On the feasibility of a negative polarity electric sail

Abstract

An electric solar wind sail is a recently introduced propellantless space propulsion method whose technical development has also started. In its original version, the electric sail consists of a set of long, thin, centrifugally stretched and conducting tethers which are charged positively and kept in a high positive potential of 20 kV by an onboard electron gun. The positively charged tethers deflect solar wind protons, thus tapping momentum from the solar wind stream and producing thrust. Here we consider a variant of the idea with negatively charged tethers. The negative polarity electric sail seems to be more complex to implement than the positive polarity variant since it needs an ion gun instead of an electron gun as well as a more complex tether structure to keep the electron field emission current in check with the tether surface. However, since this first study of the negative polarity electric sail does not reveal any fundamental issues, more detailed studies would be warranted.

Full text

Ann. Geophys., 27, 1439–1447, 2009
www.ann-geophys.net/27/1439/2009/
© Author(s) 2009. This work is distributed under
the Creative Commons Attribution 3.0 License.
Annales
Geophysicae
On the feasibility of a negative polarity electric sail
P. Janhunen
Finnish Meteorological Institute, Finland
Received: 26 September 2008 – Revised: 2 March 2009 – Accepted: 6 March 2009 – Published: 1 April 2009
Abstract. An electric solar wind sail is a recently introduced
propellantless space propulsion method whose technical de-
velopment has also started. In its original version, the elec-
tric sail consists of a set of long, thin, centrifugally stretched
and conducting tethers which are charged positively and kept
in a high positive potential of 20kV by an onboard electron
gun. The positively charged tethers deflect solar wind pro-
tons, thus tapping momentum from the solar wind stream and
producing thrust. Here we consider a variant of the idea with
negatively charged tethers. The negative polarity electric sail
seems to be more complex to implement than the positive
polarity variant since it needs an ion gun instead of an elec-
tron gun as well as a more complex tether structure to keep
the electron field emission current in check with the tether
surface. However, since this first study of the negative polar-
ity electric sail does not reveal any fundamental issues, more
detailed studies would be warranted.
Keywords. Interplanetary physics (Instruments and tech-
niques) – Magnetospheric physics (Storms and substorms)
– General or miscellaneous (New fields (not classifiable un-
der other headings))
1 Introduction
The electric sail (Janhunen, 2004; Janhunen and Sandroos,
2007) is a recently discovered, completely novel type of
space propulsion system concept which uses the solar wind
dynamic pressure for producing spacecraft thrust. The tech-
nical development of the spinning electric sail (Janhunen,
2006) commenced in 2006, currently already a long way to-
wards realisation. The spinning electric sail uses the centrifu-
gal force todeploy and stretch out a number of thin, longcon-
ducting tethers from the spacecraft (Fig. 1). The tethers are
Correspondence to: P. Janhunen
(pekka.janhunen@fmi.fi)
then charged positively by an onboard electron gun so that
their static electric field perturbs the trajectories of the inci-
dent solar wind protons, resulting in a momentum transfer
from the solar wind plasma stream to the tethers. The force
law of the electric sail (Janhunen and Sandroos, 2007) has
been used to calculate successful and efficient mission tra-
jectories in the solar system for realistic payloads and other
spacecraft characteristics (Mengali et al., 2008a).
The electric sail proposes to use the solar wind dynamic
pressure which is ∼5000 times weaker (about 2nPa at 1AU)
than the solar radiation pressure used by solar photon sails.
The electric sail is, however, able to overcome this appar-
ent shortcoming because the “sail” that intercepts the plasma
flow is not a physical obstacle, but a virtual structure made
by the electrostatic fields of the charged tethers. The virtual
electric sail that forms around each charged tether is typi-
cally tens or hundreds of metres in radius which is millions
of times larger than the physical width of the tether wires
(some tens of micrometres). It is mainly for this reason that
the electric sail can be clearly more efficient(i.e. have a larger
thrust per propulsion system mass) than a solar photon sail.
In this paper, we consider another variant of the electric
sail where the tethers are charged negatively. Like positively
charged tethers, also negatively charged bodies are able to
perturb the trajectories of solar wind ions, although the de-
tails of the interaction differ from the positive case, as we
will see below.
The structure of the paper is as follows: Firstly, after
briefly reviewing the original positive polarity electric sail
concept, we go on to present a semiquantitative analytic the-
ory for the plasma physics of a negatively charged tether
placed in solar wind. Secondly, we proceed to estimate the
three main current components (ion current, photoelectron
current and electron field emission current) that a negatively
chargedtether gathers from the solar wind. The current is im-
portant to evaluate because it determines how much electric
power it takes to maintain the tethers at the wanted negative
potential. After that, follows a brief survey of some technical
Published by Copernicus Publications on behalf of the European Geosciences Union.

