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‘ TRW‘Tech\ Report No. 43856-6O0'» UT-00
FINAL REPORV: RESEARCH STUDY OF SPACE PLASMA
Principal Investigator: E. W. Greenstadt
Co-Investigator: W. W. L. Taylor
(lASi-CB- 174351) BISIABCB S10£l CF SPICE 185-19823
PUSBA BOOIOAiX PEOCESSBS final Bepoct, 1
Oct. 1983 - 30 Set. 1964 (3BB Space
lechnology Labs.) 45 p BC iu3/HF A01 Onclaa
CSCL 201 G3/75 14206
Period of Performance:
1 October 1983 through 30 September 1984
(third year of study period)
Washington, D.C. 20546
October 23, 1984
Applied Technology Division
Bldg. Rl, Room 1176
TRW Space and Technology Group
One Space Park
Redondo Beach, California 90278
TABLE OF CONTENTS
1. INTRODUCTION 1
2. OBJECTIVES 2
3. HISTORY 2
4. STATUS ON 1 SEPTEMBER 1983 3
5. PROCRESS SINCE 1 SEPTEMBER 1983 4
6. SUMMARY 9
7. RECOMMENDATIONS 10
APPENDIX 1 20
APPENDIX 2 37
FINAL REPORT: RESEARCH RTUDY OF SPACE PUSMA
Principal Investig(Jor: E. W. Oreenstadt
Co-fnvestigator: W. W. L. Taylor
This is the final report of the third year of an investigation into the feasibil-
ity and development of computer graphic representations of plasma boundaries
in space. It is not unreasonable to declare the project a success, especially in
view of the evolving goals the project itself has fostered, ffe started out to
develop three-dimensional conceptuedizations of plasma processes in and
around the magnetosphere as an aid to our ongoing research efforts, and wound
19 making animated fflms of the bow shock in the solar wind. Although the ani-
mation objective and the animation itself are supported separately by TRWs IR
k. D funds, we have found it necessary to devise our conceptualizations with ani-
mation in mind, because the physics we want to use our graphics for reqmres an
understanding of the variability of space plasma processes. This variability is
difficult to comprehend just by comparing static "spacescapes" and recon-
structing their evolution mentally. Given this diversion, or expansion, of pur-
pose. we are well on our way toward developing the techniques of computer-
graphic sketching of plasma processes in a way that has greater potential than
we originally anticipated.
The following sections describe the objectives and history of the project and
the progress of this year's program. We close with our recommendations for
- 2 -
The general objective of this project is to develop symbolic representations,
in three dimensional computer^generated images, of plasma boundaries and
processes in the Earth's magnetosphere and in the interaction region between
the magnetosphere and the solar wind. The purpose of such images is to pro-
mote rapid comprehension of complicated relationships among various elements
the Earth's plasma environment that can be obtained only by visual means.
We are interested in the gases, wakes, electromagnetic fields, shocks, and mag-
netohydrodynamic (MHD) waves that are present everyvdiere in space: How they
should be visualized; how diverse data needed for a comprehensive description
of space plasma phenomena can be gathered, correlated, and presented.
Our specific objective has been the creation of forms for representing the
bow shock and magnetopause and their geometrically determined macrostruc-
ture on both large and small scales, and, with emphasis, the utilization of such
forms as research tools. We are expressly concerned with both the composition
of the images and the physics underlying them. Shock physics in particular, is
enjoying a period of rapidly improving understanding, so that a significant part
of this project is devoted to studying and deriving some of the current results
whose properties we wish to represent.
This project began some years ago with an attempt to represent the global
distribution of quasi-perpendicular and quasi-parallel structures of the Earth's
bow shock. The original intent was simply to generate a persuasive picture of the
shock's nonunifcrmity, to encourage other investigators not to overemphasize
the nominal solar ecliptic plane cross section at the expense of the three-
dimensional nature of the shock. By the time we had developed a respectable
computer sketch, the need for it had largely subsided, but another problem
emerged. There seemed to be a serious need to emphasize the constant change
in the ncmuniformity caused by solar wind variation. The variation was appreci-
ated, but our own computer sketches of the global distributions of shock struc-
ture convinced us that no one. including us, understood, or was capable of ima-
gining, how imposing the complexity of the shock would be when literally seen as
a dynamic responder to solar wind variation. We conceived the notion of animat-
ing the shock, and by straightforward extrapolation, the magnetopause and any
other surface, boundary, or process in the Earth's plasma environment too com-
plicated to envision statically, let alone dynamically, without visual assistance.
The key to successful depiction, in three-dimensional renderings, of tha
plasma phenomena in vdiich we are interested is the choice of computer-
generated symbols that evoke rapid recognition of boundaries and other ele-
ments when viewed by an informed colleague with a minimum of expltjiation.
The selection, coding, and perfection of such symbols is the task we set for our-
selves in this project; the animation itself is supported principally by a TRW IR &
D Program. We began with a desktop computer operating a four color pen
plotter, programmed in Basic, and progressed to a VAX/11-750 controlling an
Evans k Sutherland vector graphic, co’or workstation, programmed in "C". Our
symbolic selections have been revised and improved to accomodate each new
process, conception, and system as we've advanced.
4 OTATUS ON 1 SEP1QIBER 1BB3
We had succeeded in completely redesigning our three-dimensional symbol-
ism for the bow shock and its global geometric division. The redesigned visual
model had been reprogrammed in "C"-language for a VAX/UNIX system operat-
ing an Evans and Sutherland (E k S) graphics console, and the program had
been tested and debugged. Ibe new symbolism was chosen to (a) minimize Moir6
patterns in the shock representation, (b) take advantage dT the color pallette of
the E & S system, (c) enable the depiction of the shock at higher sampling reso-
lution than had previously been en^>loyed, (d) speed up considerably the pro-
cess of generating each image, and (e) facilitate the use of images for animation
(details in Annual Report, November 1983).
& PROGRESS SnCE 1 SEPTEUEER 1063
A. Otaphic Development. Based on the conviction that computer-animated
modeling of space plasma objects and processes is the inevitable technique of
future data analysis, we added to our conceptualizations of the bow shock the
requirement that graphic symbolism be suitable for representation of not only
static, but dynamic, conditions as well. That is, con^>uter-created images of
space plasma processes, which change as the input plasma conditions vary with
time, must be contused of symbolic elements that lend themselves to incre-
mental changes from image to image so that rapid viewing of image sequences
presents the appearance of continuous, or at least smooth, physical variation.
We proceeded with this requirement in mind.
Two data sets were selected from ISEE-1 and I SEE-3 magnetometer and
plasma records. These sets appeared adequate to test the new symbolism’s clar-
ity and its suitability for animation, and at the same time to test some of the
assumptions underlying both the shock model itself and the way we presently
conceive of letting the variable solar wind modify it. One data set war the same
one used for our first, cruder atten^)t at animation last year, which demon-
strated well the need for a dynamic requirement separate from those for suc-
cessful static representations. This first set covers a two-and-a-half-hour interval
of ISEE-3 data in which the IMF varied radically and continually from its average
stream angle; the set ideally illustrates the global changes of q-perp/q-par.
pattem on the shock that can occur, and how much the real shock can differ
from the "typical" shock customarily used for presenting or visualizing results.
