aeq, Vd = 300 V, Ps = 0 – 1500 W. Uncertainty in Isp was better than 6% of the averaged value.
TE D
0
10
6
EP
η,%
8
4
J$1 , Aeq 0.5 (Z ≤ 1) 1.0 (Ζ ≤ 1) 1.0 (Ζ ≤ 2)
AC C
2
0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
263 264 265 266
Ps / (JdVd) FIG. 12. Thrust efficiency η vs. input power ratio Ps/(JdVd). Ĵ2 = 0.36 Aeq, Vd = 300 V, Ps = 0 – 1500 W. Uncertainty in η was better than 11% of the averaged value.
267
Figure 12 shows the η dependence on Ps/(JdVd), which is the RF power ratio against the electrostatic acceleration power.
268
In the Ĵ1 = 0.5 Aeq case, Z ≤ 1 is assumed, i.e., the exhaust plume consists of only singly charged ions. By varying Ps/(JdVd),
269
η achieved a peak value of 6.6% at Ps/(JdVd) ≈ 1.0, which corresponds to Ps = 300 W. Yamagiwa et al41. analyzed the relation
13
ACCEPTED MANUSCRIPT 270
between the effective ion generation cost ci,eff. and η in a double-stage electrostatic thruster. Based on the energy conservation
271
relation, ci,eff. is defined by c i,eff ≡
(9)
Using ci,eff. and Ps/(JdVd), η can be represented by η= =
Ji J i Ei ⋅ ⋅ (cos θ Jˆ1 + Jˆ 2 Ps + J dVd
)2
1 + Ps (J dVd ) − ci, eff Vd ⋅ J i J d Ji ⋅ ⋅ (cos θ 1 + Ps (J dVd ) Jˆ1 + Jˆ 2
RI PT
272
Ps + J dV d − E i J i Ji
)2
(10)
From Eq. (10), η is the product of the ion current ratio against the total supplied working gas flow rate, energy conversion
274
efficiency, and ion beam divergence efficiency. As described in Section III A, <θ> had only a small dependence on both Ĵ1
275
and Ps, and was equal to 46° ± 2°, which corresponds to (cos<θ>)2 ≈ 0.48. In the Ĵ1 = 0.5 Aeq operation, as shown in Fig. 5(a),
276
Ji was saturated at Ĵ1 + Ĵ2 and, as shown in Fig. 10, Ji/Jd varied between 0.4 and 0.6. By substituting Ji, Ei(0), and Jd in Eq. (9),
277
ci,eff. can be calculated. When Ps/(JdVd) < 1.0, with the increase in Ps, Ji/(Ĵ1+Ĵ2) increased rapidly from 0.08 to 0.81 and ci,eff.
278
varied between 390 and 840 W/A. Therefore, the increase in the first term of Eq. (10) mainly affected η. Conversely, when
279
Ps/(JdVd) > 1.0, with the increase in Ps, Ji/(Ĵ1+Ĵ2) slightly increased from 0.71 to 0.91 and ci,eff./Vd increased from 870 to 2190
280
W/A. In this case, the decrease in the second term of Eq. (10) mainly affected η. Consequently, η had a peak value at the
281
optimum input power ratio, which depends on both the ion generation and effective ion generation cost.
TE D
M AN U
SC
273
In the Ĵ1 = 1.0 Aeq case, assuming Z ≤ 1, η exhibited the same dependence on Ps/(JdVd) as in the Ĵ1 = 0.5 Aeq case; η
283
increased rapidly with the increase in Ps/(JdVd) from 0 to 0.6. In the 0.6 ≤ Ps/(JdVd) ≤ 0.9 region, η maintained a constant
284
value and started to decrease from Ps/(JdVd) > 0.9. In the 0.6 ≤ Ps/(JdVd) ≤ 0.9 region, η had a maximum value of 8.7%.
285
Considering doubly charged ions (Z ≤ 2), with the increase in Ps from 500 to 700 W, Ps/(JdVd) increased from 0.53 to 0.67
286
and η increased from 6 to 7%. Therefore, without taking into account the doubly charged ions, η can be overestimated to 17–
287
20%. This overestimation comes from the thrust calculation in Eq. (6). In the Ĵ1 = 1.0 Aeq and Ps = 700 W operation, the
288
calculated F in the Z ≤ 1 and Z ≤ 2 cases were 13 and 11 mN, respectively. As discussed in section III C, the doubly charged
289
ions have a low effective acceleration voltage. The average momentum flux in the exhaust plume decreased and, as a
290
consequence, the Isp and η values decreased.
291
V.
AC C
EP
282
Conclusion
292
In the operation of a helicon electrostatic thruster, the effects of RF power for plasma source on the ion generation and
293
electrostatic acceleration characteristics were evaluated. The RF power had different effects on thruster operation
294
characteristics in different power range under constant discharge voltage and working gas flow rate. For the discharge voltage 14
ACCEPTED MANUSCRIPT of 300 V and argon gas flow rate of 0.5 Aeq operation, in the RF power range of 0 to 80 W, the RF power increment was
296
utilized for working gas ionization in the plasma source and then enhance the electrostatic acceleration through an axial
297
electric field from the end of the diverging magnetic field. In this power range, ionization enhancement contributed to
298
improve ion acceleration performance. However, in the RF power range of more than 80 W, the ion beam current and ion
299
beam energy were both gradually saturated at 93% of total flow rate and 88% of discharge voltage equivalent, respectively.
300
In this case, injected working gas was ionized with high effective ionization cost of up to 2190 W/A. Meanwhile, in the 1.0
301
Aeq operation, the ion beam current exceeded the total supplied working gas flow rate of 1.36 Aeq by inputting the RF power
302
more than 400 W. The RF power increment was consumed for low energy, doubly charged ions generation. The thrust
303
efficiency was governed by the RF power ratio against to electrostatic acceleration power. In both flow rate, the thrust
304
efficiency reached maximum value at the RF power ratio against to electrostatic acceleration power of 0.6 – 1.0.
SC
RI PT
295
REFERENCES
[1] D. Y. Oh, J. S. Snyder, D. M. Goebel, R. R. Hofer, T. M. Randolph, Solar electric propulsion for Discovery-class missions, J. Spacecraft Rockets 51 (2014) 1822–1835.
[2] Rainer Killinger, Ralf Kukies, Michael Surauer, Angeo Tomasetto, Leo van Holtz, Artemis Orbit Raising Inflight Experience with Ion Propulsion, Acta Astronaut (2003) 53 607-621.
TE D
[3] Peter Rathsman, Joakim Kugelberg, Per Bodin, Giuseppe D. Racca, Bernard Foing, Luca Stagnaro, SMART-1: Development and lessons learnt, Acta Astronaut. 57 (2005) 455-468.
[4] Alexey Lazurenko, Vanessa Vial, Andre Bouchoule, Alexandre Skrylnikov, Vyacheslav Kozlov, Vladimir Kim, Dual-Mode Operation of Stationary Plasma Thrusters, J. Propul. Power 22 (2006) 38-47. [5] E. Chesta, D. Estublier, B. Fallis, E. Gengembre, J. Gonzalez del Amo, N. Kutufa, D. Nicolini, G. Saccoccia, L. Casalino, P.
EP
Dumazert, M. Prioul, J. P. Boeuf, A. Bouchoule, N. Wallace, G. Noci, M. Berti, M. Saverdi, L. Biagioni, S. Marcuccio, A. Cadiou, F. Darnon, L. Jolivet, Flexible variable-specific-impulse electric propulsion systems for planetary missions, Acta Astronaut. 59 (2006) 931-945.
[6] J. Snyder, D. M. Goebel, R. R. Hofer, J. E. Polk, N. C. Wallace, H. Simpson, Performance evaluation of the T6 ion engine, J.
AC C
306
M AN U
305
Propul. Power 28 (2012) 371–379.
