1

Numerical Analysis of a Miniature Microwave Discharge Ion Thruster

Using Water as Propellant

By Kengo NAKAMURA,1) Hiroyuki KOIZUMI,2) and Yoshinori TAKAO3)

1)Department of Systems Integration, Yokohama National University, Yokohama, Japan

2)Department of Advanced Energy, The University of Tokyo, Tokyo, Japan 3)Division of Systems Research, Yokohama National University, Yokohama, Japan

We propose a small ion thruster using water as the propellant, which can remove the high-pressure gas storage system. Since the detail of the discharge characteristics is not well known yet, we have investigated the characteristics under various absorbed power conditions using three-dimensional particle-in-cell method with Monte Carlo collisions (PIC/MCC) for the kinetics of charged particles, finite-difference time-domain method (FDTD) for the electromagnetic fields of microwaves, and a finite element analysis for magnetic fields of permanent magnets. The numerical results indicate that the electron density, the potential, and the electron temperature are the highest near the ECR region, and higher absorbed power is required compared with the results using xenon as the propellant in order to obtain similar electron density.

Key Words: Ion Thrusters, PIC/MCC, Water, ECR discharge

Nomenclature

B : magnetic field E : electric field : electrostatic potential : charge density

0 : permittivity of free space

r : relative permittivity

0 : magnetic permeability of free space j : plasma current density m : mass P : power q : charge v : velocity x : position t : time n : density

eT : electron temperature Subscripts

ES : electrostatic EM : electromagnetic ST : magnetostatic abs : absorption e : electron i : ion

1. Introduction

Commercial use of CubeSats by which the development costs and terms can be reduced has been increased recently. Even deep space exploration missions can be carried out by CubeSats1) or microspacecraft.2) However, CubeSats have limits of weight, volume and power, it is required that thrusters mounted on them must be miniaturized significantly. Ion

thrusters can be one of the candidates for a small and high-performance propulsion system. The research and demonstration of a miniature propulsion system for 50-kg-class microspacecraft such as HODOYOSHI-4, which mounted a miniature ion propulsion system (MIPS), were conducted in Japan in 2014. The MIPS employs electron cyclotron resonance (ECR) discharges with ring-shaped permanent magnets for ion source and neutralizer.3–5) Since the MIPS utilizes xenon as the propellant so do the conventional ion thrusters, the gas storage and feed system occupy most weight of the spacecraft, which is difficult to be miniaturized further. Then, we propose a small ion thruster using water as liquid propellant, which can remove the high-pressure gas storage system. The preliminary operation of the thruster was already demonstrated by the University of Tokyo,6) while the details of the discharge characteristics are not well known yet. In this study, we have analyzed discharge characteristics of water using three-dimensional particle simulations to optimize the discharge conditions, to investigate the dependence on the absorbed power, and to compare with the previous results which used xenon as the propellant.

Fig. 1. Calculation flow of PIC/MCC simulation.

STEMESqdt

dm BνEE

v

Move particles

ii vv 'Monte Carlo collisions

0 ESE

Poisson’s eq. for

xqnSkji ,,

Obtain charge densityand plasma currents

Microwave electric field

Magnetostastic field

Initial conditions

ESE

EME

STB

t

2

2. Numerical model 2.1. Configuration Figure 1 shows the flow chart of the simulations. We have employed three-dimensional particle-in-cell methhod with Monte Carlo collisions (PIC/MCC) to analyze the kinetics of charged particles, together with finite-difference time-domain method (FDTD) for the microwave elecrtomagnetic field EEM, and the finite element analysis software, ANSYS EmagTM for the magnetostatic field of the permanent magnets BST as shown in Fig. 2.

Figures 3 (a) and (b) show the calculation model, where the size of the discharge chamber is 20 × 20 × 4 mm3 with the ring-shaped antenna located at z = 1.0 mm. The inside of the coaxial waveguide is filled with the dielectiric of boron nitride (BN). The microwave power is fed to the ring antenna through the four spokes. It should be noted that the BN region is also included in the electromagnetic field calculation of microwaves, although the simulation area for the motion of charged particles is only the plasma region.

