Download Studies on non-linear heating of the lower ionosphere

Indian Journal of Radio & Space Physics
Vol. 34, December 2005, pp. 413-416
Studies on non-linear heating of the lower ionosphere during
interaction between HF and ELF signals
S S De, S K Adhikari, A Debnath & P Das
Centre of Advanced Study in Radio Physics and Electronics, University of Calcutta, Kolkata 700 009, India
and
BKDe
Tripura University, Suryamaninagar 799 130, Tripura West, India
Received 18 June 2004; revised 19 November 2004; accepted 29 July 2005
Non-linear interaction between Schumann resonances (SR) and high frequency round-the-world signals (RWS) in the
lower ionosphere yields the ELF spectra that correspond to the three first modes of Schumann resonances. The phenomenon
resembles Luxembourg effect between Schumann resonances and HF signals. The intensity of natural electromagnetic field
(SR field) produced by thunderstorm activity is strong enough to give rise to non-linear effects in the 0-layer. As a result,
there will be heating of electrons by the ELF oscillations of SR fields (£,). The fair-weather electric field (£0 ) also initiates
the process of heating in the 0-layer. The influence of this field gives a linear dependence of electron temperature
fluctuations on the field strength on SR. These lead to non-linear effects comprising the variations of electron temperature,
effective collision frequency and conductivity of the medium. Also, there will be modulation of HF waves by ELF signals.
Keywords: Lower ionospheric heating, HF Signal, ELF Signal, Ionospheric heating
PACS No: 92.60.Ta; 92.70-j
1 Introduction
Experimental results on ionospheric conductivity
modulation by high power amplitude modulated
waves are well-knownl.2. Due to the conductivity
modulation, waves in ULF, ELF and VLF range are
generated efficiently.
The electrical properties of the inhomogeneous
medium above the earth vary with height. At the
upper D-region of the lower ionosphere, height
greater than 67 km, the influence of geomagnetic field
on the medium charged particles cannot be ignored.
Here, the variation of electrical properties are related
to the changes in relative magnitudes of the
displacement current and conduction current giving
rise to changes in the relative magnitudes of the
different components of the conductivity tensor.
The upper atmospheric medium below 67 km has
Pedersen conductivity (cr 1) smaller than the
longitudinal conductivity (cr0). 3 Above this height, the
magnitude of the longitudinal conductivity is much
larger than the transverse Pedersen conductivity and
Hall conductivity (cr2) . The conductivity component
cr0 (longitudinal or Cowling conductivity) is effective
for direction parallel to the geomagnetic field. The
component cr 1 applies to the direction perpendicular to
the geomagnetic field. The Cowling conductivity (cr0)
characterizes energy dissipation per unit volume for
the current density that is flowing in a plane
perpendicular to the geomagnetic field. The effect of
Hall currents, responsible for Hall conductivity, is to
generate a secondary disturbance characterized by an
azimuthal electric field and a magnetic field with
radial and vertical components near the ground 3 . The
effect increases with height.
Interaction
experiment
between
Schumann
resonance and HF (15 MHz) rou.nd~the-world signals
(RWS) in the lower region of the ·ionosphere (Dlayer) shows· peaks at the Schumann resonance
frequencies in the spectra of the HF signals4 . This
establishes the effect of cross-modulation between
ELF and HF radio waves. The intensity of Schumann
resonance fields produced by global thunderstom1
activity introduces non-linear effects in the D-layer5•6 .
As a result, there will be heating of electrons by the
ELF oscillations of SR fields (Es) in the lower
ionosphere7 , which initiates the modulation of
electron collision frequency and conductivity of the
medium 3•8 . The HF wave during its passage through
such non-linear region gets attenuated. Natural
ionospheric currents that pass through the heated
region are modulated by the conductivity changes.
The agreement between the RWS and SR spectra
414
INDIAN J RADIO & SPACE PHYS, DECEMBER 2005
confirms the existence of non-linear interaction
between HF and ELF signals4 •
Because of worldwide weather activities, the high
potential difference between the surface of the earth
and the highly conductive ionosphere is always
maintained, leading to the development9 of fairweather electric field (E0). A vertical conduction
current is also present because of the finite
conductivity of the medium. Thus a de global circuit
is built-up.
During fair-weather electricity, there would be no
charge separation taking place in the atmosphere and
the electrical phenomenon is reasonably steady9 .
