1 JSTS 　　　Vol. 25,　 No. 2

Research and Development of Plasma Simulation Tools

in JEDI/JAXA

Takanobu MURANAKA*, Iku SHINOHARA*, Ikkoh FUNAKI*, Yoshihiro KAJIMURA*, Masakatsu NAKANO**, and Ryoji TAKAKI*

* Japan Aerospace Exploration Agency, Sagamihara, Kanagawa 252-5210, Japan.

** Tokyo Metropolitan College of Industrial Technology, Tokyo 116-0003, Japan Tel: +81-50-3362-4363, Fax: +81-42-759-8405

E-mail: muranaka.takanobu@jaxa.jp

Abstract Activity on numerical plasma simulations by JAXA’s Engineering Digital

Innovation (JEDI) Center is overviewed. Currently, R&D of two major numerical tools is conducted. First one is spacecraft charging analysis tool that can compute charging status of a spacecraft solving charged particle motions precisely. Using this information, we can evaluate onboard measurement of electrostatic probes or consider better configuration of onboard equipment of a spacecraft. Computation example of the interactions between solar wind plasma and a solar sail is shown in this paper. Second one is a numerical tool called JIEDI (JAXA's Ion Engine Development Initiative), which aims to reduce the cost and the time required for an ion thruster life test. The JIEDI tool can numerically estimate ion bombardment to an ion thruster’s grid material to predict the erosion rate of the grid material, and preliminary analysis by the JIEDI tool showed good agreement with the real-time life test of a microwave ion thruster.

Nomenclature

A : relevant area of current collection, m2

!

B : magnetic field, T C : capacitance, F dt : temporal width, s dx

: spatial grid size, m

!

E : electric field, V/m

!

e : elementary electric charge, C I : current, A J : current density, A/m2 k : Boltzmann constant, J/K

!

m : mass of a particle, kg n : number density of charged particle, m-3

!

q : charge of a particle, C T : temperature of charged particle, K t : time, s V : voltage, V

!

v : velocity of a particle, m/s

Vs : floating potential of a spacecraft, V

Vp : ambient plasma potential, V X : coordinate and grid number in X-axis

!

x : position of a particle, m Y : coordinate and grid number in Y-axis Z : coordinate and grid number in Z-axis ε0 : permittivity of vacuum, F/m

!

" : electric potential, V

ρ : charge density, C/m3 ωpe : electron plasma frequency, s-1

Subscripts e : electron i : ion j : particle index

net : net value of the physical property ph : photoelectron SC :spacecraft

ⓒ Japanese Rocket Society

2

1. Introduction

JAXA's Engineering Digital Innovation Center (JEDI) center aims at contributing to space development by applying information technology and simulation technology. The development of plasma simulation tool is one of R&D topics in JEDI/JAXA, and currently, two research projects are conducted as shown in Fig. 1. First one is the development of a spacecraft charging analysis tool that can compute charging status of a spacecraft solving charged particle motions precisely. Spacecraft charging is a crucial issue for satellite engineers because charging-arcing problem could cause a serious accident including a total loss of a spacecraft. Numerical software had been developed in order to analyze spacecraft charging quantitatively in its orbit environment. NASCAP-2k (Ref. 1) in U.S., SPIS (Ref. 2) in Europe are the next-generation charging analysis tools in the world. In Japan, Kyushu Institute of Technology and JAXA had developed the spacecraft charging analysis tool called MUSCAT (Ref. 3). MUSCAT computation provides us charging status of a spacecraft at Geosynchronous Orbit (GEO), Low Earth Orbit (LEO), and Polar Orbit (PEO). The latest version of MUSCAT is designed so that we can estimate the differential voltage of a spacecraft, the difference between spacecraft body potential and local insulator potential, with a commercial workstation (Ref. 4). For a space science mission or a recent space exploration mission, however, precise charged particle distribution and the potential structure in the vicinity of a spacecraft are required. The space potential measurement by the GEOTAIL spacecraft in the magnetosphere, 10-3 V/m order of the electric field should be measured between the spacecraft body and the probe sensor onboard it (Ref. 5). Meanwhile, interactions between spacecraft and solar wind plasma should be studied for some of the spacecraft payload design for the next-generation interplanetary-flight spacecraft such as a solar sail (Ref. 6, 7) and a solar power sail (Ref. 8) consisting of a huge membrane. In order to contribute to these space missions, we have developed an electrostatic full particle code that can compute precise charged particle motions and electrostatic potential including spacecraft potential. In this paper, we introduce the present status of the code: numerical feature, validation of the code for its fundamental functions, spacecraft-plasma interaction analysis of a solar sail assuming the IKAROS spacecraft (Ref. 9) in chapter 2.