[7] C. D. Child, Discharge from hot CaO., Phys. Rev. 32 (1911) 492-511. [8] Irving Langmuir, The effect of space charge and initial velocities on the potential distribution and thermionic current between parallel plane electrodes, Phys. Rev. 21 (1923) 419-435. [9] D. M. Goebel, I. Katz, Fundamentals of Electric Propulsion: Ion and Hall Thrusters, John Wiley & Sons, 2008, pp. 429–446. [10] Kimiya Komurasaki, Yoshihiko Arakawa, Performance calculation of Hall thrusters, Acta Astronaut. 38 (1996), 185-192. [11] N. Koch, H. P. Harmann, G. Kornfeld, Development and test status of the THALES high efficiency multistage plasma (HEMP) thruster family, in Proceedings of the 29th International Electric Propulsion Conference, Princeton, USA (2005), IEPC Paper No. 2005-297. [ 12 ] Gerd Krülle, Monika Auweter-Kurtz, Akihiro Sasoh, Technology and Application Aspects of Applied Field Magnetoplasmadynamic Propulsion, J. Propul. Power 14 (1998), 754-763.
15
ACCEPTED MANUSCRIPT
[13] Carlos M. Xisto, José C. Páscoa, Paulo J. Oliveira, Numerical analysis of real gas MHD flow on two-dimensional self-field MPD thrusters, Acta Astronaut. 112 (2015) 89-101. [14] Richard R. Hofer, Peter Y. Peterson, Alec D. Gallimore, A High Specific Impulse Two-Stage Hall Thruster with Plasma Lens Focusing, in Proceedings of the 27th International Electric Propulsion Conference, Pasadena, USA (2001), IEPC Paper No. 2001-036.
RI PT
[15] Grishin, S. D., Erofeev V. D., Zharinov A. V., Naumkin V. P., Safronov I. N., Characteristics of a two-stage ion accelerator with an anode layer, J. Appl. Mech. Tech. Phys. 19 (1978) 166-173.
[16] Xu Zhang, Hong Li, Liqiu Wei, Yongjie Ding, Zhongxi Ning, Daren Yu, Effect of double-stage discharge on the performance of a multi-mode Hall thruster, Vacuum 131 (2016) 312-318.
[17] E. Ahedo, F. I. Parra, A model of the two-stage Hall thruster discharge, J. Appl. Phys. 98 (2005) 023303.
SC
[18] Shaowei Qing, Peng E, Guangqing Xia, Ming-Chun Tang, Ping Duan, Optimized electrode placement along the channel of a Hall thruster for ion focusing, J. Appl. Phys. 115 (2014) 033301.
[19] M. V. Silnikov, K. S. Kulakov, S. L. Kulakov, and D. V. Panov, “Correction thruster development based on high-current surface discharge in vacuum,” Acta Astronaut. 109 (2015) 177-181.
M AN U
[20] Adam Shabshelowitz, Alec D. Gallimore, Performance of a Helicon Hall Thruster Operating with Xenon, Argon, and Nitrogen, J. Propul. Power 30 (2014) 664-671.
[21] S. Harada, T. Baba, A. Uchigashima, S. Yokota, A. Iwakawa, A. Sasoh, T. Yamazaki, H. Shimizu, Electrostatic acceleration of helicon plasma using a cusped magnetic field, Appl. Phys. Lett. 105 (2014) 194101.
[22] A. Uchigashima, T. Baba, D. Ichihara, A. Iwakawa, A. Sasoh, T. Yamazaki, S. Harada, M. Sasahara, T. Iwasaki, Anode geometry effects on ion beam energy performance in helicon electrostatic thruster, IEEE. Trans. Plasma Sci. 44 (2016) 306–313. [23] J. A. Simpson, Design of retarding field energy analyzers, Rev. Sci. Instrum. 32 (1961) 1283–1293.
TE D
[24] M. L. R. Walker, R. R. Hofer, A. D. Gallimore, Ion Collection in Hall Thruster Plumes, J. Propul. Power 22 (2006) 205-209. [25] Alec D. Gallimore, Near- and Far-Field Characterization of Stationary Plasma Thruster Plumes, J. Spacecraft Rockets 38 (2001) 441-453.
[26] Rohit Shastry, Richard R. Hofer, Bryan M. Reid, Alec D. Gallimore, Method for analyzing E×B probe spectra from Hall thruster plumes, Rev. Sci. Instrum. 80 (2009) 063502.
EP
[27] Homer D. Hagstrum, Auger Ejection of Electrons from Tungsten by Noble Gas Ions, Phys. Rev. 15 (1954) 325-335. [28] D. Renaud, D. Gerst, S. Mazouffre, A. Aanesland, E×B probe measurements in molecular and electronegative plasmas, Rev. Sci. Instrum. 86 (2015) 123507.
58-70.
AC C
[29] E. O. Johnson and L Malter, “A Floating Double Probe Method for Measurements in Gas Discharge,” Phys. Rev. 80 (1950)
[30] Brian A, Smith and Lawrence J. Overzet, “Improvements to the floating double probe for time-resolved measurements in pulsed rf plasmas,” Rev. Sci. Instrum 69 (1998) 1372-1377. [31] James M. Hass and Alec D. Gallimore, “Considerations on the Role of the Hall Current in a Laboratory-Model Thruster,” IEEE. Trans. Plasma Sci. 30 (2002) 687–697.
[32] J. P. Sheehan, N. Hershkowitz, “Emissive probes,” Plasma Sources Sci. Technol. 29 (2011) 063001. [33] A. Fruchtman, D. Zoler, and G. Makrinich, “Potential of an emissive cylindrical probe in plasma,” Phys. Rev. E 84 (2011) 025402. [34] T. Shoji, Y. Sakawa, S. Nakazawa, K. Kadota, T. Sato, Plasma production by helicon waves, Plasma Sources Sci. Technol. 2 (1993) 5-10. [35] Jean-Pierre Boeuf, Tutorial: Physics and modeling of Hall thrusters, J. Appl. Phys. 121 (2017) 011101.
16
ACCEPTED MANUSCRIPT
[36] N. Oudini, G. J. M. Hagellar, J. P. Boeuf, L. Garrigues, Physics and modeling of an end-Hall (gridless) ion source, J. Appl. Phys. 109 (2011) 073310. [37] Sang-Wook Kim, Alec D. Gallimore, Plume Study of a 1.35-kW SPT-100 Using an E×B probe, J. Spacecraft Rockets 39 (2002) 904-909. [38] Ira Katz, Richard R. Hofer, Dan M, Goebel, Ion Current in Hall Thrusters, IEEE T. Plasma Sci. 36 (2008) 2015-2024.
RI PT
[39] Youbong Lim, Holak Kim, Wonho Ghoe, Seung Hun Lee, Jongho Seon, Hae June Lee, Observation of a high-energy tail in ion energy distribution in the cylindrical Hall thruster plasma, Phys. Plasmas 21 (2014) 103502. [40] Brayan Michael Reid, Ph.D thesis, University of Michigan, MS, 2009.
[41] Yoshiki Yamagiwa, Kyoichi Kuriki, Performance of Double-Stage-Discharge Hall Ion Thruster, J. Propul. Power 7 (1991)
AC C
EP
TE D
M AN U
SC
65-70.
17
ACCEPTED MANUSCRIPT
Highlights RF/electrostatic hybrid thruster has been developed with matched power balance. Even a small RF power efficiently enhances the ion beam current and energy. An excessively high RF power leads to an unfavorable increase in an ionization cost.
AC C
EP
TE D
M AN U
SC
RI PT
The thrust efficiency has a maximum at RF to DC power ratio from 0.6 to 1.0.
