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Electron and Ion Properties in the Beam and Discharge of a Helicon Plasma Source for Application in Spacecraft Propulsion

Authors:
SP2020_471
SPACE PROPULSION 2020+1 / 17  19 MARCH 2021
Electron and Ion Properties in the Beam and Discharge of a Helicon Plasma Source
for Application in Spacecraft Propulsion
Alfio E. Vinci(1) and Stéphane Mazouffre(1)
(1)Institut de Combustion, Aérothermique, Réactivité et Environnement,
Centre National de la Recherche Scientifique, 1C Avenue de la Recherche Scientifique, 45071 Orléans
Email: alfio.vinci@cnrsorleans.fr, stephane.mazouffre@cnrsorleans.fr
KEYWORDS: Helicon, Magnetic nozzle, plasma
diagnostics, electric propulsion.
ABSTRACT:
Helicon plasma sources are currently undergoing
an active research phase in the domain of low
temperature plasmas on account of several interest
ing characteristics they have for inspace propulsion
applications. This paper reports spatially resolved
ion and electron properties, which are inferred via
direct measurements performed in the nearfield
plume of a subkilowattclass Helicon source op
erating with krypton and xenon propellants. A rf
compensated Langmuir probe is displaced axially
and radially to enable spatially resolved measure
ments of plasma density, electron temperature and
plasma potential. A planar probe is employed to ac
cess the ion current density and analyze the beam
divergence at different axial locations. A 4grids Re
tarding Potential Analyzer is used to infer the ion ki
netic energy downstream the source exit. The effect
of magnetic field magnitude and topology on ions
and electrons properties is especially investigated.
1. INTRODUCTION
Electric propulsion devices represent an efficient
solution for inspace maneuvering [1, 2], namely
orbitraising, station keeping, and deep space ex
ploration. Along with the inherited technology in
cluding Ion Thrusters and Hall Thrusters, the elec
tric space propulsion community has recently ex
pressed a growing interest [39] in the intense re
search performed on Helicon Plasma (HP) dis
charges [1015]. These devices feature several
attractive characteristics for propulsion purposes,
namely a relatively simple design, no need for a neu
tralizer, expected long lifetime, easy use of alter
native propellants and high plasma densities (typi
cally >1017 m3) over a wide range of sizes and in
put powers. Despite the early development stage
of HP thrusters (HPT) [16], promising performance
measurements have been recently reported [8, 17].
Hence, HPTs have been proposed as an innova
tive alternative whose investigation can potentially
enrich the set of already available technologies for
use on small platforms [18, 19]. Furthermore, con
sidering missions which would considerably benefit
from the use of condensable propellants, it is more
likely that HPTs will represent an attractive solution
with respect to the aforementioned wellestablished
technologies, whose reliable functioning is strongly
limited by the lifetime of hollow cathodes operating
with such alternative propellants [20,21].
HP sources comprise three main components: i)
a dielectric tube as plasma discharge region, ii) a
radiofrequency (rf) emitting antenna for gas ioniza
tion and iii) an axially directed DC magnetic field
for plasma confinement and expansion throughout
its diverging region, i.e. the magnetic nozzle (MN).
Power radiated by the antenna is deposited in the
electron population as thermal energy by means
of helicon wave modes [22] and TrivelpieceGould
wave modes [23]. Energy is then spent for plasma
production and plasma transport phenomena, such
as ambipolar electric field, resulting in axial super
sonic acceleration in the MN region [24,25].
For the HPTs to be technologically competitive in
the near future, it is imperative to perform an exten
sive characterization of the generated plasma. Inci
dentally, a better understanding of the physics gov
erning such rf plasma sources is the ultimate way
to provide an exhaustive optimization of thruster de
sign and performance. These characterization ac
tivities are intended to render an comprehensive
dataset for comparison with numerical simulations
and models. This paper analyzes measurements of
a variety of plasma properties performed using kryp
ton and xenon gases in the MN region that extends
upstream the exit plane. In Section 2 a detailed de
scription of the HP reactor is provided; the set of di
agnostics which has been employed to attain ions
and electrons properties is reported in Section 3. It
includes: a rfcompensated Langmuir probe (LP) for
characterization of plasma density, electron temper
ature and plasma potential; a planar probe to attain
the plume diverge at different axial locations; a Re
tarding Potential Analyzer (RPA) to assess ions en
ergy. In Section 4 the collection of measurements is
presented and discussed. They are gathered in two
parametric analyses: a comparative study of krypton
and xenon plasma properties; a survey on the role
played by the magnetic throat axial location. Even
tually, conclusions are drawn in Section 5.
1
2. HELICON PLASMA SOURCE
The HP source employed in this work is schemati
cally depicted in Fig. 1. The discharge chamber con
sists in a vertically oriented quartz tube with
ϕ
=9 cm
inner diameter and L=58 cm length. Its open exit
defines the origin of the system axial coordinate z.
Propellant gas in injected offaxis at the top aper
ture, while the bottom part is connected to a 30 cm in
inner diameter and 50 cm in length expansion cham
ber. A turbomoleular/primary pumping system is
connected to one lateral side of the chamber thus
providing an ultimate base pressure in the order of
105mbar. Typical values of pressure during opera
tion lay in the 103mbar range.
RF power is generated by a 1 kW class power
supply at 13.56 MHz and fed into a coppermade
doublesaddle antenna through a 2 kW custom
π
type matching network. The antenna is 12 cm high
and its center is located at z
=11 cm. It is designed
such that it is directly connected to the matching net
work to reduce power transfer losses.