2.2. Numerical assumptions The present model has the following assumptions.

i). Only singly-ionized water H2O+ and electrons are treated as particles

ii). Neutral particles are spatially and temporally uniform with a Maxwellian distribution at a gas temperature of 300 K in the plasma region.

iii). The reactions between charged particles and neutrals are elastic, excitation (including rotation and vibration), and ionization collisions for electrons. On vibrational excitation of water molecule, the cross sections of the stretching modes and the bending mode have been taken into account.7) We have not considered collisions for ions.

OH+eOH+e 22 (Elastic). *

22 OH+eOH+e (Excitation). eOH+eOH+e 22 (Ionization). iv). The magnetic fields of microwaves are negligibly small

compared with the magnetostatic fields BST. v). The motion of excited-state atoms is not considered.

vi). Coulomb collisions are not taken into account. vii). Since the power of microwaves is low in this simulation,

the plasma current is neglected.8)

2.3. Electrostatic field The electrostatic field EES is given by

,ES E (1)

with the potential . The potential is derived from the space charge of charged particles. The Poisson’s equation is given by

,

,,,,

02

2

2

2

2

2

zyx

zyxzyx

(2)

where is the charge density, 0 is the permittivity of free space. Eq. (2) is solved by using the method of successive-over-relaxation (SOR) with boundary conditions of zero potential at all the walls. Once the potential is obtained, the electrostatic field is determined by the central difference from the potential. To decrease a numerical noise, we apply a digital smoothing to the space charge.9)

2.4. Electromagnetic field The electromagnetic fields of microwaves are obtained by solving Maxwell’s equations using FDTD method.

,EM t

BE (3)

,EM

0r0

t

EjB (4)

where B is the magnetic fields of microwave, j is the plasma current density, r is the relative permittivity, and is the magnetic permeability of free space. We set the relative permittivity r = 1.0 for the plasma, and r = 4.5 for the dielectric of BN. 2.5. Motion and collisions of charged particles The equations of motion for charged particles are described as

,STEMES BvEEv

m

q

dt

d (5)

,v

x

dt

d (6)

Fig. 2. Contour plot at the z-y plane of the strength of the magnetic field

by the ring-shaped permanent magnets, together with the thick lines in red

representing the resonant magnetic field of 0.15 T for 4.2 GHz microwaves.

z (mm)

y(m

m)

0 1 2 3 4-10

-8

-6

-4

-2

0

2

4

6

8

10

0.55

0.45

0.35

0.25

0.15

0.05

|B| (T)

(a) (b)

Fig. 3. Schematic diagrams of calculation model: (a) Side view (z-y/x

plane at x/y = 0 mm) and (b) Front view (x-y plane at z = 1.0 mm).

3

where q is the charge, m is the electron/ion mass, v is the velocity of charged particles. Equations (5) and (6) are solved by leap-frog method and Buneman-Boris method.10) In order to reduce calculation time, we employ the null-collision method in MCC with cross sections for electrons.11) We use fully absorbing walls as the boundary condition for both electrons and ions, so that all electrons and ions disappear at the walls and antenna. 2.6. Numerical initial conditions

In this simulation, the grid space is set at 0.1 mm. The time

steps for FDTD is Δ tEM = 1.49 × 10−13 s (1/1600 of a microwave cycle for 4.2 GHz). The time steps for PIC/MCC are Δ te = 5.95 × 10−12 s (1/40 of a microwave cycle) for electrons, and Δti = 2.38 × 10−10 s (one microwave cycle) for ions. Initial conditions are shown in Table 1. Corresponding to a mass flow rate of 35 g/s, we set the neutral gas pressure in discharge chamber 6.30 mTorr.6)

3. Results and Discussion 3.1. Discharge field at the z-y plane We have investigated the distributions of the electron density, the potential, and the electron temperature. In order to reduce the calculation time, we have conducted the simulation for a quarter region of the calculation model. Figures 4 (a)–(c)