S0094-5765(17)30634-3
DOI:
10.1016/j.actaastro.2017.06.032
Reference:
AA 6367
To appear in:
Acta Astronautica
Received Date: 5 May 2017 Revised Date:
27 June 2017
Accepted Date: 28 June 2017
Please cite this article as: D. Ichihara, Y. Nakagawa, A. Uchigashima, A. Iwakawa, A. Sasoh, T. Yamazaki, Power matching between plasma generation and electrostatic acceleration in helicon electrostatic thruster, Acta Astronautica (2017), doi: 10.1016/j.actaastro.2017.06.032. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
Power Matching between Plasma Generation and Electrostatic Acceleration in Helicon Electrostatic Thruster D. Ichihara,1,a) Y. Nakagawa,1) A. Uchigashima,1) A Iwakawa,1) A Sasoh,1) and T. Yamazaki2) 1
Department of Aerospace Engineering, Nagoya University, Nagoya, Aichi 464-8603, Japan
RI PT
2
Mitsubishi Heavy Industry ltd., 16-5 Konan 2-chome, Minato-ku, Tokyo 108-8215, Japan
The effects of a radio-frequency (RF) power on the ion generation and electrostatic acceleration in a helicon electrostatic thruster were investigated with a constant discharge voltage of 300 V using argon as the working gas at a flow rate either of 0.5 Aeq (Ampere equivalent) or 1.0 Aeq. A RF power that was even smaller than a direct-current (DC) discharge power
SC
enhanced the ionization of the working gas, thereby both the ion beam current and energy were increased. However, an excessively high RF power input resulted in their saturation, leading to an unfavorable increase in an ionization cost with doubly charged ion production being accompanied. From the tradeoff between the ion production by the RF power and the
optimal RF to DC discharge power ratio of 0.6 -1.0.
1
I.
Introduction
M AN U
electrostatic acceleration made by the direct current discharge power, the thrust efficiency has a maximum value at an
Electric propulsion has an advantage over chemical propulsion owing to its high specific impulse capability, and the
3
usefulness of electric propulsion has been demonstrated in orbit transfer1-3. Based on the space propulsion principle, thrust
4
and specific impulse have opposite dependences on the propellant mass flow rate with a constant power; in particular, a large
5
thrust is obtained with a high mass flow rate but low specific impulse, however, a high specific impulse is obtained with a
6
low mass flow rate but small thrust. This competing performance of specific impulse and thrust should offset each other in
7
the tradeoff between payload mass and working period4,5. Ion thrusters, in which accelerates only ions by an electrostatic
8
potential difference larger than 1.0 kV, have an important advantage of high thrust efficiency in a high specific impulse range
9
on the order of 3000 s or higher6. However, its thrust density is limited by the space charge limitation7,8. In other electric
10
thrusters, such as Hall thrusters9,10, highly efficient multistage plasma thrusters11, and magnetoplasmadynamic thrusters12,13,
11
where accelerate quasi-neutral plasma, the ionization and acceleration of the propellant are performed in a common channel;
12
therefore, the propellant ionization and thrust generation processes cannot be separated. Zharinov et al14. proposed a
13
double-stage Hall thruster, which has an intermediate electrode between the upstream anode and downstream cathode for
14
separating the propellant ionization and acceleration. A number of investigations into the operation characteristics15,16 and
15
optimal intermediate electrode locations17,18 were conducted. Silnikov et al19. proposed the utilization of nanosecond surface
16
discharge to produce positively-charged ions with a density of the order of 1019 to 1020 m-3 in the first stage of a double-stage
AC C
EP
TE D
2
a)
Author to whom correspondence should be addressed. Electronic mail: [email protected].
1
ACCEPTED MANUSCRIPT 17
electric propulsion thruster. Although this method can be useful for the impulse generation after the nanosecond discharge, it
18
is not suitable for a thruster of direct-current (DC) discharge operation. Adam et al 20 . investigated the operation
19
characteristics of a Hall thruster combined with an annular helicon plasma source and obtained a slight thrust increase.
20
However, the thrust–power ratio and thrust efficiency deteriorated. Harada et al21. examined the combination of a cylindrical helicon plasma source and electrostatic acceleration in a
22
helicon electrostatic thruster (HEST); a ring anode and hollow cathode in a cusped magnetic field were set in the downstream
23
region from the helicon plasma source. HEST realized DC electrostatic acceleration with maintaining a constant-rate
24
production in the helicon plasma source with a density of the order of 1019 m-3. Unlike to the ion thrusters nor the thruster
25
proposed in Ref. 19, the thrust density is not limited by the space charge limitation7, 8. By inputting 1500 W of RF power to
26
the helicon plasma source and applying 300 V of acceleration voltage, the average ion beam energy was comparable to the
27
applied voltage equivalent. Uchigashima et al22. reported anode geometry effects on the ion acceleration characteristics of
28
HEST. Nevertheless, a few open questions remain, i.e., the extent of the helicon plasma source contribution for enhancing the
29
thrust efficiency, and whether there exists an optimal RF power to acceleration power ratio. This study is aimed at
30
quantitatively investigating the power matching between RF plasma generation and electrostatic acceleration in HEST.
M AN U
SC
RI PT
21
AC C
EP
TE D
31
32 33 34 35
II.
FIG. 1 Schematic of HEST.
Experimental Apparatus and Procedure
36
Figure 1 shows a schematic of the HEST21. HEST has a radio-frequency (RF) plasma source in the upstream region and
37
electrostatic acceleration electrodes in the downstream region. The RF plasma source was comprised of a ceramic
38
(Photoveel) tube with an inner diameter of 27 mm and length of 150 mm. A Nagoya type III (m = +1) helical antenna was 2
ACCEPTED MANUSCRIPT fixed onto the axis of a water-cooled solenoid coil. The exit of the RF plasma source was located at the center of the solenoid
40
coil. The magnetic field strength was 100 mT at the coil center. A copper ring anode with an inner diameter of 27 mm and
41
thickness of 10 mm was placed 25 mm axially downstream from the coil center. In the downstream region, the magnetic field
42
was greatly modified using 16 cylindrical Nd–Fe–B permanent magnets and soft iron yokes to generate a diverging magnetic
43
field followed by a field-free region where the magnetic field strength was less than 3 mT. A commercial hollow cathode
44
(DLHC-1000, Kaufman & Robinson Inc.) was used and its orifice was placed 70 mm off-axis at 175 mm axially downstream
45
from the coil center. The RF power was supplied by an RF power source (RFK50ZH, Kyosan Electric Mfg. Co., Ltd.)
46
through an auto-matching circuit box (MBK50, Kyosan Electric Mfg. Co., Ltd.). The RF power frequency was set to 13.56
47
MHz.
SC
48
RI PT
39
To evaluate the ion beam energy Ei from an ion energy distribution function (IEDF), a retarding potential analyzer 23
49
(RPA)
50
probe24. The RPA or nude Faraday probe was fixed onto the swing system, which consists of a stepping motor and
51
250-mm-long stainless steel arm. Here, the cylindrical coordinates (r, z) for an axisymmetric configuration are defined with
52
their origin set at the axial position of the left surface of the ring anode. The swing center was at (r, z) = (0 mm, 115 mm). In
53
the horizontal plane on the center axis of the HEST, the ion current density ji as a function of azimuthal angle, θ, with respect
54
to the center axis was measured. In this paper, the definitions of Ei, Ji, and <θ> are identical to those mentioned in Ref. 22.
55
Figure 2 shows an example of Ei(θ) and ji(θ), which are normalized by Ei(0) and ji(0), respectively. Because Ei(θ) varied by
56
less than ±5% against Ei(0) in |θ| ≤ <θ>, Ei(0) is used as the representative value.
TE D
M AN U
was used. The ion beam current Ji and ion beam divergence half-angle <θ> were measured using a nude Faraday
1.2
58
AC C
Normalized ji(θ )
EP
1.0
400
ji(θ )
300
0.8
Ei(θ )
0.6
200
0.4
0.0 -150 -100
100
<θ > <θ >
0.2 -50
0
Ei(θ ) , eV
57
50
100
0 150
θ , deg.
59 60 61
FIG. 2 Dependence of the normalized ion current density ji (curve) and Ei (circle) on rotation angle θ. Ĵ1 = 1.0 Aeq, Ĵ2 = 0.36 Aeq, Vd = 300 V, Ps = 300 W.