The HP source features nine electromagnets, also
depicted in Fig. 1. The electromagnets surrounding
the expansion chamber are named GB and num
bered from 1 to 3, moving upstream. The same pro
gression is applied to those surrounding the quartz
tube, named PB from 1 to 6. Each electromagnet is
made up of a 2 mm diameter copper wire, constitut
ing 510 loops for PB16 and 430 loops for GB13.
The presence of multiple electromagnets enables
the investigation of profoundly different magnetic
field topologies. Fig. 2 illustrates the measured and
simulated magnetic field profiles that are used in
this work. Fig. 2(a) exemplifies a unique kind of
magnetic topology having the magnetic throat ex
actly at z=0with strength varying between 4 mT and
10 mT. Moreover, five different topologies are shown
in Fig. 2(b) with peak values of 10÷12 mT, which are
used to study the role played by the magnetic throat
location with respect to the antenna location. The
profiles illustrated in Fig. 2(a) are used in deriving
the results discussed in Section 4.1, while the pro
files of Fig. 2(b) refer to those discussed in Section
4.2.
0-30-60 50
z [cm]
gas
pump
GB1GB2GB3
PB1PB2PB3PB4PB5PB6
y [cm]
0
15
-15
x
Figure 1. Helicon Plasma Reactor Schematics. The
z=0position refers to the tube outlet, y=0refers to
the reactor axis.
Figure 2. Externally applied magnetic field profiles.
Shaded areas indicate the antenna location. Solid lines
represent simulation profiles, scatter points indicate
probe measurements.
3. DIAGNOSTICS
3.1. RFcompensated Langmuir probe
The rfcompensated LP is depicted in Fig. 3. Its
design is based on the results and guidelines re
ported in Ref. [2628] The probe tip is a 0.38 mm
tungsten wire with 5 mm length. A 1 mm outer diam
eter alumina tube insulates the tip from the rf com
pensating electrode made of stainless steel. The
sizing process of the compensating electrode re
lied on earlier measurements of the floating poten
tial fluctuations obtained using a capacitive probe.
The back end of the compensating electrode is sol
dered to a 1 nF axial capacitor. The probe tip and
the small capacitor are together connected to a se
ries of three chokes, each of which selfresonates
at one of the first three harmonics. The employed
chokes are: Bourns 78F270JRC for the fundamen
tal harmonic, API Delevan 102560K for the second
one and Bourns 923052RC for the third one. The
whole assembly is encapsulated in a 6 mm outer di
ameter borosilicate glass tube which also accommo
dates the coaxial cable for probe biasing and current
measuring.
Characterization of the chokes is a crucial aspect
of probe development as they are typically man
ufactured to satisfy a requirement on the induc
tance value but not on the selfresonating frequency.
Figure 3. rf-compensated Langmuir Probe.
2
5 10 15 20 25 30 35 40
103
104
105
106
107
Figure 4. Impedance of 1st,2nd and 3rd harmonic
chokes.
0 10 20 30 40
-30
-20
-10
0
Figure 5. rf-compensated LP characterization.
Therefore, an Agilent 4264A precision analyzer has
been used to characterize the choke for the funda
mental harmonic. It also allowed validation of a more
easily accessible method hereafter described which
has been used to characterize the other two chokes.
A10 V amplitude sine wave is fed to one lead of
the testing choke. The other lead is connected to
a resistor (46.52 kis used in this setup) and the se
ries circuit closes to the ground. Input frequency is
changed while the voltage drop across the resistor
is measured and used to calculate the current flow
ing in the circuit. The frequency at which the current
is minimum is the selfresonating frequency of the
choke. The voltage drop across the choke is max
imum at resonance. Impedance is then computed
using Ohm’s law. Chokes characterization results
are reported in Fig. 4. The blue solid line repre
sents the impedance profile obtained using the Agi
lent 4264A precision analyzer and blue squares are
obtained with the aforementioned method, showing
good agreement. The theory illustrated in Ref. [26]
-100 -50 0
0
0.5
1
1.5 10-6
0 5 10 15
10-5
10-4
10-3
10-2
10-1
100
Figure 6. Typical (a) squared ion current and (b) elec-
tron current vs. probe potential. Curves obtained for
P
IN =750 W, ˙m=1mg/s Kr, 10 mT peak value of the
external B field (cf. Fig. 2(a)).
allows stating that this configuration of chokes se
ries and compensating electrode enables proper rf
compensation for plasma potential fluctuations up to
99.5 V in krypton and 85.1 V in xenon. The whole
probe is characterized by applying a 10 V amplitude
sine wave to the tip at different frequencies. The
probe output is illustrated in Fig. 5 in dB units, show
ing local minima for the desired harmonics (dash
dotted vertical lines indicate first and second har
monics).
The rfcompensated Langmuir probe is displaced
both radially and axially, allowing direct evaluation
of plasma density np, electron temperature Teand
plasma potential Vpreported in Section 4. IV char
acteristics are obtained by using an automated con
trol unit by Impedans Ltd and afterwards interpreted
using the OML theory [28]. An example is provided
in Fig. 6. Ion current squared is plotted versus probe
potential and fitted by a straight line, enabling the
evaluation of np(assuming local quasineutrality).
The ion current fit is subtracted to the total current to
obtain a better estimation of the electron current. As
suming that the electron population is described by
a MaxwellBoltzmann distribution function, the log
arithmic curve of the electron current is fitted by a
straight line. Teis deduced from the slope of the
linear fit and Vpis consequently inferred using the
electron current equation with the known values of
npand Te.