The development of a computer tool for ion thruster is the next topic in this paper. Currently, ion thrusters are frequently used for North-South orbit control of geostationary satellite and also for orbital transfers. In

Fig. 1. R&D of plasma simulation tools in JEDI/JAXA.

Ion Engine System

Spacecraft-Plasma Interactions

Exp.

Sim.Vs.

JIEDI Tool

Spacecraft Charging Analysis Tool

•  R&D for Ion Engine grid system •  Ion beam trajectories in the ion thruster •  Ion thruster life test by the evaluation of

Grid erosion

•  Spacecraft charging •  Spacecraft payload design •  Onboard Electrostatic

potential measurement

Computer Simulation for Spacecraft R&D

Space science mission

Deep space exploration

3 JSTS 　　　Vol. 25,　 No. 2

JAXA, asteroid sample return mission HAYABUSA (Ref. 10) and Engineering Test satellites (ETS-6 (Ref. 11), Communications and Broadcasting Engineering Test Satellite (COMETS)(Ref. 12), and ETS-8 (Ref. 13)) succeeded in on-orbit operation of ion thruster systems, and a variety of future space missions are planned such as super low altitude satellite (Ref. 14), Mercury explorer (BepiColombo), and HAUABISA follow-on missions (Ref. 15). For these missions, ion thrusters greatly contribute to shorten mission trip time, or to increase a payload ratio. The thrust created in ion thrusters is, however, very small compared to conventional chemical rockets. Accordingly, to take advantage of ion thruster’s high specific impulse and high efficiency, long operation more than 10,000 hours is required. The cost for a lifetime qualification test of an ion thruster is hence quite high, and this situation prevents quick development and introduction of an optimal ion thruster for a specific mission. If numerical simulation can replace some of ion thruster’s life tests, cost and time for the development of an ion thruster can be drastically reduced. Following this concept, numerical tools for the lifetime evaluation of ion thruster’ ion optics were studied by researchers (Ref. 16-24). Nevertheless, it is still challenging for these numerical tools to serve as a design tool because the physical model to accurately predict the lifetime is not established. Under these circumstances, the development of a numerical tool called JIEDI (JAXA’s Ion Engine Development Initiative) started in JEDI/JAXA to assess the lifetime of the acceleration grid of an ion thruster within affordable computational resources and computational time. In the present paper, development status of the JIEDI tool is described in chapter 3. 2. Spacecraft Charging Simulations by Full Particle-in-cell Code 2.1 Fundamental Features of the Charging Analysis Code We have developed a three dimensional electrostatic full-Particle-In-Cell (full-PIC) code to compute the charging status of a spacecraft with the precise charged particle motion around the spacecraft. In the computation, we solve the electrostatic field consistent in the charged particle profile as a result of charged particle motions at each numerical step, which means no robustness is included in the computation. We compute charged particles originated not only in the space environment but also spacecraft surface such as photoelectrons. The spacecraft potential is calculated from the total charge onto the spacecraft surface obtained by the sum of each current component onto it. The saturation value of the spacecraft potential is determined when the net current onto the spacecraft becomes zero at the potential. The basic equations for the computation are as follows. The equation of motion of the charged particles is explicitly described as,

d 2 !x jdt2

=qjmj

!E + !vj !

!B( )

d !x jdt

= v!j

. (1)

Three-Dimensional PIC method (Ref. 25) is adopted to exchange quantities between individual particles and the electrostatic field to solve the equation of motion. We only update the electrostatic field in Eq. (1), as mentioned before, that is self-consistent with the charged particle motion. The static magnetic field in the equation is determined as the initial condition of the numerical system. The electrostatic potential in the numerical system is obtained to solve the Poisson equation,

!"0#2$ = % . (2)

Equation (2) is computed by the Fast Fourier Transform (FFT) method under the Dirichlet boundary condition, that is, the electrostatic potential at the boundary is fixed to be zero. The electric field is determined by the gradient of the electric potential as follows,

!

