# Application of Ionospheric Topside-Sounding Results to Magnetospheric Physics and Astrophysics

> Robert F. Benson
>
> Laboratory for Extraterrestrial Physics
>
> NASA/Goddard Space Flight Center

Greenbelt, Maryland 20771 USA

> Vladimir A. Osherovich
>
> Laboratory for Extraterrestrial Physics
>
> L3 CAC/Goddard Space Flight Center

Greenbelt, Maryland 20771 USA

## ABSTRACT

A brief review is presented to illustrate how the knowledge and
experienced gained from investigations of ionospheric topside-sounder
ionograms has benefited scientific research beyond the ionosphere. In
particular, to the interpretation of (1) natural radio emissions from
space plasmas, (2) sounder-stimulated echoes and plasma emissions, and
plasma diagnostics in planetary magnetospheres and (3) X-ray spectra of
disks around neutron stars and black holes. The relevant data are from
sixty satellite-years of ionospheric topside-sounder operations by the
four satellites of the International Satellites for Ionospheric Studies
(ISIS) program from 1963 through 1989. Not all of these data were
reduced to ionograms on 35-mm film. An ongoing effort at the
NASA/Goddard Space Flight Center is producing digital topside-sounder
ionograms directly from a selected subset of the original telemetry
tapes. More than 300,000 digital ionograms are now in the National Space
Science Data Center at the NASA/GSFC
(http://nssdc.gsfc.nasa.gov/space/isis/isis-status.html).

### BACKGROUND

The Alouette 1 & 2 and ISIS 1 & 2 satellites were launched into polar
orbits in 1962, 1965, 1969 and 1971 at 1,000, 500-3,000, 550-3500 and
1400 km altitudes, respectively. Alouette 1 & 2 each produced topside
ionograms for 10 years; ISIS 1 & 2 for 21 and 19 years, respectively.
The ISIS program, NASA\'s first international space program, was a
spectacular success. Nearly 700 scientific papers based on the ISIS
data, mainly dealing with ionospheric physics, were published through
the end of 1985 \[*Jackson*, 1986\] and many more have been published
since that date. Not all of the data were reduced to the ionogram format
(virtual range of the intensity-modulated echo amplitude vs. sounder
frequency) on 35 mm film. In 1996, a subset of the original 7-track
analog telemetry tapes were shipped from Canada to the NASA/Goddard
Space Flight Center (GSFC) for analog-to-digital (A/D) conversion in
order to produce digital topside-sounder ionograms. The subset consisted
of 13,800 tapes selected from time intervals centered on the solstice
and equinox dates from 24 telemetry stations chosen (with the assistance
of H. G. James and D. Bilitza) so as to obtain global coverage over a
solar cycle \[*Benson*, 1996\]. The main coverage was for the interval
from 1972 to 1983. Another 4,500 tapes were deposited in the National
Archives in Canada; the bulk of the tapes (81,500) went to a Canadian
landfill. The goal of the Goddard A/D effort was to preserve as many of
the long-term ionospheric records as possible, within projected cost
constraints, in a format suitable for digital retrieval and analysis
techniques. All of the selected ISIS-II analog topside-sounder data have
been reduced to digital topside-sounder ionograms (approximately
300,000) and have been deposited in the National Space Science Data
Center at the NASA/GSFC and ISIS-1 digital ionograms are being produced.
The data, and search and analysis software, are available from
http://nssdc.gsfc.nasa.gov/space/isis/isis-status.html. The search page
enables efficient retrieval of desired data. The analysis program allows
the user to (1) view the ionograms in detail in either the ionogram
format or the amplitude vs. time delay (at a selected frequency) format,
(2) invert ionospheric reflection traces into vertical topside
electron-density (N~e~) profiles, (3) produce N~e~ contours along the
satellite orbit from the satellite altitude down to the altitude of the
ionospheric N~e~ peak and (4) scale and identify sounder-stimulated
plasma resonances. These capabilities were used by *Benson and
Grebowsky* \[2001\] in a study involving ISIS-2 digital ionograms
recorded over the polar cap which suggested that the absence of an
F-layer N~e~ peak may be common at high latitudes. The ISIS-2 ionograms
are currently being used as input to a program that automatically
inverts the ionospheric reflection traces into vertical N~e~ profiles
\[*Bilitza et al*., 2002\]. The resulting topside profiles are being
used to improve the International Reference Ionosphere model which is in
dire need of this input to supplement its ground-based N~e~ profile data
base in order to improve total electron content model results. Such
information is necessary for optimum performance of communication and
navigational satellite systems.