62
In order to measure the beam currents of singly and doubly charged ions, an E × B probe25 was used. Figure 3 shows a
63
schematic of the E × B probe, which consists of a metal mesh (0.28 mm × 0.28 mm square, solidity of 56 %), entrance orifice, 3
ACCEPTED MANUSCRIPT E × B deflection section, exit orifice, and ion collector. The entrance orifice, which has an inner diameter of 4.2 mm and
65
thickness of 6 mm, was connected to the E × B deflection section entrance. Inside the E × B deflection section, a uniform
66
magnetic field was applied. The magnetic field strength was set to 110 mT using Nd–Fe–B permanent magnetic plates and
67
soft iron yokes. An electric field, perpendicular to both the magnetic field and exhaust direction, was applied between the pair
68
of stainless steel electrode plates. The electrode plate has a length of 100 mm and width of 10 mm. The inter-electrode
69
distance was set to 10 mm. The exit orifice, which has an inner diameter of 2.0 mm and length of 7 mm, was placed at the E
70
× B deflection section exit. The ion collector has an effective collection diameter of 5 mm and was located 8 mm axially
71
downstream from the exit orifice. The electrode plates were connected to a function generator (SG-4322, IWATSU Electric
72
Co., Ltd.) through a power amplifier (NF Corporation) to supply a voltage difference VE×B, which varied from 0 to 100 V at
73
0.02 Hz. The ion collector was grounded through a serially connected resistor (15 kΩ ± 1.0%) to measure the collected ion
74
current JE×B. In order to increase the signal-to-noise ratio, a low-pass filter with a cutoff frequency of 33 Hz was used. Figure
75
4 shows an example of the measured JE×B, which is normalized by the maximum value. The E × B probe was fixed at the
76
same position as the RPA, i.e., (r, z) = (0 mm, 350 mm). The normalized JE×B was smoothly fit to superimposed Lorentzian
77
functions using the least squares method. The ion current fraction of each charge state was estimated from each Lorentzian
78
function peak height26. The secondary electron emission coefficients, i.e., 0.1 and 0.4 for singly and doubly charged ions,
79
respectively27, were used to correct the current fraction estimation. In the case shown in Fig. 4, the current fraction of singly
80
charged ions (red dashed line) and doubly charged ions (blue dashed line) was 76 and 24%, respectively. The effective
81
acceleration voltage of each charge-state ion was estimated from the VE×B value at the peak28 of the corresponding
82
Lorentzian function.
SC
M AN U
TE D
EP AC C
83
RI PT
64
84 85 86
FIG. 3 Schematic of E × B probe. 4
ACCEPTED MANUSCRIPT
Normalized JE×B
1.2 Normalized JE×B Fit Fitting curves
1.0 0.8 0.6 0.4
0.0 0
20
40
60
80
VE×B , V
87
RI PT
0.2 100
FIG. 4 Dependence of the normalized-corrected ion current JE×B on the swing voltage VE×B of the E × B probe measurement. Ĵ1 = 1.0 Aeq, Ĵ2 = 0.36 Aeq, Vd = 300 V, Ps = 600 W.
92
tip was made of tungsten wire with a diameter of 0.3 mm and effective length of 3.0 mm. The measured probe current (I) –
93
voltage (V) curve was fitted by a theoretical formula29.
SC
88 89 90 91
M AN U
The electron number density, ne, and electron temperature, Te, were measured using a double probe. The double probe
V + c1V + c 2 . I = I sat ⋅ tanh 2 kTe e
(1)
Here, Isat is ion saturation current, k is Boltzmann constant, and e is elementally charge. The coefficient c1 corresponds to
95
sheath expansion in the ion saturation region and c2 reflects any offset currents owing to stray capacitance30. Te and Isat were
96
determined as a fitting parameters. Electron number density was calculated from Eq.(2).
TE D
94
ne =
I sat κAeff
mi . kTe
(2)
Here, κ (= 0.61), and Aeff are density decrement inside pre-sheath, and effective current correction area, respectively. In order
98
to take the sheath thickness into account, an iterative process31 was used to estimate Aeff. To measure the space potential Vs
99
with respect to the cathode potential, a floating emissive probe32 was used. The emissive probe tip was made of a
100
1%-thoriated tungsten wire with a diameter of 0.185 mm. The emissive probe tip was semicircular shape with a diameter of
101
2.0 mm. To emit a sufficient amount of thermionic electrons, the emissive probe tip was Joule heated by supplying a heater
102
current of 5.5 A. Because of the space charge limitation7, 8, the floating voltage Vf of the emissive probe was corrected by a
103
factor of ψckTe/e33 to calculate Vs.
AC C
EP
97
Vs = V f + Ψc kTe e
5
(3)
ACCEPTED MANUSCRIPT 104
The correction factor ψc varied from 0 to 1.5 for argon gas. The double probe or emissive probe was mounted on a stepping
105
motor, and the probe sweep time at each point was shorter than 0.3 s. The probe axis was oriented to the center axis of the
106
thruster.
107
III. Results and Discussion
108
A.
RI PT
Operating conditions
All experiments were conducted in a 3.2-m-long, 1.2-m-diameter, stainless steel vacuum chamber. The chamber was
110
evacuated by a cryogenic pump with an exhaust speed of 8400 l/s, which was backed by a dry pump with an exhaust speed of
111
120 l/s. The ambient pressure in the vacuum chamber, measured by an ionization gauge, was maintained lower than 10 mPa
112
with a total working gas flow rate of 1.36 Aeq. The working gas flow rate supplied to the plasma source Ĵ1 was set to 0.5 or
113
1.0 Aeq, and the RF power to the plasma source Ps was increased every 20 W from 0 to 300 W and every 100 W from 300 to
114
1500 W. The discharge voltage Vd was set to 300 V in the Ei(0), Ji, and discharge current Jd measurements, and 200 V in the
115
probe measurements. The hollow cathode was operated with a working gas flow rate, Ĵ2, of 0.36 Aeq, and the keeper current
116
Jk was set to 2.0 A. Each operation condition for measuring Ei(0), Ji, <θ>, Jd, and keeper voltage Vk was repeated at least
117
twice. In the following figures, the circles represent the average value. The error bars in Ei(0) correspond to the standard
118
deviation defined in Ref. 22, whereas those in Ji, Jd, and <θ> correspond to the standard deviation (±σ) obtained from the
119
number of trials. The uncertainty of Te was estimated based on the standard deviation of the theoretical-curve (Eq. (1)) fitting
120
and that of ne and Vs were estimated by applying the low of propagation of error in Eqs. (2) and (3), respectively. The
121
working gas supplied through both the plasma source and hollow cathode was argon (purity 99.9999%). The operation time
122
was at least 3.5 s at each operating condition.
123
B.
TE D
M AN U
SC
109
EP
Ion current and energy characteristics in Ĵ1 = 0.5 Aeq operation Figure 5(a) shows the variation of Ji with Ps for the Ĵ1 = 0.5 Aeq and Vd = 300 V operation. Ji increased with Ps. In
125
particular, Ji increased from 0.07 to 0.36 A as Ps increased from 0 to 40 W. When Ps > 40 W, Ji increased more gradually. At
126
Ps = 1500 W, Ji was equal to 0.80 A, which is 93% of the total supplied flow rate Ĵ1 + Ĵ2. Figure 5(b) shows the variation of
127
Ei(0) with Ps with Ĵ1 = 0.5 Aeq and Vd = 300 V operation. Ei(0) decreased from 133 to 107 eV as Ps increased from 0 to 40
128
W. Conversely, while Ps increased from 40 to 80 W, Ei(0) increased rapidly from 107 to 188 eV. At Ps = 1500 W, Ei(0)
129
reached 265 eV, which is 88% of Vd. In Ref. 20, by combing the annular helicon plasma source with a Hall thruster, the ion
130
beam current increased up to 50% of Ĵ1 + Ĵ2 with the increase in helicon plasma source input power. However, the ion beam
131
energy decreased to 80% of Vd. In this experiment, Ji and Ei(0) increased by a factor of 11 and 2, respectively, as Ps increased
AC C
124
6
ACCEPTED MANUSCRIPT 132
from 0 to 1500 W. Therefore, in the Ĵ1 = 0.5 Aeq operation case, the RF plasma source contributed to both the ion generation
133
and electrostatic acceleration.