! E = "#$ . (3)

The surface potential corresponds to the electric charge on the spacecraft is determined to solved the following tensor equation,

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5 JSTS 　　　Vol. 25,　 No. 2

2.2 Code Verification for Fundamental Functions We verified the fundamental solver functions using a simple cubic conductor model focusing on the current collection onto the cubic conductor (spacecraft) surface and the computation of the electrostatic field. Here, we introduce the comparison of the numerical and theoretical results for the saturation value of the floating potential and the spatial distribution of electrostatic potential under thin-sheath plasma condition. Those comparisons under the thick-sheath plasma condition are shown in Ref. 27. The thin-sheath plasma condition corresponds to a Low-Earth-Orbit (LEO) plasma environment in space, where the Debye length of the ambient plasma is much smaller than the scale length of a spacecraft. In the LEO plasma environment, the Debye length is of the order of 10-3 m, meanwhile the spacecraft scale length is of the order of 1.0 m. Table 1 shows the calculation parameters used in this simulation. The plasma in the numerical domain is spatially uniform at initial time step, and its velocity distribution is determined by the Maxwell-Boltzmann distribution. The ions and electrons flow into the system from the outer boundary with their thermal flux. The number of computation particle was each 16/cell for electrons and ions.

Table 1. Computation Parameters for Thin-Sheath Plasma Environment.

plasma density, m-3 3x1012 plasma temperature, eV 2 ion mass ratio (Xe) 240516 Debye length, m 6.0x10-3 numerical domain, grid 64x64x64 cubic conductor model size, grid 10x10x10 grid size, m 7.0x10-3 time width, s 3.0x10-9

Figure 4 (a) shows the time evolution of the floating potential and current components of the ambient ions and electrons. The numerical result shows that the saturation value of the floating potential Vs is -9.6 V in Fig. 4 (a), and we can also recognize the plasma oscillation in the temporal profile of Vs. The periods of electron and ion plasma oscillations are 6.43x10-8 s and 3.15x10-5 s, respectively. In the simulation, the Debye length is almost the same size as dx, and the one side of the conductor cube is 10 times of dx. Figure 4 (b) shows that the sheath is formed around the conductor whose thickness is about 2 times of dx. The saturation value of the ion current in Fig. 4 (a) increases up to about 3 times of its initial thermal current. It is considered that the increase of the ion current is due to a three-dimensional expansion of the current collection area as a result of the sheath around the model. If we assume that the surface is nearly planar relative to the sheath dimensions, the floating potential is obtained from the current balance between conserved ion thermal flux and decreased electron one at the floating potential,

j0i + j0e exp !e(Vp !Vs )

kTe

"

#$

%

&' = 0

, (5) where j0e and j0i are given by the following equation as particle velocity vector follows Maxwell-Boltzmann distribution,

j0e,i = ene,i kTe,i / 2!me,i . (6) Considering the plasma potential to be zero, then the floating potential is described as follows,

Vs = ! kTe / e( ) ln mi / me( )1/2 . (7) We obtain Vs of -12.40 V from Eq. (7) as the theoretical value from the thin-sheath limited condition. Although the numerical result of that does not completely agree with the theoretical one, we can simulate the sheath with reasonable thickness, and the current collection. We consider that the difference of Vs obtained

