A recent space experiment confirmed sheath-wave propagation of a kilometer-long insulated wire in the ionosphere, oriented parallel to the Earth's magnetic field. This space tether experiment, Oedipus-A, showed a sheath-wave passband up to about 2 MHz and a phase velocity somewhat slower than the velocity of light in a vacuum, and also demonstrated both ease of wave excitation and low attenuation. The evidence suggests that, on any large structure in low Earth orbit, transient or continuous wave electromagnetic interference, once generated, could propagate over the structure via sheath waves, producing unwanted signal levels much higher than in the absence of the ambient plasma medium. Consequently, there is a need for a review of both electromagnetic interference/electromagnetic compatibility standards and ground test procedures as they apply to large structures in low Earth orbit

Balmain, K. G.

Bantin, C. C.

James, H. G.

English

NASA Technical Reports Server

ND -20VZ3 1-
MAGNETOPLASMA SHEATH WAVES ON A CONDUCTING TETHER
IN THE IONOSPHERE, WITH APPLICATIONS TO EMI PROPAGATION ON
LARGE SPACE STRUCTURES
K.G. Balmain, Department of Electrical Engineering, University of Toronto,
Toronto, Canada, M5S 1A4
H.G. James, Communications Research Centre, Ottawa, Canada
C.C. Bantin, University of Toronto, Toronto, Canada
ABSTRACT
Electromagnetic waves called "sheath waves" can pro-
pagate with low attenuation in the ion sheath, a region of
low electron density that separates any conducting surface
from an ionized-gas plasma in which it is immersed.
Cold-plasma theory predicts propagation in a passband
from zero frequency up to 1/_2"- times the electron plasma
frequency for isotropic plasmas and up to 1/-,/'2"-times the
upper hybrid frequency for anisotropic plasmas permeated
by a magnetic field in the direction of propagation. A
recent space experiment has confirmed sheath-wave propa-
gation on a kilometer-long insulated wire in the ionosphere,
oriented parallel to the earth's magnetic field. This space-
tether experiment, OEDIPUS-A, showed a sheath-wave
passband up to about 2 MHz and a phase velocity some-
what slower than the velocity of light in a vacuum, and also
demonstrated both ease of wave excitation and low
attenuation. The evidence suggests that, on any large struc-
ture in low earth orbit, transient or continuous-wave elec-
tromagnetic interference, once generated, could propagate
over the structure via sheath waves, producing unwanted
signal levels much higher than in the absence of the
ambient plasma medium. Consequently there is a need for
a review of both EMI/EMC standards and ground test pro-
cedures as they apply to large structures in low earth orbit.
INTRODUCTION
An ionized gas plasma in contact with a solid surface is not
homogeneous near the surface. Rather, it is inhomogene-
ous, forming a thin layer which contains ions from the
plasma but very few electrons, so it is known as the "ion
sheath". At the frequencies of interest, the ions are massive
enough to be almost immobile, so it is the electrons that
govern sheath behavior. Because the sheath is electron-
depleted, to a first approximation it may be regarded as a
vacuum gap. If the solid surface in question is a metal,
then the picture that emerges is that of a vacuum gap
separating a good conductor from a plasma which is also a
conductor, albeit a very complex one. It is plausible that a
vacuum gap between these two conductors can act as a
guiding channel for an electromagnetic wave, and indeed
this is known to be the case, the waves being called "sheath
waves".
Early theoretical studies of sheath waves on a cylindrical
conductor were done by Seshadri [1965], and by Miller
[1968] who analyzed the case with a static magnetic field
parallel to the conductor axis. Experimental studies were
included in the papers by Ishizone et al. [1969, 1970a,
1970b], Lassudrie-Duchesne et aL [1973], Meyer et al.
[1974], Marec [1970, 1974] and Marec and Mourier [1970,
1972]. Recently, Laurin et aL [1989] analyzed sheath-
wave propagation over a planar surface, propagating in a
direction parallel to the ambient static magnetic field, and
they compared their analysis with laboratory experimental
results for a thin wire in a magnetized plasma. Their con-
clusion was that sheath waves propagate in a frequency
range from zero to 1/-_/-2-times the upper hybrid frequency,
at least for the special case of wave propagation parallel to
the magnetic field. Moreover they concluded that the
waves propagate with a phase velocity that is slower than
the velocity of light in a vacuum and approaches a nearly
