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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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