1440 P. Janhunen: On the feasibility of a negative polarity electric sail
SW p
e−
Fig. 1. Schematic description of the original spinning, positive
polarity electric sail. Charged, centrifugally stretched tethers gather
momentum from the solar wind. The charging is maintained by an
electron gun mounted on the spacecraft (middle).
ways for implementing the tether. The paper ends with dis-
cussion and conclusions. Plasma simulations of the negative
polarity electric sail are outside the scope of this paper, as
are quantitative comparisons between the positive and nega-
tive polarity variants of the electric sail.
2 Positive polarity electric sail
We begin by reviewing the operating principles of the origi-
nally proposed positivepolarity electric sail (Janhunen, 2004,
2008; Janhunen and Sandroos, 2007). Consider a long, pos-
itively charged wire or tether placed in unmagnetised solar
wind. We take the solar wind to flow perpendicular to the
wire. This is not a restrictive assumption, because any paral-
lel flow component produces no effect since the ion equation
of motion in the parallel direction is trivial and not coupled
to the rest of the dynamics.
The positively charged wire creates an electron sheath
around itself where the potential of the cylindrical wire is
approximately
V (r) = V
w
ln

1 + (r
0
/r)
2

ln

1 + (r
0
/r
∗
w
)
2

(1)
Fig. 2. A four-wire Hoytether. Wire bonding sites are shown by
dots.
where
r
0
= 2λ
De
= 2
s

o
T
e
n
o
e
2
. (2)
Here λ
De
is the electron Debye length, T
e
is the solar wind
electron temperature (on average T
e
=12eV at 1 AU), n
o
is
the undisturbed solar wind electron density (n
o
=7.3cm
−3
on average at 1AU) and r
∗
w
is the effective electric radius
of the wire, typically r
∗
w
≈1mm. The effective electric ra-
dius (Janhunen and Sandroos, 2007) of the tether is larger
than the physical radius of the wires r
w
≈20µm of which
the micrometeoroid-resistant multiline tether (Hoyt and For-
ward, 2001) is constructed (Fig. 2). The potential of the
tether relative to the surrounding plasma is V
w
.
The mechanical lifetime of a multiline tether in space de-
pends on its geometry and on the number of wires; four wires
typically providing enough long lifetime for the electric sail
case according to our numerical estimations based on the mi-
crometeoroid flux model of Gr
¨
un et al. (1985) (∼1% break-
ing probability per 2000km of tether during 5 years). The
multiline tether can break by two main mechanisms, firstly
by numerous small impacts (impactors of ∼1/3 of wire width
or larger) which break single wires and secondly by one big,
centimetre-size impactor which cuts the whole tether at one
blow. Clearly, a wide tether is more resistant towards large
impactors while a narrow tether handles small impactors bet-
ter. The optimal tether width in the four-line case is, accord-
ing to our estimations ∼2–3cm at 1AU. The optimal width
is somewhat wider for asteroid belt missions where the mi-
crometeoroid flux consists of larger particles and narrower
for near-Sun missions where the average grain size is smaller
(Jehn, 2000). It is also beneficial if the multiline tether is
designed to assume a somewhat three-dimensional (i.e. not
completely planar) shape in space after deployment, since
a completely planar tether could be broken completely by
a single small impactor arriving exactly in the tether plane.
Differenttypes of multilinetethers and theirlifetimes are dis-
cussed by Hoyt and Forward (2001).
The solar wind ions experience the potential (Eq. 1) and
are deflected in their motion. In the frame of reference of the
wire, the total energy of the ion is conserved. Thus, the par-
ticle has the same speed after exiting the interaction region
than it had originally. Because the direction of the velocity
of the ion changes, the particle loses some of its momen-
tum x-component, where x is the coordinate along the solar
Ann. Geophys., 27, 1439–1447, 2009 www.ann-geophys.net/27/1439/2009/

P. Janhunen: On the feasibility of a negative polarity electric sail 1441
wind direction. This lost particle momentum is the reason
for the thrust that the tether experiences. The momentum
is transferred to the tether by an electric field due to piling
up of ions on the sunward side of the tether (i.e., a positive
charge cloud) and a corresponding ion depletion region (neg-
ative charge cloud) on the antisunward side. Thrust is ob-
tained because the electric field formed between the charge
clouds (typically ∼1 V/m in magnitude) pushes the positively
charged tether in the antisunward direction.
According to Janhunen and Sandroos (2007), the force per
unit length of the tether is given by
dF
dz
=
Km
p
n
o
v
2
r
0
r
exp
h
m
p
v
2
eV
w
ln(r
0
/r
∗
w
)
i
− 1
(3)
where v is the solar wind speed (typically 400km/s). Equa-
tion (3) is derived by finding at which r the potential energy
eV (r) of Eq. (1) is equal to the kinetic energy (1/2)m
p
v
2
of
incoming protons and multiplying this distance (the ion de-
flection distance) by the dynamic pressure of the solar wind
and by K. Here K is a dimensionless calibration coefficient
whose likely value is between 2 and 3. A test particle calcula-
tion of the momentum loss of solar wind protons in potential
V (r) of Eq. 1) gives the value K=3.09 (Janhunen and San-
droos, 2007). Plasma particle-in-cell (PIC) simulations gives
a result which is consistent with K≈3. However, Janhunen
and Sandroos (2007) also showed that an analysis of the
PIC result for different values for the electron temperature
T
e
gives a result which is not quite consistent with the func-
tional form of Eq. (3). One can explain away this inconsis-
tency by postulating that due to numerical noise the effective
value of the electron temperature in the PIC simulation elec-
tron sheath is higher than in the solar wind. If one assumes
that this postulate is true, then the PIC simulation results are
more consistent with K≈2 than with K≈3. Ultimately, only
experiments made in space or in the laboratory can give a
certainty of the value of K. Typical numerical values at 1AU
are V
w
=20kV, r
0
=20m and dF /dz=50−100nN/m as pre-
dicted by Eq. (3).
We assumed above that the solar wind is unmagnetised.
This is a good assumption because the ratio of the electron
Larmor radius to the electron Debye length is
r
Le
λ
De
=
s
m
2
e
v
2
e
n
o