(a) 3.0 W (b) 3.0 W (c) 3.0 W

(d) 5.0 W (e) 5.0 W (f) 5.0 W

Fig. 4. Time-averaged distributions of (a) the electron density, (b) potential, (c) electron temperature at Pabs = 3.0 W, (d) electron density (e) potential

(f) electron temperature at Pabs = 5.0 W at the z-y plane for a quarter region.

z(mm)

y(mm)

0 1 2 3 40

2

4

6

8

10ne(1017/m3)

2.92.72.52.32.11.91.71.51.31.10.90.70.50.30.1

z(mm)

y(mm)

0 1 2 3 40

2

4

6

8

10

48464442403836343230282624222018161412108642

(V)

z(mm)

y(m

m)

0 1 2 3 40

2

4

6

8

10Te(eV)

181716151413121110987654321

z(mm)

y(m

m)

0 1 2 3 40

2

4

6

8

10ne(1017/m3)

2.92.72.52.32.11.91.71.51.31.10.90.70.50.30.1

z(mm)

y(m

m)

0 1 2 3 40

2

4

6

8

10

48464442403836343230282624222018161412108642

(V)

z(mm)

y(m

m)

0 1 2 3 40

2

4

6

8

10Te(eV)

181716151413121110987654321

Table 1. Initial conditions for water as the propellant.

Microwave frequency 4.2 GHz

Plasma density 1.0 ×1016 m−3

Neutral gas pressure 6.30 mTorr

Neutral temperature 300 K

Electron temperature 2.0 eV

Ion temperature 0.05 eV

Absorbed power 3.0 W, 5.0 W

4

(a) 3.0 W (b) 5.0 W

Fig. 5. Distributions of electron density at (a) Pabs = 3 W, (b) Pabs = 5 W at x-y plane at z = 2.3 mm for a quarter region.

x(mm)

y(m

m)

-10 -5 0 5 10-10

-5

0

5

10

ne(1017/m3)

2.1521.851.71.551.41.251.10.950.80.650.50.350.20.05

x(mm)

y(m

m)

-10 -5 0 5 10-10

-5

0

5

10

ne(1017/m3)

3.12.92.72.52.32.11.91.71.51.31.10.90.70.50.30.1

(a) 0.3 W (b) 0.3 W (c) 0.3 W

(d) 0.7 W (e) 0.7 W (f) 0.7 W

Fig. 6. Time-averaged distributions of (a) electron density, (b) potential, (c) electron temperature at Pabs = 0.3 W, (d) electron density (e) potential (f)

electron temperature at Pabs = 0.7 W at the z-y plane for all region, where xenon is employed as the propellant.

z (mm)

y(m

m)

0 1 2 3 4-10

-8

-6

-4

-2

0

2

4

6

8

10

2.3

2.1

1.9

1.7

1.5

1.3

1.1

0.9

0.7

0.5

0.3

0.1

ne (1017 m-3)

z (mm)

y(m

m)

0 1 2 3 4-10

-8

-6

-4

-2

0

2

4

6

8

10

27

25

23

21

19

17

15

13

11

9

7

5

3

1

(V)

z (mm)

y(m

m)

0 1 2 3 4-10

-8

-6

-4

-2

0

2

4

6

8

10

15

13

11

9

7

5

3

1

Te (eV)

z (mm)

y(m

m)

0 1 2 3 4-10

-8

-6

-4

-2

0

2

4

6

8

10

2.3

2.1

1.9

1.7

1.5

1.3

1.1

0.9

0.7

0.5

0.3

0.1

ne (1017 m-3)

z (mm)

y(m

m)

0 1 2 3 4-10

-8

-6

-4

-2

0

2

4

6

8

10

27

25

23

21

19

17

15

13

11

9

7

5

3

1

(V)

z (mm)

y(m

m)

0 1 2 3 4-10

-8

-6

-4

-2

0

2

4

6

8

10

15

13

11

9

7

5

3

1

Te (eV)