The second set covers a one-hour interval in which ISEE-1 was subject to
repeated crossings of the bow shock, some of which appeared to represent q-
perpendicular and some q-parallel structures. The IMF, measured indepen-
dently upstream by lSEE-3 at eight times the sampling rate of the first case,
showed, in contrast to the first case, only small variation about an average
direction not far from the average stream angle.
An animation film (and videotape) was made, supported by TRW’s IR & D
funds, for each data set described above. I:i the second case, the location of
ISEE-1 at the shock was represented by an asterisk that was made to blink on
and off when the local structure was q-parallel at ISEE-1 and to change color
between white and red, depending on vdiether ISEE-1 was outside or inside the
bow shock. Thus the ISEE-3 solar wind data, vdiich were used to define graphi-
cally the bow shock's position and structural distribution, became a "predictor"
(rf what local conditions were to be expected at ISEE-1, and the latter became a
"tester" of the predictions and hence of the assumptions underlying them. The
1. The uniformity of the solar wind and IMF over the distance from
ISEE-3 to ISEE-1;
2. The delay time from ISEE-3 to ISEE-l;
3. The model for global shock scaling of magnetopause and shock
standoff distances (from earth);
4. The bow shock’s shape;
5. The criterion for q-perpendicular /q-parallel separation (we used
'»Bn = «•);
6. The arrival directions of solar wind plasma and IMF variations
(we took both to be directly along Vg^).
The three attached color Figures 1, 2, 3 illustrate the images we are
- 8 -
currently using and show our capability for arbitrary zoom and ^dewpoint selec-
tion. Figure 4 displays the configuration of the spacecraft and the shock and
solar wind assumptions used in constructing each image from a sequence of
The animation test was reasonably successful in general. The predicted q-
perp/q-par. division was located close to ISEE-1. as the latter's data demanded,
but not close enough to cross the spacecraft whenever it should have. Similarly,
the average shock envelope did not cross ISEE-1 out- or inbound exactly as
predicted. This discrepancy seemed to be correctable by adjusting the assumed
delay between the two spacecraft. We are contemplating the rest of the assump-
tions as this is written. The most outstanding success seems to have been that
our guesses about how to produce decent animation were essentially right in
that the first try with the new symbolism resulted in smooth, visually acceptable
Two presentations of our graphics, in the form of animations, were made
since September, the first as incidental accompaniment to a review paper, at
the Napa Conference, the second as a report to the geophysical community, at
the May AGU meeting in Cincinnati. The purpose of these reports has been to
exhibit our technique, to display physical insights clarified by the technique, and
to solicit views of other experts on numerical simulations regarding state of the
art improvements applicable to our technique. The specific meetings at vdiich
presentations were made were:
AGU Chapman Conference on Coliisionless Shocks in the Heliosphere:
"Oblique, parallel, and quasi-parallel morphology" by E. W.
Greenstadt (Invited review), Napa, 20-24 February, 1904.
AGU Spring Meeting: "Animated simulation of global bow shock
structure" by E. W. Greenstadt and K. F. Yee (Poster session on
Numerical simulation of space plasmas), Cincinnati, 14-17 May,
KPhyaicaL /Voctsms. Having satisfied ourselves that the new symbolic
representations of the bow shock were suitable to animation with the E & S for-
mat, we turned our attention to expanding the inventory of plasma phenomena
we can simulate. We engaged in numerous activities, supported in part by other
funded programs, to keep current and active in the physics of space plasmas.
One important result has just emerged from this part of our effort. We have
demonstrated clearly that the earth’s bow shock must include a region in which
quasi-perpendicular and quasi-parallel structures coexist locally, or, more accu-
rately. must alternate in a periodic pattern in the shock surface to form a third,
"transition" section of the shock. Figure 5 shows the kind of variations of ‘dgjj
that occur at the shock iidiere ave> of 2 ^^ 3 ,^ is 45°, when typical foreshock yraves
of quite modest amplitude 6B/B = 0.2 or 0.4 (b/B in the figure) are convected to
it by a typical solar wind.
Instantaneous ‘dg,, differs from its average for appreciable intervals of time
and surface distance. One report describing the result and some of its conse-
quences has just been finished and submitted for publication; a draft of this
paper is attached as Appendix 1. The result described in ^pendix 1 will neces-
sarily have p major impact on the construction of bow shock images and on
foreshock images we plan to construct in the future. We are preparing a second
draft report describing an important consequence of the foregoing result, epe-
cially for computer graphic sketches, namely that the conventional depiction of
the bow shock, and therefore the magnetosheath and foreshock as well as two
mutually exclusive quasi-perpendicular and quasi-parallel sections must be
modified to include the transition sections too. If we are interested in the quasi-
parallel structure, we must now ask what part of the shock will At in this
category regardless of the presence of large amplitude waves with their changes
in . That is, vdiat part of the shock is always quasi-parallel, even when the
. 0 .
local waves impose a maximal excursion on .
Figure 6 shows two subareas of the shock, viewed from the sun’s direction
as projected on the y-z plane. The circle at the center marks the outline of the
shock in the y-z plane (at x s 0); the large area still open at the left edge of the
figure, is the region where the shock structure should be q-parallel in the pres-
ence of waves of relative amplitude 6B/B = 0.5. The smaller oval encloses the
region vdiere the shock should be q-parallel even in tha presence of waves of
relative amplitude 6B/B = O.B. We assume in drawing these sketches that the
average field is at the 45° stream angle. The important message here is that the
tnu q-parallel part of the shock occupies a great deal less than the left half that
might naively have been imagined.
We believe the areas defined above are at best approximate in that, strictly
speaking, is not the best criterion for dividing regions. The areas were
derived by finding the loci where < 45° at the maximal excursion ct waves of
the respective amplitudes. Aside from the issue of whether 45° is an accurate
discriminator of shock structure, the correct angle should not be that between
B and the three-dimensional normal to the shock, n. but that between B and the
normal iic to the intersection C of the shock with ihe plane containing B and the
x-axis. As B changes with the wave, so also does the &x plane and Df Ths loci
enclosing the invariant q-parallel structure taking into account this effect,
defined by = arcos(B(t) • nc(t)), are much more ccxnplicated to derive than
the simple ones illustrated in Fig. 6, and have not yet been worked out.
The addition of further details to images of the bow shock will be of little
value unless the transition area is included. More importantly, the graphic char-
acterization of downstream regions, such as the part oi the magnetosphere
affected by q-parallel structure transmitted through the magnetosheath, will
have to be carefully delineated with subregions of the shock in mind.
- 9 -
C. OthMT ActivUiaM, Mr. Greeniiadt served as Editor of the chapter produced
by the Working Group 10, vdiich he chaired, at the Solar Terrestrial Physics
Workshop in Coolfont, West Virginia, last year (see below). He also serves t s a
member of the Data Systems Users Working Group (DSUWG). Dr. Taylor has con-
tinued as a member of the DSUWG, and contributes directly to our constant
efforts to keep abreast of technological developments in computer data reduc-
Uoa analysis, and networking, and to acquire and apply new equipment to this
project whenever possible.
D. Haports. Two presentations including graphics results were listed above.
Written repoKs, prepared or published are as follows:
"Scale lengths in quasi-parallel shocks", by J. D. Scudder, L F.
Burlaga, and E. W. Greenstadt, J. Ceophys. Res., 69. 7545. 1964.