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by the computation and the theoretical estimation is arisen by the three-dimensional effect on the current collection mentioned before. (a) (b) Fig. 4. (a) Temporal evolution of the floating potential of the conductive cube model and the currents of ambient ions and electrons onto the cubic conductor (spacecraft) surface, (b) Numerical result of the spatial distribution of the electric potential on the YZ-plane. 2.3 Application of the Charging Analysis Code to the Spacecraft R&D in JAXA We aim to apply our code to spacecraft research and development (R&D) e.g. spacecraft payload design, and validation of onboard scientific instruments in terms of interactions between charged particles and a spacecraft. First we had applied this tool to simulate an onboard electric field measurement probe (Ref. 28) whose mechanism is based on a Langmuir probe. We also applied this code to evaluate the correlation between spacecraft potential and the photoelectron energy distribution function in the Earth’s tenuous magnetospheric plasma (Ref. 29). The correlation was studied to evaluate the observation data by the GEOTAIL spacecraft (Ref. 30). In this subsection, we will introduce the numerical analysis of the electrostatic potential structure around a solar sail as an application of the charging analysis code to the R&D of a next-generation spacecraft for interplanetary flight. 2.3.1 Analysis of Electrostatic Potential Structure around Solar Sail Solar sail is a next-generation spacecraft that is regarded as a candidate for interplanetary flight. Solar sail consists of a strong large membrane that is typically made of metal-coated polymer material. The conductive surface of the membrane reflects the solar radiation, which results in converting the solar radiation pressure into the spacecraft thrust. If the electricity of a solar sail is supplied by solar cells, this type of a solar sail is called solar power sail. Today, JAXA had launched the IKAROS spacecraft (Ref. 9), the first demonstration spacecraft of solar power sail, in May 2010 into the Venus transfer orbit. The IKAROS spacecraft, its picture is shown in Fig. 5, had achieved the interplanetary flight for more than 12 months for May 2011. The scale of the membrane is estimated from 10 x 10 m2 to 100 x 100 m2 to obtain sufficient thrust from the solar radiation pressure, (e.g. 10-6 Pa at 1.0 AU). During interplanetary flight, a solar sail is exposed to the solar wind plasma whose density and temperature vary depending on the solar activity and the distance from the sun. Photoelectron current from the sunlit surface of a spacecraft that is the dominant current source in the environment also varies depending on the solar flux intensity. In addition to the Debye length of the solar

Z, grid

Y, g

rid

!, V

7 JSTS 　　　Vol. 25,　 No. 2

wind plasma is comparable to the scale of the sail, the charged particle profiles such as the photoelectrons are unique around a solar sail. Hence, the sail is expected to have the significant potential structure in the vicinity of itself. Therefore, it is of importance to study the potential structure around the sail for its payload design, such as the locations of scientific instruments and solar arrays. Garrett and Minow had provided an overview on the charging issue of solar sails (Ref. 31) in the solar wind and in the ionosphere. We tried a further investigation of the interactions between charged particles and a solar sail by using our full-PIC charging analysis code. The analyses were performed focusing on the potential structure around the sail including the space charge effect of photoelectrons as well as the solar wind. We also performed charging analysis using MUSCAT, a spacecraft charging analysis software, to estimate the differential voltage between the local insulator component and the body potential of the spacecraft. Here, we will report the characteristics of the charged particle profiles and the potential structure around a solar sail, which will be of importance for a solar sail or a solar power sail payload design.

Fig. 5. Picture of the Solar Power Sail “IKAROS”. The shape of the membrane is a 14 m-square. 2.3.2 Characteristics of Interactions between Solar Sail and Solar Wind Plasma The first order estimation of the plasma interaction with a solar sail can be determined by assuming the sail as a thin conducting aluminum sheet. The floating potential of the solar sail relative to the ambient solar wind plasma is determined so that the net current onto the sail is equal to zero at a body potential of the sail (Ref. 31, 32),

Inet (Vs ) = 0= Ie + Ii + I ph= !Ae " Je(Vs,Te,ne )+ Ai " Ji (Vs,Ti,ni )+ Aph " Jph (Vs,Tph, Jph0 ) . (8)

Equation (8) only includes the current balance between ambient solar wind plasma and photoelectron. Other current sources such as secondary electron are neglected in this study. We can easily estimate each current component in Eq. (8) considering the characteristic parameters of the solar wind plasmas and the solar sail geometry at zero potential of the spacecraft. For typical solar wind plasma at 1.0 AU whose density is 6x106 m-3 and temperature is 10 eV with the drift velocity of 470 km/s, the thermal velocities for the electron and ion (H+) are 1.87x106 m/s and 4.37x104 m/s, respectively. Thus, the current density of the thermal electron onto a solar sail can be estimated as 5.08x10-7 A/m2 by the following equation (Ref. 33),

Je = !e "ne "

14(8kTe /!me )

1/2

, (9) for ions, on the other hand, we can simply estimate the current density as 4.51x10-7 A/m2 by the product of its charge, density and drift velocity because the drift velocity is much greater than the thermal velocity.

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Meanwhile, the photoelectron current density for aluminum at 1.0 AU is of the order of 10-5 A/m2 that is about 100 times greater than the electron and the ion current densities. Hence, the floating potential of the solar sail saturates at a positive potential as a result of the current balance described Eq. (8). The spacecraft at a positive potential is shielded by the ambient electrons and its characteristic scale is almost comparable to the solar sail IKAROS. Figure 6 shows the schematics showing the steady state of the charged particle distributions around a solar sail and potential structure. In the upstream region of the sail, existence of the photoelectron cloud would affect the potential structure. In the downstream region, an ion wake is formed and that will make a wake potential.

