1

Effect of Improvement in Neutral Depletion on Propulsion Performance

in Electrodeless Thruster

By Kazuki TAKASE,1) Kazunori TAKAHASHI,2) and Yoshinori TAKAO3)

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

2)Department of Electrical Engineering, Tohoku University, Sendai, Japan 3)Division of Systems Research, Yokohama National University, Yokohama, Japan

The effect of neutral gas injection from downstream side of the thruster is numerically investigated by two-dimensional axisymmetric particle-in-cell simulations with Monte Carlo collisions algorithm (PIC/MCC) for charged particles, and direct simulation Monte Carlo (DSMC) for neutrals. In this paper, we have employed an improved calculation model (downstream-expansion model), and compared with the results of the previous model (fully-closed model) to perform quantitative evaluations of the effects of gas injection. The numerical results show that the force to the lateral wall decreases in the improved model. Therefore, we overestimated the force in the previous model. However, the results with the improved model also show the tendency of the improvement of the propulsion performance with increasing downstream gas injection, indicating good agreement with experimental results qualitatively.

Keywords : Electric Propulsion, Helicon Plasma Thruster, Neutral Depletion, PIC/MCC, DSMC

Nomenclature

v : velocity x : position ρ : charge density j : plasma current density B : magnetic field E : electric field Q : neutral gas flow rate

Subscripts ex : external up : upstream down : downstream

1. Introduction

Researches of high-power electric thrusters have been performed owing to a trend of developing all-electric satellites and space probes in the world. For example, Boeing already developed a 5 kW-class XIPS mounted on 702SP,1) and JAXA has been developing 6 kW-class hall thrusters mounted on Engineering Test Satellite Ⅸ (ETS-Ⅸ).2) While this enlargement of existing thrusters is interesting, helicon plasma thrusters (HPTs),3,4) which consist of a high-density helicon plasma source and a magnetic nozzle, could be also one of the candidates for such thrusters. Since high density plasma is generated in HPTs, it is expected to generate large thrust. However, the propulsion performance of HPTs stays at low-level compared to conventional thrusters. We previously reported that the non-negligible momentum loss resulted from neutral depletion at downstream region of the thruster leads to the low performance from both the experiments and numerical simulations.5,6) Then, Takahashi et al.7) proposed that neutral

gas injection from not only upstream side but also downstream side of the thruster improves propulsion performance due to reduction of neutral depletion effect in their experiments. We also confirmed this effect from numerical simulation with a simple calculation model. 8) In this study, we have conducted further simulation with improved calculation models and compare the results. 2. Numerical model We have conducted two-dimensional axisymmetric particle-in-cell simulations with Monte Carlo collisions algorithm (PIC/MCC) for charged particles, and used the direct simulation Monte Carlo (DSMC) method for neutrals. In this section, we describe numerical model and condition for each simulation. 2.1. DSMC simulation In this simulation, only xenon atoms were treated as particles. The total gas flow rate was maintained at 0.1 sccm, and six types of flow ratios of upstream (Qup) to downstream (Qdown) gas injection were employed: only upstream, 20:1, 3:1, 1:1, 1:3, and 1:20. Since the mean free path is much larger than the size of the thruster, it is assumed that collisions between atoms are negligible. Detail simulation method, model and results are described in Ref. 9). 2.2. PIC/MCC simulation

Figure 1 shows a schematic of the calculation model for the PIC simulation. It is composed of the thruster, the double-turn rf antenna, and the solenoid coil. The size of thruster is 0.5 cm in radius and 3.0 cm in width. The center of rf antenna and solenoid coil is located at z =1.5 cm and 2.4 cm, respectively. Although we employed a fully-closed (FC) model in our previous paper,8) we have conducted the simulations using improved calculation model including the inside of the thruster

2

and its downstream region. Then we refer to the new model as a downstream-expansion (DE) model in this paper. Figure 2 shows a calculation flow for the PIC/MCC simulations. Since the detail calculation flow and method are described in Refs. 10–12), we describe those briefly here. Major calculation conditions are shown in Table 1. Moreover, we have conducted the simulations with the following assumptions:

i) Only singly-ionized xenon and electrons are treated as particles. The neutral distributions obtained from the DSMC simulation are fixed on the grids and no dynamics are taken into account in the PIC simulation.

ii) The reactions of charged particles are elastic and charge exchange collision for ions and elastic, excitation, and ionization collision for electrons.

iii) The boundary conditions of potential are zero at all the walls.

