Full PIC Simulation of Ion Beam Neutralization
Hideyuki Usui, Akihiko Hashimoto and Yohei Miyake

Graduate School of System Informatics, Kobe University, 1-1 Rokkoudai, Nada, Kobe 657-8501, Japan
1Introduction

Ion beam emission and its neutralization by thermal
electrons in electric propulsion is one of the most fundamental
problems in spacecraft plasma interactions. By emitting thesame amount of electrons as the beam ions, the charge
neutralization can be basically achieved in the spacecraft
environment. However, because of large difference between
electron and ion dynamics, the understanding of theneutralization process remains at a rather primitive level.
Although the previous works handled uniform ion beam which
has an infinite cross section[1,2], we consider a situation inwhich an ion beam is emitted with a finite radius from aspacecraft[3-6] and simultaneously thermal electrons are
released from a different position from the ion emitter [3] for thecharge neutralization. Our focus is on the transient process ofelectron mixing and trapping in the ion beam region in the very
vicinity of the ion engine. To examine the transient process indetail, we performed Particle-In-Cell[7] simulations in which
both electrons and ions are treated as macro-particles. In Section
2, we introduce our simulation model and parameters used in thesimulations. In Section 3, we show some results obtained in thesimulation in terms of electron dynamics in the ion beam region.
Section 4 contains a summary.
2Simulation Model

To examine the detail of electron dynamics in the ion beam
region in the vicinity of spacecraft, we performed full ParticleIn-Cell simulations by using our original simulator software
called “EMSES”[8] which we developed for the analysis ofspacecraft plasma environment. Like other conventional PIC
simulation codes, EMSES basically solves Maxwell’s equationfor electromagnetic fields and the equation of motion for a large
number of macro-particle with the FDTD scheme. One of theunique features of EMSES is that it can define some internal
conduction boundaries which correspond to spacecraft surfaceand solve interaction with the surrounding plasma. Figure 1
shows the simulation model for the current study. The locationsof ion beam emitter and electrons neutralizer are separate. To
keep the charge neutrality inside the spacecraft, total fluxes ofion beam and thermal electrons are the same to each other. The
ratio of the electron thermal velocity to the ion beam velocity isInjection Plane
Electron
2cm×2cm
Ion
10cm×10cm

Z

0.54 m108 Grids

Electrons
Ion beamO

0.54 m108 Grids

Y
1.08 m
216 Grids

X

Fig. 1 Simulation model

1.25. The ion thermal velocity is much lower than the ion drift
velocity. In such a situation, we are interested in the transient
response of emitted electrons to the ion beam in the vicinity ofion engine.
3Transient Response of Electrons

We show some snapshots of charge densities measured on ax-z plane including the ion beam. The ion beam basically
propagates away from the emitter as time elapsed. Althoughsome diffusion of ions is seen at the beam front as in the bottom
panel, the ion beam propagation is generally simple and straightbecause of ion's large inertia. On the contrary, emitted electrons
show very complex signature of density as shown in the rightpanels. Thermal electrons are emitted from the upper side of theyellow body representing an ion engine. The emitted electrons
are overall attracted to the ion beam and propagate along with
the ion beam propagation in the x direction. Most of theelectrons are trapped by positive potential created by the ion
beam. Nevertheless the density profile is not uniform orasymmetric with respect to the ion beam axis. Non-uniform
density profiles of electrons are caused by the dynamic electron
response to the ion beam. As soon as electrons are emitted fromthe neutralizer they are quickly attracted to the core of the ion
beam and are initially accelerated to the negative z direction.
Then most of them penetrate the core part of the ion beam.
However, when they pass through the beam, the electrons aredecelerated, stagnate, and are accelerated again toward the ionbeam. In such a manner, the emitted electrons, which basically
propagate with the beam in the x direction, oscillate in the z
direction. One of the interesting points seen in the panels is thatthe electron density values are relatively high at the surface
surrounding the ion beam. Since the potential has a peak at thecore of the ion beam, electrons are accelerated to the beam coreand pass the center of the beam at the maximum velocity. Oncethey pass the beam core, they start to be decelerated and finallystagnate at the other side of beam surface. This stagnation cancause relatively high density near the surface of the ion beam.
The electrons again start to be accelerated back to the beam coreby the electric field and this process seems repeated multiple
times before the electrons reach at the beam front. In figure 3,
we plot a contour map of normalized electrostatic potential andthe corresponding electron dynamics in a x-Vx phase space.
Because of large electron thermal velocity the ion beam region
is not perfectly neutralized and has slightly positive potential as
shown in the upper panel. By the presence of the positive
potential region, most of the electrons are electrostaticallytrapped. As shown in the lower phase diagram of Fig. 3,electrons emitted from the neutralizer are quickly accelerated
along the beam direction and some electrons escape from thebeam front. However, the most electrons are quickly decelerated
at the beam front and move back to the opposite direction to thebeam propagation. Although not displayed in a figure, a profileof distribution function of the electron velocity along the beam
direction measured near the beam front is not a single
Maxwellian but consists of two components. One has positive
velocity and its peak has three times larger than the ion beam
velocity. The other has negative velocity reflected back at theIons

Electrons pe t  100

 pe t  150

 pe t  250

 pe t  350

Fig.2 Normalized densities of ion beam and thermal electrons measured on a x-z plane including the ion beam propagation
at different times.
ion beam front. The velocity difference between the peaks of thetwo components seems larger than the width of each distributionfunction. In such a situation, electron two-stream type instability
may occur near the beam front and causes the local
enhancement of the electric field and eventually electron heating.
Moreover, there may be some interactions between a cold ion
beam and the accelerated electrons stated above. However, since
the trapped electrons basically move back and force in thepotential well of ion beam multiple times, the electron
distribution tends to be smeared out and the clear velocity
function which has two peaks can be seen only near the beam
front. In such a situation, no two-stream instability may be
expected because, according to the linear theory, the mostunstable electrostatic mode has a wavelength which is much
longer than the region where the above velocity distribution isformed.
4Conclusion

We have been studying the transient behavior of electrons
emitted for ion beam neutralization in electric propulsion by
performing full PIC simulations with EMSES. We found someinteresting signature of electrons in the neutralization process toion beam. Unlike simple dynamics of ion beam, the behavior ofthermal electrons emitted from the neutralizer is very complex.
They basically propagate along with the ion beam to neutralize
the positive charge. However, in the beam region, electrons areelectrostatically trapped and move back and forth in the both
directions parallel and perpendicular to the beam propagation.
This complex trapping motion of electrons directly causes theelectrostatic heating of electrons or the increase of the electron
temperature just outside the ion acceleration grid of ion engine.
Although counter-streaming electron components are found in
the present case, no plasma instability may be expected becausesuch unstable velocity distribution is formed only near the ion
beam front. We need further analysis on this point.
Acknowledgements
The computation in the present study was performed with
the KDK system of Research Institute for Sustainable
Human sphere (RISH) at Kyoto University.

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[2]
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Fig 3. A contour map of normalized electrostatic
potential on a x-z plane including the ion beam propagation(Upper panel) and the corresponding electron dynamics in ax-Vx phase space (lower panel).

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