Fig. 6. Schematics of the charged particle profiles and the potential structure around a solar sail. 2.3.3 Numerical Analysis of Interactions between Solar Sail and Solar Wind Plasma We performed numerical experiments in order to determine the charged particle profiles and the potential structure around a solar sail in 1.0 AU solar wind plasma environment using a three-dimensional electrostatic full PIC code that we had developed. The motion of individual ions and electrons is explicitly solved, and the electrostatic field is computed self-consistently in the charging analysis code. We focused on the quantitative analyses of the charging status of a solar sail, space charge effect of the photoelectrons in the upstream region, and wake potential in the downstream region. The differential voltage on the downstream insulator surface of the sail was optionally computed using MUSCAT. Table 2 shows the computation parameters and Fig. 7 shows the numerical domain of the simulation. The plasma parameters used are also shown in Table 2. The sail is assumed an aluminium conductor plate whose area is of 14x14 m2 and thickness is of 0.5 m. The thickness of the sail model is comparable with the Debye length of the photoelectrons but much smaller than

Fig. 7. Numerical domain of the full-PIC charging analysis for a solar sail.

Ele

ctric

Pot

entia

l

x

0

Solar Flux Solar Wind

2) Ion wake

1) Electron sheath

3) PhotoelectronsSolar Sail (@ positive potential)

Space charge effect Wake

potentialconductor

insulator

Overall of Spatial Profilesinsulator charging

9 JSTS 　　　Vol. 25,　 No. 2

that of the ambient plasma. The direction of solar flux and the ambient plasma flow is normal to the surface of the sail in this simulation. As simplicity, we neglect ambient magnetic field. The emitting photoelectrons are considered to have double Maxwellian distribution as a better representation of the distribution in tenuous plasma environment (Ref. 29, 30).

Table 2. Numerical parameters used in the charging analysis of solar sail.

plasma density, m-3 6x106 plasma temperature, eV 10 plasma drift velocity, km/s 470 photoelectron (PE) current flux, µA/m2 40 PE1 temperature, eV 1.5 PE2 temperature, eV 5.0 flux ratio, PE1:PE2 9:1 ion mass ratio (H) 1836 numerical domain, grid 256x128x128 solar sail (Al plate) size, grid 1x28x28 grid size, m 0.5 time width, s 1.0x10-7 ωpe dt 0.0138

In this solar wind plasma environment at 1.0 AU, the Debye length of the plasma is 9.6 m that is corresponding to 0.69 times the scale of the sail. The ratio of the solar wind drift velocity to the ion thermal velocity is 10.8. Figure 8 shows the numerical results of the spatial distribution of the charged particles: (a) ambient electrons, (b) ambient ions, (c) photoelectrons, and (d) the electric potential at 2500 time steps. The saturation value of the floating potential of the sail is determined to be +8.3 V by the computation. A large

(a) (b)

(c) (d)

Fig. 8. Spatial distributions of the charged particles and the electric potential around the solar sail at 1.0 AU at 2500 time steps. The open rectangular located at the center of each contour graph represents the solar sail. Contours show (a) the number density of the ambient electrons, (b) the ambient ions, (c) the photoelectrons and (d) electric potential in XY-plane at Z=64. The electric potential is obtained relative to the boundary of 0 V.

