The development of solar wind shock models with tensor plasma pressure and the comparison of some of the shock models with the satellite data from Pioneer 6 through Pioneer 9 are reported. Theoretically, difficulties were found in non-turbulent fluid shock models for tensor pressure plasmas. For microscopic shock theories nonlinear growth caused by plasma instabilities was frequently not clearly demonstrated to lead to the formation of a shock. As a result no clear choice for a shock model for the bow shock or interplanetary tensor pressure shocks emerged

Abraham-Shrauner, B.

English

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https://ntrs.nasa.gov/search.jsp?R=19750021905 2020-03-22T20:54:48+00:00Z
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Final Technical Report
Grant Title:
"Development of Solar Wind Shock Models with Tensor
Plasma Pressure for Data Analysis"
Princ_pal Investigator - Barbera Abraham-Shrauner
Period Covering Aueust 1, 1970 - December 31, 1975
N
Grant Numher NGL-008-057
Technical Supervisor - Dr. David Cauffman (present)
Dr. Larry Kavanz,ugh (previous)
Department of Electrical Engineering
Washington University
St. Louis, Missouri	 63130
	
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- 1 -
Introduction
The purpose of this grant was first to develop solar
wind shock models wit;t tensor plasma pressure and then to
compare some of the shock models with the satellite data
from Pioneer 6 through Pioneer 9.
The results have been described in two renewal proposals,
( play, 1971 and June, 1973) and in four semi-annual status
reports. This final technical report is submitted in lieu
I	 of recent semi-annual status reports.
Theoretically we found difficulties with non-turbulent
fluid shock models for tensor pressure plasmas. For microsc aic
shock theories nonlinear growth caused by plasma instabilities
has frequently not clearly been demonstrated to lead to the
formation of a shock. As a result no clear choice for a
shock model for the bow shock or interplanetary tensor
pressure shocks emerged. Hence, we decided to look at
actual data across interplanetary shocks. We did find that
further theoretical work on shock normals was necessary
since the available procedures did not offer sufficient
accuracy. In the course of our research we did loot: at
Lepping and Argentino's method l for determination of more
accurate shock normals but decided not to use their method.
First we were interested in looking for a simpler procedure
where hopefully the shock normal is given by a triple vector
product. Second we could not use their subset of shock
conditions for the tensor pressure case without a better
- 2 -
knowledge of the electron and helium pressure than we expected
to have.
When we looked at the plasma probe data and calculated
plasma parameters, no calculation of the tensor pressure
i
components had been done for our times of interest. Furthermore,
none could be done for Pioneer 6 and 7 because of the expense
at that time (Jun g , 1971). Hence we found some shocks and
j	 analyzed them using MUID shock conditions. We showed that
s
(1) shocks were observed by the Ames plasma probe,
(2) the magnetic coplanarity shock normal is often
inaccurate unless additional information is used,
(3) apparently some of the cv, nts identified by Taylor
did not exhibit the classic shock, structure where
he used magnetic coplanarity as the criteria of
choice,
(4) the agreement of the data with the "AHD shock
f conditions can be greatly improved if certain
vectors that appear in shock normals are selected
to be perpendicular by varying the time span of
the data,
(5) and the sensitivity of the shcz; y normals and MIID
jump conditions to the
	 span fj , the data
chosen on both sides of the shock suggests that
the method of averaging the fluctuations may be
important.
The shock events identified on Pioneer 8 and 9 could
not be checked for tensor pressure since the data analysis
41
_..
1 1
- 3 -
was not performed at Ames Research Center. Our inability to
obtain this data has been very frustrating but we may be
able to find some Vela data at Los Alamos suitable for
analysis. Naturally we could not do part of the project
proposed without this data.
Discussion of Research
Theoretical Analvsis
We first tried to check existing theories for shocks
with tensor or anisotropic pressure (temperature) that could
apply to the earth's bow shock or to interplanetary shocks
in the solar winds.