The total thrust for simple HPTs are defined as the sum of the

force to the back plate Ts, to the lateral wall Tw, and the Lorentz force onto the magnetic nozzle TB.13) In this simulation, we focus on Tw and Ts in order to evaluate propulsion performance. They are estimated by calculating only the ion momentum to the boundary in the simulation. 2.3. External magnetic field

We employed two types of external magnetic field strength Bex, which is 0 and 200 G at the solenoid center on z-axis. Figure 3 (a) shows the contour distribution of Bex and the magnetic field lines by solid lines. Axial magnetic field strength Bz on the central axis is also shown in Fig. 3 (b).

3. Results and discussion 3.1. Effect on the distribution of plasma density Figure 4 shows the distributions of electron density in steady state for each profile of Bex and gas injection ratio. These results indicate that the increase in Qdown lead to significant shifts of the plasma distribution to downstream region, and the increase in Bex also lead to concentration of the distribution to just beneath the electromagnetic coil and generation of higher density plasma. These results show a similar tendency of the FC model. In the recent experiment,14) applying strong magnetic field also led to shifts of the distribution from upstream to downstream. However, there was no remarkable change as shown in Fig. 4. It is considered that this difference is resulted from the present calculation model. As described above, the PIC/MCC and the DSMC simulations were conducted separately, where the neutral is fixed and not consumed when a high-density plasma is generated. Coupling between the PIC/MCC and the DSMC is left for an important issue to work on in the future. 3.2. Effect on propulsion performance Figure 5 shows Ts, Tw, and total thrust Tw+Ts for each gas injection ratio, where solid lines are the DE model and dashed lines are the FC model. As shown in Figs. 5 (a)-(b), although Ts is not significantly changed, Tw for Bex = 200 G becomes lower

Fig. 1. Schematic diagram of the simulation area for the PIC/MCC simulation.

Fig. 2 Flow chart of the PIC/MCC simulation.

0

0.5

3.00 6.0z (cm)

r (cm)

2.4

solenoidrf antenna

dielectric tubeback plate

Obtain charge density and plasma current

Solve Poisson Eq. to obtain electric and magnetic field

Collision with MCC

Move particles

𝒙,𝒗 → 𝜌, 𝒋

𝜌, 𝒋 → (𝑬,𝑩) (𝑬,𝑩) → 𝒗 → 𝒙

𝒗𝒊′ → 𝒗𝒊

Initial distribution of particles Neutral density distributionfrom DSMC simulation

External magnetic field 𝑩ex

Δ𝑡

Fig. 3 (a) External magnetic field strength Bex by solenoid coil in the simulation area (contour) and magnetic field lines (solid lines). (b) Axial magnetic field strength Bz on the central axis.

20 60 100 140 180 220

0 1 2 3 4 5 60

0.5

B (G)

0 1 2 3 4 5 60

50

100

150

200

radi

al d

ista

nce

r (cm

)

axial distance z (cm)

B (G

)

(a)

(b)

Table 1. Calculation conditions for PIC/MCC simulation.

RF frequency 80 MHz Initial plasma density 1.0×1017 m-3

The number of superparticles 1.5×106 Time step for ion 5.0×10-10 s

Time step for electron 5.0×10-12 s

Absorbed power 1.0 W Grid spacing 1.0×10-4 m

3

clearly. It is considered that we overestimated Tw in the FC model. The total thrust shown in Fig. 5 (c) also decreases with a decrease in the Tw for Bex = 200 G. However, a tendency that the downstream gas injection leads to the increase in total thrust agrees with the experimental results. 4. Conclusion We have conducted two-dimensional axisymmetric PIC/MCC simulations with an improved calculation model to perform more quantitative evaluations of the effects of the gas injection. Improvement of calculation model shows that the distribution of electron density expands to downstream region significantly. Moreover, it is found that we overestimated the force to the lateral wall Tw, in the previous model. However, the tendency that the downstream gas injection leads to the increase in total thrust agrees with the experimental result. 5. Acknowledgments This work was supported in part by JSPS KAKENHI Grant Number JP16H04084. Part of the computer simulation was performed on the KDK computer system at Research Institute for Sustainable Humanosphere, Kyoto University.

References

1) Feuerborn, S., Neary, D. and Perkins, J.: Finding a way: Boeing’s “All Electric Propulsion Satellite”, 49th AIAA/ASME/SAE/ASEE Joint Propulsion Conf., AIAA-2013-4126, 2013.

2) Funaki, I., Iihara, S., Cho, S., Kubota, K., Watanabe, H., Fuchigami, K. and Tashiro, Y.: Laboratory Testing of Hall Thrusters for All-electric Propulsion Satellite and Deep Space Explorers, 52nd AIAA/SAE/ASEE Joint Propulsion Conf., AIAA-2016-4942, 2016.