A statistical analysis is performed to evaluate
the uncertainty associated with the assessment of
plasma properties: i)the rfcompensated LP is
placed onaxis at z=5 cm and z=10 cm;ii)at
each location twenty IV characteristics are recorded
in different moments of the day, randomly switch
ing between the magnetic configurations reported in
Fig. 2; iii)values of np,Teand Vpare computed as
previously discussed, together with the associated
mean value
µ
and standard deviation
σ
;iv)the er
ror is evaluated as the ratio
σ
/
µ
. An example of
data dispersion is provided in Fig. 7. It results that
all plasma properties are inferred with an error al
ways below 2% for all operating conditions.
0 20 40
0.95
1
1.05
0 20 40
0.95
1
1.05
0 20 40
0.95
1
1.05
Figure 7. Uncertainty analysis of inferred plasma prop-
erties. Typical normalized a) plasma density, b) elec-
tron temperature and c) plasma potential with respect
to
µ
. Red dashed lines represent unitary
µ
, black dash-
dotted lines represent normalized ±
σ
. Input parame-
ters: P
IN =750 W, ˙m=1mg/s Kr, 4 mT peak value
of the external B field (cf. Fig. 2(a)).
3
3.2. Planar Probe with a Guard Ring
The planar probe with a guard ring (PPGR), also
known as Faraday probe, mainly comprises a disk
shape collector surrounded by a metallic ring. The
role of the guard ring is to concentrate sheath edge
effects far from the collector, thus ensuring that the
ion collection area exactly corresponds to the col
lector geometrical area [29]. Both components are
made of stainless steel. The collector is 5.6 mm in di
ameter and 1 mm in thickness, while the ring width is
1 mm. The two electrodes are electrically insulated
by a gap of 100 µm. They feature separated elec
trical connection for polarization and current mea
surement. The collector is biased and its current is
measured using a Keithley 2410 SourceMeter, while
the guard ring is biased using a TTIEX752M power
supply. Both devices are carefully connected to the
common facility ground to ensure the same refer
ence voltage. Design requirements include: i) the
collector thickness must be as small as possible to
minimize ion collection on the sides; ii) the guard
ring width must be much larger than the local plasma
sheath thickness to effectively fulfill his role; iii) the
gap between the two electrodes must be smaller
than the local sheath thickness to introduce negli
gible potential irregularities; iv) the collector surface
roughness must be minimized in order to not over
estimate the collected current density.
The PPGR is displaced radially to infer the ion
current density ji. IV characteristics obtained at
(r=0 cm;z=15 cm) are illustrated in Fig. 8(a)(e)
for five magnetic configurations, cf. Fig. 2(b), with
and without guard ring, i.e. with biased and float
ing guard ring. Other operating parameters were:
750 W input power and 1 mg/sKr. Saturation of the
ion current is achieved for configurations CDE at
voltages lower than about 40 V, while no complete
saturation is recorded for configurations A and B,
due to the fact that the guard ring width is not com
patible with the local values of the sheath thickness.
-80 -40 0
-0.08
-0.04
0
-80 -40 0
-0.12
-0.06
0
-80 -40 0
-2.4
-1.2
0
-80 -40 0
-6
-2
2
-80 -40 0
-3
0
Figure 8. a) - e) Ion current profiles at (r=0,z=15)
cm for the five magnetic configurations A - E shown
in Fig. 2(b). Curves obtained for P
IN =750 W, ˙m=1
mg/s Kr.
024
0
0.4
0.8
024
0
0.4
0.8
024
0
0.15
0.3
024
0
0.15
0.3
024
0
0.15
0.3
Figure 9. a) - e) Debye length, floating and high-
voltage sheath thickness at z=15 cm for the five mag-
netic configurations A - E shown in Fig. 2(b). Curves
obtained for P
IN =750 W, ˙m=1mg/s Kr.
This can be shown by using the data later reported
in Fig. 2024 for npand Te, and by computing the
local values of the characteristic lengths. Results
are shown in Fig. 9(a)(e) as function of the radial
coordinate. Floating and high voltage sheath thick
ness, sfand shv respectively, are computed in ac
cordance with Ref. [30], using 75 V for the mag
netic configurations AB and 50 V for CDE. It is
evident that values of shv for configurations CDE
are much smaller than the guard ring width, while
those for configurations A and B approach its size.
It has to be noted that a perfectly flat ion current pro
file is beyond the scope of the following PPGR mea
surements, which do not focus on indirect propulsive
performance estimation but rather are used to per
form a more qualitativelike comparison of the five
magnetic configurations.
3.3. Retarding Potential Analyzer
The RPA, also known as Retarding Field Electro
static Analyzer (RFEA), used in this work consists of
four mesh grids with 0.4 mm mesh size: the entrance
grid (G1), the electron repeller grid (G2), the ion fil
tering grid (G3) and the secondary electron repeller
grid (G4). A collector (C) is placed downstream the
grids assembly to enable ion current measurement.
-20 0 20 40 60 80 100
0
2
4
610-7
0
5
10
10-8
Figure 10. Typical RPA (blue-axis) ion current and
(red-axis) its first derivative. P
IN =750 W, ˙m=0.2
mg/s Xe, 7 mT peak value of the external B field
(cf. Fig. 2(a)).