The importance of the ionosphere to such systems, and the magnetic storm
effects on power grids and long-distance cable operations, is well known
\[*Lanzerotti et al*., 1998\]. Our goal here is to emphasize the
importance of also considering the ionosphere as the nearest space
plasma that is available for cost-effective research. This research
provides knowledge and experience pertaining to fundamental space-plasma
processes that are relevant to our understanding of the terrestrial
magnetosphere and planetary and astrophysical plasmas in addition to the
terrestrial ionosphere. Our discussion will emphasize the plasma
resonances stimulated by ionospheric topside sounders.

### ISIS-2 EXAMPLE AND RESONANCE INTERPRETATION

Figure 1 shows an ISIS-2 topside ionogram that displays the
intensity-modulated amplitude of the various signal returns that are
received during the 22 ms listening period following the transmission of
a short (0.1 ms) sounder pulse as a function of the sounder frequency.
Two scales are presented on each axis, i.e., the delay time can be
expressed in terms of apparent range out to 3,000 km (assuming
propagation at the free-space velocity of light) and the swept frequency
(from 0.1 -- 10 MHz in this example) is a function of time after the
start of the ionogram (from 3.3 to 14 s in this example) The first 3.3 s
is dedicated to fixed-frequency sounding (at 1.0 MHz in this example).
Most of the signal returns observed in Figure 1 are due to either
short-range electrostatic (es) echoes or long-range electromagnetic (em)
echoes. The former, called plasma resonances, are observed at

nf~H~(kHz) ≈ n{0.028 \|**B**(nT)\|} (n = 2, 3, 4, ...) (1)

f~N~(kHz) ≈ {80.6 N~e~(cm^-3^)}^1/2^ (2)

f~T~ = (f~N~^2^ + f~H~^2^ )^1/2^ (3)

where f~H~ is the electron cyclotron frequency, f~N~ is the electron
plasma frequency, f~T~ is the upper hybrid frequency, \|**B**\| is the
ambient magnetic field strength, and N~e~ is the ambient electron
density (see, e.g., reviews by *Muldrew* \[1972a\] and *Benson*
\[1977\]). One member of a sequence of resonances know as Qn resonances
is present in Figure 1. This sequence is observed at frequencies between
the nf~H~ harmonics and above f~T~ given by the approximate expression

f~Qn~ ≈ f~H~{n + (0.464/n^2^)(f~N~^2^/f~H~^2^)} (4)

using the es approximation to the dispersion relation with a Maxwellian
electron distribution \[*Warren and Hagg*, 1968\]. They are due to
sounder-stimulated es Bernstein-mode waves with group velocity **v~g~**
nearly matched to the satellite velocity **v~s~** \[*Muldrew* 1972b\]. A
resonance is also observed at f~H~ (i.e., n = 1 in (1) above) in
Figure 1. The associated propagation conditions have not been determined
for this fundamental resonance \[*Muldrew* 1972a\]. Resonances at nf~H~
with n up to 5 are observed in Figure 1; they are designated by the
numerals 1 -- 5 at the top of the ionogram.

![](media/image1.png){width="6.739583333333333in"
height="4.013888888888889in"}

Figure 1. An ISIS-2 digital ionogram produced from a telemetry tape
recorded at Kashima, Japan on 23 May 1979 at 1023:41 UT.

The two free-space long-range electromagnetic (em) echoes, one
corresponding to the ordinary mode (O) and one to the extraordinary mode
(X), extend out to the 10 MHz limit in Figure 1. They have cutoff
frequencies at the satellite given by (2) and by

f~X~ = (f~H~/2) {1 + (1 + 4 f~N~^2^/f~H~^2^)^1/2^}, (5)

respectively. There is also a slow branch of the X mode, called the Z
mode (Z), which is confined to the ionospheric plasma with a maximum
possible frequency given by (3) and a cutoff frequency of

f~Z~ = f~X~ - f~H~ (6)

(see, e.g., Stix \[1992\]; Goertz and Strangeway\[1995\]). In Figure 1,
this cutoff merges with the intense low-frequency edge of the 2f~H~
resonance.