134 350 300 Ei (0) , eV
Ji , A
1.5 Ji = J$ 1 + J$2
1.0
250 200 150 100
0.5
50
(a) 0.0
(b)
0 500
1000
1500
0
500
1000
1500
SC
0
Ps , W Ps , W FIG. 5. Ps dependence with Ĵ1 = 0.5 Aeq, Ĵ2 = 0.36 Aeq, and Vd = 300 V. (a) Ji vs. Ps, (b) Ei(0) vs. Ps. Uncertainty in Ji was better than ± 2% of the averaged value.
M AN U
135 136 137
Ei (0) = Vd
RI PT
2.0
Figure 6 shows the distribution of ne, Te, and Vs on the center axis for the Ps = 0 and 300 W, and Vd = 200 V operation.
139
Owing to a low signal-to-noise ratio, the ne and Te values at z > 150 mm were not obtained except for the center axis. In the
140
Ps = 0 W operation, ne was equal to 2.0 × 1017 m−3 at z = 0 mm and decreased toward the downstream region. However, it had
141
a local minima of 6.3 × 1016 m−3 at z = 85 mm and a local maxima of 1.5 × 1017 m−3 at z = 125 mm. Meanwhile, in the Ps =
142
300 W operation, at z = 0 mm, ne = 3.0 × 1018 m−3. This is more than 10 times higher than that of the operation at Ps = 0 W. ne
143
then decreased monotonically toward the downstream direction. Shoji et al34. measured the variations in electron number
144
density with the change in RF power. By using a Nagoya type III antenna (m = + 1), a steep density increase was observed at
145
approximately 400 W of RF power in the argon gas operation. They also reported that the required RF power to produce a
146
steep density increase was smaller when the RF power frequency was close to the lower hybrid frequency ωLH, which can be
147
calculated as in Eq. (4).
AC C
EP
TE D
138
ωLH ≡ ωci ⋅ ωce
(4)
148
Here, ωci and ωce are the ion cyclotron frequency and electron frequency, respectively. For a singly charged argon ion,
149
ωLH = 10.3 MHz at B = 100 mT. This is close to the RF power frequency (13.56 MHz). Therefore, the HEST also exhibited a
150
density jump in the same RF power range to that reported in Ref. 34; as a result, Ji increased from 0.07 A at Ps = 0 W to 0.61
151
A at Ps = 300 W (see Fig. 5(a)).
152
In the Ps = 0 W operation, Te had a peak value of 20 eV at z = 85 mm. Conversely, in the Ps = 300 W operation, Te had a
153
local peak of 16 eV at z = 85 mm and a maximum of 27 eV at z = 125 mm. The electron temperature distribution relates to
154
the space potential distribution. In the Ps = 0 W operation, Vs at z = 0 mm was 99 V and started to decrease from z = 85 mm, 7
ACCEPTED MANUSCRIPT which is the same location to where Te had the peak value. At z = 350 mm, Vs was 26 V. Through this potential drop, the
156
thermionic electrons diffused from the hollow cathode gained kinetic energy and then lost it by ionization collision with the
157
injected working gas. These energy gain and loss mechanisms affect the electron peak temperature and distribution31. In the
158
Ps = 300 W operation, Vs at z = 0 mm was 198 V, which is almost identical to the discharge voltage (200 V). At z = 85 mm,
159
Vs started to monotonically decrease toward the downstream direction and reached 38 V at z = 350 mm. The measured Vs
160
values at z = 0 and 350 mm were consistent with the IEDF, i.e., in the Ps = 300 W operation, the ion beam potential and space
161
potential were 184 and 41 V, respectively. The above results indicate that the ions were electrostatically accelerated from
162
near the anode potential and obtained an average energy of Ei(0), as shown in Fig. 5(b).
RI PT
155
SC
163 1019 Ps=300W
M AN U
ne , m
-3
1018 1017
0W
1016 15 1040
Hollow cathode position
Te . eV
30 20
0 250 200
Vs = Vd
150 100
50
EP
Vs from cathode , V
TE D
10
0
0
100
200
300
400
168
Figure 7 shows the color contours of ne, Te, and Vs for the Ps = 300 W and Vd = 200 V operation. The ne distribution is
169
affected by the diverging magnetic field. As shown in Fig. 7(a), ne was confined within r ≤ 20 mm. From z = 70 mm, the end
170
of the diverging magnetic field, the low electron number density region spread within r ≤ 20 mm. As shown in Fig. 7(b), in
171
the r ≥ 20 mm region, Te maintained a constant value along the magnetic lines of force because electrons have a considerably
172
larger mobility in the direction parallel to the magnetic lines of force than that in the perpendicular direction35. Conversely, in
173
the r ≤ 20 mm region, Te varied along the magnetic lines of force. From Fig. 7(c), Vs decreases toward the downstream
AC C
164 165 166 167
z , mm FIG. 6 ne, Te, and Vs distribution on axis. Ĵ1 = 0.5 Aeq, Ĵ2 = 0.36 Aeq, Vd = 200 V. Uncertainty in ne, Te, and Vs were better than +15%/-23%, ± 8.7%, and ± 4% of the averaged value, respectively.
8
ACCEPTED MANUSCRIPT 174
direction and the axial electric field was generated. Oudini et al36. reported that if the electron temperature and/or plasma
175
density gradients are large, the magnetic lines of force will no longer be equipotential. As shown in Figs. 7(a) and (b), ne and
176
Te varied along the magnetic lines of force, particularly, within z ≤ 20 mm and r ≤ 20 mm. Therefore, the space potential also
177
varied along the magnetic lines of force and decreased in the axial direction.
TE D
M AN U
SC
RI PT
178
FIG. 7. Distribution of (a) ne, (b) Te, and (c) Vs. Ĵ1 = 0.5 Aeq, Ĵ2 = 0.36 Aeq, Vd = 200 V, Ps = 300 W. Uncertainties in ne, Te, and Vs were no more than +14%/-22%, ± 10%, and ± 5% of the averaged value, respectively. Linear interpolation was applied among probe measurement points.
184
C.
EP
179 180 181 182 183
AC C
Ion current and energy characteristics in Ĵ1 = 1.0 Aeq operation
185
Figure 8(a) shows the variations of Ji with Ps in the Ĵ1 = 1.0 Aeq and Vd = 300 V operation. In the Ps = 0 W operation, Ji
186
was equal to 1.0 A, which is 77% of Ĵ1 + Ĵ2. In general, Ji increased with Ps. However, Ji had a local minimum at Ps = 40 W.
187
When Ps > 40 W, Ji increased with Ps. At Ps = 400 W, Ji was equal to the value of Ĵ1 + Ĵ2, and, at Ps = 1500 W, Ji was 1.2
188
times larger than Ĵ1 + Ĵ2. According to the current fraction of each charge-state ion measured by the E × B probe, the doubly
189
charged argon ion current had 22% of Ji at Ps = 500 W and increased to 27% at Ps = 700 W.
190
Figure 8(b) shows the variations of Ei(0) with Ps for the Ĵ1 = 1.0 Aeq and Vd = 300 V operation. When Ps ≤ 200 W, Ei(0)
191
maintained approximately 60 eV and then increased from Ps = 200 W. However, Ei(0) was gradually saturated at
192
approximately 220 eV, which is 73% of Vd. From the E × B probe measurement in the Ps = 600 W operation (see Fig. 4), the 9
ACCEPTED MANUSCRIPT effective acceleration voltage of a singly charged and doubly charged argon ion were 186 V and 143 V, respectively. Kim et
194
al37. measured the effective acceleration voltage on the axis of a Hall thruster. The effective acceleration voltage of a doubly
195
charged ion was 10–30 V lower than that of a singly charged ion. From simulations by Katz et al38., the doubly charged ions
196
were generated at a lower space potential region than that of the singly charged ions. Youbong et al39. measured the effective
197
acceleration voltage of each charge-state ion in a cylindrical Hall thruster and reported an up to 30 V lower acceleration
198
voltage of doubly and triply charged ions than that of singly charged ions. In our experiments, the doubly charged ions had a
199
43 V lower effective acceleration voltage than that of the singly charged ions. As shown in Fig. 6, the space potential of the
200
HEST decreased monotonically from the upstream anode potential toward the downstream direction. Therefore, as described
201
in Ref. 38, doubly charged ions were generated in a low space potential region, and, as a result, the effective acceleration
202
voltage was also lower than that of singly charged ions. These results indicate that, in this Ĵ1 = 1.0 Aeq operation, the
203
contribution of Ps to the increase of Ei(0) was limited because of the generation of low-energy doubly charged ions.