4
The whole assembly is encapsulated in an aluminum
body with 4.5 cm outer diameter and 1 cm entrance
orifice. The gap between all the elements is kept
constant at 1 mm. In principle, this is not compati
ble with the expected value of Debye length in the
bulk of the plasma (in the order of 102mm), imply
ing a requirement on the grid spacing to be smaller
than about 0.15 mm to avoid space charge limited
flow [31]. Such a grid spacing is technologically dif
ficult to achieve. Hence, to reduce the plasma flux
entering the probe, i.e. the plasma density inside the
probe itself, an additional grid (G0) is placed in con
tact with the outer body. This allowed to significantly
increase the quality of the measured IV signal. The
grid polarization scheme with respect to ground is:
G0 at 0 V; G1 at 0 V; G2 at 60 V; G3 swept from
20 V to 100 V with 0.2 V step size; G4 at 30 V; C at
3 V. A typical IV characteristic is shown in Fig. 10
together with its first derivative.
4. EXPERIMENTAL RESULTS AND DISCUS
SION
All the spatiallyresolved measurements presented
hereafter are obtained by feeding 750 W rf power to
the antenna. When not explicitly reported, reflected
power is typically below 2.5 %. Krypton and xenon
are injected at 1 mg/sand 0.2 mg/s, respectively. As
suming the two gases have the same molar volume,
the neutral density is about 8 times larger for krypton.
These mass flow rate values are implicitly assumed
in the following when not specified.
Figure 11. On-axis evolution of (a) plasma density,
(b) electron temperature and (c) plasma potential for
different magnetic strengths. P
IN =750 W, ˙m=1mg/s
Kr, r=0mm.
The diagnostics presented in Section 3 is man
ually actuated using a singleaxis translation stage
with a resolution of 10 µmand 150 mm stroke. Probes
are individually employed and displaced with a step
size of 5±0.05 mm. Probe alignment is ensured by
use of a crossline laser pendulum.
4.1. Krypton vs. Xenon Plasma Properties
In this section, characterization of plasma properties
has been carried out using the diagnostics described
in Section 3 as function of the propellant and the ex
ternal magnetic field strength. The used propellants
are krypton and xenon. The tested magnetic field
strengths have been previously reported in Fig. 2(a).
Measurements involving the rfcompensated LP
are performed both axially and radially. Onaxis
scans of np,Teand Vpare reported in Fig. 11(a)(c)
and Fig. 12(a)(c) using krypton and xenon, respec
tively. Electron pressure peis computed using the
measured density and temperature. Notably, sub
stantial differences between the two propellants are
drawn. In Fig. 11(c), it is shown that the plasma po
tential changes from a rapidly dropping profile to an
almost constant profile as the strength of the exter
nal magnetic field is increased. Furthermore, with
reference to Fig. 11(a), the plasma density peak
moves downstream. Quantitative explanation of
this phenomenon is later provided when discussing
Fig. 15 and 16. Visual inspection of the plasma
source in operation agrees with these results. In
deed, at 4and 5 mT, it is observed that plasma con
Figure 12. On-axis evolution of (a) plasma density,
(b) electron temperature and (c) plasma potential for
different magnetic strengths. P
IN =750 W, ˙m=0.2
mg/s Xe, r=0mm.
5
Figure 13. Radial profile of (a) plasma density, (b) electron temperature, (c) plasma potential and (d) electron
pressure for different magnetic strengths. P
IN =750 W, ˙m=1mg/s Kr, z=3cm.
Figure 14. Radial profile of (a) plasma density, (b) electron temperature, (c) plasma potential and (d) electron
pressure for different magnetic strengths. P
IN =750 W, ˙m=0.2mg/s Xe, z=3cm.
centrates just below the antenna region, with almost
null light emission elsewhere [32]. On the contrary,
a visibly homogeneous plasma column appears at
10 mT extending over several antenna lengths. This
strongly suggests that a magnetic field between 7
and 10 mT is somewhat a threshold external param
eter characterizing the transition from inductively
coupled regime to a wavemode regime. Differ
ently, when the plasma source operates with xenon,
no mode transitions have been recorded. Qualita
tively speaking, this is clearly shown in Fig. 12(a),(c)
where the density and potential profiles shift up as
the external magnetic field strength is increased.
It has been previously reported the presence of
density peaks at low externally applied magnetic
fields [33]. In this particular experimental setup, ei
ther using krypton or xenon as working gas, no larger
plasma density at lower magnetic fields has been
recorded.
Detailed plasma properties measurements were
also performed in the radial direction at z=3 cm for
the four different magnetic profiles. In accordance
with the reference system in Fig. 1, the measure
ments were performed along the xaxis. The results
are given in Fig. 13(a)(d) and Fig. 14(a)(d) for kryp
ton and xenon respectively. Scatter points represent
6
2.4
2.4
2.4
2.6
2.6
2.8
2.8
3
3
3.2
3.2
3.4
3.4
3.6
3.6
0123
-4
-2
0
2
4
6
8
10
3
3
3.2
3.2
3.2
3.2
3.4
3.4
3.4
3.6
3.6
3.6
3.8
3.8
4
4.2
4.4
0123
-4
-2
0
2
4
6
8
10
10.5
10.5
11
11
11
11
11
11
11
11.5
11.5
11.5
12
0123
-4
-2
0
2
4
6
8
10
0.12
0.13
0.14
0.14
0.15
0.15
0.16
0.16
0.16
0.17
0.17
0.17
0.17
0.18
0.18
0.18
0.19
0.19
0.19
0.2
0.2
0123
-4
-2
0
2
4
6
8
10
Figure 15. Contour plot of (a) plasma density, (b) electron temperature, (c) plasma potential, (d) electron pressure.
Input parameters are: P
IN =750 W, ˙m=1mg/s Kr, 10 mT peak value of the external B field.