Within such fair-weather condition (quasi-static
state), electric field, current density and conductivity
over the surface of the earth are subjected to both
global and local variatior.s. Global variations are
associated mainly with tropical thunderstorms. The
large-scale fair-weather electrical phenomena include
the global circuit, and solar and other large-scale
effects on its circuit parameters, whereas the smallscale phenomena may be fluctuations of the electric
field and the air-earth current perturbed by ionisation
and aerosols produced locally.
Heating of the D-region of the ionosphere by ELF
oscillations leads to vanatwns of electron
temperature, effective collision frequency and
conductivity of the medium. Because of attenuation of
HF signals in the medium, the RWS is amplitude
modulated quasiperiodically by ELF oscillations.
Without E0 , the modulation effect would be much
weaker in the D-layer. Also, the RWS spectrum
fluctuations depend on the presence of E0 . The results
do not agree with observations4 without E0 • Thus, the
influence of E0 enhances the non-linear process of
heating along with the SR fields and as a result there
will be heating in the atmosphere4 • In this
presentation, the fluctuation of temperature due to
electron heating including the influence of small-scale
fair-weather electric field has been studied
theor~tically. The temperature enhancement has been
estimated numerically.
where, Tis the temperature of the neutral particles, m
the electronic mass, e the electronic charge,
8 = 2m/M, the fraction of energy given by the
electrons to the heavy particles through collisions, w
the frequency of the heating field and vk the effective
collision frequency of electrons.
Due to electron heating by SR fields, the expression
of the modulated electron collision frequency can be
written as
vk = NvQ(v)
... (2)
where, N is the neutral particle density, v the electron
velocity and Q(v) the velocity dependent momentum
transfer cross-section. For wide energy range of the
electrons, the collision frequency would be averaged
over the Maxwellian distribution of electron
velocities.
Within the stated height range, the collision
between N 2, 0 2 and Ar are important for the
determination of effective collision frequency.
Electron-neutral particle collisions are strongly
dependent on Te. Values of Q for N 2 , 02 and Ar may
be expressed as 8
... (3)
Te is the electron temperature. The constants a, b, c
and d are dependent on the scattering length,
polarisability of the target and different gas constants.
Values of a, b, c and dare listed in Table 1.
The fluctuation of temperature due to electron
heating, including the influence of fair-weather
electric field may be written as
1'1T =T -T =T
e
( E0 + E )
s
£2
2
... (4)
p
The fair-weather electric field is given by
v
Eo=-cr 0 R
... (5)
Table !-Values of a, b, c and d of expression (3)
2 Mathematical formulation
The main dissipation of .SR energy occu~s . within
the height range 45-80 km of the upper atmosphere.
The plasma fields (Ep) in thi~:-.beight range is given
by!O,
.'· ~ .:· '
... (1)
Species
a
b
c
d
Oz
0.51468
(- 16)
0.14597
(- 16)
-0.12554
(- 18)
0.35801
(- 21)
Nz
0.85924
(- 16)
0.12275
(- 16)
0.12679
(- 18)
-0.16887
(-20)
Ar
0.78638
(- 15)
-0.39515
(-16)
0.65673
(- 18)
-0.35480
(-20)
DE et al.: NONLINEAR HEATING OF LOWER IONONOSPHERE
where, V is the ionosphere-earth potential difference,
R the columnar resistance and cr0 the longitudinal
conductivity (Cowling conductivity).
The term cr0 can be expressed as
. .. (6)
where
Nk. ek and mk are the number density, charge and mass
of the k'h species, E 0 the free space permittivity and B0
the static magnetic field of the Earth.
Using Eqs (1)-(3), (5) and (6) in Eq. (4), one can
get
... (7)
where
and
415
The value of Er within the height range 60-80 km
varies 11 from 2 X 10-2 V/m to 2.6 X w - l V/m andEs at
the surface of the earth 12 is taken as 3x10-4 V/m. It is
assumed to remain constant up •o the upper boundary
of Schumann resonance cavity. The value of Eo is
about 3 x 10- 1 V/m at the height of D-layer 13 • The
electric field exhibits dependence on local influences.