M AN U
SC
RI PT
193
204
350
2.0
Ji = J$1 + J$2 1.0 0.5
TE D
Ji , A
Ei (0) , eV
300
1.5
(a)
0.0 0
1000
1500
250 200 150 100
50
(b)
0 0
500
1000
1500
Ps , W Ps , W FIG. 8. Ps dependence with Ĵ1 = 1.0 Aeq, Ĵ2 = 0.36 Aeq, and Vd = 300 V. (a) Ji vs. Ps, (b) Ei(0) vs. Ps. Uncertainty in Ji was better than ± 1% of the averaged value.
EP
205 206 207
500
Ei (0) = Vd
Figure 9 shows the color contours of ne, Te, and Vs for the Ĵ1 = 1.0 Aeq, Ps = 300 W, and Vd = 200 V operation. By
209
increasing Ĵ1, the maximum value of ne increased to 6.9 × 1018 m−3 at (r, z) = (0 mm, 0 mm). As shown in Fig. 9(a), the
210
electrons were confined by the diverging magnetic field as well as the Ĵ1 = 0.5 Aeq operation (see Fig. 7(a)). However, in the
211
Ĵ1 = 1.0 Aeq operation, the local peak of electron temperature vanished and the maximum electron temperature decreased to
212
16 eV at (r, z) = (20 mm, 5 mm). This ne increase and Te decrease with increasing working gas flow rate have also been
213
observed in Hall thrusters40. As shown in Fig. 9(c), in the r ≥ 5 mm region, Vs maintained a constant value along the magnetic
214
lines of force. In the r ≤ 5 mm region, Vs varied along the magnetic lines of force because of the large ne and Te gradient36;
215
this also occurs in the Ĵ1 = 0.5 Aeq operation (see Fig. 7(c)). In general, Vs decreased from the upstream to downstream
216
regions, and an axial electric field was generated. At (r, z) = (0 mm, 0 mm) and (0 mm, 350 mm), Vs was equal to 159 and 35
AC C
208
10
ACCEPTED MANUSCRIPT 217
V, respectively. In the Ĵ1 = 0.5 Aeq operation, ions were accelerated from the anode potential (see Fig. 6). However, by
218
increasing Ĵ1, the working potential difference decreased and, as a result, the acceleration performance deteriorated, as shown
219
in Fig. 8(b).
TE D
M AN U
SC
RI PT
220
221
FIG. 9 Distribution of (a) ne, (b) Te, and (c) Vs. Ĵ1 = 1.0 Aeq, Ĵ2 = 0.36 Aeq, Vd = 200 V, Ps = 300 W. Uncertainties in ne, Te, and Vs were better than +14%/-23%, ± 3.7%, and ± 1.8% of the averaged value, respectively. Linear interpolation was applied among probe measurement points.
226
IV. Thruster Performance
227
A.
AC C
EP
222 223 224 225
Current characteristics
228
Figure 10 shows the dependence of Ji on Jd and Ĵ1 for the Ps = 0 – 1500 W and Vd = 300 V operation. Being independent
229
of Ĵ1 and Ps, Ji was almost a linear function of Jd. Ji/Jd was adequately fit to a gradient of 0.4–0.6, which indicates that the
230
discharge current was composed of 40 - 60% of the ion beam current from the plasma source, and the rest was the electron
231
backflow from the hollow cathode.
232
11
ACCEPTED MANUSCRIPT 2.0 1.5
0.6
0.4
1.0
Ji /Jd = 0.2
0.5 0.0 0.0
1.0
2.0
3.0
RI PT
Ji , A
1.0 0.8
J$1 , Aeq 0.5 1.0
4.0
233 234 235
Jd , A FIG. 10. Ji vs. Jd. Ĵ2 = 0.36 Aeq, Vd = 300 V, Ps = 0 – 1500 W. Uncertainty in Jd was better than ± 3% of the averaged value.
236
B.
SC
238
In this section, the thruster performance such as thrust F, specific impulse Isp, and thrust efficiency η are estimated. From the energy conservation law, the average Z-charged ion velocity ui,Z can be calculated as
M AN U
237
Input power dependence of thruster performance
1 mi u i,2Z = eZηa,Z Vd 2
(5)
239
Here, mi, e, and ηa,ZVd are the ion mass, elementary charge, and effective acceleration voltage of Z-charged ions, respectively.
240
By combining the law of the conservation of momentum, F can be calculated as
TE D
J J i, Z F ≈ ∑ m i i u i, Z eZ Ji Z
cos θ
(6)
Here, Ji,Z/Ji is the current fraction of Z-charged ions. The ηa,ZVd and Ji,Z/Ji values are obtained by the E × B probe
242
measurement. In reality, the Ji,Z/Ji value is a function of θ37, but, in this paper, it is represented by a center axis value. The
243
cos<θ> value is also assumed to have no dependence on Z. The definition of Isp and η can be expressed as follows22:
244
AC C
EP
241
η=
I sp =
F F = ˆ m& g mi J e ⋅ g
F2
2 m i Jˆ e ⋅ (Ps + J dVd + J k V k )
(7) (8)
Here, ṁ and g are the mass flow rate and gravitational acceleration, respectively.
245
Figure 11 shows the variation of Isp calculated using Eq. (7) from the probe measurement data with the variation in Ĵ1 and
246
input energy of each working gas particle (Ps+JdVd+JkVk)/(Ĵ1+Ĵ2). In the Ĵ1 = 0.5 Aeq case, Z ≤ 1 is assumed, i.e., the exhaust
247
plume consists of only singly charged ions. Isp increased with (Ps+JdVd+JkVk)/(Ĵ1+Ĵ2) and started to saturate at about 2400 s
248
because Ji and Ei(0) reached the saturation point with the increase in Ps (see Fig. 5). In Fig. 11, the slope from the origin
249
corresponds to the thrust–power ratio and the slope started to decrease at (Ps+JdVd+JkVk)/(Ĵ1+Ĵ2) ≈ 800 W/Aeq. As shown in
250
Fig. 6, in the Ps = 300 W operation, ne at the anode inlet increased by 10 times that of the Ps = 0 W operation, and the 12
ACCEPTED MANUSCRIPT generated ions were electrostatically accelerated from near the anode potential. Therefore, when (Ps+JdVd+JkVk)/(Ĵ1+Ĵ2) < 800
252
W/Aeq, the plasma source contributes to the ion acceleration. However, when (Ps+JdVd+JkVk)/(Ĵ1+Ĵ2) > 800 W/Aeq, the
253
increasing Ps has a limited contribution to the enhancement of the ion acceleration, and the thrust–power ratio decreases.
254
Assuming that Z ≤ 1, the Ĵ1 = 1.0 Aeq case behaves identically to the Ĵ1 = 0.5 Aeq case. The Isp value reached 3100 s at Ps =
255
1500 W and the slope started to decrease at (Ps+JdVd+JkVk)/(Ĵ1+Ĵ2) ≈ 1000 W/Aeq. Considering doubly charged ions (Z ≤ 2)
256
in the Ĵ1 = 1.0 Aeq case, the Isp value decreases at most by 10% from that of the Z ≤ 1 assumption because ηa,2Vd is lower than
257
ηa,1Vd.
