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Time-evolution of the ion velocity distribution function in the discharge of a Hall effect thruster


Abstract and Figures

The temporal characteristics of the Xe$^+$ ion axial Velocity Distribution Function (VDF) were recorded in the course of low-frequency discharge current oscillations ($\sim$~14 kHz) of the 5 kW-class PPS$\circledR$X000 Hall thruster. The evolution in time of the ion axial velocity component is monitored by means of a laser induced fluorescence diagnostic tool with a time resolution of 100 ns. As the number of fluorescence photons is very low during such a short time period, a hom-made pulse-counting lock-in system was used to perform real-time discrimination between background photons and fluorescence photons. The evolution in time of the ion VDF was observed at three locations along the thruster channel axis after a fast shut down of the thruster power. The anode discharge current is switched off at 2 kHz during 5 $\mu$s without any synchronization with the current oscillation cycle. This approach allows to examine the temporal behavior of the ion VDF during decay and ignition of the discharge as well as during forced and natural plasma oscillations. Measurements show that the distribution function of the axial component of the Xe$^+$ ion does change periodically in time with a frequency close to the current oscillation frequency in both forced and natural cases. The ion density and the mean velocity are found to oscillate whereas the velocity dispersion stays constant, which indicates that ionization and acceleration layers have identical dynamics. Finally, variations over time of the electric field are for the first time experimentally evidenced in a crossed-field discharge.
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arXiv:0902.1432v1 [physics.plasm-ph] 9 Feb 2009
Time-evolution of the ion velocity distribution function in the
discharge of a Hall effect thruster
S. Mazouffre, D. Gawron, N. Sadeghi,
February 9, 2009
ICARE, CNRS, 1C avenue de la Recherche Scientifique, 45071 Orl´eans, France.
LSP, Joseph Fourier University - CNRS, 140 Av. de la Physique, 38402 St Martin d’H`eres, France.
The temporal characteristics of the Xe+ion axial Velocity Distribution Function
(VDF) were recorded in the course of low-frequency discharge current oscillations (14 kHz)
of the 5 kW-class PPSrX000 Hall thruster. The evolution in time of the ion axial veloc-
ity component is monitored by means of a laser induced fluorescence diagnostic tool with
a time resolution of 100 ns. As the number of fluorescence photons is very low during
such a short time period, a hom-made pulse-counting lock-in system was used to perform
real-time discrimination between background photons and fluorescence photons. The evo-
lution in time of the ion VDF was observed at three locations along the thruster channel
axis after a fast shut down of the thruster power. The anode discharge current is switched
off at 2 kHz during 5 µs without any synchronization with the current oscillation cycle.
This approach allows to examine the temporal behavior of the ion VDF during decay and
ignition of the discharge as well as during forced and natural plasma oscillations. Mea-
surements show that the distribution function of the axial component of the Xe+ion does
change periodically in time with a frequency close to the current oscillation frequency in
both forced and natural cases. The ion density and the mean velocity are found to oscil-
late whereas the velocity dispersion stays constant, which indicates that ionization and
acceleration layers have identical dynamics. Finally, variations over time of the electric
field are for the first time experimentally evidenced in a crossed-field discharge.
Submitted to Physics of Plasmas
1 Introduction
A Hall Effect Thruster (HET) is a gridless ion accelerator that finds applications in the field
of spacecraft propulsion [1, 2]. Such a type of electric propulsive device is especially suited for
long duration missions and for maneuvers that require a large velocity increment. HETs are
at present mostly employed for geostationary communication satellite orbit correction and
station keeping. Other fields of application are envisaged for the near future. Low power
Hall thrusters seem suited for drag compensation of observation satellites that operate on a
low-altitude Earth orbit. The use of high power Hall thrusters for orbit raising and orbit
topping maneuvers of communication satellites would offer significant benefits in terms of
launch mass, payload mass and operational life. In addition, large Hall thrusters appear as
good candidates to be used as the primary propulsion engine for robotic space probes during
interplanetary journeys towards far-off planets and asteroids.
A Hall effect thruster is a low-pressure DC discharge in crossed electric and magnetic fields
configuration [2, 3, 4]. Xenon is generally used as a propellant gas due to its high atomic mass
and low ionization energy. A schematic of a HET is depicted in Fig. 1. The anode is located
at the upstream end of a coaxial annular dielectric channel that confines the plasma. The
cathode is situated outside. A set of coils combined with magnetic parts provide a radially
directed magnetic field Bof which the strength is maximum in the vicinity of the channel
exhaust. The magnetic field is chosen strong enough to make the electron Larmor radius much
smaller than the channel characteristic sizes, but weak enough not to affect ion trajectories.
The gas injected through the anode is ionized inside the channel by electron impacts. As the
magnetic field considerably slows down the electron motion towards the anode, the applied
potential concentrates in a restricted area at the channel entrance. The corresponding axial
electric field Ethen accelerates ions out of the channel, which generates thrust. The ion
beam is neutralized by a fraction of electrons emitted from the cathode. The crossed Eand
Bgeometry is at the origin of a large electron azimuthal drift – the Hall current – that is
responsible for the efficient ionization of the supplied gas. When operating near 1.5 kW, a
HET ejects ions at 20 km s1and generates 100 mN of thrust with an overall efficiency of
about 50 % [5].