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ion wake structure is formed in the downstream region of the sail as shown in Fig. 8 (b). The number density of the ambient electrons shown in Fig. 8 (a), on the other hand, decreased in the vicinity of the sail and in the wake region, although degradation of the density is much smaller than that of the ions. A wake potential whose minimum value is -3.0 V is formed due to the difference of the charge density between ions and electrons shown in Fig. 8 (d). We can see the photoelectron cloud of its scale is comparable to the sail whose density is more than that of the ambient electrons. The dense layer of the photoelectron in the vicinity of the sunlit surface is observed whose density is of 100 times greater than that of the ambient electrons. The emitted photoelectrons from the upstream surface diffuse around the sail even to the surface although the negative wake potential obstructs the diffusion shown in Fig. 8 (c). We had determined the space charge effect of the photoelectron cloud on the potential structure around the sail by the comparative computations with or without photoelectron emission. The computation without photoelectrons was performed at the fixed spacecraft potential of +6.2 V that had been obtained as the floating potential of the sail by the computation using the single Maxwellian photoelectrons whose temperature was 1.5 eV. Figure 9 shows the one-dimensional distributions of the electric potential with or without photoelectron emission in X-axis at Y=Z=64 at 3000 steps. The significant potential drop is shown with photoelectron emission in the region between X=80 and X=131 compared to the result without photoelectron emission. (Note that the location of the photoelectron emitting surface in the upstream region is X=131.) It is assumed that the photoelectron cloud can lead to the reduction of the electron sheath, in other words, the compression of the potential near the sail. Fig. 9. One-dimensional distributions of the electric potential of the solar sail with or without photoelectron emission in X-axis at Y=Z=64 at 3000 steps. A robust charging analysis to estimate the differential voltage on the insulator surface of the sail had been made using MUSCAT, a spacecraft charging analysis software. We obtained the differential voltage of -15 V on the insulator surface of Kapton® whose relative dielectric constant and thickness are of 3.5 and 7.5x10-6 m, respectively. Although the magnitude of the differential voltage is not serious for charging-arcing problem, the differential voltage would affect the wake potential and suppress the diffusion of the photoelectrons to the downstream region. 3. Tool for Life Time Evaluation of Ion Thruster (JIEDI Tool) 3.1 Ion Thruster’s Ion Optics and its Physical Modeling

An ion thruster uses positively charged ions as a propellant. These ions are exhausted from the thruster at

sail location

solar wind solar flux

grid number

11 JSTS 　　　Vol. 25,　 No. 2

an extremely high speed by accelerating them through an electrostatic field. Due to electrostatic acceleration, an ion thruster can easily create high-velocity ions (> 30 km/s) so that high specific impulse (> 3,000s) much larger than that of chemical thrusters (typically ~310s) is possible. To produce ions, xenon gas is introduced into an ion source (ionization chamber) like the one shown schematically in Fig.10, where the gas is ionized when absorbing microwave power. These ions are then accelerated through an electrostatic field created by charged plates that have many holes in them. The positively charge plate is referred to as the “screen” grid, the negatively charge plates referred to as the “accelerator” grid, and the last grid (“decelerator” grid) is equal to the engine’s ground. These grids are sometimes referred to as ion thruster’s “ion optics”. Ion optics geometry of for µ10 (Hayabusa’s ion thruster) is shown in Fig. 10b), and 1/12 model of a single grid hole is illustrated in Fig. 11.

Fig. 10. Schematic diagram of microwave ion thruster and its ion optics.

To evaluate the lifetime of ion thruster’s ion optics, the JIEDI tool performs a “numerical wear test”

for a single pair of grid aperture. Numerical procedure is summarized in Fig. 12. After initial mesh is prepared by GRID-SHAPE routine, OPT-J in the JIEDI tool first of all model ion beamlet trajectories through a single pair of grid apertures in the self-consistent electric potentials found by solving Poisson’s equation. In addition to high-energy ions from the upstream boundary, OPT-J treats

Upstream Plasma

Ion Beam

Downstream Beam Plasma

Beam Emitting Surface (Sheath)

Pote

ntia

l

distance in beam direction

Net Voltage for Acceleration

Total Voltage

Screen grid (!3.0mm) Accelerator

Grid (!1.8mm)

0

b)

Decelerator Grid (!2.4mm)

SmCo Magnet Rings

Ion Beam

Circular Waveguide

Antenna

Circular Waveguide (Al)

! 45mm

Fe-Yoke

Xe

Ion Source

Neutralizer

Electron

Microwave

Screen Grid

DC Break

DC Break

ECR line

Accelerator P.S.

Screen P.S.

C/C Grids ! 100mm

Decelerator Accelerator

XeCoaxial Cable

trapped electron in mirror magnet

e

Microwave

a)

Magnified view of single aperture

Fig. 11. Computational domain of µ10 ion thruster’s ion optics.

The mesh is generated by Pro-STAR, which is a commercial pre-post processor of STAR-CD.