RI PT
251
258
SC
3500 3000 2000
M AN U
Isp , sec
2500 1500
J$1 , Aeq 0.5 (Z ≤ 1) 1.0 (Ζ ≤ 1) 1.0 (Ζ ≤ 2)
1000 500 0
259 260 261 262
500 1000 1500 2000 2500 3000 (Ps+JdVd+JkVk) / (J$1+J$2) , W/Aeq FIG. 11. Specific impulse Isp vs. specific input power (Ps+JdVd+JkVk)/(Ĵ1+Ĵ2). Ĵ2 = 0.36 Aeq, Vd = 300 V, Ps = 0 – 1500 W. Uncertainty in Isp was better than 6% of the averaged value.
TE D
0
10
6
EP
η,%
8
4
J$1 , Aeq 0.5 (Z ≤ 1) 1.0 (Ζ ≤ 1) 1.0 (Ζ ≤ 2)
AC C
2
0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
263 264 265 266
Ps / (JdVd) FIG. 12. Thrust efficiency η vs. input power ratio Ps/(JdVd). Ĵ2 = 0.36 Aeq, Vd = 300 V, Ps = 0 – 1500 W. Uncertainty in η was better than 11% of the averaged value.
267
Figure 12 shows the η dependence on Ps/(JdVd), which is the RF power ratio against the electrostatic acceleration power.
268
In the Ĵ1 = 0.5 Aeq case, Z ≤ 1 is assumed, i.e., the exhaust plume consists of only singly charged ions. By varying Ps/(JdVd),
269
η achieved a peak value of 6.6% at Ps/(JdVd) ≈ 1.0, which corresponds to Ps = 300 W. Yamagiwa et al41. analyzed the relation
13
ACCEPTED MANUSCRIPT 270
between the effective ion generation cost ci,eff. and η in a double-stage electrostatic thruster. Based on the energy conservation
271
relation, ci,eff. is defined by c i,eff ≡
(9)
Using ci,eff. and Ps/(JdVd), η can be represented by η= =
Ji J i Ei ⋅ ⋅ (cos θ Jˆ1 + Jˆ 2 Ps + J dVd
)2
1 + Ps (J dVd ) − ci, eff Vd ⋅ J i J d Ji ⋅ ⋅ (cos θ 1 + Ps (J dVd ) Jˆ1 + Jˆ 2
RI PT
272
Ps + J dV d − E i J i Ji
)2
(10)
From Eq. (10), η is the product of the ion current ratio against the total supplied working gas flow rate, energy conversion
274
efficiency, and ion beam divergence efficiency. As described in Section III A, <θ> had only a small dependence on both Ĵ1
275
and Ps, and was equal to 46° ± 2°, which corresponds to (cos<θ>)2 ≈ 0.48. In the Ĵ1 = 0.5 Aeq operation, as shown in Fig. 5(a),
276
Ji was saturated at Ĵ1 + Ĵ2 and, as shown in Fig. 10, Ji/Jd varied between 0.4 and 0.6. By substituting Ji, Ei(0), and Jd in Eq. (9),
277
ci,eff. can be calculated. When Ps/(JdVd) < 1.0, with the increase in Ps, Ji/(Ĵ1+Ĵ2) increased rapidly from 0.08 to 0.81 and ci,eff.
278
varied between 390 and 840 W/A. Therefore, the increase in the first term of Eq. (10) mainly affected η. Conversely, when
279
Ps/(JdVd) > 1.0, with the increase in Ps, Ji/(Ĵ1+Ĵ2) slightly increased from 0.71 to 0.91 and ci,eff./Vd increased from 870 to 2190
280
W/A. In this case, the decrease in the second term of Eq. (10) mainly affected η. Consequently, η had a peak value at the
281
optimum input power ratio, which depends on both the ion generation and effective ion generation cost.
TE D
M AN U
SC
273
In the Ĵ1 = 1.0 Aeq case, assuming Z ≤ 1, η exhibited the same dependence on Ps/(JdVd) as in the Ĵ1 = 0.5 Aeq case; η
283
increased rapidly with the increase in Ps/(JdVd) from 0 to 0.6. In the 0.6 ≤ Ps/(JdVd) ≤ 0.9 region, η maintained a constant
284
value and started to decrease from Ps/(JdVd) > 0.9. In the 0.6 ≤ Ps/(JdVd) ≤ 0.9 region, η had a maximum value of 8.7%.
285
Considering doubly charged ions (Z ≤ 2), with the increase in Ps from 500 to 700 W, Ps/(JdVd) increased from 0.53 to 0.67
286
and η increased from 6 to 7%. Therefore, without taking into account the doubly charged ions, η can be overestimated to 17–
287
20%. This overestimation comes from the thrust calculation in Eq. (6). In the Ĵ1 = 1.0 Aeq and Ps = 700 W operation, the
288
calculated F in the Z ≤ 1 and Z ≤ 2 cases were 13 and 11 mN, respectively. As discussed in section III C, the doubly charged
289
ions have a low effective acceleration voltage. The average momentum flux in the exhaust plume decreased and, as a
290
consequence, the Isp and η values decreased.
291
V.
AC C
EP
282
Conclusion
292
In the operation of a helicon electrostatic thruster, the effects of RF power for plasma source on the ion generation and
293
electrostatic acceleration characteristics were evaluated. The RF power had different effects on thruster operation
294
characteristics in different power range under constant discharge voltage and working gas flow rate. For the discharge voltage 14
ACCEPTED MANUSCRIPT of 300 V and argon gas flow rate of 0.5 Aeq operation, in the RF power range of 0 to 80 W, the RF power increment was
296
utilized for working gas ionization in the plasma source and then enhance the electrostatic acceleration through an axial
297
electric field from the end of the diverging magnetic field. In this power range, ionization enhancement contributed to
298
improve ion acceleration performance. However, in the RF power range of more than 80 W, the ion beam current and ion
299
beam energy were both gradually saturated at 93% of total flow rate and 88% of discharge voltage equivalent, respectively.
300
In this case, injected working gas was ionized with high effective ionization cost of up to 2190 W/A. Meanwhile, in the 1.0
301
Aeq operation, the ion beam current exceeded the total supplied working gas flow rate of 1.36 Aeq by inputting the RF power
302
more than 400 W. The RF power increment was consumed for low energy, doubly charged ions generation. The thrust
303
efficiency was governed by the RF power ratio against to electrostatic acceleration power. In both flow rate, the thrust
304
efficiency reached maximum value at the RF power ratio against to electrostatic acceleration power of 0.6 – 1.0.
SC
RI PT
295
REFERENCES
[1] D. Y. Oh, J. S. Snyder, D. M. Goebel, R. R. Hofer, T. M. Randolph, Solar electric propulsion for Discovery-class missions, J. Spacecraft Rockets 51 (2014) 1822–1835.
[2] Rainer Killinger, Ralf Kukies, Michael Surauer, Angeo Tomasetto, Leo van Holtz, Artemis Orbit Raising Inflight Experience with Ion Propulsion, Acta Astronaut (2003) 53 607-621.
TE D
[3] Peter Rathsman, Joakim Kugelberg, Per Bodin, Giuseppe D. Racca, Bernard Foing, Luca Stagnaro, SMART-1: Development and lessons learnt, Acta Astronaut. 57 (2005) 455-468.
[4] Alexey Lazurenko, Vanessa Vial, Andre Bouchoule, Alexandre Skrylnikov, Vyacheslav Kozlov, Vladimir Kim, Dual-Mode Operation of Stationary Plasma Thrusters, J. Propul. Power 22 (2006) 38-47. [5] E. Chesta, D. Estublier, B. Fallis, E. Gengembre, J. Gonzalez del Amo, N. Kutufa, D. Nicolini, G. Saccoccia, L. Casalino, P.
EP
Dumazert, M. Prioul, J. P. Boeuf, A. Bouchoule, N. Wallace, G. Noci, M. Berti, M. Saverdi, L. Biagioni, S. Marcuccio, A. Cadiou, F. Darnon, L. Jolivet, Flexible variable-specific-impulse electric propulsion systems for planetary missions, Acta Astronaut. 59 (2006) 931-945.