5

and (d)–(f) show the results at z-y plane for Pabs = 3.0 W and 5.0 W, respectively. Here, the results are averaged over 50000 microwave cycles. As the absorbed power increases, maximum values of the electron density and the potential increased, and the area of high electron temperature expanded. Peak value of electron density was located at z = 2.3 mm, which is near the ECR region, and the electron temperature was more than 17 eV at the area. We consider that the ionization reactions occur in the arcuate high temperature region since the threshold energy of ionization is 13.76 eV. Moreover, the electrons move along the magnetic field lines due to confinement by the mirror magnetic fields, so that it is considered that the arcuate high electron temperature region is formed. 3.2. Distribution of the electron density at the x-y plane We have investigated the time-varying distribution of the electron density. The results in this section were averaged over 100 microwave cycles. Figures 5 (a) and (b) show the distributions of electron density for Pabs = 3.0 W and 5.0 W for x-y plane at z = 2.3 mm, where the peak value of electron density was observed for the z-y plane. These distributions indicate that the electron density becomes the highest in the ECR region near the antenna with an outer diameter of 5.6 mm. Furthermore, we found the characteristic structures such as rotating stripe and gear shape patterns. As the absorbed power increases, these characteristic structures appeared more clearly. In addition, we also found these structures in the distribution of the potential and electron temperature. 3.3. Comparison with the result for xenon propellant

In the previous study, we have used xenon as the propellant. 12,13) In the previous simulation, we treated all region for the grid space of 0.2 mm and a quarter region for the grid space of 0.1 mm. The time steps for FDTD are ΔtEM = 2.98 × 10−13 s (1/800 of a microwave cycle for 4.2 GHz) for 0.2 mm, and ΔtEM = 1.49 × 10−13 s (1/1600 of a microwave cycle) for 0.1 mm. The time steps for PIC/MCC are Δte = 5.95 × 10−12 s (1/40 of a microwave cycle) for electrons and Δti = 2.38 × 10−10 s (one microwave cycle) for ions. Initial conditions are shown in Table 2. Moreover, Corresponding to a mass flow rate of 35 g/s, we set the neutral gas pressure in discharge chamber 1.0 mTorr. Figures 6 (a)–(c) and (d)–(f) show the distributions of the electron density, the potential, and the electron temperature for xenon at z-y plane for Pabs = 0.3 W and 0.7 W, respectively.12) Comparing Figs. 4 and 6, the value of the potential differs by about twice. The absorbed power is more required when water is used as the propellant, in order to obtain the same order of the electron density. We consider that there are three possible reasons of this difference: (i) cross section, (ii) the potential, and (iii) the electron temperature. While xenon is a monoatomic molecule, water is a polyatomic molecule. For polyatomic molecule, it is necessary to consider rotational and vibrational excitation, which cause a lot of loss at low energy.14) Due to the high potential for water, we consider that more ions have reached the Bohm velocity. Hence, more ions in the water case are lost to the wall than in the xenon case. Ionization energy of water is 13.76 eV, while that of xenon is 12.13 eV. These are nearly the same ionization energy. However, the area of high electron temperature for water is wider than that for xenon. Hence, we consider that more energy is required for water to maintain the plasma. At the x-y plane, using xenon as the propellant, we also found the characteristic structures shown in Fig. 7.13) This is similar to the result using water as the propellant. In future works, we will analyze this structure. 4. Conclusion In this study, we have conducted the analysis of discharge characteristics of water as the propellant using three-dimensional particle simulations (PIC/MCC) for a miniature microwave discharge ion thruster. As a result, it is found that the electron density, the potential, and the electron temperature have maximum values in the ECR region near the antenna. Compared with xenon as the propellant, in order to obtain the same electron density, the absorbed power is more required. In addition, we observed the rotating stripe patterns for both water and xenon. In future work, we will also consider ion species such as OH+, H+ and so on, because we assumed that ion species produced by ionization was only H2O+ in the present study. Acknowledgments This work was supported in part by JSPS KAKENHI Grant Number JP16H06370. Part of the computer simulation was

Fig. 7. The distribution of electron density using xenon as the

propellant at Pabs = 0.3 W at x-y plane at z = 2.0 mm for a quarter region.

x(mm)

y(mm)

-10 -5 0 5 10-10

-5

0

5

10

ne(1017/m3)

21.851.71.551.41.251.10.950.80.650.50.350.20.05

Table 2. Initial conditions for xenon as the propellant.