"The structure of oblique subcritical bow shocks: ISEE 1 and 2
observations", by M. M. Melloit and E. W. Greenstadt. J. Geophys.
Res.. 89. 2151-2161, 1984.
"Collisionless shock waves in the solar terrestrial environment". Chapter
10. E. W. Greenstadt. ed., in "Solar Terrestrial Physics: Present and
Future". D. M. Butler, and K Papadopoulos, eds., NASA Reference Publication
"Oblique, parallel, and quasi-parallel morphology of collisionless shocks ',
by E. W. Greenstadt. in "Cullisionless Fl.ock Waves in the Heliosphere". B.
Tsurutani and R Stone, eds., in preparation for the Am. Geophys. Union,
"Variable in the shock-foreshock boundary observed by
ISEIE-1 and -2". by E. W. Greenstadt and M. M. Mellott. submitted to
J. Geophys. Res.. 1964.
Cover pages of the foregoing papers are reproduced in Appendix 2. except for
the last, which is attached in its entirety as Appendix 1.
Vector, computer graphic representations ot the global distributions of bow
shock structures, and elementary animation of the dynamics of those distribu-
tions in the changing solar wind, for selected cases, now exist as results of this
- 10 -
project The programming tooli and codei developed for theie reiulti are
adaptable to other caiei and can be applied in a rudimentary way to other
features of the plasma environment.
We can make several recommendations independent of continuation of this
particular project. First, we are convinced that our objective, computer graphic
representations of space physical processes, is a desirable, viable, and produc*
tive goal. Real-time animation, although distant, is even more to be desired, so
that representations suitable to animation should be part of computer graphic
Second, speed of image production is not currently adequate for real-time
animatioa Assembly, or development, of equipment capable of higher graphic
calculation and production rates should be supported. However, development of
appropriate symbolic representations can be carried out separately, as long as
attention is given to creating images likely to be independent of particular
hardware and software solutions to the speed problem.
Third, computer graphic representations should be developed for a wider
assortment of space plasma phenomena than has been dealt with so far. We
would expect new problems to arise that have not yet appeared in our work.
Finally, computer techniques should be expanded to iijclude, or incor-
porate. raster graphic figures with color fill symbols, hidden line removal for
vector graphic sketches, and shading algorithms for raster sketches. These
methods all involve foreseeable problems of one kind or another. For example,
hidden line removal slows down vector image generation considerably. There will
be unforeseen problems as well. We do not therefore underestimate the effort
needed to bring these techniques under usable control, but we think it wiil
• 11 -
rviult in « valuable approach to data analyiii. At the moment we favor at an ini-
tial expanvion an attempt to blend vector and raster elements kite composite
pictures that will get around some of the problems we envision without adding
too serious a burden of number crunching.
We recommenc broad support for the application of computer graphic
development to space plasme data analysis, taking into account all the above
observations. We believo. liowever, that the fundamentals of animation have been
sufticiently advanced to Justify reluming the focus of attention to the problem
of three-dimensional representations of a diversity of magnetospheric
phenomena. Thus, we also have recommendations for speciftc tasks related to
our own original approach:
Q-F^rptnUcular/Q-ParnUnK TVtsnsifion. As already noted, recent calcula*
tions suggest that a substential region of transition exists separating
purely q-perp from purely q*par sections of the bow shock (Appendix 1
and Fig. 6) above) This region shoulJ be characterized by locally
periodic, or nearly periodic, alternation between the two structures,
because of large-amplitude waves impinging on the shock from upstream.
We believe a representation of this additional region must now be incor-
porated in any graphic shock model.
AbresAock. The foreshock as an implicit substructure of the q-parallel.
collisionless shock, so that no depiction of the shock is truly complete
without a foreshock element. At the Napa shock conference. Scudder
introduced a three-dimensional graphic representation of foreshock
boundaries extending like visors into the upstream region from the bow
shock surface. This representation should be examined carefully,
modifled, if necessary, and a foreshock configuration should be added to
- 12 -
bow shock images.
Vfcnus. As there is reason to believe that there may be significant
differences between the distributions of structural forms on the Venus
and Earth bow shocks, the model we have been developing should be
appropriately modiffed to produce images of Venus' shock.
Magnetopause. As we have noted in the past, a representation of the mag-
netopause has already been included in our graphic programs for this
study. We have not, however, defined what physical distinctions we wish to
make in our representations of the magnetopause surface. Noting the
rapid progress being made in reconnection studies, and interest
expressed by magnetospheric experts in the possible use of our tech-
niques. other investigators should be consulted on this matter, and the
adaptation of our programs to magnetopause modeling should be
Vbftffne Represent aiions. Thus far, we have confined our model represen-
tations to surfaces only. But the physical processes in which we are
interested, of course, involve whole volumes of space. We are thinking
particularly of the foreshock, the magnetosheath, and the magneto-
sphere. We urge exploration of the more difficult problem of representing
processes within these important volume elements of the space plasma
environment. This is a serious challenge to computer graphics technology
in general, and efforts should be expanded to include raster graphics
apparatus and techniques, which we believe will be necessary to meet the
Propagatior of IMF Varialions. The weakest assumption underlying our
eflorts to produce sequences of bow shock images governed by the flowing
solar wind has been the modeling of the IMF as a series of sampled incre-
ments uniform in planes, or slabs, perpendicular to the flow direction, i.
e.. perpendicular to the sun-earth line. 1)118 assumption is suitable for the
solar wind plasma under most circumstances, but fluctuations of the IMF
are likely to propagate along the average IMF at least half the time, thus
approaching the bow shock from a direction usually about 45° away from
that of the solar wind itself. The programs we have developed should be
modified to take this effect into account.
Figure 1. Earth's bow shock, with quasi-perpendicular (bl'ie) and
quasi-parallel (green) sections determined from ISEE-3 solar wind
data, and ISEE-1 at asterisk position. Red asterisk means the
satellite was inside the shock. oArc
Figure 2. Zoom, i.e., magnified view of bow shock. White asterisk
means the satellite was outside the shock.
• CLOSEUP OF
COLOR P^ C'OORAPH
Figure 3. Side view, showing satellite outside shock after solar
wind has pushed shock inward, causing travelling surface wave, visible
at the edge near the bottom.
SHOCK: 79i25}*— 3BBR] ~10<s<|i^
'™‘ a,.[i«u^ yv* lnh' r.»
*0 W O
0 U h
« « «
M U Ki
•-I h p.
O 0 I
0 t-l O*
•0 O TJ
0 0 0
J3 0 U
4J 0 <rt
•H -H -O
iH *0 Q.
■0 0 0
9 iH o.
J3 ^ 0
CO U *H
0 0 >
M •H <H
•rl I 0
PROPOSAL NO. 43836. OOIRI
k • l« 10*^ em*^ V..* §0 km/t 45*
. b/D • 1
T' • 40 MC
V • 2.3 Rf
B/D > .68
V • 334 BBC
V *6.8 Rg
Figur« 5. C<mput«d tbIubb of thB Bhoek normBl Bngls for typlcBl vbvb
B nd BOlBr Vlad pBTBMtBrB Bt tvo rBprBBBntBtlVB loCBtiODB on thB bow
Bhock (BkBtcbBB Bt right).