o
T
e
B
2
=
r
m
e
m
i

c
v
A

. (4)
At 1AU, typically v
A
≈80km/s (corresponding to B=10nT
and n
o
=7.3cm
−3
) while
√
m
e
/m
i
=0.023. Thus at 1AU,
r
Le
/λ
De
≈901. When moving radially outward from the
Sun, this ratio does not change since it is proportional to the
Alfv
´
en speed v
A
. The Alfv
´
en speed does not vary because
ρ∼1/r
2
and B∼1/r in the equatorial plane. Thus the mag-
netic field can be neglected when considering electron mo-
tion in the sheath region. For ions, the Larmor radius is still
larger by factor ≈70 so they can be assumed to be unmagne-
tised as well.
The induced electromotive force, due to the solar wind
magnetic field, is generally insignificant compared to the
tether voltage. For example, for a typical 10nT field,
400km/s solar wind speed and 20 km long tethers, the max-
imum induced potential along the tether is only 80V. For
missions going near the Sun, e.g. at Mercury distance, the
field can sometimes be as large as 60nT, which would give
a 0.5 kV potential difference. Since typical voltages are
∼20kV for the positive polarity sail, one can conclude that
the induced voltage by the magnetic field is not significant
and, in most cases, can be ignored when analysing electric
sails.
The outward surface electric field on the tether wires is
typically 100–200MV/m. This field is still not high enough
for it to cause a significant emission of ions or ion clusters
from the surface. It is conceivable that some local micro-
scopic protrusions (e.g. whiskers) may be torn away by the
electrostatic force. Such protrusions might exist on the metal
surface originally or be caused by micrometeoroid cratering
in space. If this happens, it should not cause any problems,
since the expelled positively charged particles and fragments
exit permanently to space. Only an electric field, which is in
the range 5–10GV/m or even higher, could be able to extract
larger amounts of ions from a metal surface without the field
being amplified by local protrusions.
Equation (3) is formulated to agree with one- and two-
dimensional self-consistent plasma simulations of Janhunen
and Sandroos (2007). The plasma simulations are not sta-
tionary, but include explicitly the ramp-up phase of the tether
voltage. During the ramp-up phase, a certain fraction of
ambient electrons get trapped in the potential well. Conse-
quently, Eq. (3) includes the extra shielding effect of these
trapped electrons. As shown by Sanmart
´
ın et al. (2008), if
trapped electrons were absent, the potential structure would
be wider. Presumably, the thrust would also then be larger
than predicted by Eq. (3). After the present paper was
submitted, arguments were found supporting the view that
trapped electrons actuallytend to be removed by orbitchaoti-
sation in a realistic electric sail geometry and that the positive
polarity electric sail thrust could be roughly five times larger
than predicted by Eq. (3) (Janhunen, 2009). In the present
paper, performance comparisons of the positive and negative
sails are not attempted and from now on we concentrate on
analysing the negative sail variant as a standalone concept.
3 Negative polarity electric sail
A negatively charged tether attracts solar wind ions and re-
pels electrons so that an ion sheath gets formed around the
tether. Electrons (temperature ∼10eV) are cold compared
to the solar wind ion bulk flow kinetic energy (∼1keV) and
to the tether potential (>1 kV). They are thus pushed out to
www.ann-geophys.net/27/1439/2009/ Ann. Geophys., 27, 1439–1447, 2009