1.6
1.7
1.8
1.8
1.9
1.9
2
2
2.1
2.1
2.1
2.2
2.2
2.2
2.2
2.3
2.3
2.3
2.4
0123
-4
-2
0
2
4
6
8
10
2.8
3
3
3
3.2
3.2
3.4
3.4
3.4
3.6
3.6
3.6
3.8
3.8
3.8
4
4
4
4.2
4.2
4.2
4.4
4.4
4.6
4.6
0123
-4
-2
0
2
4
6
8
10
12.5
12.5
12.5
12.5
13
13
13
13
13.5
13.5
14
14
14
14.5
14.5
0123
-4
-2
0
2
4
6
8
10
0.08
0.09
0.1
0.1
0.1
0.11
0.11
0.12
0.12
0.12
0.12
0.13
0.13
0.13
0.14
0.14
0.15
0.15
0.16
0123
-4
-2
0
2
4
6
8
10
Figure 16. Contour plot of (a) plasma density, (b) electron temperature, (c) plasma potential, (d) electron pressure.
Input parameters are: P
IN =750 W, ˙m=0.2mg/s Xe, 10 mT peak value of the external B field.
measurements data and dotted lines are smoothed
profiles to enhance visualization. Density, tempera
ture and potential peak values are localized offaxis.
Similar outcomes have been previously reported for
npand Te[34,35], but not for the plasma potential
to the knowledge of the authors. It has been sug
gested that offaxis density peak is due to transport
of high temperature electrons from the plasma dis
charge along the surface of the MN [36]. Fig. 13(a)
and Fig. 14(a) show how ionization efficiency is en
hanced at stronger magnetic fields. No relevant ad
vantages in terms of electron temperature are ob
tained by increasing the applied field for krypton, as
seen in Fig. 13(b). Differently, peak value of Tein
creases by more than 20 % (4 mT vs. 10 mT) when
xenon is used, cf. Fig. 14(b). Similarly, Vpprofiles in
Fig. 13(c) and Fig. 14(c) show that a more energetic
plasma is obtained at larger B fields.
Twodimensional plasma properties are addition
ally provided for the 10 mT peak magnetic profile.
Data is collected by displacing the probe radially be
tween r=0 mm and r=30 mm and axially. Seven
axial profiles for np,Teand Vpare obtained. By inter
polation, contour plots for kypton and xenon are de
rived and shown in Fig. 15(a)(d) and Fig. 16(a)(d),
respectively. Peak values for Teare about 4.5÷5 eV
both for krypton and xenon, occurring offaxis and
few centimeters downstream the antenna. Then,
from z
=0on, the temperature decays monotoni
cally. Counterintuitively, npis peaked downstream
where Teislow. It is notable that the same qualitative
results have been previously found in numerical [37]
and experimental [14] studies using completely dif
ferent setups in terms of scale and input parame
ters, such as antenna type and associated azimuthal
mode numbers, input power frequency, magnetic
field strengths and propellant. It shall be noted that
likewise reported in [14], also in the present case this
phenomenon is due to pressure balance. In a sim
plified 1D two fluids description of the plasma, the
7
axial component of the electron momentum equation
in cylindrical coordinates reads
npeEzj
θ
eBr
pe
z=0,Eq. 1
where peis the electron pressure, Ezis the axial elec
tric field, j
θ
eis the electron azimuthal current den
sity and Bris the radial component of the applied
magnetic field. For simplicity sake, the momentum
transfer collisional term has been neglected. This
is justified by observing that the mean free path
λ
is much larger than the source diameter. Val
ues of
λ
are computed using average values for np
and Tefrom Fig. 15 and Fig. 16 together with the
available dataset for the elastic momentum trans
fer cross section [38], yielding
λ
25 m for kryp
ton and
λ
15 m for xenon. With reference to
Fig. 1, it can be observed that Br/Bz1in the
region where the scan is performed, with typical
values of Br106÷107T. The electron current
density is computed to be j
θ
e103Am2. Hence,
the electrons momentum equation reduces to a bal
ance between the volumetric electric forces term, i.e.
npeEz, and the volumetric pressure forces term, i.e.
pe/
z. By averaging the measured np(r,z),Vp(r,z)
and pe(r,z)over the radial direction, both terms of
Eq. 1 can be easily evaluated. Results are reported
in Fig. 17(a) for krypton and Fig. 17(b) for xenon. It
is shown that pressure gradient and potential gra
dient are nearly equal and opposite through all the
scanned region. Yet, this is more evident for kryp
ton than for xenon. Hence, it is concluded that the
density peak localized downstream is due to pres
sure balance. As the external magnetic field re
duces the crossfield electron mobility, a relatively
large axial conductivity ensues, which determines an
almost constant plasma potential profile, as shown
-5 0 5 10
-3
-2
-1
0
1
2
-5 0 5 10
-1
-0.5
0
0.5
1
Figure 17. Volumetric forces acting on the electrons
for (a) krypton and (b) xenon propellants. Variables ¯pe
and ¯
nprefer to radially averaged quantities.
in Fig. 11(c) and Fig. 12(c). This results in a small
pressure gradient for equilibrium reasons, cf. Equa
tion 1. The density peaks downstream because the
temperature drops.