constant value at low frequencies (i.e. it is nearly disper-
sionless). Propagation in isotropic (unmagnetized) plasma
is similar, with the plasma frequency fp replacing the
upper-hybrid frequency fu , where fu _ = fp_ + fc 2 and fc
is the electron cyclotron frequency.
THE "OEDIPUS-A" ROCKET EXPERIMENT
This project involved an ionospheric rocket which was
launched in January 1989 from Andoya, Norway. It was
separated into two parts early in its flight, the two parts
remaining connected by a thin, insulated wire (or "tether")
that unreeled from a spool in the rocket nose section, reach-
ing a maximum wire length of 985 m near apogee. During
the flight, the tether orientation stayed within 5° of being
parallel with the earth's magnetic field. A stepped-
frequency transmitter with an output level of 50 Vrms and
covering the range 50 kHz - 5 MHz was located in the nose
section and a synchronized receiver was located in the tail
646
https://ntrs.nasa.gov/search.jsp?R=19910011410 2020-03-19T19:04:05+00:00Z
section. There were several experiments on board, the one
of primary interest in this paper having the configuration
shown in Figure 1, the purpose being to measure the
transmission of signals end-to-end along the tether. The
particulars of the tether are shown in Figure 2, in which it
can be seen that the tether unreeled steadily, reaching max-
imum extension midway during the flight.
Figure 3 is a gray-scale representation of received signal
strength as a function of both frequency and elapsed time
during the flight. The dominant feature is a strong
passband from zero frequency up to a sharp cutoff fre-
quency between about 1.7 and 2.3 MHz. Above the cutoff
frequency is a strong stopband extending upward to a fre-
quency between 3 and 4 MHz where there is a return to
fairly strong signal levels. As an aid to interpretation, Fig-
ure 3 includes a graph of plasma frequency ft, (taken from
delayed-pulse measurement data supplied by one of the
authors, H.G.J.) along with a graph of cyclotron frequency
fc . Also included are graphs of upper-hybrid frequency
fu and sheath-wave cutoff frequency fs = 1/'4_ffu , as
well as harmonics of the cyclotron frequency.
The theoretical sheath-wave cutoff frequency f¢ is about
30% higher than the measured cutoff frequency. This may
be due to the expected high attenuation of sheath waves
just below the cutoff frequency. Above the cutoff fre-
quency is the stopband which extends upward to the
upper-hybrid frequency fc , as predicted by cold-plasma
theory.
Within the low-frequency passband and for the earlier part
of the flight, some very faint curved lines can be seen.
These are enhanced by adjusting the gray-scale and are
shown much more clearly in Figure 4. It is postulated that
they are resonances occurring whenever the tether length is
a multiple of a sheath-wave half-wavelength. Based on
this postulate, contours for different sheath-wave phase
velocities (refractive indices or wavenumbers) were drawn
until a reasonable fit was obtained as shown, which is for a
constant refractive index of 1.7 : this indicates that a rela-
tively non-dispersive slow wave exists on the tether, in
agreement with the sheath-wave postulate. The resonances
are clearly visible at all frequencies up to the cyclotron fre-
quency fc , above which only faint indications of reso-
nances can be seen ar_'only up to an elapsed time of about
260 seconds. It will require further study to determine
whether or not the rapidly rising attenuation (with increas-
ing frequency) as predicted by Laurin et al. [1989] is
sufficient to explainthe disappearance of the resonances at
or just above fc for the greater part of the flight duration.
As an aside, it is interesting to note that dipole-to-dipole
transmission experiments (with one dipole on the nose sec-
tion and one on the tail section) produced gray-scale plots
similar to Figures 3 and 4. In particular, the tether-length
resonances were clearly visible even though the tether was
not connected either to the transmitter or the receiver. This
indicates that there was strong excitation of sheath waves
in a situation where it was not intended.
Nose
section Transmitter
Spool
Direction
of earth's
magnetic
field
Tether
on
Tail
section
Figure 1. Diagram of the "OEDIPUS A" rocket experi-
ment configuration used for the study of sheath
waves.
647
of/i
E
o
Y
"l-
u
_r
b,.
1000
800
600
4O0
/
200 /
0
00
Figure 2.
100
Figure 3.
/
/
20,
/
/
\
300 4.00 500 600 700
Time (seconds after launch)
Tether length and altitude as functions of elapsed time. Tether wire length:
1300 meters; tether wire: No. 24 AWG, 19 strands of No. 36 copper, diame-