1442 P. Janhunen: On the feasibility of a negative polarity electric sail
a distance where the tether potential is almost completely
masked by ions. Consequently, there is an electron hole in-
side which only ions exist. Outside the electron hole, the
plasma properties do not differ markedly from the ambient
solar wind plasma.
In the positive polarity electric sail, some electrons get
trapped by the potential structure when the voltage is turned
on (Janhunen, 2004). A particle may get trapped by a poten-
tial structure only if the potential structure deepens by more
than the particle’s original kinetic energy during the time the
particle resides in the structure. Thus, only those particles
that initially moved very slowly with respect to the tether
can be trapped. The number of trapped particles does not de-
pend on the deepening rate of the potential structure. A faster
deepening rate implies a shorter duration of the process so
that fewer particles occur on the structure, but on the other
hand the width of the energy window from which particles
are trapped increases. These two effects cancel each other
out so that the number of trapped particles does not depend
on how rapidly the potential of the tether is turned on.
The solar wind electrons are approximately isotropic in the
sense that their bulk velocity (∼400 km/s) is less than their
random thermal speed (∼1600km/s). Thus, the distribution
contains a fair fraction of electrons with velocities close to
zero. The situation is completely different for solar wind
ions, because their thermal spread is only ∼10% of the bulk
speed. Thus, extremely slow ions (relative to the spacecraft)
that could become trapped are very few in the source distri-
bution. Consequently, no trapped ions are expected to exist
in the potential structure of a negatively charged tether placed
in the solar wind.
Consider an arbitrary two-dimensional negative potential
well V (x, y)≤0. Our task is now to estimate the ion den-
sity inside the potential in the absence of trapped ions. For
simplicity, we assume that there is no preferred direction in
ion velocity space, i.e. that the tether is approached by ion
streams from all perpendicular directions isotropically. This
assumption is not realistic because the solar wind ions arrive
only from one direction, but we shall make it here in order
to obtain an analytically tractable problem which hopefully
gives some rough guidelines to the real situation. The ion
distribution far from the tether is then the ring distribution,
f
o
(v
0
) =
n
o
2πv
o
δ(v
0
− v
o
) (5)
where v
o
is the ion stream speed, taken to be equal to the
solar wind bulk velocity, n
o
is the ambient ion density and
δ is the Dirac delta function. By Liouville’s theorem, which
is valid for collisonless plasma, the distribution function at
point (x, y) inside the potential structure is given by
f (x, y, v
x
, v
y
) = f
o
(v
0
)χ(x, y, v
x
, v
y
) (6)
where energy conservation fixes the original speed of the par-
ticle to be
v
0
=
q
v
2
x
+ v
2
y
+ 2eV (x, y)/m
i
(7)
and where the accessibility characteristic function
χ(x, y, v
x
, v
y
) is equal to one if backward trajectory
integration from (x, y, v
x
, v
y
) reaches a point which is
outside the potential structure and zero otherwise. From
Eqs. (5–7) we obtain
f (x, y, v
x
, v
y
) =
n
o
2πv
o
δ
"
s
v
2
x
+ v
2
y
+
2e
m
i
V (x, y) − v
o
#
χ(x, y, v
x
, v
y
). (8)
Equation (8) can be integrated to give the ion density inside
the potential structure
n(x, y) =
Z
dv
x
dv
y
f (x, y, v
x
, v
y
)
≤
n
o
v
o
Z
∞
0
dvvδ

q
v
2
+ 2eV (x, y)/m
i
− v
o

=
n
o
v
o
Z
∞
−v
o
du(u + v
o
)δ(u)
= n
o
. (9)
Here we made a change of variable
u =
q
v
2
+ 2eV (x, y)/m
i
− v
o
(10)
so that
du =
vdv
p
v
2
+ 2eV (x, y)/m
i
(11)
and made use of the fact that χ(x, y, v
x
, v
y
)≤1. Thus we ob-
tain an important and simple result that the ion density inside
the potential structure is at most equal to the ambient density
n
o
, irrespective of the functional form of the potential struc-
ture V (x, y). The result holds well for any two-dimensional
potential (Laframboise and Parker, 1973).
Knowing now that the ion density is everywhere limited
by n
o
and the electron density is approximately zero inside
some radius R and approximately equal to n
o
outside R (the
transition is sharp since the electrons are cold), we can cal-
culate the functional form of the potential V (x, y)=V (r)
under the assumption of maximum ion shielding, defined
by χ(x, y, v
x
, v
y
)=1 everywhere so that the inequality in
Eq. (11) becomes an equality. At radius R, it holds that the
ions completely shield the negatively charged tether inside,
i.e.
− eπ R
2
n
o
= λ = 2π 
o
r
w
E
0
(12)
where λ<0 is the line charge, r
w
the radius and E
0
<0 the
surface electric field of the tether. Solving Eq. (12) for R we
obtain
R =
s
2
o
r
w
(−E
0
)
en
o
. (13)
Ann. Geophys., 27, 1439–1447, 2009 www.ann-geophys.net/27/1439/2009/