Additional measurements include the investiga
tion of ion energy as function of the externally ap
plied magnetic field. In doing so, the RPA detailed
in Section 3.3 has been employed. To increase
data resolution, magnetic profiles with 6 mT and 8 mT
peak values have been added to the four ones previ
ously discussed. The probe has been placed down
stream at z=33 cm. While operating the HP source
at one specific magnetic strength, fifty IV character
istics are acquired in groups of ten. Data is firstly
smoothed and later numerically derived to obtain
the ion energy distribution function (IEDF). The most
probable ion energy (MPIE) is then extracted as
the IEDF peak value. Results in terms of MPIEs
for krypton and xenon are reported in Fig. 18 and
Fig. 19, respectively. As expected, higher ion en
ergies are measured as the external magnetic field
strength is increased, coherently with what reported
in Fig. 11(c) and Fig. 12(c). Generally speaking,
although consistent with the values of plasma po
4 5 6 7 8 9 10
0.5
1
1.5
2
2.5
3
3.5
4
Figure 18. Most probable ion energy as function of the
magnetic field. P
IN =750 W, ˙m=1mg/s Kr, z=33
cm. Horizontal mark indicates median value, thick box
delimits 25th and 75th percentiles, red marks represent
outliers.
4 5 6 7 8 9 10
4
5
6
7
8
9
Figure 19. Most probable ion energy as function of the
magnetic field. P
IN =750 W, ˙m=0.2mg/s Xe, z=33
cm. Horizontal mark indicates median value, thick box
delimits 25th and 75th percentiles, red marks represent
outliers.
8
tential, typical ion energies herein reported are very
small, suggesting low propulsive performance of the
HP source in analysis. The measured ion energies
imply electrostatic ion speeds of about 2.7 km/sfor
Kr+and about 3.5 km/sfor Xe+, both estimated for
the highest strength of the magnetic field. Higher
beam energies in the range of few tens of eV have
been reported in previous works [17, 3942]. It is
reasonable to state that this large performance dis
crepancy with respect to other HP sources comes
from a complete different set of input parameters.
The source analyzed in this work features a rela
tively large geometry and operated at relatively weak
magnetic fields and small mass flow rates.
4.2. Effect of Magnetic Throat Location
In this section, characterization of plasma properties
has been carried out using the diagnostics described
in Section 3 for the five magnetic field topologies pre
viously reported in Fig. 2(b).
The rfcompensated LP is displaced radially be
tween r=0and r=4cm and axially between
z=4 cm and z=21 cm. Five axial profiles for np,
Teand Vpare obtained for each magnetic topology
and interpolated to increase spatial resolution. Nor
malized 2D maps are reported in Fig.s 20 to 24. Nor
malization values are: 6·1017 m3for np,6 eV for Te,
25 V for Vp,0.3 Pa for pe. Solid black lines represent
computed magnetic field lines limited by the tube exit
cross section diameter.
When the reactor operates in configuration A,
most of the plasma light emission is concentrated
in the discharge tube and is reasonably lost at the
radial and back boundaries. Indeed, the down
stream expansion features a faint light emission and
is characterized by a low monotonically decreasing
npranging between 9·1015 and 1·1017 m3along
the axis, and a monotonically decreasing Teas high
024
0
5
10
15
20
024
0
5
10
15
20
024
0
5
10
15
20
024
0
5
10
15
20
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Figure 20. Normalized plasma density, electron tem-
perature, plasma potential and electron pressure ob-
tained for magnetic configuration A. Reference values
are: 6·1017 m3,6eV, 25 V, 0.3Pa. Input parameters
are: P
IN =750 W, ˙
m=1mg/s Kr.
as 3 eV. All plasma properties peaks occur onaxis
at z<0. Typical values of reflected power during op
eration were in the order of 2 %.
When the reactor operates in configuration B,
most of the light emission likewise concentrates
in the discharge tube. nppeaks onaxis at z<0
and then decays monotonically. Altogether, slightly
higher values of npare recorded with respect to con
figuration A. Tepeak moves offaxis with upper val
ues of 3.5 eV. Typical values of reflected power
were in the order of 5 %.
When the reactor operates in configuration C,
qualitatively similar results to those shown in Fig. 15
are obtained. As a matter of fact, this topology fea
tures the magnetic throat in the proximity of the tube
exit. All plasma properties peak offaxis, at z>0for
npin the order of 3·1017 m3and z<0for Teas
high as 4 eV. Measurements were not possible at
(0<r<2 cm;z<0) because of instability of the dis
024
0
5
10
15
20
024
0
5
10
15
20
024
0
5
10
15
20
024
0
5
10
15
20
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Figure 21. Normalized plasma density, electron tem-
perature, plasma potential and electron pressure ob-
tained for magnetic configuration B. Reference values
are: 6·1017 m3,6eV, 25 V, 0.3Pa. Input parameters
are: P
IN =750 W, ˙m=1mg/s Kr.
024
0
5
10
15
20
024
0
5
10
15
20
024
0
5
10
15
20
024
0
5
10
15
20
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Figure 22. Normalized plasma density, electron tem-
perature, plasma potential and electron pressure ob-
tained for magnetic configuration C. Reference values
are: 6·1017 m3,6eV, 25 V, 0.3Pa. Input parameters
are: P
IN =750 W, ˙
m=1mg/s Kr.
9
024
0
5
10
15
20
024
0
5
10
15
20
024
0
5
10
15
20
024
0
5
10
15
20
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Figure 23. Normalized plasma density, electron tem-
perature, plasma potential and electron pressure ob-
tained for magnetic configuration D. Reference values
are: 6·1017 m3,6eV, 25 V, 0.3Pa. Input parameters
are: P
IN =750 W, ˙m=1mg/s Kr.