ORIGINAL PAGE IS
Of. POOR QUALITY
Figure 6. Antl-eunverd, l.e.» solar wind's* vlsw of ths bow shock
projsctsd on ths y-r plans. Ths elrcls srotind the origin Is ths
Intersection of the hypsrbololdsl shock with ths y-s plans (at x ■ 0).
Ths two heavy curves define ths projsctsd boundaries of ths regions
within which ths local shock structure would be expected to be
q>psrsllsl* for an IMF at ths nominal strssm-sngls* even when waves
of ths respective rslstlvs amplitudes ere convsctsd to ths nominal
shock surface. Each tic Is ten earth radii.
NEW REPORT, SUBMITTED FOR PUBLICATION
VARIABLE IN THE SHOCK-FORESHOCK BOUNDARY OBSERVED BY
lSEE-1 AND -2
E. V. Greenstadt
Space Sciences Depa*-lmenl, TRV»’ Inc., Redondo Beach, CaUfo-nir-
M. M. MclloU
Department of Physics and Astro:. orr,y. University of Iowa, lov.a Cil)*. lav, a
Abstract. Saturated ULF waves in the foreshock, (5B,/B^1.0, o/Op^O. 1, are
convected by the solar wind to the quasi-parallel shock where the average field-
normal angle S45'*. Several examples from ISEE 1 and 2 magnetometer data
show waves that defined local, instantaneous very different periodically from
the average. Local geometric conditions at the nominally quasi-parallel shock
varied from nearly parallel to nearly perpendicular, at the periods of t>’pical
upstream waves. Clear magnetic shock transitions occurred when r?3jj was tem-
One of the major controlling factors of the structure of a collisionless shock
is 1J3J, , the angle between the upstream magnetic field and the local normal to
the shock surface, or w’ave envelope. When ‘d3j, is high (90“ > > 60"), the
shock is quasi-perpendicular; when 153^ is low (30“ 0®), the shock is
quasi-parallel [Greenstadt, 1904]. These terms denote, phenomenologically
[Greenstadt and Fredricks, 1974], shocks whose magnetic signatui-e.® in the
shock or spacecraH frame are characterized by abrupt, clearly defined jumps in
average field over times generally on the ordir of lc.«s than 30 seconds (q-
perpcndicular) or by lengthy upstream and downstream wavetrains, sometimes
difficult to distinguish, of large amplitude 5D/IK1 and periods of seconds to tens
of seconds (q-parallel) in which the particle shock transition is embedded
- 2 -
[Scudder et al., 1964]. The upstream wavelrains define part of an exlcnflve
region ahead of the ihock, called the foreshock, whose full development Is a
prominent feature of the q*parallei struct urc.
A ngniflcant part of these upstream wavetralns is expected to arise in an
instability in which ions reflected from shock interact with the- sntar A.-nd
[Fairfield, 1909; Barnes, 1970; Barnt et al., 1030 : Le>., 1982; W'inske and Ijcroy,
1984]. For need of a term, we shall shy the sliocl; is in a “transitionr'" condition
when dan By ^his we mean that reflected ions escaping the shock upstream
at dan <'^60'’ interact with solar wind to generate transverse waves which, in
various stages of development, are convected back to the shock where, until daj,
drops to >^40% the>' are reasonably distinguishable from the compressional
waves and pulses that mark the true quasi-parallel shock profile. Both observa-
tion [Hoppe et al., 1981] and theory [Winske and Leroy, 1984] have showm the
transverse waves develop relative amplitudes dB / Bq at least -^0.5 in the transi-
tional foreshock, w'here is the average upstream, or solar wind, field. Recall
that the angle and field variation are related by dgn = arcos (B • n), where
B»B(t) = Bb + (5B(l), dB(t) represents the wave vector, and n is the local normal.
In principal, ions rejected by one process or another, say, reflection or
post-shock heating and scattering, can leave the shock for any da<j., <*^60® and
contribute to the instability driving the upstream waves. In fact, beams must
leave for a range of d^Qj, in order to drive the instability to saturation. The ins-
tability, and wrave growth, proceed as rejected ion beams continue to be fed into
the upstream interaction while the solar wind sweeps? its field liri'. s arid their
shock-intersections across the shock toward lower d^j, . The resulting v.avt.* are
returned to the shock somewhere at appreciable amplitude, where the instan-
taneous values of dg,, cannot be dgon . but rather some dg., (t). If wavegrowth is
fast enough, the possible paradox arises in whicvi escaping pai'.i< h's cri-atr'
wavet which, when convected back to the ihock, define local '■ that pehodi*
cally diicourage or distort the escape of beams needed to maintain the instabil-
ity, thereby modifying the above, simplified upstream process in an as yet
undefined way. In applying this argument, we are thinking of with respect to
a first order "normal" defined by some model of the global shock surface. Of
course, if the local surface is itself wavy. (t) could be interpreted to encom-
pass both B(t) and n(t).
Recently. Greenstadl , using a /Ixtd local, model normr.i, displayed
the results of sample calculations of (t) indicating that the variations of
at the shock should be expected to have significant effects on local shock struc-
ture. Figure 1 illustrates a sample calculation of (t) where it has been
assumed that a "typical" transverse, upstream wave propagating parallel to
with k s .0006 [Hoppe and Russell, 1963] and dB / b 0.5 in a "typical" solar
wind carrying a at its "typical" stream angle (at 1 AU) encounters the shock
at the subsdar point. At the subsolar point, of course, the fixed, unit normal is
(1,0,0) for any model; we took our "typical" solar wind speed as 360 km/s, the
wave speed as 60 km/s, and the stream angle as 45”. Such an encounter ought
indeed to alter significantly the first order approximation b dgQ,, b 45 ‘. and
we see in the figure that dg„ varies between roughly 10” and 60”.
The purpose of this report is to document that such encounters are a real-
ity; They arc readily found in satellite data, in this case data from ISEE-1 end
ISEC-2, and, in fact, occt"* at wave amplitude s considerably larger than that
shown in Fig. 1.
DATA SELECTION AND TREATMENT
The cases we present here were selected by surveying four years of shock
crossings by ISEE-1,2 from launch in October 1977 Ihi ough December 1990. The
survey was made visually with graphs of magnetic field data, from the UCLA
• 4 -
fiuxgalei [Ruitell, 1978], averaged every 12 eeconde' and plolted every four
•econdfl. We lought well defined shocks adjacent to variable foreshock field in
which the componenti ahowed higher amplitude than did the field magnitude,
preferably ai nearly periodic oecillatione. We hoped in this manner to select
largely transverse upstream waves that \>ould permit direct comparison with
simple model waves such as those of Fig. 1.
Our search yielded more than tw'o score of potentially suitable candidate
shock crossings. We show five examples in this report, three from lSEE-1, two
from lSEE-2. The examples have been studied at quarter-second resolution, that
is, as plots of field measurements at the sampling rate of four points per second.
We use a program, more accurately a constellation of programs, developed at
UCLA to plot the data and analyze them to produce filtered plots, spectral ana-
lyses, polarization hodograms, and, most importantly for this investigation, con-
tinuous Computations of . By average , or , in this report, we mean
the angle between the average and the shock normal during four minutes of
waves recorded immediately outside the shock.