P. Janhunen: On the feasibility of a negative polarity electric sail 1443
The electric field at a radius r, r
w
<r<R is given by Gauß’
law,
E(r) =
(λ + eπn
o
r
2
)
2π
o
r
=

r
w
r

E
0
+
en
o
r
2
o
. (14)
Integrating Eq. (14) we obtain the potential
V (r) =
Z
R
r
drE(r)
= (r
w
E
0
)

ln

R
r

−
1
2

−
T
e
4e

r
λ
De

2
(15)
where we have expressed the result in terms of the electron
Debye length λ
De
=
p

o
T
e
/(n
o
e
2
).
Equation (15) defines a solution for the potential valid for
cold electrons, no trapped ions and the entire phase space
accessible for traversing ions. If the entire phase space is
not accessible for traversing ions, then χ(x, y, v
x
, v
y
) van-
ishes at some points. In this case the ion density may be-
come smaller than what was assumed in the above calcula-
tion, and the non-logarithmic terms in Eq. (15) should be
damped by some factor which is less than unity. In what
follows, we shall not consider this correction, because the
most important term in Eq. (15) is the logarithmic one. In-
cluding this correction would tend to decrease ion shielding
and therefore to increase the propulsive force, so our assump-
tion χ (x, y, v
x
, v
y
)=1 gives a lower limit for the propulsive
force.
In reality the solar wind arrives from only one direction,
so the solution is no longer symmetrical. In any case, to
roughly estimate the force acting on the tether, we must esti-
mate the extent of the potential well which is able to cause a
large-angle turning of incoming ions. This amounts to find-
ing the radial distance (ion deflection distance) r
s
such that
V (r
s
)=V
i
≡−(1/2)m
i
v
2
o
/e. The solution for r
s
can be ex-
pressed in terms of Lambert’s W -function, also called the
product log function. For any x, W (x) is defined to be equal
to a solution y of the equation
x = ye
y
. (16)
The solution for the ion deflection distance is
r
s
= R
s
−W

−exp

−2
V
i
r
w
E
0
− 1

(17)
and a rough estimate for the thrust per unit length dF /dz is
the solar wind dynamic pressure P
dyn
=m
i
n
o
v
2
o
multiplied by
the extent of the strong ion scattering region 2r
s
,
dF
dz
≈ m
i
v
2
o
s
8
o
e
n
o
V
0
W

−exp

−
m
i
v
2
o
e|V
0
|
− 1

(18)
where the potential parameter V
0
=r
w
E
0
. For V
0
not much
larger than V
i
, Lambert’s W -function in Eq. (18) is evaluated
at a small negative argument for which it is enough to take
the first term in W ’s Taylor series
W (x) = x − x
2
+ (3/2)x
3
+ O(x)
4
. (19)
Thus, with W (x)≈x, Eq. (18) becomes
dF
dz
≈ m
i
v
2
o
r
8
o
e
n
o
|V
0
|exp
−
m
i
v
2
o
2e|V
0
|
−
1
2
!
= 1.72P
dyn
s

o
|V
0
|
n
o
e
exp
−
(1/2)m
i
v
2
o
e|V
0
|
!
. (20)
where we used
√
8e
−1/2
=1.72. Recall that the solar wind
dynamic pressure is P
dyn
=m
i
n
o
v
2
o
.
The potential of the tether, with respect to the surrounding
plasma, is obtained from Eq. (15) by setting r=r
w
. In this
case, the last term which is proportional to T
e
is vanishingly
small and we obtain
V
w
= V (r
w
) = V
0

ln

R
r
w

−
1
2

(21)
Equation (20), or alternatively the more accurate version
Eq. (18), is the main result of this section. It tells us that
the effective electric sail width of a negatively charged tether
contains, as the essential factor, an “effective Debye length”
λ
eff
D
=
s

o
|V
0
|
n
o
e
(22)
where instead of the electron temperature the potential pa-
rameter V
0
=r
w
E
0
appears (recall that E
0
is the wire surface
electric field). This length λ
eff
D
is potentially large, leading to
a potentially large force per tether length. For example, in
average solar wind at 1AU and with V
0
=1kV, λ
eff
D
=87m.
However, before being able to realise the potential thrust
benefit of the negative polarity electric sail, several questions
need to be addressed: How large a current does a negatively
charged tether gather from the solar wind plasma? How large
a surface electric field E
o
can be safely maintained without
a risk of an electric breakdown of some sort? Is the ion gun,
which is necessary to maintain the negative potential, dif-
ficult to construct? Does one need significant amounts of
propellant to create the ions? We will now consider these
questions.
To control the motion of the tethers, the tether potentials
must be known and controllable. This can be accomplished
by monitoring thespacecraft potential with respect to the sur-
rounding plasma by using a particle detector (ion detector in
negative polarity sail, electron detector in positive polarity
sail). The tether potentials are controlled by potentiometers
(tunable resistors) that are installed between each tether and
the spacecraft. For each tether, its potential is the sum of the
spacecraft potential and the potentiometer voltage. The po-
tentiometer voltage can be measured electrically and it can
be controllably changed by changing the resistance of the
www.ann-geophys.net/27/1439/2009/ Ann. Geophys., 27, 1439–1447, 2009