It is well-established that the crossed-fields discharge of a Hall effect thruster is strongly
non-stationary [3, 6]. This specific type of magnetized plasma displays numerous types of
oscillations, which encompass many kinds of physical phenomena, each with its own length and
time scales [6]. Current and plasma fluctuations, of which the frequency range stretches from
10 kHz up to 100 MHz, play a major role in ionization, particle diffusion and acceleration
processes. Low-frequency plasma oscillations in the range 10-30 kHz, so-called breathing
oscillations, are especially of interest as they carry a large part of the power [7]. Breathing
oscillations find their origin in a prey-predator type mechanism between atoms and ions
as shown by Boeuf and co-workers [8]. In short, these oscillations originate in a periodic
depletion and replenishment of the neutrals near the exhaust of the thruster channel due to
the efficient ionization of the gas. The frequency is then linked to the time it takes for atoms
to fill in the ionization region. With an atom thermal speed of 300 m/s and a region size of
20 mm, one finds a frequency of 15 kHz. The breathing phenomenon not only disturbs the
discharge current but also has a strong impact on several quantities. The plume shape and
the ion beam divergence change during an oscillation cycle of the current as was shown by
means of CCD imaging [9]. A time variation of the ion beam energy in a Hall thruster far
field was evidenced using a retarding potential analyzer [11]. The electron density and the
plasma potential oscillate at low frequency [10]. Conversely, the electron temperature stays
unchanged. Oscillations of the aforementioned quantities are most likely connected with a
time variation of the potential distribution or, in other words, with the variation with time
of the accelerating electric field. Therefore, it appears of great interest to investigate the
temporal behavior of the electric field that certainly hides a rich and intricate dynamics.
Across the acceleration layer, the medium is collisionless, i.e. ion-ion and ion-atom collision
events are scarce. As a consequence, the electric field can be directly inferred from the Xe+
velocity which then becomes the quantity to be examined.
Laser Induced Fluorescence (LIF) spectroscopy in the near infrared has often been used in
the past few years to measure the time-averaged velocity distribution function (VDF) of Xe+
ions in the plasma of a Hall effect thruster [12, 13, 14, 15]. LIF spectroscopy is a non intrusive
diagnostic tool that enables an accurate determination of the local velocity of atoms along the
laser beam direction by measuring the Doppler shift of absorbed photons. The metastable
Xe+ion VDF is recorded by collecting fluorescence radiation at 541.9 nm after excitation
of the 5d 2F7/26p 2Do
5/2transition at λ= 834.7233 nm [14]. A phase sensitive detection
method is often used to capture the fluorescence signal. However, this method, which is
powerful enough for the extraction of a signal in an environment with a high background
noise level, offers a poor time resolution. To achieve the measurement of the time-resolved
Xe+ion VDF in the plasma of a Hall effect thruster, it is necessary to develop a bench able
to detect LIF photons with a time resolution around 1µs. In normal operating conditions
for a HET, the number of fluorescence photons observed at 541.9 nm with a continuous laser
beam tuned at 834.7233 nm with about 1 mW/mm2power density is on the order of 102per
µs. Under identical experimental conditions, the number of background photons generated
by the plasma at 541.9 nm during 1 µs is typically 1, which means a ratio of 100 between the
two signal amplitudes. The laser system must therefore be able (i) to detect a tiny amount
of photons hidden in a strong background (ii) to determine with a high accuracy the exact
moment in time fluorescence photons have been produced. One must therefore turn to a
photon-counting technique.
In this contribution, we present time-resolved measurements of the Xe+ion axial VDF in
the discharge of the 5 kW-class PPSrX000 Hall thruster fired at 500 V discharge voltage and
6 mg/s xenon mass flow rate. The evolution in time of the VDF was recorded at several loca-
tions during the transient regime that follows a fast anode discharge current ignition in order
to investigate the ion dynamics during forced and free low frequency current oscillations. The
current is switched off during 5 µs at a 2 kHz repetition rate without any synchronization with
the discharge current oscillation cycle. The outline of this paper is as follows. In Sec. 2, the
LIF optical assembly is described and the pulse-counting technique is introduced. Section 3
shows contour plots of the time-varying Xe+ion VDF as well as traces of various velocity
groups at the thruster outlet. In Sec.4, the temporal behavior of macroscopic quantities
like the density, the mean velocity and the velocity dispersion, is examined and discussed.
Section 5 reports on variation over time of the accelerating electric field in the crossed-field
discharge of a Hall thruster. Finally, concluding remarks will be presented in Sec. 6.
2 Diagnostic technique
2.1 Optical bench and collection branch
The LIF optical assembly is extensively described in Ref. [15]. The laser beam used to
excite Xe+metastable ions at 834.7 nm is produced by an amplified tunable single-mode
external cavity laser diode. The wavelength is accurately measured by means of a calibrated
wavemeter whose absolute accuracy is better than 100 MHz, which corresponds to 90 m/s.