Microwave frequency 4.2 GHz

Plasma density 1.0 ×1016 m−3

Neutral gas pressure 1.0 mTorr

Neutral temperature 300 K

Electron temperature 2.0 eV

Ion temperature 0.05 eV

Absorbed power 0.3 W, 0.7 W

6

performed on the KDK computer system at Research Institute for Sustainable Humanosphere, Kyoto University.

References

1) Mars Cube One (MarCO) Mission Overview, NASA JPL, http://www.jpl.nasa.gov/cubesat/missions/marco.php (accessed December 14, 2016)

2) Koizumi, H., Kawahara, H., Yaginuma, K., Asakawa, J., Nakagawa, Y., Nakamura, Y., Kojima, S., Matsuguma, T., Funase, R., Nakatsuka, J., and Komurasaki, K.: Initial Flight Operations of the Miniature Propulsion System Installed on Small Space Probe: PROCYON, Trans. JS A SS, Aerospace Tech. Japan, 14. ists30 (2016), pp. Pb_13-Pb_22.

3) Kuninaka, H., Nishiyama, K., Funaki, I., Yamada, T., Shimizu, Y., and Kawaguchi, J.: Powered Flight of Electron Cyclotron Resonance Ion Engines on Hayabusa Explorer, J. Propul. Power, 23 (2007), pp. 544-551.

4) Kuninaka, H. and Satori, S.: Development and Demonstration of a Cathodeless Electron Cyclotron Resonance Ion Thruster., J. Propul. Power., 14 (1998), pp. 1022-1026.

5) Koizumi, H. and Kuninaka, H.: Miniature Microwave Discharge Ion Thruster Driven by 1 Watt Microwave Power, J. Propul. Power., 26 (2010), pp. 601-604.

6) Nakagawa, Y., Kawahara, H., Koizumi, H., and Komurasaki, K.: Fundamental Experiments with Liquid Propellants for the Microwave-discharge Ion Thruster, Space Propulsion 2016, Roma, Italy, SP2016-312540, 2016.

7) Yousfi, M. and Benabdessadok, M.D.: Boltzman equation analysis

of electron-molecule collision cross sections in water vapor and ammonia, J.Appl. Phys., 80 (1996).

8) Takao, Y., Eriguchi, K., Ono, K., Sugita, Y., Koizumi, H., and Komurasaki, K.: A Validation Study of a 3D PIC Model for a Miniature Microwave Discharge Ion Thruster, 50th AIAA/ASME/SAE/ASEE Joint Propulsion Conf., AIAA-2014-3829, 2014.

9) Veboncoeur, J. P.: Particle simulation of plasmas: review and advances, Plasma Phys. Control. Fusion, 47 (2005), pp.A231–A260.

10) Birdsall, C. K. and Langdon, A. B.: Plasma Physics via Computer Simulation, IOP Publishing, Bristol, U. K., 1991.

11) Vahedi, V. and Surendra, M.: A Monte Carlo collision model for the particle-in-cell method: applications to argon and oxygen discharges, Comput. Phys. Commn., 87 (1995), pp. 179-198.

12) Takao, Y., Koizumi, H., Komurasaki, K., Eriguchi, K., and Ono, K.: Three-dimensional particle-in-cell simulation of a miniature plasma source for a microwave discharge ion thruster, Plasma Sources Sci. Technol., 23 (2014), pp. 064004-1-11.

13) Hiramoto, K., Nakagawa, Y., Koizumi, H., Komurasaki, K., and Takao, Y.: 3D Particle Simulation for Electron Extraction Mechanisms of a Miniature Microwave Discharge Neutralizer, 52nd AIAA/SAE/ASEE Joint Propulsion Conference, Salt Lake City, USA, AIAA 2016-4946, 2016.

14) Itikawa, Y. and Nigel, M.: Cross Sections for Electron Collisions with Water Molecules, J. Phys. Chem., 34 (2005), pp. 1-22.