ter 0.020"; tether wire coating: irradiated polyolefin, diameter 0.057",
e, = 2.32; wire resistance: < 100 ohms over 1300 meters; spool-to-chassis
resistance: > 3 x 10 TM ohms; contact: slip ring; braking: constant-torque of
6.5 oz-in.
200 300 400 500 600 700
Time (seconds after launch)
Received signal strength (darker gray scale means higher signal level) show-
ing the cyclotron frequency fc and its harmonics, the plasma frequency fp,
the upper-hybrid frequency fu, and the nominal sheath-wave cutoff fre-
quency fs = fu /_l'Z.
ORIGINAL PAGE iS
OF POOR QUALITY
4"i-
v
_Z
O)
2
O"
h_
0
1 O0 20O 300 400 500 600 700
Time (seconds after launch)
Figure 4. Received signal strength with gray-scale adjusted to show tether-length reso-
nances. Lines show where tether is a multiple of a half wavelength long,
assuming a wavenumber of 1.7.
Figure 5 shows received amplitude plotted against fre-
quency at four different times during the flight. The
features already discussed are evident, but most prominent
is the high level of the low-frequency passband and the
depth of the stopband, the difference in levels being of the
order of 70 dB.
A particularly interesting feature visible in Figs. 3, 4 and 5
is the association of gray-scale boundaries with the har-
monics of the cyclotron frequency. This suggests that
cyclotron-harmonic waves which propagate across the
magnetic field play a part in sheath-wave attenuation, say
by carrying energy away from the tether (a suggestion
made by one of the authors, H.G.L). There are two impli-
cations, the first that this is a "leaky wave" phenomenon
(and that the tether has become a leaky-wave antenna), and
the second that kinetic theory will be required to explain
fully the phenomenon of sheath waves.
Highly simplified theory may still be helpful, however,
especially in view of the scarcity of theoretical develop-
ments adequate for the computation of fields due to given
sources in finite-temperature anisotropic plasmas. Con-
sider isotropic, cold plasma : existing thin-wire computer
programs for lossy media can be adapted readily to cover
this case, for example the program developed by Richmond
[1974] and improved by Tilston and Balmain [1990]. This
program can model isotropic cold plasma and a vacuum-
gap sheath surrounding any interconnected network of thin
wires. Its utility in application to anisotropic plasma will
always be limited but, for the case of a wire parallel to the
magnetic field, the strong radial electric field is always per-
pendicular to the magnetic field. This means that the per-
pendicular permittivity will predominate, with its zero at
the upper-hybrid frequency rather than at the plasma fre-
quency as would be the case with no magnetic field. This
suggests that isotropic cold-plasma theory could be useful
as a rough first approximation provided that the numerical
value of the upper-hybrid frequency is substituted for the
plasma frequency. The result of doing this is shown in Fig-
ure 6 in which the sheath-wave refractive indices deduced
from measured resonances (ranging from 1.20 to 1.75) are
bracketed by theoretical values computed by selecting two
isotropic plasma frequencies spanning the range of upper
hybrid frequencies in the experiment.
ORIGINAL PAGE iS
OF POOR QUALITY
649
tl
i-
Recotv_l S3g_J _L t-270 raN;
'
-2
-4.- --_
-5
-e.
-0
-9
-|0 I
-11 1
--t2
0.0 1.0 2.0 3,0
I " | I
4,0 5.0
O_PUg A F141ht
Received ._;gr,o( o_ t-31_ se¢ R_md _¢mQI at t-384 me¢
-12
0.0 1,0 2.0 3.0 4.0 5.0 CLO 2,0 3.0
_mc,uer_ (ur_,z) _ (ue,z)
!
i
1.0 4._0 5.0
Figure 5. Frequency sweeps of received signal level at elapsed times 234 sec., 270
sec., 318 sec., and 384 sec.
650
o
2_
4.0
3.0
2.0
1.0
0.0
.'I
f
0.0
[] Ist
fp=2.5MHz
_-
f'p=3.gMHz
0.5 1.0 1.5 2,0
Frequency (MHz)
A 2nd reson. O 3rd reson. X 4th reson. -- MM resultsresort.
Figure 6. Wavenumbers derived from various resonances, together with moment-
method calculations of wavenumbers in isotropic plasma, using two different
values of plasma frequency intended to span the actual experimental values
of upper hybrid frequency. The assumed sheath radius is 2.5 cm.
651
The use of gridded end-plates to represent the rocket nose
and tail in this cold-plasma numerical calculation enables a
calculation of typical transmitted signal level along with a
free-space comparison as shown in Figure 7. The low-
frequency passband and the transition to a deep stopband
around 70 dB lower are clearly evident, along with tether-
length resonances. The calculated cutoff frequency fs at
2.6 MHz is clearly too high (compared with the measured
value of 1.8 MHz at an elapsed time of 590 see.).
Nevertheless, the calculations up to 1 MHz or somewhat