A plane scanning Fabry-Prot interferometer with a 1.29 GHz free spectral range is used to
real-time check the quality of the laser mode and to detect mode hops. The primary laser
beam is modulated by a mechanical chopper at a low frequency 20 Hz before being coupled
into a 50 m long optical fib er of 50 µm core diameter. The fiber output is located behind the
thruster. Collimation optics are used to form a narrow beam that passes through a small hole
located at the back of the PPSrX000 thruster. The laser beam propagates along the channel
axis in the direction of the ion flow. Typically, the laser power density reaches 3mW/mm2,
which warrants a weak saturation effect on the studied transition.
A collection branch made of a 40 mm focal length lens, which focuses the fluorescence light
onto a 200 µm core diameter optical fiber, is mounted onto a travel stage perpendicular to
the channel axis. The magnification ratio is 1, meaning that the spatial resolution is 200µm
in axial direction. A 16 mm long slit was made in the channel dielectric outer wall in order to
carry out measurements inside the channel. The fluorescence light transported by the 200 µm
fiber is focused onto the entrance slit of a 20 cm focal length monochromator that isolates the
541.9 nm line from the rest of the spectrum. A photomultiplier tube serves as a light detector.
2.2 Lock-in photon-counting device
The pulse (or photon) counting technique allows the detection of a very low level signal with
an excellent time resolution. When combined with a modulation of the laser light intensity,
the pulse counting technique can distinguish between LIF photons and spontaneous emission
photons. The technique is known as the time-resolved pulse counting lock-in detection tech-
nique. In this work, a customized pulse-counting system is used to measure time-dependent
ion VDF [16]. Here we briefly outline the main characteristics and settings of the system.
A block diagram of the pulse counting system is shown in Fig. 2. Photons are detected by
means of a high gain and low dark noise PMT (R7518-P from Hamamatsu). A fast amplifier
and discriminator module (9302 from Ortec - 100 MHz counting rate) is used to screen out
dark current from PMT dynodes, to limit the pulse rate thereby avoiding saturation of the
pulse counter, and to transform any single event – here the arrival of a photon – into either
a NIM or a TTL pulse. Pulses are subsequently treated by the lock-in pulse counter device,
which counts events as a function of time. A trigger starts the counter which segments photon
count data into sequential time bins. Notice that up to 32 kbins are available. The width of
the bins can be set from 10 ns to 655 s. The instrument records the number of photons that
arrive in each bin. In order to greatly improve the signal-to-noise ratio, the counter is able
to operate in real-time addition-subtraction mode. The laser beam intensity is modulated at
low frequency (20 Hz) by means of a mechanical chopper. Each pulse recorded when the
laser is propagating through the plasma (laser-on mode) is added to the time series; the signal
corresponds to LIF photons plus background photons. Each pulse recorded when the laser
is suspended (laser-off mode) is subtracted from the time series: in that case the signal is
solely composed of background photons. A 2 kHz trigger signal generated by the counter itself
was used to define the start of the measurement cycle. The time resolution, i.e. the width
of each bin, was set to 100 ns and 5000 bins were used. The duration of one measurement
cycle is therefore 500 µs, corresponding to about 6 times the period of low-frequency current
oscillations of the PPSrX000 thruster operating at 500 V and 6 mg/s. In order to obtain a
reasonable signal-to-noise ratio, light was accumulated over 1 million cycles.
The procedure to obtain the time-resolved ion VDF is the following:
the laser is fixed at a given wavelength λcorresponding to a certain ion velocity group
δv. The extent (dispersion) of the velocity group results from the spectral width of the
laser beam and from the thermal expansion of the laser cavity. A feedback loop allows a
minimization of the shift of the laser wavelength. The dispersion is thus around 10 m/s.
The pulse counter is used to record the number of fluorescence photons induced by
excitation of metastable ions at λ. That means we follow the temporal evolution of the
velocity group δv.
After about one million discharge current disconnection cycles the laser wavelength is
changed and a new measurement starts.
To obtain a smooth ion VDF about 15 to 20 different wavelengths are used.
3 Temporal characteristics of the ion VDF
3.1 Experimental conditions - Ion emission light
All measurements were performed in the PIVOINE-2g test-bench. The PPSrX000 Hall effect
thruster was equipped with BN-SiO2channel walls and with a carbon anode. All thruster
parameters were kept unchanged during the experiments: The applied voltage Udwas set to
500 V, the anode xenon mass flow rate Φawas fixed at 6 mg/s and the magnetic field strength
Bwas 150 G. The mean discharge current is 5.4 A and the oscillation frequency is found to
be 13.7 kHz. The temporal characteristics of the ion VDF were recorded for three locations
along the channel centerline. Each position defines a distinct area in terms of electric field
magnitude [15]. The position x= -15 mm corresponds to a zone through which the electric
field is almost zero and the ionization is strong. At x= -2.5mm, the electric field is large and
ionization is maintained. The channel exit plane, x= 0 mm, corresponds to a region where
ionization ceases and the electric field strength is high with E300 V/cm.