[6] J. Snyder, D. M. Goebel, R. R. Hofer, J. E. Polk, N. C. Wallace, H. Simpson, Performance evaluation of the T6 ion engine, J.
AC C
306
M AN U
305
Propul. Power 28 (2012) 371–379.
[7] C. D. Child, Discharge from hot CaO., Phys. Rev. 32 (1911) 492-511. [8] Irving Langmuir, The effect of space charge and initial velocities on the potential distribution and thermionic current between parallel plane electrodes, Phys. Rev. 21 (1923) 419-435. [9] D. M. Goebel, I. Katz, Fundamentals of Electric Propulsion: Ion and Hall Thrusters, John Wiley & Sons, 2008, pp. 429–446. [10] Kimiya Komurasaki, Yoshihiko Arakawa, Performance calculation of Hall thrusters, Acta Astronaut. 38 (1996), 185-192. [11] N. Koch, H. P. Harmann, G. Kornfeld, Development and test status of the THALES high efficiency multistage plasma (HEMP) thruster family, in Proceedings of the 29th International Electric Propulsion Conference, Princeton, USA (2005), IEPC Paper No. 2005-297. [ 12 ] Gerd Krülle, Monika Auweter-Kurtz, Akihiro Sasoh, Technology and Application Aspects of Applied Field Magnetoplasmadynamic Propulsion, J. Propul. Power 14 (1998), 754-763.
15
ACCEPTED MANUSCRIPT
[13] Carlos M. Xisto, José C. Páscoa, Paulo J. Oliveira, Numerical analysis of real gas MHD flow on two-dimensional self-field MPD thrusters, Acta Astronaut. 112 (2015) 89-101. [14] Richard R. Hofer, Peter Y. Peterson, Alec D. Gallimore, A High Specific Impulse Two-Stage Hall Thruster with Plasma Lens Focusing, in Proceedings of the 27th International Electric Propulsion Conference, Pasadena, USA (2001), IEPC Paper No. 2001-036.
RI PT
[15] Grishin, S. D., Erofeev V. D., Zharinov A. V., Naumkin V. P., Safronov I. N., Characteristics of a two-stage ion accelerator with an anode layer, J. Appl. Mech. Tech. Phys. 19 (1978) 166-173.
[16] Xu Zhang, Hong Li, Liqiu Wei, Yongjie Ding, Zhongxi Ning, Daren Yu, Effect of double-stage discharge on the performance of a multi-mode Hall thruster, Vacuum 131 (2016) 312-318.
[17] E. Ahedo, F. I. Parra, A model of the two-stage Hall thruster discharge, J. Appl. Phys. 98 (2005) 023303.
SC
[18] Shaowei Qing, Peng E, Guangqing Xia, Ming-Chun Tang, Ping Duan, Optimized electrode placement along the channel of a Hall thruster for ion focusing, J. Appl. Phys. 115 (2014) 033301.
[19] M. V. Silnikov, K. S. Kulakov, S. L. Kulakov, and D. V. Panov, “Correction thruster development based on high-current surface discharge in vacuum,” Acta Astronaut. 109 (2015) 177-181.
M AN U
[20] Adam Shabshelowitz, Alec D. Gallimore, Performance of a Helicon Hall Thruster Operating with Xenon, Argon, and Nitrogen, J. Propul. Power 30 (2014) 664-671.
[21] S. Harada, T. Baba, A. Uchigashima, S. Yokota, A. Iwakawa, A. Sasoh, T. Yamazaki, H. Shimizu, Electrostatic acceleration of helicon plasma using a cusped magnetic field, Appl. Phys. Lett. 105 (2014) 194101.
[22] A. Uchigashima, T. Baba, D. Ichihara, A. Iwakawa, A. Sasoh, T. Yamazaki, S. Harada, M. Sasahara, T. Iwasaki, Anode geometry effects on ion beam energy performance in helicon electrostatic thruster, IEEE. Trans. Plasma Sci. 44 (2016) 306–313. [23] J. A. Simpson, Design of retarding field energy analyzers, Rev. Sci. Instrum. 32 (1961) 1283–1293.
TE D
[24] M. L. R. Walker, R. R. Hofer, A. D. Gallimore, Ion Collection in Hall Thruster Plumes, J. Propul. Power 22 (2006) 205-209. [25] Alec D. Gallimore, Near- and Far-Field Characterization of Stationary Plasma Thruster Plumes, J. Spacecraft Rockets 38 (2001) 441-453.
[26] Rohit Shastry, Richard R. Hofer, Bryan M. Reid, Alec D. Gallimore, Method for analyzing E×B probe spectra from Hall thruster plumes, Rev. Sci. Instrum. 80 (2009) 063502.
EP
[27] Homer D. Hagstrum, Auger Ejection of Electrons from Tungsten by Noble Gas Ions, Phys. Rev. 15 (1954) 325-335. [28] D. Renaud, D. Gerst, S. Mazouffre, A. Aanesland, E×B probe measurements in molecular and electronegative plasmas, Rev. Sci. Instrum. 86 (2015) 123507.
58-70.
AC C
[29] E. O. Johnson and L Malter, “A Floating Double Probe Method for Measurements in Gas Discharge,” Phys. Rev. 80 (1950)
[30] Brian A, Smith and Lawrence J. Overzet, “Improvements to the floating double probe for time-resolved measurements in pulsed rf plasmas,” Rev. Sci. Instrum 69 (1998) 1372-1377. [31] James M. Hass and Alec D. Gallimore, “Considerations on the Role of the Hall Current in a Laboratory-Model Thruster,” IEEE. Trans. Plasma Sci. 30 (2002) 687–697.
[32] J. P. Sheehan, N. Hershkowitz, “Emissive probes,” Plasma Sources Sci. Technol. 29 (2011) 063001. [33] A. Fruchtman, D. Zoler, and G. Makrinich, “Potential of an emissive cylindrical probe in plasma,” Phys. Rev. E 84 (2011) 025402. [34] T. Shoji, Y. Sakawa, S. Nakazawa, K. Kadota, T. Sato, Plasma production by helicon waves, Plasma Sources Sci. Technol. 2 (1993) 5-10. [35] Jean-Pierre Boeuf, Tutorial: Physics and modeling of Hall thrusters, J. Appl. Phys. 121 (2017) 011101.
16
ACCEPTED MANUSCRIPT
[36] N. Oudini, G. J. M. Hagellar, J. P. Boeuf, L. Garrigues, Physics and modeling of an end-Hall (gridless) ion source, J. Appl. Phys. 109 (2011) 073310. [37] Sang-Wook Kim, Alec D. Gallimore, Plume Study of a 1.35-kW SPT-100 Using an E×B probe, J. Spacecraft Rockets 39 (2002) 904-909. [38] Ira Katz, Richard R. Hofer, Dan M, Goebel, Ion Current in Hall Thrusters, IEEE T. Plasma Sci. 36 (2008) 2015-2024.
RI PT
[39] Youbong Lim, Holak Kim, Wonho Ghoe, Seung Hun Lee, Jongho Seon, Hae June Lee, Observation of a high-energy tail in ion energy distribution in the cylindrical Hall thruster plasma, Phys. Plasmas 21 (2014) 103502. [40] Brayan Michael Reid, Ph.D thesis, University of Michigan, MS, 2009.
[41] Yoshiki Yamagiwa, Kyoichi Kuriki, Performance of Double-Stage-Discharge Hall Ion Thruster, J. Propul. Power 7 (1991)
AC C
EP
TE D
M AN U
SC
65-70.
17
ACCEPTED MANUSCRIPT
Highlights RF/electrostatic hybrid thruster has been developed with matched power balance. Even a small RF power efficiently enhances the ion beam current and energy. An excessively high RF power leads to an unfavorable increase in an ionization cost.
AC C
EP
TE D
M AN U
SC
RI PT
The thrust efficiency has a maximum at RF to DC power ratio from 0.6 to 1.0.