1444 P. Janhunen: On the feasibility of a negative polarity electric sail
potentiometer. The turning of the sail is possible using an al-
gorithm resembling helicopter flight control where the tether
potentiometer settings are modifying cyclically and in sync
with the rotation when one wants to tilt the sail (Janhunen,
2006).
4 Current gathered by negatively charged tether
Consider a negatively charged tether immersed in solar wind
plasma. Our task is to estimate how much current per unit
length the tether gathers from the plasma if it is kept at po-
tential V
w
.
We consider three sources of gathered current: the ther-
mal ion current arriving from the surrounding plasma, cur-
rent carried by solar ultraviolet (UV) radiation induced pho-
toemission of electrons from the tether surface and finally
current due to field emission of electrons (Fowler-Nordheim
current) at the tether surface.
4.1 Thermal ion current
Because the solar wind is very tenuous, the plasma is col-
lisionless to a very good approximation. The tether acts as
a cylindrical probe immersed in plasma and the ion current
can be calculated by the orbital motion limited (OML) theory
(Allen, 1992). The current per unit length is

dI
dz

th.
= en
o
s
eV
w
m
p
2r
w
. (23)
For a self-contained derivation of this expression, see Ap-
pendix B of Janhunen and Sandroos (2007). This current is
p
m
e
/m
p
≈43 times smaller than the corresponding electron
current in the positive electric sail case and can nearly always
be neglected.
4.2 Photoelectron current
A sunlit object, such as a conducting tether, emits photoelec-
trons due to solar UV radiation. If the tether is positively
charged, the photoelectrons cause no macroscopic current
since they are rapidly attracted back to the tether. When the
tether is negatively charged, however, photoelectrons are re-
pelled by the tether and therefore they contribute directly to
the current gathered by the tether. Notice that the photoelec-
tron current is independent of the tether voltage, but depends
only on the tether surface properties, the solar UV spectrum
and the solar distance.
Grard (1973) estimated the photoelectron emission at
1AU from selected materials as follows: aluminium ox-
ide 42µAm
−2
, gold 29µAm
−2
, stainless steel 20µAm
−2
,
graphite 4µAm
−2
. The spacecraft photoelectron yields
inferred from orbital data are typically somewhat higher
than those based on laboratory measurements of Grard
(1973). For example, Nakagawa et al. (2000) determined
the photoelectron current for the GEOTAIL spacecraft to be
85±33µAm
−2
. Our present baseline material for construct-
ing electric sail tethers is aluminium whose surface has the
natural oxidation layer formed by atmospheric oxygen. We
shall here adopt Grard’s aluminium oxide value as represen-
tative for the tethers so that we have

dI
dz

photoel.
= 42µAm
−2
× 2r
w

1AU
r

2
. (24)
With average solar wind density at 1 AU and with V
w
=20kV,
the photoelectron current is 43% of the electron current of the
corresponding positive electric sail case.
Both the thermalplasma current and the photoelectron cur-
rent scale as 1/r
2
where r is the distance from the Sun. Thus
both the ion thermal current and the photoelectron current
are conveniently modest in magnitude. They do not appear
to present a problem for the realisation of a negative polarity
electric sail.
4.3 Electron field emission current
A negatively charged electrode may emit electrons at a much
lower surface field than a positively charged electrode can
emit ions. Electron emission from sharp, well-cleaned tips
follows closely to the Fowler-Nordheim field emission law
and its later modifications taking into account finite temper-
ature and other refinements (
Alpert et al., 1964; Noer, 1982;
Halbritter, 1983) and takes place typically at 1–2GV/m sur-
facefield. (Since the dependence of the current density on the
electric field E is proportional to E
2
exp(−1/E), the emis-
sion increases rapidly from insignificant to large values.) For
broad-area electrodes containing attached dust, local impu-
rities and adsorbed gases, however, significant electron field
emission is typically observed already at ∼100 times smaller
fields of order 10MV/m (Noer, 1982; Halbritter, 1983).
Basically, all experimental investigations of electron field
emission have taken place in ground-based laboratories
rather than in space. In the laboratory, there are always two
electrodes present, anode and cathode. There are experimen-
tal indications that the onset and nature of electron field emis-
sion at the cathode also depends on the properties of the an-
ode (Noer, 1982). The physical mechanism is possibly that
relatively weak but very localised electron beams initially
emitted by the cathode knock loose some ions from the an-
ode upon impacting it. The ions are then accelerated by the
electric field back to the cathode and impact it near the origi-
nal electron emission spot. This may cause further secondary
electron emissions at the cathode local emission site. Ions in
the space between the electrodes can also be produced by
electron impact ionisation of neutral atoms outgassed from
the anode by local heating caused by the cathode-emitted
electron beams.
These complicated interaction and feedback phenomena
between the cathode and anode, while always present in the
laboratory, are absent in space where the other electrode is
Ann. Geophys., 27, 1439–1447, 2009 www.ann-geophys.net/27/1439/2009/