12

ions/neutrals generated by elastic scattering as well as charge exchange collisions in a grid aperture to account for the impingement of both ions and neutrals (Ref. 19, 34). Using OPT-J, ion beam trajectories and potential distribution are calculated for initial grid geometry at the beginning of thruster operation (0 hour). When a focused ion beamlet is properly formed, no impingement on grid surface is expected, but when some ions/neutrals are generated in the grid aperture due to collisions and hit the walls of grid apertures, the wall surfaces are eroded. Such ions/neutrals impinging on each grid wall are estimated based on the results of OPT-J. After this calculation, the amounts of grid erosion after 1,000-hours are evaluated, and consequently, the shape of grid after 1,000-hours of operation is decided by the GRID-SHAPE routine. In the next step, another mesh is generated by the Pro-STAR, and erosion rate calculation of each grid is repeated to estimate the grid shape at 2,000-hours. In order to evaluate the lifetime of the ion thruster, this kind of evaluation should continued until the grid aperture is severely eroded and the shape is considerably changed from beginning-of-life (BOL). When performance of ion thruster is considerably degraded from BOL, the thruster encounters its end-of-life (EOL).

To estimate an erosion rate accurately, the physics associated with grid erosion by ions/neutrals should be carefully included. The physical processes included in the JIEDI tool are schematically explained in Fig.13 (Ref. 35). Among these processes, ion collision with particles and walls are of importance. As for ion collision with particles, the elastic scattering and charge-exchange collisions were incorporated and their reaction rates were evaluated using the number density of neutrals, the primary ion beam current and its velocity, and the reaction cross sections. The number density of neutrals is determined using Direct Simulation Monte Carlo (DSMC) method for a rarefied flow. The ion and neutral beams produced by elastic scattering and charge-exchange collisions are moved using the same technique as that for the primary ion beams. They are tracked until they escape from the simulation domain or collide with one of the grid surfaces. When a beam impacts a grid surface, the sputtered grid mass and the injection directions of the sputtered grid materials are calculated using the differential sputtering yield, which is a function of the energy of a sputtering ion (or neutral) and its

Fig. 12. Outline of numerical wear test by JIEDI tool.

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angle to the grid surface. For a carbon/carbon composite grid system, the sputter yield of Williams et al (Ref. 36, 37). was used. Sputtered grid materials are also traced until they hit a grid surface or escape from the computational domain. When the sputtered grid materials hit a grid surface, some of the materials stick to the grid surface. The ratio of sticking materials to materials hitting a grid surface is called “redeposition rate” in this paper. The redeposition rate of sputtered C/C materials was taken as 0.78 from the study by Marker et al (Ref. 38).

Fig. 13. Erosion mechanism in ion thruster’s ion optics.

3.2 Calculation of Grid Erosion by JIEDI Tool A numerical wear test is conducted for ion optics of µ10 ion engine. As shown in Fig.10, the hole

diameters were different for each grid: 3.0 mm for the screen grid, 1.8 mm for the accelerator grid, and 2.4 mm for the decelerator grid. About 700 holes (grid apertures) were located in a 3.5-mm pitch on flat, circular plates, 150 mm in diameter and 1 mm in thickness. Spacing between the grids was kept at 0.35 mm for the accelerator-screen grids gap and 0.5 mm for the accelerator- decelerator grids gap. The screen grid was biased to +1500 V with respect to ground, and the accelerator grid was set to

350 V, and the decelerator grid is equal to the engine’s body. Results for µ10’s engineering model (110 mA beam current for Xe propellant) are provided in Figs.14, 15 and 16. See Ref. 39 for detail of experimental conditions. Figure 14 (a) is an electric potential distribution (upper) and ion beam trajectories (lower) at 0 hour (when ion thruster’s operation started). After 20,000 hours of continuous operation, the ion beam trajectories are significantly diverged as indicated by the white dotted circle in Fig.14 (b). Here, accelerator grid is the key component to properly focused ion trajectories, and beam divergence is as a result of eroded acceleration grid.

Figure 15 shows the geometry of the screen, accelerator, and decelerator grids at the beginning of operation (0 hour) and after 20,000-hours operation, where black indicates a high surface erosion rate and white represents a low erosion rate. The screen grid experiences almost no erosion, whereas the accelerator and decelerator grids are substantially eroded, and as a result, the grid aperture after 20,000 hours is expanded like a horn towards the downstream direction. To see if the grid surface erosion rate is simulated correctly, the time history of accelerator grid mass change in µ10 ion thruster (Ref. 39) is plotted in Fig.16. It should be noted that wear test condition in Fig.16 is switched at 2,700 hours in the experiment: the potential voltage of the screen grid is given as 1.0 kV from 0 to 2700 hours, and then, after 2700 hours, the potential voltage of the screen grid is given as 1.5 kV. Due to this change of operational parameter, grid weight change shows rather peculiar curve, and it is not a monotonic profile. As for numerical wear test, the solid line in Fig.16 indicates the simulation result for the redeposition rate of 0.78, the dotted line indicates the case without redeposition. Simulation result considering redopisition shows fairly good agreement with the experimental results whereas the