The theories were either fluid theories of which the
Chew-Goldberger-Low2 (CGL) model was the principal example
or microscopic plasma models where certain instabilities
were postulated for the dissipative mechanisms. The latter
are of more recent origin and can only be shown to exhibit
shocks by computer models with the present formalis::,s. The
microscopic plasma models are useful if the dissipative
mechanism is being studied and details of the shock- structure
(such as seen in bow shock crossings) are desired. The
derivation of hyperbolic fluid equations in the conservation
form from tt.ese theories whose solutions obey the evolutionary
condit4cns has not been done rigorously for most of the
miLr.oscopic mechanisms.
The fluid models we checked are variations of the CGL
equations. These were Lynn's shock model 3 , the 'Morioka and
- 4 -
Spreiter 4 calculations fur perpendicular and parallel magnetic
fields (direction is with respect to shock front normal.) and
the polytrope models. Lynn's model was intended to be valid
only for very weak shocks and was therefore not applicable
to the earth's row shock or most interplanetary shocks. In
addition his requirement of magnetic moment conservation	
r^
through the shock was not consistent with the magnetic field
parallel to the shock front for the CGL equations since the
uncoupled energy equations gave a sufficient number of
equations. The condition was consistent with the normal
magnetic field case.
The Morioka and Spreiter shock model did not appear to
agree with the bow shock results of December 16, 1965 as
seen by Pioneer 6. 5 The parallel temperature (T IC ) for the
magnetic field perpendicular to the shock normal was not
conserved as expected across the shock front according to
the data. However, the determination of T II is difficult
particularly behind the bow shock. Also the bow shock at
this crossing was not exactly a perpendicular shock.
Nevertheless, one expects that plasma turbulence coupled the
parallel and perpendicular energy fluxes and hence changed
TII across the shock.
The polytrope modifications of the CGL equations 6 were
used for perpendicular shocks but T I C across the shock.
The polytrope n:-Iiifications of the CGL equations 6 were
used for perpendicular shocks but T II decreased rather than
increased across the shock as expected. All the above
w?;
5theoretical analysis led us to suspect that plasma turbulence
must be considered for most interplanetary shocks and the
probability of their being laminar shocks is small. However,
we did not begin to calculate dissipative mechanisms for
turbulent shocks because the list of possibilities seemed so
large and would entail years of study. Gary' has done a
number of calculations for perpendicular shocks which would
be interesting to compare with .interplanetary shock data.
We decided to check the satellite data for a hint of
possible shock mechanisms. Since only isotropic pressure
data was available we concentrated on comparing satellite
data with the M11D shock jump conditions. The basic idea was
to check the agreement of the data with the MEAD shock
conditions first and then explain any discrepancies.
However, the accurate determination of the- sh ,-)ck surface
normal turned out to be more difficult than expected.
Mihalov et al. 5 had first pointed out tr- discrepancies in
the shock normal results in the paper 	 . e Pioneer 6,
December 16, 1965 bow shock crossing. Ti,L-y attributed the
errors in the magnetic coplanarity stock normal to errors in
the magnetic field data behind the bow shock_. Then we
derived an expression for the shock normal of a stationary
bow shock. where only the magnetic fiend ahead of the shock
was used. In addition, another sourcF , of error in the
magnetic coplanar..1 t: I; q -10 1 :k normal i!; the small angle between
the magnetic field ahead of and behind the shock. The error
in the an,Ile can frequently be as large as the angle itself
r
Mor th(, shock direction is very inaccurate.	 j
A general method for finding shock normals using plasma
and maUnct.ic field data for MHD shocks and triple vector
products was found and a paper $ published in the Journal of
Geophysical Research on that subject. The advantage of some
mixed data expressions is that the angles between the vectors
are 90 1 or close to it theoretically. Hence, the effects of
errors in the data are minimized. Also additional criteria
for iecogniz.ing a good fit of the data to theory are available
because certain vectors from plasma and magnetic field data
must be mutually perpendicular.