There are also plasma resonances that correspond to incoherent plasma
emissions stimulated by the sounder pulses (as opposed to coherent es
echoes). An important class of these are observed at frequencies between
the nf~H~ harmonics and below f~T~ and are know as Dn resonances
\[*Nelms and Lockwood*, 1966; *Oya*, 1970\]. *Osherovich and Benson*
\[1991\] showed that they can be described by the following equations:

f~Dn~ = 0.95 (f~N~f~H~)^1/2^n^1/2^ (7)

f~Dn~^+^ = (f~Dn~^2^ + f~H~^2^)^1/2^ (8)

f~Dn~^-^ = (f~Dn~^2^ - f~H~^2^)^1/2^. (9)

The D1 and D1+ resonances present in Figure 1 satisfy the hybrid
relationship given by (8) just as f~N~ and f~T~, also clearly observed
in Figure 1, satisfy the hybrid relationship given by (3).

Since the parameters defined in (1) - (9) depend only on f~H~ and f~N~
it is useful to present them in a normalized (by f~H~) form as a
function f~N~/f~H~ (Figure 2). In this representation, a self-consistent
interpretation of the resonance and cutoff phenomena of (1) - (9)
correspond to the vertical line appropriate for the f~N~/f~H~ value for
the corresponding ionogram. Thus accurate determinations of ambient
plasma parameters can be made. In Figure 1, most of these phenomena are
identified and there is an additional feature just below the 0.75 MHz
frequency marker that approximately corresponds to f~T~/2. It is
observed when f~T~/2 ≈ f~N~ --f~H~ \[*Hagg and Muldrew*, 1970\]. The
normalized frequencies of the features observed in Figure 1 correspond
to a value of f~N~/ f~H~ = 2.4 in Figure 2.

![](media/image2.pct){width="6.748611111111111in"
height="4.872916666666667in"}

Figure 2. Normalized Qn and Dn frequencies relative to f~X~, f~T~, f~N~
and f~Z~. The Qn frequencies were based on solutions of the es
dispersion equation rather than the approximation given by (4) as in
*Benson et al*. \[2001\].

### SCIENTIFIC APPLICATIONS BEYOND THE IONOSPHERE

The knowledge and experience gained from ionospheric topside sounding
has been applied to the interpretation of natural wave emissions,
sounder-stimulated echoes and plasma emissions, and plasma diagnostics
in space plasmas other than the ionosphere. It has also stimulated an
entirely new interpretation of the X-ray spectra of exotic objects.

The ISIS observations have been applied to at least three types of
natural emissions. First, high-altitude ISIS-1 observations made the
first determination that f~N~/f~H~ \<\< 1 in the Auroral Kilometric
Radition (AKR) source-region \[*Benson and Calvert*, 1979\]. These
observations were of fundamental support to the cyclotron maser
generation mechanism of *Wu and Lee* \[1979\] which has been applied to
the interpretation of solar, planetary and stellar radio emissions
\[see, e.g., *Wu*, 1985\]. The astrophysical application of this
mechanism has been modified and extended based on the comprehensive
source-region measurements using the FAST satellite \[*Ergun et al*.,
2000\]. Second, lower-altitude ISIS-2 observations demonstrated that
wave emissions often identified with f~T~ in planetary magnetospheres
are seldom observed at that frequency in the terrestrial auroral region;
rather, the emission peak is more often at f~N~ or at a frequency
between f~N~ and f~T~ \[*Benson*, 1993\]. Third, *Fredricks* \[1971\]
suggested a relationship between magnetospheric banded emissions
observed between the harmonics of f~H~ and sounder-stimulated plasma
emissions with similar frequency patterns. Evidence for a close
relationship between the sounder-stimulated emissions and the natural
emissions, which have been observed in all planetary magnetospheres, has
been presented by *Oya* \[1972\], *Benson and Osherovich* \[1992\] and
*Benson et al*. \[2001\].

The experience gained from interpreting the wave cutoff and resonant
phenomena observed by ionospheric topside sounders, as described by
(1)-(9), has been applied to the interpretation of sounder records in
planetary magnetospheres. These interpretations have been used to
determine f~N~, and hence N~e~, to within a few %. In the terrestrial
magnetosphere they have been used to provide the starting points for the
inversion process leading to N~e~ polar-cap profiles measured by the
Radio Plasma Imager (RPI) on the Imager for Magnetopause-to-Aurora
Global Exploration (IMAGE) satellite \[*Reinisch et al*., 2001\]. In
Jupiter\'s Io plasma torus they have been used to interpret Ulysses
relaxation-sounder observations and determine N~e~ along the trajectory
of the spacecraft \[*Osherovich et al*., 1993\]; an alternate
interpretation of these observations was presented by *LeSager et al*.
\[1998\].