20
-2O
i
higher still are the best available theoretical results that
include approximate representations of the rocket nose and
tail sections. In particular, the comparative plasma-with-
sheath and free-space calculations deserve attention. With
the sheath, the signal level in the plasma is 30 dB to 60 dB
higher than in free space, at frequencies below 1 MHz. It is
this strong coupling that has implications for EMI/EMC on
large structures such as the Space Station. Without the
sheath, Figure 7 shows essentially no coupling, as
expected.
-40
-80
-100
-120
-140
-160
-180
1, IIWi'I_C I_.hSklA _ SHF_AT
A .",
^ /U
-240
0 1 2 fs 3 fP 4 5
Frequency (MHz)
.4 m sq.
Figure 7.
,4 r'n sq.
2Kohm 50V 10Oohm
SOURCE LOAD
Moment-method calculation of coupling from one end of the tether to the
other, for both free space and plasma environments, the latter for two condi-
tions, with no sheath and with a 2.5 cm diameter sheath. The tether length is
300 m.
652
The coupling factor is potentially important because
EMI/EMC standards and test methods are based on the
assumption of a free-space environment. Therefore a
source of interference at one point on the Space Station
will couple to a susceptible instrument at a distant point
much more strongly than might be anticipated, implying
that tighter standards would be needed either for emission
or immunity, for interference with significant spectral
content below about 1.5 MHz. The above computations
using a computer program valid for isotropic dielectric
media suggest that such programs could be useful in get-
ting a first estimate of interference levels.
Another relevant aspect of EMI/EMC is ground test pro-
cedure for emission or susceptibility. Putting a large part
of the Space Station in a plasma chamber is clearly out of
the question when it comes to deciding whether a given
unit emits excessive unwanted radiation. Because at low
frequencies the plasma can be regarded as a conductor and
because it is separated from any surface by the sheath
region which is a few centimeters thick, it is postulated that
a first-order laboratory equivalent model would consist of a
wire mesh completely surrounding the part of the Space
Station under test and separated from it by a few centime-
ters. To represent the cutoff frequency and the stopband, it
is postulated that the wire mesh could be segmented and
the segments separated by appropriately synthesized
lumped-element networks, as shown in Figure 8. If the
equivalence of this wire-mesh configuration could be esta-
blished, then relevant emission and susceptibility test
methods and standards could be derived.
CONCLUSIONS
The OEDIPUS-A ionospheric rocket flight involving radio
transmission along a conducting tether parallel to the
earth's magnetic field has established the existence in the
ionosphere of sheath waves on the wire and revealed some
of their properties, including passbands, stopbands and
phase velocities. The existence of tether-length-dependent
resonances shows that the sheath waves can propagate with
little attenuation, especially at frequencies below the elec-
tron cyclotron frequency. Existing cold-plasma theory
explains in part the properties of the sheath waves but
kinetic theory analysis ultimately will be needed for in-
depth understanding.
The ease of coupling between widely separated parts of a
long structure in the ionospheric plasma has implications
for EMI/EMC standards applicable to systems on the Space
Station. Some EMI/EMC calculations probably can be
done with sufficient accuracy using existing computer pro-
grams valid for isotropic, lossy dielectrics. Ground test for
EMI/EMC compliance may be possible using a modified
wire mesh envelope to represent the sheath-plasma boun-
dary.
Wire mesh envelope
Conducting strut or ann
Figure 8. Proposed ground-test configuration with a wire mesh representing the sheath
edge and the plasma beyond it. The lower part of the figure shows how syn-
thesized impedance loading of the mesh might be employed to improve
simulation in the vicinity of the primary stopband.
653
ACKNOWLEDGMENTS
The authors are indebted to Dr. Guy Hulbert of York
University, Toronto, for providing pre-processed
OEDIPUS flight data. This work was supported by the
National Research Council of Canada, by the Natural Sci-
ences and Engineering Research Council of Canada, and by
the Ontario Institute for Space and Terrestrial Science.
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Magnetoplasma sheath waves on a conducting tether in the ionosphere with applications to EMI propagation on large space structures

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