P. Janhunen: On the feasibility of a negative polarity electric sail 1445
formed by the surrounding space plasma. It might, therefore,
be the casethat a broad-areacathode in spacetolerates higher
surface fields than in the laboratory. There is in practice no
other way to find this out other than to perform an experiment
in space with a thin cathode wire.
All materials, including metals, outgas to some extent in a
vacuum. Part of the outgassed molecules can become ionised
by solar UV radiation while moving out from the tether. If
ionisation takes place while the molecule is inside the poten-
tial structure of the tether, it may form a trapped ion. We have
estimated the magnitude of this effect and found that under
some circumstances, such outgassing produced ions might
produce unwanted trapped ions to an extent that matters. An
easy fix to this potential problem, if it occurs, is to reset the
potential periodically to clean out the unwanted trapped ions
from the potential structures of the tethers.
5 Technical design
5.1 Ion gun
The negative polarity sail needs an ion gun instead of an elec-
tron gun to keep itself charged. Although an ion gun is a
more complicated device than an electron gun, its construc-
tion should not present any fundamental problems. Impor-
tantly, the number of ions that one must emit over a reason-
able operational lifetime of the electric sail (some years), is
not so large that the mass of the propellant from which the
ions are created would be a significant item in the spacecraft
mass budget. The ion gun is effectively equivalent to a very
high specific impulse ion engine. Such a deviceneeds mainly
power, but does not consume much propellant. Since the aim
is to produce current rather than mass flow, light ions would
be preferable to heavy ones in this case, in order to min-
imise propellant mass. Since ion engines typically use xenon
(atomic mass 131), we shall consider it also here, however. If
the electric sail tethers are charged to 20kV, the speed of the
emitted Xe
+
ions is 170km/s. Recent developments of four-
gridded ion engines should make such high exhaust speeds
reachable (Fearn, 2005). At such a high specific impulse,
even a high-powered engine uses relatively little propellant.
As noted above, by replacing xenon by a lighter element such
as argon, the propellant mass consumption could be lowered
further if needed. Overall, then, if and when the power is
available to feed it, the ion gun which is needed to keep the
negative polarity electric sail charged should not present in-
surmountable problems.
The extra thrust provided by the ion gun is almost negligi-
ble (less than 1mN even if using xenon) in comparison with
the electric sail thrust, because the ion gun specific impulse
is very high and its power is only modest.
5.2 Tubular tether
Consider a hollow tubular tether with radius r
w
, wall thick-
ness h (hr
w
), material mass density ρ
m
and conductivity
σ . The tether mass per unit length is
dm
dz
= ρ
m
πh(2r
w
− h). (25)
If we use surface electric field E
0
, the tether generates force
per unit length
dF
dz
= 1.72P
dyn
s

o
|V
0
|
n
o
e
exp
−
(1/2)m
i
v
2
o
e|V
0
|
!
(26)
where V
0
=r
w
E
0
. Assuming that the surface electric field is
such that electron field emission current is negligible, other
current components except the photoelectron current (Eq. 24)
can be neglected. The power consumption per unit length
is then the current obtained from Eq. (24) multiplied by the
tether voltage (Eq. 21). The result can be written in the form
dP
dz
=

42µAm
−2

× 2r
w
V
0
"
ln
λ
eff
D
r
w
!
−
1 − ln2
2
#
(27)
where λ
eff
D
is defined by Eq. (22).
As a performance metric, we use the specific accelera-
tion a
spec
, defined here to be the obtained thrust divided by
the mass of the tether as obtained from Eqs. (25) and (26),
or a
spec
=(dF /dz)/(dm/dz). Figure 3 shows the specific
acceleration a
spec
and the specific power [consumed power
divided by obtained thrust, (dP /dz)/(dF /dz)] as a func-
tion of the tether radius of a tubular aluminium tether with
10µm wall thickness in average solar wind at 1AU, for
two values of the allowed surface electric field E
0
=5 and
10MV/m. One sees that the result depends strongly on the
valueof E
0
adopted. For E
0
=10MV/m, for example, we ob-
tain at the optimum point a specific acceleration of 8mm/s
2
at ∼20kV voltage, consuming only ∼1.3W/mN of electric
power. Assuming that the spacecraft has e.g. 100 tethers of
20km length each, we obtain in this case a total thrust of
0.42N, tether mass 50 kg and power consumption 530 W. If
the power system, tether reels and ion gun would weigh an-
other 50kg and the payload e.g. 300kg so that the total mass
would be 400kg, the propulsive acceleration would be about
1mm/s
2
. This level of acceleration is already adequate for
performing many manoeuvres in the solar system (Mengali
et al., 2008a,b).
The tether mass for a tubular tether is directly proportional
to the wall thickness which was here assumed to be 10 µm.
For example, with a thinner 5µm wall the specific accelera-
tion would be two times higher and in the above example the
tether mass would be 25kg instead of 50kg.
The quantity a
spec
is useful because it is simple to calculate
and does not depend on other parameters. In a more detailed
performance analysis, one should use a more advanced figure
www.ann-geophys.net/27/1439/2009/ Ann. Geophys., 27, 1439–1447, 2009