The upper-hybrid relationship, which is well known in space plasma
physics, has recently been applied to the field of astrophysics to
explain X-ray spectra of the accretion disks around neutron stars and
black holes. Two examples of the upper-hybrid relationship have been
discussed in connection with Figure 1 and equations (3) and (8). (A
similar relationship is expressed in (9), after rearranging terms, and
the corresponding ionogram examples have been presented by *Osherovich
and Benson* \[1991\].) There are astrophysical analogs to the f~N~ and
f~T~ of plasma physics as expressed by (2) and (3), respectively. In
plasma physics, f~N~ describes the frequency oscillation of a test
charged particle displaced from its point of equilibrium in a neutral
plasma. In astrophysics, a neutral test particle of small mass displaced
from the center of a sphere of constant density (a zero-order model for
a star) will oscillate at the frequency f ^1/2^ \[*Allen*, 1973\] in
analogy with the expression for f~N~ in (2). Mathematically, these
problems are equivalent. Outside this sphere, a test particle located at
a distance r from the center will rotate with the Keplerian frequency
f~K~ r^-3/2^. The astrophysical analogy with the upper-hybrid frequency
in a magnetized plasma is with the quasi-periodic oscillations in the
accretion disk surrounding a neutron star. (Twenty soft x-ray sources
are now known to have such quasi-periodic oscillations \[*van der Klis
et al*., 1997\].) This analogy is based on the well-known analogy
between the Lorentz force/unit mass q**v** x **B** in a plasma with
magnetic field **B** and the Coriolis force/unit mass 2 x **v** in a
frame rotating with angular velocity , where for the Lorentz force **v**
is the velocity of a particle with charge q while for the Coriolis force
**v** is the velocity of a particle in the rotating frame. An electron
under the simultaneous influence of Langmuir plasma oscillations given
by (2) and the Lorentz force will oscillate at the upper-hybrid
frequency given by (3). A blob of mass near an accretion disk in a
magnetosphere rotating about a neutron star with angular velocity is
simultaneously subject to radial oscillations at f~K~ and oscillations
due to the Coriolis force resulting in hybrid oscillations with a
frequency given by \[f~K~^2^ + (\|/)^2^\]^1/2^. It is important to note
that the magnetospheric rotation frequency \| is different from f~K~
because, according to Ferraro\'s theorem \[*Alfven and Falthammar*,
1963\], \|depends only on the magnetic structure surrounding the star
(if the electrical conductivity is high). Thus the rotating
magnetosphere introduces a frequency that is different from f~K~ that,
when combined with f~K~, leads to hybrid oscillations. These
oscillations formed the basis of a two-oscillator model of the twin-peak
phenomena observed in the x-ray spectra of neutron stars \[*Osherovich
and Titarchuk*, 1999\]. This model, which has been recently applied to
the spectra of black holes \[*Osherovich and Fainberg*, 2002\], provided
a radical new approach to explain a fundamental observational problem in
astrophysics. Its genesis was based on recognizing the importance of the
upper-hybrid relationship to the interpretation of ionospheric topside
ionograms by one of the authors (Osherovich) and applying this
experience to another field of science.

### SUMMARY

In addition to the well-known applications of ionospheric research to
scientific problems associated with the ionosphere and applications to
technological systems, the significance of this research to other space
plasmas has been highlighted. Particular emphasis has been placed on the
scientific spin-offs from obtaining a proper understanding of the plasma
resonances stimulated by ionospheric topside sounders. A large data base
of digital topside ISIS ionograms are now available for analysis, using
state-of-the-art analysis techniques, in addition to those available on
35 mm film. The scientific spin-offs include the determination of
electron densities in planetary magnetospheres, the interpretation of
natural emissions from magnetized space plasmas and the interpretation
of x-ray spectra associated with neutron stars and black holes.

**Acknowledgements**. The digital ISIS ionograms (as used in Figure 1)
were produced with the support of NASA/OSS Applied Systems and
Information Research Program (AISRP) RTOP Grant \# 370- 03-00-04. We are
grateful to W. Schar, G. Burgess and P. Rozmarynowski for assistance in
the data presentations.

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