In this study, the ion flow dynamics was investigated before and after a fast shut-down of
the anode discharge current. It was therefore possible to examine the temporal characteristics
of the ion VDF during plasma breakdown and ignition as well as during forced and free current
oscillations. The anode current is switched off during 5 µs at 2 kHz by way of an optically
controlled fast power switch based on a MOSFET [9]. The power switch is directly driven by
the counter, as shown in Fig. 2. There is no synchronization between the power cut cycle and
the discharge current waveform. In other words, the anode current is switched off randomly
at any time with respect to the discharge current natural oscillations.
Figure 3 displays the intensity of the 541.9 nm ion line as a function of time observed
at x= -2.5 mm recorded with the photon-counting device operating in addition mode only.
A snapshot of the anode current waveform is also shown. Measurement reveals the time
evolution of natural plasma emission. The power is always switched off at t= 0 µs (reference
time). The plasma decays with a 1/etime of 2.1 µs. However, it does not fully vanish as
charged-particle recombination and diffusion processes timescales are not infinitely shorter
compared to the 5 µs current-off time period. On the contrary, both the anode current and
the Hall current cancel in a few hundreds of ns [17]. This point is specifically addressed
in the next sections. A large amount of light is quickly produced at the re-ignition stage,
as can be seen in Fig. 3. In like manner, a discharge current burst always occurs at re-
ignition [9, 17]. This forced plasma oscillation originates in the sudden ionization of the great
amount of propellant atoms accumulated inside the channel when the discharge is off. The
plasma oscillates with a mean period of about 83 µs that corresponds to a 12 kHz frequency.
As can be observed in Fig. 3, the amplitude of light oscillations diminishes with time, and
the signal finally approaches a constant level. This phenomenon is due to the fact that, the
current disconnection cycle is not synchronized with the natural current oscillations, while
data acquisition is a cumulative process over thousand of cycles.
3.2 Contour map
Figure 4 shows contour plots of the time evolution of the Xe+ion velocity distribution func-
tions for three positions along the thruster channel axis, respectively x= -15 mm, x= -2.5 mm,
and x= 0 mm. All velocity groups vanish quickly after the current is switched off on a time
scale on the order of a few 100 ns. This property indicates the electric field cancels almost
instantaneously when the current is stopped. As a consequence, the discharge current as
well as the Hall current disappear over an extremely short time period, as experimentally
observed [17]. Yet, very slow ions do not fully disapp ear in 5 µs as recombination, ambipolar
diffusion to walls and drift out of the acceleration zone are slow processes. In Fig. 4, the
fluorescence signal is significantly above zero after 5 µs for x= -15 mm. The remark holds
also true for the ion emission signal, see Fig. 3. Note that a Xe+ion travels 1.5 mm in 5 µs
at the thermal speed vth 300 m/s. Very slow ions, i.e ions with the atom speed, are always
produced first at re-ignition as electrostatic acceleration is not an instantaneous process. In
Fig. 4, slowest ions are indeed observed first and the mean velocity gradually increases up
to a limit. Ions moving with a velocity close to the thermal speed are not visible in Fig. 4
for x= -2.5 mm and x= 0 mm as the ion VDF is truncated due to a lack of data points.
The large production of ions at plasma ignition originates from the fact that the channel
is entirely filled up with xenon atoms, as previously explained. As can be seen in Fig. 4,
the Xe+ion VDF in axial direction changes in time, especially during the first two plasma
oscillations. This phenomenon indicates that the acceleration potential, and thus the electric
field, is likely to vary in time with a frequency on the order of the main discharge current
oscillation frequency.
3.3 Velocity groups
Examination of the temporal characteristics of the ion VDFs provides a general outline of
the ion dynamics in the discharge of a Hall thruster. In contrast, a critical analysis of the
temporal behavior of ion velocity groups reveals in great detail the intricate character of the
physics at work. The time evolution at the channel outlet of eight well-identified ionic velocity
groups δv is shown in Fig. 5. The temporal evolution is monitored at the thruster channel
exhaust. Graphs correspond to horizontal cross-sections of the lower contour plots in Fig. 4.
All velocity groups quickly vanish as soon as the power is switched-off: the mean 1/edecay
time for all δv is 1.5 µs. The discharge current as well as the Hall current decay in about
the same time period [17]. Nonetheless, fastest ions disappear out of the acceleration region
first: the 1/edecay time is 1.1 µs at 12960 m/s. On the contrary, slowest ions are produced
first when the discharge current is re-ignited. In Fig. 5, the group δv = 9515 m/s is detected
at 9 µs and it reaches its highest amplitude at 19 µs whereas the group δv = 13390 m/s is
detected at 20 µs and it goes through a maximum at 39 µs. All velocity families oscillate
nonetheless with the same period of time T73 µs, that means with a frequency around
14 kHz.