14

case without redeposition is considered to show the most eroded profile, i.e., the worst scenario. Selecting parameters such as the redeposition rate is therefore significantly for evaluating the grid erosion rate, and they should be carefully checked before the code servers as a design tool.

(a) (b) Fig. 14. Numerical wear test of ion optics by using JIEDI tool (µ10 ion thruster EM). (a) Electric potential distribution (upper) and ion beam trajectories (lower) at the beginning of operation (0 hour), (b) Electric potential distribution (upper) and ion beam trajectories (lower) after 20,000 hours of operation.

0 hr 20,000 hrs Fig. 15. Side views of the calculated grid in each grid surface and the contour plot of erosion rate (/m2·s) (Ref. 40).

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4. Summary and Future Plan

Full particle-in-cell simulation tools are developed to evaluate spacecraft charging phenomena associated with JAXA’s space missions. Full particle simulation gives us information on precise charged particle profiles and electrostatic potential structure around a spacecraft as well as the charging status of a spacecraft. The information is of importance for charged particle related scientific instruments and payload design of a spacecraft. We introduced the application of the charging analysis code to these analyses for a solar sail to contribute payload design of a future solar power sail that will have electric devices such as solar cells, scientific instruments, and ion engines. We found that the thin dense layer of photoelectrons in front of the sunlit surface of a solar sail, and rear insulator charging as a result of an ion wake should be especially considered for a payload design although charging itself was not serious. In near future, we will introduce following functions for further utilities of the code: 1) adopting a graphical user interface to the parameter input to reduce the user’s effort, 2) applying a multi-grid system to handle a multi-scale density of plasmas efficiently. Also, JEDI/JAXA develops a numerical tool called JIEDI (JAXA's Ion Engine Development Initiative). The JIEDI tool is to be used for qualification processes of ion thruster’s ion optics; it is anticipated in the near future that combination of a limited duration test (2,000-3,000 hours) and a numerical wear test by the JIEDI tool will replace a full-time (> 10,000 hours) endurance test of an ion thruster. For that purpose, numerical accuracy, robustness, and computer resources required for the tool must be intensively tested. It is shown in this paper that the full life-test result of a microwave ion thruster (µ10 engineering model) was successfully reproduced by the JIEDI code. For further improving accuracy, the following revision to the code are now in progress: 1) to incorporate a new and accurate low-energy sputtering model, 2) replacing computational domain to full three-dimensional geometry of a single grid aperture to evaluate the effect of misalignment, and 3) proper error analysis to indicate 3σ of numerical wear tests. To perform a numerical wear test, current JIEDI tool takes only one week using an entry-class personal computer, so drastic reduction in cost and time is possible in comparison with full-time endurance tests.

Fig. 16. Time history of accelerator grid mass change per hole in the case of µ10 ion thruster's engineering model with and without redeposition effect; γ=0.2 is doubly charged ions ratio (Ref. 40).

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Acknowledgements This study is supported by JAXA's Engineering Digital Innovation (JEDI) Center. The authors are grateful to Dr. Hiroko O. Ueda of MUSCAT Space Engineering, Co. Ltd., Prof. Masaki Okada of National Institute of Polar Research, and Prof. Hideyuki Usui of Kobe University for their contributions to the development of the full-PIC charging analysis code. The authors would like to acknowledge the contributions to the JIEDI tool development from Prof. Hitoshi Kuninaka of JAXA, Prof. Yoshinori Nakayama of National Defense Academy of Japan, Prof. Toru Hyakutake of National Yokohama University, Prof. Takeshi Miyasaka of Gifu University, Dr. Yasushi Okawa of JAXA, Profs. Motoi Wada and Takanori Kenmotsu of Doshisha university, and Prof. Tetsuya Muramoto of Okayama university of science. References 1) Mandell, M. J., Davis, V.A., Cooke, D. L. and Wheelock, A.T., NASCAP-2k Spacecraft

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