Data Analvsis
Laboratory Data
First we took some of Paul's 9 laboratory data or, cylindrical,
perpendicular smocks. They measured only isotropic temperatures
but we tried to check possible values of Y, the g as constant
as a possible hint for polytrope indices. For his data
Y = 5/3 seemed the best fit though small errors caused
large changes in the results. On the other har:l Kornherrl0
found	 = 2 a better fit for ions in higher 6 shocks. There
had been a lon g, controversy about the proper choice of , for
the bo%., shock. This calculation was not published because
the spread in the results was too great to give a definitive
result for ),. However, since the laboratory data was more
accurate than space data, a good guess for ) was more likely
to be made from laboratory data.
I- 7 -
Bow Shock
We already mentioned the Pioneer 6 bow shock data for
the December 16, 1965 crossing. We calculated different
shock normals and found improvement using some mixed data
shock normals as compared to other shock normals used.
I
Interplane tary Shocks
Our main project was the detection and analysis of
interplanetary shocks from Pioneer 6 and 7 satellite data.
Ile used data from the Ames Research Center plasma probe of
Dr. John Wolfe's group and the Goddard Space Flight Center
magnetometer of Dr. Norman Ness. The events were identified
by using a p:,per by Taylor ll who identified shocks seen by
IMP1 durinc; this period using magnetometer data.
Dr. J. Feynman suggested we use Taylor's paper.- Allowing
for expected time lags, we checked the original NASA data
books for computer runs of the 7-minute full flux mo p e scan.
A hiatus in the plotted data frequently occurred because any
sharp jump in current flux from one 50 second sector to the
next caused the computer to reject the data because of a
time aliasing criteria. Since shacks usually pass by in
t
less than 50 seconds and the current jump is from 2 - 4
fold, only by looking at the current fluxes observed in the
instrument could the shocks be identified. Later Dr. John
Mihalov in Dr. John Wolfe's group did special 50 second
computer calculations of the maximum flux mode through the
shock.
4 J
1- 8 -
Six events were originally identified and a seventh one
on January 7, 1966 was later identified but not analyzed.
only fast shocks were searched for and it is dubious that
slow shocks could be identified given the computer errors.
The dates of the events were December 18, 1965 and January 21,
1966 for the Pioneer 6, August 29, 1966, August 30, 1966,
September 19, 1966 and September 23, 1966 for the Pioneer 7
events. Most of the events appear to be the same event seen
by Taylor using the time lags. Three of th r- Gix events do
not exhibit the classic sharp jump in density and flow
velocity expected. These may be nonlinear waves in the
p rocess of steepening as suggested by Chao 12 . The magnetic
field maqnitude for the August 30, 1966 event on Pioneer 7
resembles a solitary wave.
The method of analysis and results are discussed in a
preprint 13 . These are given in summary form here. The
events were assurled to be fast magnetohydrodynamic (MID)
shocks since only scalar pressure was measured. No electron
data was available. Bence, the normal momentum and energy
flux conservation equations f ,)r the Rankine-IIugonict equations
were not considered because the electron temperature must be
known to d;termine the total pressure.
The events were tested by first calculating shock
normals and then by fitting the proton and magnetic field
data ahead and behind the shock to the Rankine-Hugoniot jump
conditions. Six shock normals were used. Thk2 two spacecraft
shock normal did not give very good agreement of data with
cmm
r .-4
! .	 .
- 9 -
theory for any of the events probably because the interplanetary
shocks bent as they passed the earth's bow shock and ma(Inetosphere.
For the December 1' 1965 shock the two spacecraft were
really too close together for c,00d time resolution.
The velocity coplanarity shock normal is only approximate
except for perpendicular shoc':s and as expected did not give
results for the data that agreed well with the theory.
Three mixed data shock normals were used where both
magnetic and proton data were used. These gave the best
agreement between data and theory. The magnetic copla-..arity
shock normal was expected to be inaccurate because the angle
between the magnetic field vectors ahead of and behind the
shock was small leading to large errors in *.heir vector
product.
Median avera ges of all quantities except the density
were taken on both sides of the shock. Medians rather means
were used because they tend to give better statistical
results. The usual period for averaging was 8-10 minutes
where shorter periods of time gave worse results.