When the power is turned on again, ionization immediately takes place, see Fig. 3. Dis-
charge and Hall current are restored in less than 1 µs and ions are gradually accelerated as
shown in Fig. 5. All these facts indicate that the electric field is established on a microsecond
timescale at re-ignition. However, it seems at first sight in manifest contradiction with the
time it takes to detect fast ions inside the thruster channel. The time of flight of a given
ion velocity group across the acceleration layer after plasma re-ignition can be assessed by
numerically solving the particle motion equation in an external electric field E:
(1) dv =e
mE dt,
where eis the elementary charge and mis the mass of a xenon ion. For simplicity’s sake,
the electric field is first set constant in space and in time through the whole acceleration
region (from x= -10 mm to 20 mm) with a magnitude of 170 V/cm [15]. Moreover, the
field is assumed to be instantaneously created and the ionization process is stationary and
homogeneous. The initial velocity v0is fixed as the thermal speed vth. Computations reveal
that the group δv = 13390 m/s appears at the exit plane at t= 1.05 µs. Ions have then
travelled 7.2 mm, a distance compatible with the acceleration layer size L30 mm. However,
this velocity group is observed first at t= 20 µs, see Fig. 5. Another approach consists of
taking a steady electric field distribution similar to the measured one [15]. When ions are
created about 19 mm inside the channel, computations indicate that the group δv = 13390 m/s
is indeed observed at x= 0 mm for t20 µs. Yet ions moving at 9515 m/s are solely seen a
few hundreds of ns earlier, in contradiction with experimental outcomes.
One way to better duplicate reality consists for instance of considering that the ionization
profile or the electric field can evolve in the course of time. With a stationary electric field
profile similar to the measured one [15], numerical simulations using Eq. 1 show that ions
must be created first in the vicinity of the channel outlet and the ionization front must move
towards the anode with a speed on the order of 500 m/s to reproduce trends that are ex-
perimentally observed in Fig. 5. Propagation of an ionization wave through the acceleration
layer was proposed to explain experimental results acquired by means of time-resolved optical
emission spectroscopy with a fiber comb [11] as well as CCD images of the plume behavior
with a sp eed around 1-2 km/s.
Figure 6 shows the time evolution of the velocity group δv = 9550 m/s for two locations,
respectively x= -2.5 mm and x= 0 mm. The ion family is first observed at the channel
exit plane at t= 8 µs before being detected inside the channel at t25 µs. The highest
amplitude is attained for t= 19 µs and t= 45 µs at x= 0 mm and x= -2.5 mm, respectively.
Results indicate that ions are created within a broad region inside the channel: ions created
close to the exit plane are indeed detected first. Nevertheless, experimental outcomes cannot
be correctly simulated when assuming that an ionization wave travels from the plume near
field towards the anode while the electric field distribution stays unchanged. On the contrary,
results suggest that the ionization front as well as the acceleration layer change in time to-
gether. Numerical simulations, though basic, and experimental data are therefore in favor of
complex plasma dynamics within the discharge of a Hall thruster. It is worth noticing that
the behavior of Xe+ion velocity groups during a forced oscillation that follows a power-off
period may not directly image the normal behavior during a natural plasma oscillation from
the viewpoint of amplitude of the observed phenomena.
4 Evolution in time of the density, mean velocity and disper-
The time evolution of various averaged quantities is plotted in Fig. 7, 8 and 9 for three
positions along the channel axis, respectively x=15 mm, x=2.5 mm and x= 0 mm.
The relative metastable Xe+ion density is given by the area of the VDF. The mean velocity
and the velocity dispersion are computed from, respectively, the first and the second order
moments of the velocity distribution. The velocity spread is in fact expressed in terms of p
parameter [14, 15]. The latter reads:
(2) p= 2 p2Ln(2) ×σ2.335 ×σ,
where σis the standard deviation. The quantity pis equal to the FWHM in the case of a
Gaussian profile.
As can be seen in Fig. 7, the ion density is oscillating in time with a frequency of about
16 kHz whatever the position. Changes in the ion density are connected with temporal charac-
teristics of the ionization rate. The latter is driven by a prey-predator kind of process between
atoms and charged particles [6, 18, 19]. Besides, Langmuir probe measurements have shown
that the electron density periodically varies in time with the discharge current oscillation
frequency [10]. The fact that in Fig. 7, the first maximum of the ion density waveform is
shifted in time with respect to the first maximum of the 541.9 nm line intensity profile for
x=2.5 mm and x= 0 mm is an experimental artefact due to the truncation of the measured
The time evolution of the mean velocity is shown in Fig. 8. At x= -15 mm, the velocity
slightly oscillates around zero as the observation point is outside the acceleration layer. At
x=2.5 mm and x= 0 mm, the mean velocity oscillates around a constant value, which
corresponds with a reasonably good agreement to the value obtained by means of time-
averaged LIF spectroscopy at the same location [15]. The small difference is due to the
power-switch disturbance. As shown in Fig. 8, the velocity changes in time are however
small. In terms of kinetic energy the largest gap is 10 eV at -2.5 mm, respectively 25 eV at
the channel exit plane. Energy variation of a few tens of eV during a low-frequency current
oscillation cycle was recorded in the plume far-field of a SPT100-ML Hall thruster using
a repulsing potential analyzer [11]. Hybrid fluid/kinetic models also predict low-amplitude
periodical variation of the ion velocity [18, 19] with a strong correlation between discharge
current and ion velocity temporal behavior. The observed oscillations of the mean ion axial
velocity can solely be explained by a back and forth motion of the ionization and acceleration
layers and/or a change in the electric field magnitude, as already suggested by the analysis
of ion velocity groups characteristics as a function of time.