Figure 2 is a full magnetic characterization of one example of the encounter
of upstream UU* waves with the shock. The magnetic context can quickly be
assessed by reference to the total field magnitude shown in the bottom graph of
the left panel, where thr shock is visible as a sharp jump near the far right of
the plot. The shock w«s preceded by a long period wavetrain (r<"* 4r*«ec) most
clearly delineated in the By and B, components of the field. Other wove frequen-
cies were obviously also present at lesser amplitudes. Tlie charact'.T of the
waves is evident in the hodograms of the two right pa.oels and was substantially
in the I-J plane-of-maximul-variance (upper right), where the superposition of
the whole sequence of low-pass-ftltered cycles is displayed. Tlie wavetram was
• 6 •
not txclufively irantvvrie. but included a compreuional contribution, etpe*
cially near the shock. Angle between the direction of propagation (the direr*
tion of minimal variance) and the field was about 22*, essentially, but not
entirely, parallel to . The essentially transverse wave in this case had an
amplitude dB 0 6 Bq . The angle 1/30^ between the average jpstrran: B*vector
and the nomina> model normal was 46*.
l>ie graph at the top of the left panel is a plot of instantaneo'.r calcu*
lated from the ISEX-1 data, showing the direction of every measured field vector
with respect te the local model normal, and the average ni a dashed
horizontal line. The dominant ULT periodicity of the waves is readily apparent in
this representation, where the average period is about 38 sec. The solid cunre is
a plot of theoretical i)j|„ calculated for the same idealized, ’’typical" transverse
wave as in Figure 1, but with S^/ Bq s 0.6, and for the analogous location on a
nominal shock. That is. for a point at the same angle to the solar-ecliptic x-axis
on a model shock scaled by the parameters we used for Fig. 1, as the point at
which the data of the figure were obtained. The model we use is
.04 [(*-586)* -304 682], a cylindricrl coordinate version of the best fit ter-
restrial bow shock derived by Slavin et al. , wherep*^v^4■s^
Three more examples are shown in Figure 3. where we plot only the field
magnitude and angle 1)3,, (t). The regularity of the oscillations of 03,, (t). as of
the foreshock waves themselves, varied apj;»-ccicbly from case to case, with only
tSe Sept. 6 case, in the middle, having waves as close to monochromatic a« those
of .\o\*. 6 (Kig. 2). in every instance, however, the difT'-rmr e of inst;in',.i;» 'ous 153^
from its average is abundantly evident. It is especially important that the value
of d3„ at the instant of shock encounter war not necessarily anywhere n»-nr the
average. Table 1 summarizes the parameters attached to the data of Figures 2, 3
- 6 -
Although the main purpose oi this report has been served by display of Pig-
ures 2 and 3. we call attention to several characteristics of the data that have
appeared as a "bonus" in examining these plots and that we believe will be of
considerable significance in further investigations of quasi-parallel shock struc-
First, we see that the instantaneous value of iSaj, at the shock encounters
(marked by vertical solid lines), w'as in every case equal to or greater than the
average ■jJgQj, , marked in the figures. In effect, the local shock, insofar as it
appeared as an abrupt, quasi-perpendicular jump in the field, always occurred
while tJqj, (t) defined temporarily a locally quasi-perpendicular geometry. Figure
4 illustrates a second very clear example, like that of the center panel of Fig. 3.
where iJgj, (t) at shock encounter was >60°, unmistakably well above iS 3 qjj , which
was 3 Qj, ~ 37° (35° in Fig. 3b).
Second, as a sort of complement to the foregoing observation, we see in
three of the four cases of Figs. 2 and 3 (in all but the last) that one or tw'o bursts
of high frequency oscillations (shaded bars) occurred near the shock. These
bursts took place when (t) was at the bottom of its cycle, i.e., when the
instantaneous defined a temporary, unambiguous, quasi-parallel geometry.
This suggests that bursts of waves associated writh a locally parallel magnetic
profile may have prevailed perioilica'.ly when “dg,, (t)~0°.
Third, relative elevations in the magnitude B. i.e. compressiorial increases
in B in the figures, occurred during lliose portions of the dg., (t) cycles when the
angle was above the average; in other words, significant compressions occurred
only w'hen dg., (t) was high, meaning the local geometry was quasi-pcrpcndicular.
The converse was not evident: not every rise of dg„ (t) was accompanied by a
compression. The correlation has been emphasized in the figures by the vertical
The graphs of Fig. 2 demonstrate that the the theoretically and empirically
implied encounter of large amplitude, transverse, foreshock waves with their
associated shocks at transitional average field normal angles of ~ 45“ actually
occurs in nature at the earth’s bow' shock in a pattern reminiscent of the ideal*
ized one, and that instantaneous values of tJqjj differ radically from the average.
Ihus there is a definite region of the bow' shock in which quasi’perpendicular and
quasi-parallel geometries alternate semi-periodic ally; i.e., angle (v.) may be
close to either 0“ or 90“ at the point where the shock is forming. The character
of the magnetic record in our cases suggests that the shock structure may vary
locally, depending on the time variation of 153 ^ .
One further implication is that, since the high- “d 3 jj sections of the wave
cycles are staggered in space, the quasi-perpendicular "envelope" of the shock
has an undulating surface, perhaps consistent with the one inferred from early
data by Fredricks et al. . This wrould then imply that calculations of t? 3 jj (t)
should also have taken into account the compounding effect of n(t), if a model of
such variation of the normal were available. Curiously, however, abrupt shock
jumps appeared at high, q-perpendicular d 3 j, calcvlaied from fixed n. thus intro-
ducing a consistency w^ith the first order approximation that would deny the
seemingly straightforward implication that a higher order calculation is needed.
Kesolulion of these contradictor)’ "consislcncie?" remains for more comprehen-
Examination of the figures encourages additional speculations. First, ques-
tions of quasi-parallel shock potential, electron potential gain, ion potential gain,
and subshock formation in fully developed structures [Goodrich and Rc udder,
1984; Kennel et al., 1984; Quest. 1984; Scudder et al., 1984] must be addressed
- 8 -
both in terms of the long magnetic scales of quasi-parallel proflles and the short
scales of what appear the local, temporary quasi-perpendicular shock jumps.
Second, it takes little imagination to infer that the mixed values of
close to the shock, accompanied as we see by mixed high and low frequency
magnetic waves, are probably associated with plasma waves and t\ith mixed dis-
tributions of upstream ions, some scattered downstream by waves further
upstream, some reflected or emitted upstream from nearby q-parallel shock
encounters, and some trapped in adjacent q-perpendicular shock encounters.
■Rie ion flux oscillations at typical w'ave periods in the foreshock described by
Potter  may have resulted from modulated emissions at the shock source.