1446 P. Janhunen: On the feasibility of a negative polarity electric sail
a)
0
1
2
3
4
5
6
7
8
mm s−2
Specific acceleration
b)
0
5
10
W/mN
Specific power
c)
100 10
3
rw/um
0
10
20
30
40
kV
Voltage
Tubular tether
Fig. 3. Specific acceleration (a), specific power consumption (b)
and voltage (c) of a tubular, negatively charged aluminium tether
with 10µm wall thickness. The logarithmic horizontal axis is the
radius r
w
of the tether in micrometres. Solid curves correspond
to allowed surface electric field E
0
=5MV/m and dashed curves
to E
0
=10MV/m. Points of maximum specific acceleration are
marked on the curves.
of merit which takes explicitly into account the mass of the
spacecraft power system, tether reels and the ion gun. How-
ever, for applications where the payload mass is in any case
rather large compared to the sail propulsion system mass, the
exact mass of the propulsion system is not too significant. In
this type of application, it is more important that the electric
sail propulsion system can generate enough thrust without
having to make the total tether length excessive.
In practice, instead of a tubular tether, one might prefer
to use related but somewhat different tethers such as quasi-
tubular “wiresock” tethers constructed by wire-wire bonding
from e.g. 10–30 metal wires of ∼20µm thickness. However,
analysing this and other kinds of tether structures, is outside
the scope of this paper.
The most important parameter whose exact value remains
unknown is the allowed surface electric field E
0
, i.e., how
large surface electric field E
0
the tether tolerates before field
emission from the tether (probably mainly from points dam-
aged by micrometeoroids) becomes comparable to or larger
than the photoelectron current. We think it is likely that a
value E
0
=5MV/m should be rather safe, but it is not out of
the question that also larger values could be used. Experi-
ments would be needed to ascertain this.
6 Discussion and conclusions
The negative polarity sail current has three components: ion
current, photoelectron current and electron field emission
current. The ion current is small and it scales by the so-
lar wind density (1/r
2
). The photoelectron current is larger
(roughly similar to typical current in positive polarity sail)
and it also scales as 1/r
2
. The sum of ion and photoelectron
currents, therefore, scales as 1/r
2
and is nearly independent
of the tether voltage, because the ion current part is small.
Currents that scale as 1/r
2
are nice because their associated
power consumption then scales in the same way (1/r
2
) as the
power produced by solar panels. The electron field emission
current is independent of r, but it depends strongly on the
tether voltage. The level of usable surface electric field E
0
,
before significant electron field emission sets in at some point
on the tether, is the main parameter in the negative electric
sail concept whose exact value remains inaccurately known,
due to lack of experimental data on long cathode wires with-
out nearby anodes in the ultra-high vacuum of space.
Recently, Choini
`
ere and Gilchrist (2007) studied the
sheath extent and current collection of negative tethers in
moving plasma by self-consistent steady state 2-D Vlasov
simulation and under the assumption of no trapped particles.
Their calculation method could probably be easily extended
to produce more accurate thrust estimates than what we have
provided here.
In principle, the thrust of the negative polarity electric sail
also receives a contribution from the impulse given by ions
that hit the wires. This thrust contribution can be estimated
to be negligibly small, however, for typical parameter values,
so we do not discuss it explicitly.
If significant electron field emission occurs, it takes place
at a few points containing dielectric impurities, micromete-
oroid damage or other anomalies along the tether. We might
speculate with the possibility of “cleaning” the tetherof some
of the high field emission sites by running it in high positive
polarity mode for some time, hoping that Coulomb repulsion
extracts the unwanted material from the surface. This possi-
bility, while speculative, would in any case be accessible to
experimental investigation.
In conclusion, the negative polarity electric sail might be
a feasible concept to implement in its own right, although
it has a set of issues mainly related to electron field emis-
sion from negatively charged wires that would need to be ad-
dressed. The question of whether the negative polarity vari-
ant would provide some performance benefit compared to
the original positive polarity electric sail depends mainly on
whether trapped electrons exist or not in the positive polarity
sail. This question is presently under active study and one
should wait for the answer before drawing final conclusions.
In any case, the thrust level of both the positive and nega-
tive electric sail concepts has the potential to be quite high in
comparison to presently existing space propulsion methods.
Ann. Geophys., 27, 1439–1447, 2009 www.ann-geophys.net/27/1439/2009/

P. Janhunen: On the feasibility of a negative polarity electric sail 1447
Acknowledgements. The author thanks Petri Toivanen and
Arto Sandroos for many discussions related to the topic and
acknowledges the much larger international electric sail team for
background support. The work was supported by the Academy of
Finland. The author also wants to express special thanks to both
referees for their thorough scrutiny of the paper using a multitude
of approaches.
Topical Editor I. A. Daglis thanks two anonymous referees for
their help in evaluating this paper.
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