As can be seen in Fig. 9, the velocity dispersion does not vary much in time other than
at current shut off and restart. At the thruster channel exhaust, the velocity dispersion (p
parameter) is almost constant with a value of 2950 m/s. In terms of energy spread it is 47 eV.
In previous investigations [14, 15], it was clearly demonstrated that in a Hall thruster environ-
ment the velocity dispersion originates mostly in the spatial overlap between the ionization
and the acceleration layers. As the velocity dispersion stays unchanged with time whereas
the ion density and velocity do vary, one can conclude the ionization front and the electric
field distribution have a correlated dynamics. For instance, assuming the form of the two
profiles stay unchanged, the two layers would have to move along at once together in the
axial direction. Actually, computer simulations indicate that both the shape and the location
of the ionization and electric field profiles change with time [18].
5 Low-frequency electric field oscillations
The oscillation in time of the accelerating electric field can be assessed from the time-
dependent profile of the Xe+ion mean velocity ¯v, see Fig. 8, assuming a collisionless medium.
The electric field is computed according to the formula:
(3) E(t) = mXe+
2e¯v(x1, t)2¯v(x2, t)2
where xis the position and drefers to the distance. The time-dependent electric field is plotted
in Fig. 10 for the area that ranges between -2.5 mm and the exit plane. The electric field is
found to oscillate with a period T90 µs, i.e. f11 kHz, around a mean value of about
215 V/cm disregarding the power-off period. This value is close to the value of 245 V/cm
found by way of time-averaged laser spectroscopy [15]. The amplitude of the field oscillations
is, however, relatively weak. Over the first free oscillation that extends from t= 75 µs until
t= 165 µs the amplitude varies at most from 190 V/cm to 240 V/cm, therefore, the electric
field variation is in the range ±10 % ahead of the thruster channel exhaust. Finally, in Fig. 10,
one can also notice the slow rise of the electric field magnitude from 100 V/cm at 10 µs to
250 V/cm at 30 µs. This temporal evolution is likely to be connected with the time it takes
for the establishment of an equilibrium state for both the discharge and the Hall currents.
6 Conclusions
The examination of the temporal characteristics of the Xe+ion velocity distribution func-
tion in the magnetized discharge of a Hall effect thruster reveal the complex dynamics of
the ionization and the acceleration processes. Three results are especially of great interest.
First, the ionization profile and the electric field distribution are unstationary. Second, the
ionization and acceleration layers vary in time in such a way that their spatial overlap stays
almost unchanged as the ion velocity spread does not change much after ignition. Third, the
amplitude of the low-frequency electric field oscillations ahead of the channel exit plane is
Even though this study has brought new facts about the physics of a Hall effect thruster,
it appears necessary to carry on this type of experiments aiming at building-up of a larger
set of data. The latter is actually necessary to improve our understanding of the time and
space evolution of the electric field in a Hall thruster. Measurements of the time-dependent
ion VDF must be performed with a better signal-to-noise ratio at many locations along
the thruster channel centerline. Measurements must also be carried out for several thruster
operating conditions and various power levels. Finally, experimental results must be critically
compared with numerical outcomes of PIC models of Hall thruster behavior.
Works are performed in the frame of the joint-program CNRS/CNES/SNECMA/Universities
3161 entitled “Propulsion par plasma dans l’espace”. They are also financially supported by
the French National Research Agency in the frame of the 06-BLAN-0171 TELIOPEH project.
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Figure 1: Cross-section view of a Hall effect thruster. The symbol estands for electron, afor atom
and ifor ion. The channel exit plane is referred to as x= 0 in this work.
Figure 2: Block diagram of the lock-in pulse counting system used in this work to measure the time-
resolved Xe+ion VDF by means of LIF spectroscopy. The PMT is placed behind a 20 cm focal length
monochromator. The anode discharge current switch is externally driven by the counter.
Figure 3: (Top) Snapshot of the anode current waveform. The discharge current is switched for 5 µs
at t= 0 µs. (Bottom) Change in time of the ion emission at 541.9 nm observed using the photon
counting technique at x= -2.5 mm. The inset panel displays enlargement of the emission signal from
50 µs until 350 µs. The oscillation frequency is 12 kHz.
Figure 4: Contour map of the Xe+ion axial VDF as a function of time for three locations along the
channel axis of the PPSrX000 Hall thruster fired at 500 V: x= -15 mm, x= -2.5 mm and x= 0 mm.
Figure 5: Trace of the time evolution of eight ionic velocity groups at the channel exit plane (x= 0
Figure 6: Time evolution of the velocity group δv 9 550 m/s for two lo cations: x=-2.5 mm and
δv = 9605 m/s (solid line) and x= 0 mm and δv= 9515 m/s (circle).
Figure 7: Time evolution of the metastable Xe+ion relative density for three positions along the
channel axis of the PPSrX000 Hall thruster. The density is given by the VDF area. Also shown is
the emission profile at 541.9 nm (blue line).
Figure 8: Time evolution of the Xe+ion mean axial velocity for three on-axis positions. The time-
averaged velocity measured in a previous study at x=2.5 mm and 0 mm is 9300 m/s and 13100 m/s,
respectively [15]. Also shown is the profile of the light emission at 541.9 nm (blue line).