The results are given in tables I - VI in ref. 1.3. Two
shocks are nearly perpendicular. Two events that did not
a ppear to be classic shocks do not give the proper Mach
number ahead and behind the discontinuity for a fast shock.
One event is not included as it did not appear to be a shock	
i
at all. 1111 events are quasi-perpendicular (that is the
angle between the m.:ignt:-tic field and calculated shock normal
is g reater thcin 50'.
Y .^.^ ..
W.
- 10 -
All ti.e computer results are not given because they are
lengthy. However, the August 29, 1966 shock normals (Table IV)
are given because many others have calculated shock normals
for this event. Our mixed data shock normal 3 differs by
i
only 10° from the statistical result found by Lepping and
Argentino.
For the December 18, 1965 low Mach number, nearly
perpendicular, laminar shock the theoretical predictions for
the angles between data vectors are quite closely obeyed for
the vectors gaming into the mixed data shock normals.
Pioneer 8 and 9 Tensor Pressure Shocks
We obtained Ames proton bulk processor data from the
National Data Center for Pioneer 8 and 9 satellites. Seven
events of the classic shock form were identified. Plasma
parameters with scalar pressure were calculated by Dr. John
Mihalov for two of the most promising shocks.
1-.e have riot been able to complete the intended aim of
the grant, especially that for the second renewal, because
the data analysis for the shocks with tensor pressure was
never done at Ames Research Center. Dr.. John Wolfe finally
said that it would be too expensive. Dr. Larry Kavanaugh
1	 and our interim technical advisor Dr. Frederick Berko both
tried to obtain the analyzed data but they were unsuccessful.
The lack of tensor pressure data has been very disappointing.
b
- 11 -
References
1. R.P. Lepping and P.D. Argentino, J. Geophys. Res. 76,
4349 (1971) .
2. G.F. Chew, M.D. Goldberger and F.E. Low, Proc. Roy. Soc.
236, 112 (1956).
3. Y.M. Lynn, Phys. Fluids 10, 2278 (1967).
4. S. Morioka and J.R. Spreiter, J. Plasma Phys. 2,
449 (1968).
5. J.D. Mihalov, C.P. Sonett and J.H. Wolfe, J. Plasma
Phys. 3, 449 (1969).
6. B. Abraham-Shrauner, Plasma Phys. 15, 375 (1973).
7. S.P. Gary, J. Plasma Phys. 4, 753 (1970); 6, 551
(1971); and 7, 417 (1972).
8. B. Abraham-Shrauner, J. Geophys. Res. 77, 730 (1972).
9. J.W.M. Paul, ERSIN Study Group on Collision-Free
Shocks in Laboratory and Space, Frascati, (June, 1969).
10. M. Kornherr, Z. Physik 237, 37 (1970).
11. H.E. Taylor, Solar Phys. 6, 320 (1969).
12. J.K. Chao, J. Geophys. Res. 78, 5411 (1973).
13. B. Abraham-Shrauner and S.h. Yun, "Interplanetary shocks
seen by Ames plasma probe on Pioneer 6 and 7", J. Geophys.
Res. (submitted for publication)
w,
- 12 -
Personnel supported:
Principal Investigator - Barbara Abraham--hrauner
Research Assistants (graduate students):
Seh-Noon Yun, M.S. received June, 1973
Kuo-Mei Ling, M.S. graduate student started June, 1975
John Rice - computing assistance	 ,
Papers
Barbara Abraham-Shrauner, "Determination of Magnetohydrodynamic
Shock Normals", J. (7eophys. Research, 77, 736 (1972).
Barbara Abraham-Shrauner, "Interplanetary Shocks observed on
Pioneer 6 and 7 by Ames plasma probe", AGU annual Spring
meeting, Supplementary program p. 42, June, 1975.
Barbara Abraham-Shrauner and Seh-Boon Yun, "Interplanetary
shocks seen by Ames plasma probe on Pioneer 6 and 7",
J. Geophys. Res. (submitted for publication).
FOP-


Development of solar wind shock models with tensor plasma pressure for data analysis

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