024
0
5
10
15
20
024
0
5
10
15
20
024
0
5
10
15
20
024
0
5
10
15
20
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Figure 24. Normalized plasma density, electron tem-
perature, plasma potential and electron pressure ob-
tained for magnetic configuration E. Reference values
are: 6·1017 m3,6eV, 25 V, 0.3Pa. Input parameters
are: P
IN =750 W, ˙m=1mg/s Kr.
charge as the probe approached this region. Typical
values of reflected power were in the order of 3 %.
When the reactor operates in configuration D,
a narrow bright plasma beam is visibly recogniz
able downstream the antenna. It is evident from
Fig. 23 how npfollows the axial gradient of the
magnetic field, thus featuring its maximum value
of 5·1017 m3in correspondence of the mag
netic throat. It is prominent to notice the trans
port pattern of a relatively hot electron population
(Te3.5÷4.2 eV) localized at the external surface
of the magnetic nozzle, which is clearly guided
along the magnetic field lines towards the throat at
z
=10 cm. Typical values of reflected power were
about 1 %.
When the reactor operates in configuration E, a
bright slender plasma column is visible throughout
the expansion chamber. Highest values of npof
about 5.5·1017 m3are recorded when the reactor
operates with this magnetic topology. Density and
temperature profiles clearly follow the magnetic field
lines, cf. Fig. 24, showing that most of the electrons
with Te3 eV are concentrated in a beam of about
3 cm in radius at z
=10 cm. Typical values of reflected
power were less than 1 %.
In order to asses which of the employed magnetic
topologies better complies with the typical needs of
propulsion, it is relevant to consider the problem of
plasma confinement. To do so, diffusion in the di
rection perpendicular to the applied magnetic field
is analyzed by calculation of the classical crossfield
diffusion coefficient D, which reads [43]
D=
η
pe
B2Eq. 2
where
η
is the crossfield plasma resistivity com
puted assuming singly charged ions [43], peis
the electron pressure and Bis the magnetic field
strength. Axial profiles of Dare computed for the
five magnetic profiles shown in Fig. 2(b) using on
axis profiles of npand Teextracted from Fig. 20
24. Results are shown in Fig. 25. In the range
of zhere considered, all profiles experience a large
range of values between 0.1and marginally 10 2m/s.
Differently, the profile related to configuration D ex
ceptionally remains within a relatively narrow range,
roughly between 0.3and 0.72m/s. In accordance
with these results, advective diffusion parallel to the
magnetic field is better promoted over the cross
field diffusion for magnetic configuration D, mean
ing that less kinetic energy is lost in the radial di
rection. This consideration suggests that, in general
terms, there exists an optimal distance between the
antenna and the magnetic throat to be carefully ac
counted for throughout the design of a HP device.
A similar outcome has been drawn in [44], where
plasma confinement is analyzed as function of the
magnetic strength and discharge chamber length.
Plume divergence is also studied by employing
the PPGR previously described in Section 3. The
probe is placed at z=5and z=15 cm and actuated
along the xaxis. Measured values of jiare illus
trated in Fig. 26(a) and 26(b). A lowcurrent high
divergence ion beam is extracted from the plasma
source when operating with configurations A and B.
0 5 10 15 20
10-1
100
101
Figure 25. Computed profiles of cross-field diffusion
coefficient at r=0for the five magnetic configurations
A - E shown in Fig. 2(b).
10
-12 -10 -8 -6 -4 -2 0
100
101
102
-12 -10 -8 -6 -4 -2 0
100
101
102
Figure 26. Ion current density at a) z=5cm and b)
z=15 cm for the five magnetic configurations A - E
shown in Fig. 2(b).
Differently, the ion beams obtained with topologies
CDE present a similar lowdivergence profile of ji
close to the tube exit, cf. Fig. 26(a), yet plasma con
finement for configuration C is rapidly reduced down
stream, as shown in Fig. 26(b). Altogether, high
est values of jiare recorded for configuration E, in
agreement with the previously discussed values of
npreported in Fig. 24.
When dealing with space propulsion devices, effi
cient conversion of input energy into resulting thrust
is attained when high levels of propellant utilization
fraction and plasma confinement are achieved. By
accounting for the indirectly inferred values of D
and the measured profiles of ji, it is pointed out that
magnetic topologies D and E represent the preferred
operating choices for this particular HP source.
5. CONCLUSION
Plasma properties have been inferred via direct
measurements in a HP source operating with kryp
ton and xenon as propellants.
The two gases are compared as function of the
externally applied magnetic strength. It is found that
plasma potential axial profiles exhibit qualitative and
quantitative differences when using krypton for dis
tinct strengths of the magnetic field. This suggests
that the plasma source operates in inductive mode
below a threshold value of the applied field. In con
trast, no qualitative differences have been recorded
when using xenon. Measurements along the radial
direction revealed that all plasma properties peak
offaxis for all the tested magnetic strengths. Kryp
ton and xenon plasma properties are 2Dmapped
when the source operates with a magnetic field peak
value of 10 mT at the exit cross section of the dis
charge chamber. It is found that the electron tem
perature peaks offaxis just before the exit cross sec
tion, while the peak in plasma density occurs sim
ilarly offaxis but downstream where the electrons
are cooler. This phenomenon is quantitatively at
tributed to pressure balance effects. Ion energy is
measured as function of the applied magnetic field
strengths, showing that xenon performs better. Nev
ertheless, low ion energies are recorded.
Five different magnetic topologies have been an
alyzed to study the effect of the magnetic throat lo
cation with respect to the antenna location. The
plasma plume has been 2Dmapped for all the mag
netic geometries. It is found that a lowcurrent
highdivergence plume is extracted from the plasma
source when the magnetic throat is located up
stream the antenna, thus implying that the gener
ated plasma is lost at the radial and back bound
aries. As the magnetic throat is moved downstream,
higher currents and higher levels of plasma confine
ment are attained. This suggests that there exists an
optimal length between the antenna location and the
magnetic throat location to be accounted for when
designing an optimized HPT.