Figure 9: Time evolution of the Xe+ion axial velocity dispersion (pparameter) for three positions
along the channel axis of the PPSrX000 Hall thruster. Also shown is the profile of the light emission
at 541.9 nm (blue line).
Figure 10: Electric field temporal characteristics ahead of the PPSrX000 thruster channel exhaust
(between 0 and -2.5 mm). The field strength is determined from the mean Xe+ion axial velocity.
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The nature of oscillations in the 1 kHz–60 MHz frequency range that have been observed during operation of Hall thrusters is quantitatively discussed. Contours of various plasma parameters measured inside the accelerating channel of a typical Hall thruster are used to evaluate the various stability criteria and dispersion relations of oscillations that are suspected to occur. A band by band up-to-date overview of the oscillations is carried out with a description of their observed behavior and a discussion of their nature and dependencies through comparison of the calculated contours to reported observations. The discussion encompasses the excitation of low frequency azimuthal drift waves that can form a rotating spoke, axially propagating “transit-time” oscillations, azimuthal drift waves, ionization instability-type waves, and wave emission peculiar to weakly ionized inhomogeneous plasmas in crossed electric and magnetic fields.
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The operation of a laboratory version of the flight-qualified SPT-100 stationary plasma thruster is compared for four different discharge chamber wall materials: a boron nitride–silica mixture (borosil), alumina, silicon carbide, and graphite. The discharge is found to be significantly affected by the nature of the walls: changes in operating regimes, up to 25% variations of the mean discharge current, and over 100% variations of the discharge current fluctuation amplitude are observed between materials. Thrust, however, is only moderately affected. Borosil is the only material tested that allows operating the thruster at a low mean current, low fluctuation level and high thrust efficiency regime. It is suggested that secondary electron emission under electron bombardment is the main cause of the observed differences in discharge operation, except for graphite, where the short-circuit current inside the walls is believed to play a major role. It is also suggested that the photoelectric effect, which has apparently not been given attention before in the Hall thruster literature, could increase the cross-field electron current. © 2003 American Institute of Physics.
Full-text available
Closed drift thrusters are reviewed. The publications on these thrusters constitute a large body of information. This article can therefore include only the most prominent theoretical and experimental features of closed drift thrusters. In some regards, this article is also an attempted synthesis of the differing views of these thrusters found in literature, as well as in our own work. In a closed drift thruster, the electric field that accelerates the ions is established by an electron current that passes through and is impeded by a magnetic field. The precessing electrons in this magnetic field follow a closed drift path giving this thruster its name. Closed drift thrusters are divided into magnetic layer and anode layer types, based both on the geometrical and material differences in the discharge channels of the two types, and on the different physical processes that take place within the discharge plasma. Considered as a whole, the publications on closed drift thrusters constitute an impressive body of information that, for the most part, was generated in Russia independently of US research on electric thrusters.
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Hall-effect thruster plasma oscillations recorded by means of probes located at the channel exit are analyzed using the empirical mode decomposition EMD method. This self-adaptive technique permits to decompose a nonstationary signal into a set of intrinsic modes, and acts as a very efficient filter allowing to separate contributions of different underlying physical mechanisms. Applying the Hilbert transform to the whole set of modes allows to identify peculiar events and to assign them a range of instantaneous frequency and power. In addition to 25 kHz breathing-type oscillations which are unambiguously identified, the EMD approach confirms the existence of oscillations with instantaneous frequencies in the range of 100– 500 kHz typical for ion transit-time oscillations. Modeling of high-frequency modes 10 MHz resulting from EMD of measured wave forms supports the idea that high-frequency plasma oscillations originate from electron-density perturbations propagating azimuthally with the electron drift velocity. © 2005 American Institute of Physics.
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The results of a study of laser-induced fluorescence velocimetry of neutral and singly ionized xenon in the plume and interior portions of the acceleration channel of a Hall thruster plasma discharge operating at powers ranging from 250 to 725W are described. Axial ion and neutral velocity profiles for four discharge voltage conditions (100V, 160V, 200V, 250V) are measured as are radial ion velocity profiles in the near-field plume. Ion velocity measurements of axial velocity both inside and outside the thruster as well as radial velocity measurements outside the thruster are performed using laser-induced fluorescence with nonresonant signal detection on the xenon ion 5d[4]7/2–6p[3]5/2 excitation transition while monitoring the signal from the 6s[2]3/2–6p[3]5/2transition. Neutral axial velocity measurements are similarly performed in the interior of the Hall thruster using the 6s[3/2]0 2–6p[3/2]2transition with resonance fluorescence collection. Optical access to the interior of the Hall thruster is provided by a 1-mm-wide axial slot in the insulator outer wall. While the majority of the ion velocity measurements used partially saturated fluorescence to improve the signal-to-noise ratio, one radial trace of the ion transition was taken in the linear fluorescence region and yields a xenon ion translational temperature between 400 and 800K at a location 13mm into the plume.
