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I. SUPPLEMENTARY NOTES
This work was sponsored by the Defense Nuclear Agency under Subtask
S99QAX fC66) Work Unit 12 and Work Unit title, "Late Time
Electrostatic Investigations."
19. KEY WORDS (Continue on revere elde If neceeeary and Identify by
block number)
Ionospheric conductivity High altitude nuclear explosion Late time
electrostatics / ~ ~(t"4'i' '
20. ABSTRACT (Continue an reveee fdle If neceesary and Identify
by'biock number)
y , -In thiepo - e nductivity formulas for the disturbed
ionosphere. These formulas are recommended for use m HANE
simulation studies and for other disturbed ionospheric con-
ditions.
DD I 1473 EDITION Of I NOV 6 1S OBSOLETE S/N 0102-LF-014.6601
SECURITY CLASSIFICATION OPP THIS PAGE (Wotn Date Entered)
iC
Formulas for the perpendicular DC ionospheric plasma
conductivities
have been presented previously by numerous authors. 1 ,2 ,3 ,4 ,5
Use of these
published formulas under normal ionospheric conditions for the E
and F regions
leads to accurate, reliable results. However, under certain extreme
condi-
tions (i.e., a high altitude nuclear explosion) these approximate
formulas
can lead to inaccurate and even unphysical results for the
conductivities.
In this memo report we present a new set of exact formulas which do
not
suffer these deficiencies. They yield accurate and usable results
under the
most extreme circumstances of plasma and neutral densities and
temperatures.
We therefore recommend use of the formulas presented here for
extreme or
unusual ionospheric conditions.
Derivation
We begin with the electron and ion momentum equations considering
only
the Lorentz term and frictional terms
m + V'e x ) en Ve + V i(v e Vi) 1e
-(E+ v x~)' V + V(V-v) (2)m i i in *i ie i e
Here is the magnetic induction and ithe electric field strength;
v-"e and v
are the electron and ion velocities; m e and m i are the electron
and ion mass;
e is the electron charge; and ven V ~,and Vi are the
electron-neutral, the
ion-neutral, the electron-ion, and the ion-electron collision
frequencies.
We eliminate from (1) and (2) the cross product terms between the
velocities
and the magnetic induction resulting in
t Manuscript submitted July 7, 19801
L(V + V ) 2 -V 2 + n2J +-2en ei e i e ve en e TB7 e-By
mi i -- V (V Ven)i (3) meii i e
[(Vi + V ) 2 -Vi 2 + pi2] v = Vn~i + Ti2 2
m m + m C Vei(V -in m Van )e (4)
i in m e
where 1e eB/met ni = eB/mi, and Vie = (m fin) Vei have been
used.
We next solve (3) and (4) for ve and v. explicitly which yieldse
1
(did + c2) (diae +_ caE)
me
e B
a i V in 0= a. e0e =i mia en
2
ie e m
c=Vei(Vin - m Ven)
d (Vin + V ie)2 V ie 2 + 2 d e (ven + V ei)2 V2 + 2 ie e- e en ei
el e"
Use of equations (5) and (6) in Tne ( v now yields the Pederson
and
Hall conductivities.
We write
a 1- e - ded + c 2 ) (8)
ne debi - dib e + 2c(be bi) ah = E dide + C2 ' (9)
and n is the plasma number density.
The conductivity tormulas presented above are considerably more
compli-
cated than those previously published in the literature. For
instance, the
4 formulas of V51k and Haerendel ignore the effects of collisions
between
ions and electrons which can be of considerable importance for very
high
5 plasma densities. Similarly, Francis and Perkins while including
electron-
ion collisions in the electron momentum equation, ignore their
effect on the
ion momentum equation. The result of these types of simplifications
is
either incorrect or even unphysical conductivities for the
ionosphere under
R extreme plasma conditions. The exact formulas presented above do
not suffer
these difficulties.
Summary
In the preceding section we have presented the derivation of
exact
formulas for the perpendicular DC ionospheric conductivity. These
formulas
are usable and present accurate results under the most extreme of
iono-
spheric conditions, a high altitude nuclear explosion. We therefore
recom-
3
mend their use in computations for unusual or extreme ionospheric
conditions.
Collision frequencies for use in the equations can generally be
found in the
standard reference texts on the ionosphere and aeronomy 3,6
4
1~?
References
Whitten, R. C. and I. G. Poppoff, Fundamentals of Aeronomy, John
Wiley,
New York (1971).
2 Rowe, J. F. Jr. and J. D. Mathews, "Low Latitude Nighttime E
Region
Conductivities", J. Geophys. Res., 73, 7461 (1973).
Rishbeth, H. and 0. K. Garriott, Introduction to Ionospheric
Physics,
Academic Press, New York (1969).
4 V5ik, H. J. and G. Haerendel, "Striations in Ionospheric Ion
Clouds",
J. Geophys. Res., 76, 4541 (1971).
Francis, S. H. and F. W. Perkins, "Determination of Striations
Scale
Sizes for Plasma Clouds in the Ionosphere," J. Geophys. Res., 80,
3111
(1975).
Banks, P. M. and C. Kockarts, Aeronomy, Part 1, Academic Press,
New
York (1973).
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