We inspected one example of ion data from a quasi-parallel shock already
described in the literature: Gosling et al. [19B2] recorded two samples of specu-
larly reflected ions "similar in nature to the g>rating ion beams observed within
the quasi-perpendicular bow shock [Paschmann et al.. 1982]". 'Hie purity of their
reflection signatures in a region w’here diffuse distributions might have been
expected, but where "no evidence for such particle debris in the contours" w’as
noted, suggests that the signatures may have been created during a temporarily
q-perpendicular. and released during a temporarily q-parallel, interval of local
W'e ran tJgj, (t) plots for the waves surrounding the cases of Gosling et al.,
and found variations comparable to those illustrated in Figures 2 and 3 of this
report, with the addition of considerable variations; at higher frequency. Tlie
data for those cases >vere obtained al IFEF’s iiighest sampling rate, so the plots
were too long and too detailed to reproduce in this letter. The samples selected
by Gosling et al. occurred two minuses aw«y from the actual shock crossing,
somewhat removed from the largest oscillations of the field direction. During
each three-second ion sample, the direction change was relatively small, com-
■omewhat removed from the largest oscillations of the field direction. During
each three-second ion sample, the direction change was relatively small, com-
pared to surrounding intervals, and the field was close to its average upstream
orientation. Certainly the possibility is open that the observed ion distributions
were produced elsewhere at nonaverage . Comprehensive investigation of
(t). plasma, and plasma wave data in high bit rate cases, where iun distribu-
tions can be distinguished, is the obvious next step.
AclenowledgeTrLents. This study was funded by NASW-3690 and -3836 (at TRW)
and NAS5-26819 (at Univ. of Iowa). The data library, processing techniques, and
advice of C. T. Russell have been essential, as was the help of R C. Elphic, L.
Baum, and K Yee in effecting the analysis. The in^>ortance of (t) has been
espoused by C. F. Kennel for years in private discussions; its calculation was
added to the UCLA data analysis programs at the suggestion of J. T. Gosling.
Bame, S. J., J. R Asbridge, J. T. Gosling, G. Paschmann. and N. Sckopke,
Deceleration of the solar wind upstream from the earth's bow shock and athe
origin of diffuse upstream ions, J. &ophys. Res., 65, 2961, 1980.
Barnes, A, Theory of generation of bow-shock-associated hydromagnetic waves
in the upstream interplanetary medium, Cbsmic ELectrodyn., 1, 90, 1970.
Fairfield, D. H., Bow shock associated waves observed in the far upstream inter-
planetary medium, J. Qeophys. Res., 74, 3541, 1969.
Fredricks, R W., G. M. Crook, C. F. Kennel, I. M. Green, F. L Scarf, P. J. Coleman,
and C. T. Russell, Ogo 5 observations of electrostatic turbulence in bow shock
magnetic structures, J. Geophys. Res., 19, 3751-3768, 1970.
- 10 -
Goodrich, C. C., and J. D. Scudder, The adiabatic energy change of piasma elec-
trons and the frame dependence of the cross-shock potential at collisionless
magnetosonic shockwaves. J. Qtaphys. Rbs., 69. 6654-6662, 1964
Gosling. J. T.. M. F. Thomsen. S. «. Bame. W. C. Feldman, G. Paschmann. and N.
Sckopkc, Evidence for specularly reflected ions upstream from the quasi-
parallel bow shock, Oeophys. Rts. Utt.. 9. 1333, 1962.
Greenstadt, E. W., Oblique, quasi-parallel, and parallel morphology of collision-
less shocks, CbUisiordess Stocks in the Heliosphere, AGU Monograph, 1984.
Greenstadt, E. W., and R W. Fredricks. Shock systems in collisionless space plas-
mas, in 5olar System Plasma Riysics: A Twentieth Anniversary Review, vol. 3,
edited by C. F. Kennel, L J. Lanzerotti, and E. N. Parker, p.4. North-Holland.
Hoppe. M. M.. and C. T. Russell, Whistler mode wave packets in the earth's
foreshock region. Nature, 267, 407-420, 1980.
Hoppe, k. U.. and C. T. Russell Plasma rest frame frequencies and polarizations
dl the low-frequency upstream waves: ISEE 1 and 2 observations, J. Geophys.
Res., 66. 2021-2028, 1983.
Hopp>e, M. M.. C. T. Russell, L A. Frank, T. E. Eastman and E. W. Greenstadt.
Upstream hydromagnetic waves and their association with backstreaming ion
populations: ISEE 1 and ISEE 2 observations. J. Geophys. Res., 66, 4471-4492.
Kennel C. F.. J. P. Edmiston. and T. Hada, A quarter century of collisionless
shock research, Collisionless Shocks in the Heliosphere, AGU Monograjh, 1984.
Lee. M. A.. Coupled hydromagnetic wave excitation and ion acceleration
upstream of the earth’s bow shock. J. Geophys. Res., 67, 5063, 1982.
- 11 -
Paschmann, G., N Sckopke, S. J. Bame, and J. T. Gosling, Observations of gyrating
ions in the foot of the nearly perpendicular bow shock, Oeophys. Fts. Latt., 9,
Potter, D. W„ High time resolution characteristics of intermediate iondistribu-
tions upstream of the Earth's bow shock, in press, J. Gaophys. Res . , 19B4.
Quest, K. B., A review of simulation of quaseparallel collisionless shocks, submit-
ted, CbUisiordess Shocks in tha HaLosphara, AGU Monograph,, 19B4.
Russell, C. T., The ISEE-1 and -2 fluxgate magnetometers, EEE Trans. Gkosci.
Electronics, GE-16, 239-242, 1978.
Scudder, J. D., L F. Burlaga, and E. W. Greenstadt, Scale lengths in quasi-parallel
shocks, J. Gaophys. Res., 89, 7545-7550, 19B4.
Slavin, J. A. R E. Holzer, J. R Spreiter, and S. S. Stahara, Planetary Mach cones;
theory and observation, J. Gaophys. Res., 69, 270B-2714, 19B4.
¥Tinske, D., and M. M. Leroy, Diffuse ions produced by electromagnetic ion beam
instabilities, J. Gaophys. Ra»., 89, 2673-26BB, 19B4.
R^nce of i5»,.
1 iSb„ at shock
Fic. no. 1
22 Dec. 77
6 Nov. 78
6 Sep. 79
18 Nov. 79
25 Nov. 79
- 12 -
Figure 1. Plot of instantaneous fleld-normal angle vs fraction (t/T or 1/X’) of
apparent period T* or wavelength V. in a shock or spacecraft frame stationary
with respect to the solar wind, for a tjrpical transverse foreshock wave of fre-
quency 0.10 and amplitude dB/B=0.5.
Figure 2. Left, magnetic field data (lower four plots) and corresponding field-
normal angle (irregular upper plot), vs. time for the 6 November 1978 case.
A model calculation of for a foreshock wave of amplitude dB/B=0.P is super-
posed as the smooth periodic curve in the upper panel. The solid vertical arrow
marks the shock crossing. The horizontal dashed line marks the average
upstream ;the vertical dashed lines mark the centers of compressional
excursions of R the hatched box marks a burst of high frequency oscillations
close to the shock. Right, hodograms of the observed wave, showing dominant
planar polarization, as assumed in the calculated behavior dt the foreshock
Figure 3. Three case of wave-shock encounter, shovdng field magnitude and
(t) computed from the data. Symbols and lines have the same meanings as in
Figure 4. A two-minute section of an additional case of shock appeal ance when
^Bn above a relatively low, post-transitional 1)30,, .
Figure 1. Plot of instantaneous field-normal angle vs fraction (t,/T or l/V) of
apparent period T or wavelength X', in a shock or spacecraft frame stationary
with respect to the solar wind, for a typical transverse foreshock wave of
frequency 0.1 and amplitude bB = .5.
Figure 2. Left, magneUc field data (lower four plots) and corresponding field-
normal angle (irregular upper plot), vs. time for the 6 November 1970 case.