3) Chen, F. F.: Helicon discharges and sources: a review, Plasma Sources Sci. Technol., 24, pp. 014001-1-25, 2015.

4) Charles, C.: A review of recent laboratory double layer experiments, Plasma Sources Sci. Technol., 16, pp. R1-25, 2015.

5) Takahashi, K., Chiba, A., Komuro, A. and Ando, A.: Axial Momentum Lost to a Lateral Wall of a Helicon Plasma Source, Phys. Rev. Let., 114, pp. 195001-1-5, 2015.

6) Takao, Y. and Takahashi, K.: Numerical validation of axial plasma momentum lost to a lateral wall induced by neutral depletion, Phys. Plasmas, 22, pp. 113509-1-6, 2015.

7) Takahashi, K., Takao, Y., and Ando, A.: Modifications of plasma density profile and thrust by neutral injection in a helicon plasma

Fig. 4. Electron density distributions in steady state for each profile of Bex and Qup:Qdown = 20:1, 1:1, and 1:20.

0 1 2 3 4 5 60

0.5

0 1 2 3 4 5 60

0.5

0 1 2 3 4 5 60

0.5

0 1 2 3 4 5 60

0.5

0 1 2 3 4 5 60

0.5

0 1 2 3 4 5 60

0.5

axial distance z (cm)

radi

al d

ista

nce

r (cm

)

𝑛𝑒 (m−3)1E+16 1E+17 1E+18

0 G, 20:1 0 G, 1:1 0 G, 1:20

200 G, 20:1 200 G, 1:1 200 G, 1:20

Fig. 5 (a) The force to the back plate Ts, (b) the force to the dielectric wall Tw, and (c) the total thrust Tw+Ts as a function of gas injection ratio Qup:Qdown for each Bex. The solid lines are the results with the DE model, and dashed lines are those with the FC model.

× ××

×× ×

0

5

10

15

20

200 G

onlyupstream

20:1 3:1 1:1 1:3 1:20

0 G

Qup : Qdown

T s(µΝ)

× × ×× × ×

-5

0

5

10

15

20

25

30

200 G

onlyupstream

20:1 3:1 1:1 1:3 1:20

0 G

Qup : Qdown

T w(µΝ)

× × × × × ×

5

10

15

20

25

30

35

200 G

onlyupstream

20:1 3:1 1:1 1:3 1:20

0 G

Qup : Qdown

T w+

T s(µΝ)

(a)

(b)

(c)

4

thruster, Appl. Phys. Let., 109, pp. 194101-1-4, 2016. 8) Takase, K., Takahashi, K. and Takao, Y.: Numerical Analysis of

Electrodeless Plasma Thrusters Using a Two-dimensional Axisymmetric Particle Model, The 57th Conference on Aerospace Propulsion and Power, 2A09 (JSASS-2017-0061), 2017, (in Japanese).

9) Takase, K., Takahashi, K. and Takao, Y.: Effects of neutral distribution and external magnetic field on propulsion performance of electrodeless plasma thrusters, The 60th Space Sciences and Technology Conference, P21 (JSASS-2016-4690), 2016 (in Japanese).

10) Takao, Y., Sakamoto, M., Eriguchi, K., and Ono, K.: Investigation of Plasma Characteristics and Ion Beam Extraction for a Micro RF Ion Thruster, Trans. JSASS Aerospace Tech. Japan, 12, pp. Pb_13-

18, 2014. 11) Takao, Y., Eriguchi, K., and Ono, K.: Effect of capacitive coupling

in a miniature inductively coupled plasma source, J. Appl. Phys., 112, pp. 093306-1-10, 2012.

12) Takao, Y., Kusaba, N., Eriguchi, K., and Ono, K.: Two-dimensional particle-in-cell Monte Carlo simulation of a miniature inductively coupled plasma source, J. Appl. Phys., 108, pp. 093309-1-8, 2010.

13) Fruchtman, A., Takahashi, K., Charles, C. and Boswell, R. W.: A magnetic nozzle calculation of the force on a plasma, Phys. Plasmas, 19, pp. 033507-1-6, 2012.

14) Takahashi, K., Charles, C. and Boswell, R. W.: Approaching the Theoretical Limit of Diamagnetic-Induced Momentum in a Rapidly Diverging Magnetic Nozzle, Phys. Rev. Lett., 110, pp. 195003-1-5, 2013.