The reported experimental results represent an
useful set of data apt to be exploited for further
progress in theoretical modeling and numerical sim
ulations of plasma expansion in a magnetic nozzle.
In order to guide the design procedure of an opti
mized thruster, a complete 2D characterization of
the plasma plume would be of interest thus to indi
rectly retrieve the device performance.
ACKNOWLEDGMENTS
This project has received funding from the European
Union’s Horizon 2020 research and innovation pro
gram under grant agreement No 870542 (HelIcon
PlasmA Thruster for Inspace Applications).
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The research challenges for electric propulsion technologies are examined in the context of s-curve development cycles. It is shown that the need for research is driven both by the application as well as relative maturity of the technology. For flight qualified systems such as moderately-powered Hall thrusters and gridded ion thrusters, there are open questions related to testing fidelity and predictive modeling. For less developed technologies like large-scale electrospray arrays and pulsed inductive thrusters, the challenges include scalability and realizing theoretical performance. Strategies are discussed to address the challenges of both mature and developed technologies. With the aid of targeted numerical and experimental facility effects studies, the application of data-driven analyses, and the development of advanced power systems, many of these hurdles can be overcome in the near future.
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In the inductively coupled plasma of the Njord helicon device we have, for the same parameters as for which an ion beam exists, measured a downstream population of high-energy electrons emerging from the source. Separated measurements of energetic tail electrons was carried out by Retarding Field Energy Analyzer (RFEA) with a grounded entrance grid, operated in an electron collection mode. In a radial scan with the RFEA pointed toward the source, we found a significant population of high-energy electrons just inside the magnetic field line mapping to the edge of the source. A second peak in high-energy electrons density was observed in a radial position corresponding to the radius of the source. Also, throughout the main column a small contribution of high-energy electrons was observed. In a radial scan with a RFEA biased to collect ions a localized increase in the plasma ion density near the magnetic field line emerging from the plasma near the wall of the source was observed. This is interpreted as a signature of high-energy electrons ionizing the neutral gas. Also, a dip in the floating potential of a Langmuir probe is evident in this region where high-energy electrons is observed.
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The existence of a theoretically predicted critical magnetic field strength for efficient plasma confinement in helicon plasma thrusters is verified experimentally in the source of a magnetic nozzle (MN) flow. Control of the plasma confinement is crucial for enhancing the mass utilization efficiency of electric propulsion systems that employ MNs. Langmuir probe measure-ments of the density at the MN throat of a helicon plasma thruster as a function of the applied magnetic field strength indicate a transition from a low-confinement operation mode, in which a majority of the plasma diffuses to the solid walls of the plasma source before emerging from the thruster, to a high-confinement operation mode, in which the plasma preferentially exhausts downstream through the MN. This transition is shown to be governed by the anisotropic Péclet number, Pe an , which is defined as the ratio of the advective (field aligned) to diffusive (cross field) mass transport rates. Experimental estimations of the mass utilization efficiency of the plasma source for various magnetic field strengths and plasma source lengths are shown to support an analytically derived scaling law, and suggest Pe an 1 as a design criterion for MN plasma sources. Index Terms— Cross-field diffusion, helicon plasma, magnetic nozzle (MN), radio-frequency (RF) plasma.
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REGULUS is a propulsion platform for CubeSats. It integrates the Magnetically Enhanced Thruster (MET) and its subsystems (i.e., fluidic line, electronics, and thermo-structural components) in a 2U envelope of weight lower than 3 kg. MET is a RF cathode-less thruster capable of providing thrust in the range 300 μN to 900 μN, with maximum specific impulse of 900 s and maximum operation power of 60 W. The performance has been measured with a dedicated thrust balance, when the thruster is operated with 0.1 mg/s of Xenon gas. REGULUS: (i) is compatible with thermal, mechanical and electrical interfaces of the CubeSat platforms available in the marked, (ii) it relies on COTS components to abate the recurrent costs, and (iii) it is based on a passive thermal control system. The main framework of application of the REGULUS platform is the propulsion of medium-to-large CubeSats (from 6U up to 27U). Such capability is here demonstrated by comparing MET with other thrusters for CubeSats offered in the market. The feasibility of two possible mission scenarios, namely drag compensation and constellation deployment, has been verified through preliminary orbit calculations. The REGULUS platform can compensate the effects of atmospheric drag on a 6U CubeSat in a 400 km altitude orbit for years. Besides, by exploiting the natural drift of the ascending node caused by the second zonal harmonic of the terrestrial gravity field, a CubeSat constellation can be deployed through several planes in some months employing small fractions of the onboard propellant.
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The azimuthal plasma current in a magnetic nozzle of a radiofrequency plasma thruster is experimentally identified by measuring the plasma-induced magnetic field. The axial plasma momentum increases over about 20 cm downstream of the thruster exit due to the Lorentz force arising from the azimuthal current. The measured current shows that the azimuthal current is given by the sum of the electron diamagnetic drift and E x B drift currents, where the latter component decreases with an increase in the magnetic field strength; hence the azimuthal current approaches the electron diamagnetic drift one for the strong magnetic field. The Lorentz force calculated from the measured azimuthal plasma current and the radial magnetic field is smaller than the directly measured force exerted to the magnetic field, which indicates the existence of a non-negligible Lorentz force in the source tube.