A model calculation of for a foreshock wave of amplitude b/B=0.B is super-
posed as the smooth periodic* curve in the upper panel. The solid vertical arrow
marks the shock crossing. The horizontal dashed line marks the average
upstream :thc vertical dashed lines mark the centers of compressions!
excursions of B; the hatched box marks a burst of high frequency oscillations
close to the shock. Right, hodogroms of the observed wave, showing dominant
planar polarization, as assumed in the calculated behavior of the foreshock
SOLAR TERRESTRIAL PHYSICS - PRESB^ AND FUTURE
COLLISIONLESS SHOCK WAVES IN THE SOLAR TERRESTRIAL ENVIRONMENT
II. Natural Shocks
III. Quasi-Perpendicular Supercritical Processes
IV. Quasi-Perpendicular Subcritical Processes
V. Quasi-Parallel Processes
VI. Ion Acceleration
VII. Outstanding Problems
VIII. Investigative Avenues
JOURNAL OF GEOPHYSICAL RESEARCH. VOL. ». NO. A9. PACES 7545-7550. SEPTEMBER 1. 19M
Scale Lengths in Quasi-Parallel Shocks
J. D. SCUDDER AND L. F. BURLAOA
NASA CodAar^l Spitce Flight Cemrr, Laboratory for Exiraterrtunal Fhyuct, Crrtnjeli, Maryland
E. W. Gpxft^stadt
TRW, Redondo Beach. Caltfomla
Eiampln of an inierplaneiary ihock and ihr earth'i bow iRock arc prcanicd to illuitralc ihc nnall-
icalr fiac L, of ihc fluid deceleration relative to the acale of the magnetii. fluciuattoni, L^. at quaii-
parallel (hock* The incrcaie in elearon and ion random energies is also illustrated to occur on the short
'inner' scale of L. The selected interplanetary and bow shock rsamples are both supercntical high-/!
shocks but have JilTereni Alivtn Mach numbers. The thickness L, in absolute and convcctcd Larmor
radii units of the lower Alfv^n Mach number interplanetary sho;k is larger (- 10 L' /n„| than that at the
bow shock ( ' 1 1 -2| I’ ' /n„|. where V is the plasma flow sp^ viewed in the normally incident shock rest
frame In both esamples the Kale of the fluid deceleration is much smaller than ihs* of the up- or
downstream magnetic fluctuations. The estsienoc of steady siaic quasi-parallel shocks requires that the
Lorenu deceleration force be much larger than the elc^roslatic deceleration force along the shock
The view of quasi-parallel shocks < 45 ) as broad and
disordered transition regions, with scale lengths at the bow
shock of several has remained uncontested in the literature
for over 10 years This characterization is l4rgel> based on the
magnetometer morphology at the earth's bow shock. Recently
observes interplanetary quasi-parallel shocks have aiso been
reported to possess broad magnetic transitions with scales in
excess of 10* km. In this paper we organize ISEE and Voyager
plasma data capable of alTirming or denying the “broad trarui-
tion“ view of such shocks by identifying the scale L, over
which the plasma decelerates across quasi-parallel shocks. We
show that this deceleration scale L, is much smaller than the
spatial scale of the magnetic fluctuations. which has been
previously "sed to characterize quasi-parallel shocks as
“broad" structures. Previously, the spatially varying system-
atic effects in ion measurements at the standing bow shock
havf precluded definitive commentary on these issues.
In the iramework of MHD theory a parallel shock is
characterized by a discontinuous increase in temperature and
a discontinuous decrease in speed in the normally incident
shock frame, neither the magnitude nor the direction of the
irugnetic field changes [Landau and Lifschii:. 1960] across
such a theoretically idealized shock (except for the limited
regime (low betai where a switch-on shock is possible, nanmly.
tf'c normally incident velocity V, bounded be-
tween <V.< (4i;.^ - 3C,^' ^ [Akhiezer ei ai. 1975]).
Shocks in nature have a finite thickness L^ which may be
taken to be the width of the necessary transition in density or
speed Across this layer, random energy increases ai the ex-
pense of the directed streaming energy This exchange is prin-
cipally initiated in quasi-perpendicular shocks by an elec-
trostatic field E localized within this layer Within in quasi-
parallel shocks there is also localized an electrostatic field, but
Its relative importance in the deceleration process for this clau
of shocks has until now not been established In either case
Copynghi I9M by the American Geophysical Union
Paper number 4AOM2
0I4I-0227/IM 004A-0M2S02 00
the distance Lg over which such an E is nonnegligible is ap-
proximately bounded by L,. Up- and downstream of shocks,
magnetic fluctuations are usually found with scale lengths
• where the plus superscripts ruler to the low-
entropy upstream regime and the minus superscripts 'efer to
the high-entropy downstream regime In the past the high-
resolution magnetometer profiles of * and L^ ' have been
operationally used to auess the thickness of collisionless
shocks, especially for those of the quasi-parallel geometry
[Cahill and Amazeen, 1963; Bernsttin el al., 1964; Creensiadi
et ai. 1970. 1977; Auer and Volk, 1973; Acuna ei ai. 1981;
Tsuritani et ai, 1983, Kennel ei ai, 1982]
Lm * at the earth's bow shock is typically several R, for a
wide range of < ^5 [Creensiadi and Fredericks, 1979].
There is. however, neither experimental nor theoretical justi-
fication that the scale of the plasma deceleration L^ is ncces-
urily synonymous with the scales of the magnetic fluctu-
ations, Lm " , Ljm * The observed relative ordering of these two
Kales will be contrasted in this paper for the first time
2. RkGiMES ot Quasi- Parallel Shock
Quasi-parallel shocks have until recently only been studied
at the earth's standing bow shock, the first detection of an
interplanetary quasi-parallel shock was reported in 1979
[Acuna ei ci, 1981] There is an important difference in the
systematics of ion measurements which make determinations
of L, more difficult at the standing bow shock than at the
propagating interplanetary shock : the plasma bulk velocity in
the spacecraft frame is (is not) supersonic with respect to ion
thermal speeds on both sides of a propagating interplanetary
(standing bow) shock
In order to assess the Kale of the fluid speed. L^ the speed
itMlf must first be determined free of spatially varying system-
atic effects. The constituent sonic Mach number of the bulk
flow in the spacecraft frame determines how much of the 4n sr
of veloaty space mu-vt be thoroughly sampled to allow direct
model independent numerical estimates of the bulk velocity of
The solid angle coverage in velocity space about the spa-
tially varying local flow direction C?(x) necessary for this deter-
JOURNAL OF GEOPHYSICAL RESEARCH. VOL 99. NO A4. PACES 2151-2161. APRIL I. I9M
The Structure of Oblique Subcritical Bow Shocks: ISEE 1 and 2 Observations
M. M. Mellott'
/fuiiiytr (jtophyuo and Plam iary Phytu %. Umifriit) of Californ a
E. W. Greenstaot
Spacf Snencet Dfpartmrm, TRW Spcrr and Technology Group
Wc have iludicd the ilruclural clemrntt. includinf ihocii rampt and prccuraor wave iraint. of a lenn
of oblique low- Mach number lerretirial bo» thockt We used mafneiic field data from the dual ISEt I
and 2 ipacecraft lo delermine the tcale lenfiht o' vanouv elcmcnii of ihock iiruciure at well at
wavcler' ht and wave polanzationt Row thock iiructure under thne condiliont it ettcniiall) that of a
larfe-ampliiudc damped whiiller mode wave which etiendt uptiream in the form of a precurtor wave
train Shock thicknrttet. which are determined by the ditpertive propertiet of the ambient plaima. are
too broad to tuppon curreni*dnven electroiiaiic wavet. rulinf out tuch lurbultnoe at the touroe of
oiuipaiion in ihete ihockt. Dittipaiive procetici are leflected in the damping of the precurtort. and
dittipative tcale lengiht are *>200 IflO km (Kvetal timet greater than thock thicknetieti Precurto.'
damping it not related lo thock normal angle or Mach number, but it correlaieb with 7, T The tource
of the dittipation in the thocki doct not appear to be wave-wave decay of the whittlert. for which no
evidence it found W'e cannot rule out the pouihility of contributiont to the Jittipation from ion acoutiic
and or lower -hybrid mode turbulence, but interaction of the whiitler ittelf with uptiream elcctront offert
a timpler and more telf-con* tent etplanaiion for the cbicrved wave train damping.