Time-resolved electrostatic probe measurements were performed in the near field of a SPT100-ML Hall effect thruster in order to investigate electron properties changes on a microsecond time scale. Such measurements allow one to monitor the electron temperature Te, the electron density ne, as well as the plasma potential Vp during a time period that corresponds to one cycle of a breathing-type plasma oscillation with f ≈ 15–30 kHz. Although Te(t) stays constant in time, ne(t) and Vp(t) oscillate with the discharge current waveform frequency. The observed time delay between ne and anode discharge current (Ida) waveforms, which is of approximately 7 μs, is linked to the ion transit time from the ionization layer to the probed near-field region. The same time gap is measured between Vp(t) and Ida(t), however Vp(t) and ne(t) are in phase opposition. The electron density reaches its highest value at the very moment ions are ejected out of the thruster discharge chamber, which also corresponds to the instant the cathode potential is the most negative. Such a behavior images the need for ion beam neutralization. Further, it is shown that there is a strong correlation between the electron dynamics and the presence of high frequency (HF) plasma oscillations in the megahertz range: HF fluctuations are the strongest when ne is the highest.
Stationary plasma thrusters are ion thrusters whose properties make them especially suitable for satellite station keeping or orbit transfer. In these thrusters, a magnetic field transverse to the electron flow towards the anode increases the electron collision frequency and makes possible the generation of a plasma at relatively low gas flow and gas density. The decrease of the plasma conductivity due to the magnetic field induces a large electric field in the plasma which accelerates the quasicollisionless ions whose trajectories are not significantly affected by the magnetic field. The purpose of this article is to clarify, using results from a simple model, the electrical properties of these thrusters and the low frequency oscillation regime which has been observed experimentally. The model is based on the assumption of quasineutrality of the plasma column and on a 1D transient hybrid treatment of electron and ion transport in the device. Electrons are considered as a fluid and ions are described with a collisionless kinetic equation. This model provides reasonable estimates of the plasma properties and is able to give a clear picture of the low frequency oscillations, qualitatively close to the experimental observations. © 1998 American Institute of Physics.
A discussion is presented on the results and predictive capabilities of a two-dimensional (2D) hybrid Hall effect thruster (HET) model. It is well known that classical (collision-induced) cross-field electron transport and energy losses are not sufficient to explain the observed HET characteristics. The 2D, quasineutral, hybrid discharge model uses empirical parameters to describe additional, anomalous electron transport and energy loss phenomena. It is shown that, for properly adjusted empirical parameters, the model can qualitatively reproduce the observed thruster behavior over a large range of operating conditions. The ionization and transit-time oscillations predicted by the model are described, and their consequences on the time-averaged thruster properties are discussed. Finally, the influence of the empirical parameters on the model results is shown, especially on quantities that can be measured experimentally. © 2004 American Institute of Physics.
This paper presents some aspects of the research developed in the frame of a coordinated program launched in France in 1996 and devoted to plasma thrusters for space technologies. Relevant results of physical studies have been selected from the literature with the addition of recent original results. The thrusters within the scope of this research are diagnostic equipped versions of industrial realizations, in a thrust level range of 0.1 N and electrical power 1.5 kW. The optical and electrical diagnostics concern studies of the thruster plasma and of the thruster plume. Transient phenomena in these two regions, related to discharge current fluctuations or oscillations on a typical time scale of 40 µs, have been space-time characterized. This has been achieved by developing a large panel of diagnostics including RFEA, Langmuir probes, OES, fast camera imaging and electron drift Hall current probe. They lead to a coherent representation of these phenomena , in rather good qualitative agreement with 1D modelling. But they emphasize also the importance of 2D effects. Insights obtained through combined LIF (on Xe+ ions) and OES diagnostics are also presented. They concern the ionization-acceleration region in the thruster plasma, where intrusive diagnostics are disturbing in nature, and open a new step for a significant improvement of the detailed understanding of these thrusters. Such improvements are required when looking at the final goal of a predicable modelling simulation able to help the design of optimized structures at various thrust levels, in spite of the important work devoted to these devices in the former USSR and by Russian teams in Moscow at the MIREA, MAI-RIAME and KOURCHATOV Institutes.
We describe a time‐resolved pulse‐counting system well adapted for the detection of continuous laser induced fluorescence (LIF) signals in repetitive phenomena, when a strong background emission is present. It consists of 256 channels coupled to a first in first out memory and interfaced to a 486 DX 33 PC, for data storage. It accepts time‐averaged count rates up to 450 kcount/s. Time between channels can be set from 12.5 ns to several μs and the dead time between two consecutive cycles of the physical phenomena is less than 20 ns. In phase with a chopper, which modulates the laser beam, it adds the observed photon signal to the channel memories when the beam is on and substracts it when the beam is stopped, acting like a lock‐in amplifier which detect only the modulated part of the signal. The minimum detectivity on the LIF signal is only limited by the shot noise of the plasma induced emission signal. As an application, we studied the time variation of the Ar<sup>+</sup>*(<sup>2</sup>G 9/2 ) metastable ions, detected by LIF, in two types of plasmas. Their radiative lifetime and collisional quenching frequencies were deduced from their decay rate in the afterglow of a pulsed Helicon reactor. We also observed the evolution of their density in a 455 kHz capacitively coupled argon discharge. © 1996 American Institute of Physics.