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Produced by the NASA Center for Aerospace information (CASi) 


‘ TRW‘Tech\ Report No. 43856-6O0'» UT-00 



Principal Investigator: E. W. Greenstadt 

Co-Investigator: W. W. L. Taylor 

(lASi-CB- 174351) BISIABCB S10£l CF SPICE 185-19823 

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) 

Prepared for 

NASA He?dquarters 
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 
(213) 536-2015 















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 - 

further work. 


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. 

a HisroRir 

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. 


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). 


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 
assumptions included: 

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 
parallel "slabs". 

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 
image changes. 

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 
1120. 1964. 

"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 

- 13- 

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. 



... -'-'O’ 


tjmGlMAi: PAG€ 


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.» 

S 0 

O • 

■H OS 
*0 W O 
0 U h 
« « « 

» S'S 

M U Ki 
0 0 
•-I h p. 
O 0 I 
0 t-l O* 

_ 0 

•0 O TJ 

I" M 
0 0 0 
0 iH 
0 0 
J3 0 U 
4J 0 <rt 
•H -H -O 
> 0 
« V 
iH *0 Q. 

0 ET 
■0 0 0 
9 iH o. 


g *3 

J3 ^ 0 
CO U *H 

iS *0 


'» *0 
• «H 

0 0 > 
M •H <H 


•rl I 0 
M vt 



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 

— BB* 


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). 



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. 





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- 
porarily quasi-perpendicular. 


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 [1964], 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. 


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. [1984], 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 

and 4. 

- 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 


dashed lines. 


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. [1970]. 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- 
sive investigation. 

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 [1984] 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 
shock geometry. 

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. 
Amsterdam. 1979. 

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, 
BBl, 19B2. 

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 





2 1 

6 Sep. 79 





3b ! 

18 Nov. 79 


0.7-0. 9 





25 Nov. 79 






- 12 - 

Hgure Captions 

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 
Fig. 2. 

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 






I. Introduction 

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 













Scale Lengths in Quasi-Parallel Shocks 


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 
that constituent 

The solid angle coverage in velocity space about the spa- 
tially varying local flow direction C?(x) necessary for this deter- 


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 [1975] 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 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 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 




E. Greenstadt, Chairman 


V. Formisano 


C. Goodrich 

University of Maryland 

J. T. Gosling 

Los Alamos National Laboratory 


University of New Hampshire 

M. Leroy 

DESPA Observatorie de Meudon 

M. Mellott 

University of California 

K. Quest 

Los Alamos National Laboratory 

A. E. Robson 

Naval Research Laboratory 

P. Rodriguez 

Naval Research Laboratory 

J. Scudder 

NASA f Goddard Space Flight Center 

J. Slavin 

Jet Propulsion Laboratory 

M. Thomsen 

Los Alamos National Laboratory 

D. Winske 

Los Alamos National Laboratory 

C. S. Wu 

University of Maryland 





I. Introduction 

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 




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 



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.