Study of the lerrcstrul bow thock is an integral part of our
attempts to understand the formation of the magnetosphere
and the energy transfer to it from the tolar wind Detailed
examination of the thock also provides us with -icreased un-
derstanding of the physical processes involved in the forma-
tion of thock waves in collisionless plasmas in general. Under
most conditions the bow thock it a complex and turbulent
structure for which comprehensive analytic theories have only
recently begun to appear [e.g., Leroy. 1983] Occasionally,
however, the shock loses much of its complexity and lends
itself to comparison with relatively uncomplicated analytic de-
scriptions In this paper we describe the relatively rare but
strucluially simple thock which results when the tolar wind >s
cold and has a relatively low flow veloaty. For oblique thock
normal angles the shocks which form under tuch conditions
are essentially laige-ampliti<de whistler mode waves which
extend upstreart in the form of phase-standing precursor wave
Important early contributiont to thock studies were made
through investigations of the precursor wave trains, the first of
which was presented by Fairfield and  They
showed that the waves found upstream of and adjacent to
low- Mach number bow shocks characteristically fell into two
frequency ranges a lower-frequency signal with periods of
tent of seconds and a higher-frcqucr.cy signal with periods of
I t Inferred properties of the low-frequency waves matched
those predicted for the whistler thock precursors Wave polar-
ixations. for example, changed from right handed for outward
moving shocks lo left handed for inward moving shocks as
expected for phase-standing whistlers Fairfield and Feldman
also investigated wavelengths, although they were onable to
' Now at Depanmcni of Phyiicv and Astrot.om). Univcrtiiy of
Copyright 1914 by the American Geophysical l^nioi
Paper number 3AI9II
0141-0227 14 /OOJA- I9IRS05 00
make direct measurements of the tcale lengths of the signals.
They did. however, calculate the wavelengths expected for
trending whistlers and inferred thock velocities using these
calculated values The in.^erred shock velocities were in reason-
ably good agreement with other estimates of thock velocities,
and to the estimated wavelengths, which averaged '-500 km
and ranged from 60 to 1600 km. were accepted at physically
reasonable. Although these and other early observations were
consistent with theory, they were all based on single-spacecraft
measurements which could not establish the absolute tcale of
the phenomena in question The present paper, in contrast,
continues work on laminar shock structure which uses the
unique cap^M-y of the ISEE I and 2 dual-spacecraft set lo
establish absolute tcale lengths and intrnisic wave polariza-
tions Use of these data hat allowed us lo make detailed quan-
titative compantons between shock theory and observations
of naturally occurring collitionless shcKk waves This analysis
demonstrates that oblique low- Much number bow shocks arc
indeed the predicted large-amplitude whistler waves and that
the low-frequency precursors are the upstream extension of
the thock structure itself
The relation of the higher-frequency waves lo thock struc-
ture i< less clear One interesting hype thesis has been that they
might have been generated by decay of the standing precur-
sors. but the properties of the high-frequency waves observed
upstream of low- Mach number ISEE shocks are not consis-
tent w ith those expected for products of decay c' the standing
whistlers On the other hand, similar higher-frequency waves
had been observed uptiream of higher Mach number shocks
[Fairfield. 1974]. and it has alternatively been suggested that
the higher-frequency waves seen upstream of low -Mach
number shocks are merely further examnlc*. of this more gen-
eral phenomenon Wc will show, howev' f. th*i n is unlikely
that the higher-fr*quency waves observed upstream of low
Mach number shocks are generated by the same mechanism
which drives the waves observed upstream of stronger shocks
Low-/! low Mach number shocks have traditionally been
designated ‘'laminar shocks." a term first applied in theoretical
COLLISIONLESS SHOCK WAVES
IN THE SOLAR TERRESTRIAL ENVIRONMENT
WORKING GROUP MEMBERS
E. Greenstadt, Chairman
University of Maryland
J. T. Gosling
Los Alamos National Laboratory
University of New Hampshire
DESPA Observatorie de Meudon
University of California
Los Alamos National Laboratory
A. E. Robson
Naval Research Laboratory
Naval Research Laboratory
NASA f Goddard Space Flight Center
Jet Propulsion Laboratory
Los Alamos National Laboratory
Los Alamos National Laboratory
C. S. Wu
University of Maryland
SOLAR TERRESTRIAL PHYSICS - PRESB^ AND FUTURE
COLLISIONLESS SHOCK WAVES IN THE SOLAR TERRESTRIAL ENVIRONMENT
II* Natural Shocks
III* Quasi-Perpendicular Supercritical Processes
IV. Quasi-Perpendicular Subcritical Processes
V. Quasi- Parallel Processes
V|. Ion Acceleration
VII* Outstanding Problems
VIII. Investigative Avenues
TRW Tech. Report No. 40789-6007-UT-00
OBLIQUE, PARALLEL, AND QUASI-PARALLEL MORPHOLOGY OF COLLISIONLESS SHOCKS
A Review for
Chapman Conference on
Shock Waves in the Heliosphere
Revised September 10, 1984
Eugene VJ. Greenstadt
Space Sciences Department
TRW Space and Technology Group
Advanced Products Laboratory
Applied Technology Division
One Space Park
Redondo Beach, CA 90278
OBLIQUE, PARALLEL, AND QUASI^PARALLEL MORPHOLOGY OF COLLISIONLESS SHOCKS
Although many of the features of natural shocks in space had been known
or surmised sane years agj, neither theoreticians nor laboratory
experimenters had quite assembled all the idealized elements into a
correct prediction of ext; aterrestrial observations. Shocks were
classified as perpendicular, oblique, and parallel before high-quality
measuranents becane available. Thus, seme nonperpendicular profiles
have appeared puzzlinr and unexpected. Are nonperpendicular, oblique
shocks disguised che bow shock system by its finite radius of
curvature? The latest research results indicate otherwise; that is,
the quasi-perpendicular/quasi-parallel division is real and intrinsic,
although some characteristics may be parameter dependent. An attempt
is made to suimarize observational results on non perpendicular shocks
with the aim of understanding the shock as an interactive structure
dependent -on the geometry of shock propagation. An elementary
suggestion is presented that may provide a foundation for reconciling
some seemingly conplicated or contradictory quasi-parallel features.