The observed field at the surface of the earth is low at
the daytime and remains relatively higher at night 14 •
The value of Eo between 60 km and 80 km has
considerable fluctuations (0.1-1 V /m) 15 • Experimental
results reveal considerable fluctuations of Eo with the
heights 15 • Hence crossD-layer ionospheric
modulation effects may be used to investigate
different physical processes in the D-region.
In the numerical analysis, the values of the
geomagnetic field at the height range 60-80 km are
taken between 0.3792 Oe and 0.3711 Oe, where
12
E 0 = 9 X 10- F/m:
4 Discussions
Numerical analysis of expression (7) is done using
the values of different parameters involved for the
upper D-region of the ionosphere (65-80 km), where
the influence of magnetic field has been introduced
through the expressions of various conductivities of
the medium. It is found that the heating by Schumann
resonance field is very poor and such heating would
not lead to any considerable non-linear effects 4 . The
influence of electric field Eo along with the SR field
produce heating at the stated height range and
maintains the observable non-linear effects. Although
the change of electron temperature is small, still it
contributes to the process of warming the lower
ionosphere.
Acknowledgements
This work is funded by Indian Space Research
Organization (ISRO) through S K Mitra Centre for
Research in Space Environment, University of
Calcutta, Kolkata, India. The authors are thankful to
Dr. A P Mitra, FRS, for going through the paper and
offering valuable suggestions.
3 Results
The expression (7) has been used for numerical
analysis. Data are taken from CIRA 72, IRI and from
different published papers. It is found that 11T is in the
range 1.802-2.605 K. The variation arises due to the
variation in the value of Eo and electron-neutral
particle collision frequency at the upper D-region
height range.
References
l
Stubbe P, Kopka H & Dowden R L, Generation of ELF and
VLF waves by polar electrojet modulation: Experimental
results, J Geophys Res (USA), 86 (1981) 9073.
2 Stubbe P, Kopka H, Rietveld M T & Dowden R L, ELF and
VLF wave generation by modulated HF heating of the
current carrying lower ionosphere, J Atmos Terr Phys (UK),
44 (1982b) 1123.
416
INDIAN J RADIO & SPACE PHYS, DECEMBER 2005
3 Greifinger C & Greifinger P, Transient ULF electric and
magnetic fields following a lightning discharge, J Geophys
Res (USA), 81 (1976) 2237.
4 Yampolski Y M, Bliokh P Y, Beley V S, Galushko V G &
Kascheev S B, Non··linear interaction between Schumann
resonances and HF signals, J Atmos & Solar-Terr Phys (UK),
59 (1997) 335.
5 Sentman D D, Approximate Schumann resonance parameters
for a two-scale-height ionosphere, J Atmos Terr Phys (UK),
52 ( 1990) 35.
6 Nicolaenko A P, Modern aspects of Schumann resonance
studies, J Atmos & Solar-Terr Phys (UK), 59 (1997) 805.
7 William E R, The Schumann resonance: A global tropical
thermometer, Science (USA) 256 (1992) 1184.
8 Aggarwal K M & Shetty C S G K, Collisions and transport
of electrons in the ionosphere, Indian J Radio Space Phys, 9
(1980) 105.
9 Ogawa T, Fair-weather electricity, J Geophys Res (USA), 90
(1985) 5951.
10 Ginzburg V L, The Propagation of Electromagnetic Waves
in Plasmas (Pergamon Press, New York, USA), 1964.
11 Gurevich A V & Shvartsburg A B, Non-linear Theory of
Propagation of Radio waves in the Ionosphere, (Nauka,
Moscow), 1973.
12 Rycroft M J, Resonance of the earth-ionosphere cavity
observed at Cambridge, England, Radio Sci (USA), 69D
(1965) 1071.
13 Reid G C, Electrical Structure of the Middle Atmosphere, in
the Earth, Electrical Environment (Studies in Geophysics,
183), (National Academy Press, Washington DC, USA),
1986.
14 Yeboah-Amankawah D, Fair weather electric field in Port
Moresby, J Atmos Terr Phys (UK), 51 (1989) 1035.
15 Bragin Y A, Kocheev A A, Kikhtenko V N, Smirnyh L N,
Tjutin A A, Bragin 0 A & Sakhmatov B F, Electrical
Structure of Stratosphere and Mesosphere on Data of Rocket
Investigations, Radio Wave Propagations and Physics of the
Ionosphere (Nauka, Moscow, Navosibirsk), 1981, 165.