Double streaming at 35 AU during the coronal mass ejections of March 1991

Ejections of March 1991

by

Thanasin V. Nampaisarn

Submitted to the Department of Physics in Partial Fulfillment of the Requirements for the Degree of

Bachelor of Science in Physics

at the

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

June 2009

Massachusetts Institute of Technology 2009. All Rights Reserved.

The author hereby grants to MIT permission to reproduce and to distribute publicly paper and electronic copies of this thesis document in whole or in part.

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Double Streaming at

35

AU during the Coronal Mass

Ejections of March 1991

Thanasin Nampaisam, MIT Class of 2009

ADVISOR: Professor John W. Belcher

ABSTRACT:

We analyze data associated with the coronal mass ejections of March 1991, with

emphasis on a remarkable double-streaming proton event observed at 35 AU. The plasma data

used in our analysis were collected by three spacecraft: Voyager 2 near 35 AU, Ulysses near 3

AU, and IMP-8 at I AU. The observations of the same CME events by three spacecraft over

such a wide range of radii gives insight into the evolution of CMEs as they propagate from the Sun to 1 AU and then into the outer heliosphere. Of the many characteristics observed, we are especially interested in the double-streaming proton events seen at Voyager 2 in June 1991 over a two day period. Such pronounced double-streaming has not previously been reported to be a

feature of CMEs at any distance, much less at distances of 35 AU, with its 120 day transit time

from the Sun. The double streaming events show a remarkably large separation between the two peaks that is close to the Alfven speed and much greater than the thermal spread of either peak. These double streaming events were followed a day later by a large scale polarity reversal in the interplanetary magnetic field at Voyager 2. This reversal is thought to be a site of magnetic reconnection, where energy in the field is being converted into particle energy. We speculate that the free energy involved in the earlier double streaming events is somehow related to this magnetic reconnection process, although we have found as yet no direct causal connection.

Acknowledgements

This thesis is a continuation of my project under the Undergraduate Research Opportunities Program (UROP) at Massachusetts Institute of Technology (MIT) under the supervision of Professor John W. Belcher. This project gave me an incredible opportunity to actually get involved in NASA's data and understanding the instruments on famous spacecraft such as the Voyager series, Ulysses, as well as the Interplanetary Monitoring Platform (IMP) spacecraft. The office of the group I have been working with is located on the sixth floor of Building 37 of MIT.

Professor Belcher is a generous man who seems to not be frustrated over my laziness. I must admit that, though I want to do a research, I lack the motivation to start my work as I can easily get distracted by my other interests. Professor Belcher, however, did not respond to my behavior with anger; in fact, he tried to remind me about what I should do, of which I have been really grateful. Despite its not-so-well-written description, this thesis is one of my very few major writings, and I realize how inexperienced at writing I am. Hence, Professor Belcher is not just my physics thesis advisor, but also he is my English teacher. Furthermore, thanks to his generosity, he accepted my request that he write a recommendation letter for my graduate school applications, and I was admitted to a wonderful program at Princeton University.

Apart from Professor Belcher, Michael L. Stevens is a graduate student who was very helpful for the completion of this thesis. Without instruction about plasma physics, I would not have been able to get a slight understanding of this field (and I still have much to learn). I wish him well after his graduation from the Ph.D. program at MIT, and I wish also that he will become a great professor in the field of plasma physics.

There are also many other professors such as my former academic advisor Professor Alar Toomre from the Mathematics Department, who has been very supportive, and my plasma astrophysics lecturer Professor Bruno Coppi, who explained me many interesting plasma

phenomena. Professor Wudhibhan Prachyabrued, Professor Piyapong Sithikong, Professor

Suwan Kusamran, and other Thai physics Olympiad supervisors are also highly credited for being among the first teachers who have attracted me to the world of physics. I am indebted Professor Narong Pannim, Professor Nittiya Pabhapote, Professor Pattanee Udomkavanich, Professor Wicharn Lewkeeratiyutkul, Professor Vichian Laohakosol, and other Thai mathematical Olympiad supervisors who have developed my mathematical skills and cultivated them to be a great tool in solving physics problems. Thanks to these great people, I have succeeded in my education up until now.

Lastly, my parents are the most wonderful persons in the world who never deny my reasonable needs. My siblings (including my pets) and my friends have been very understanding and given me strength to advocate to my intensive work (especially, Andrei Frimu and Karen Figueroa who gave me very nice back massages after my long-hour suffering at work on my laptop). I am also very thankful of all my high school teachers who are among building engineers who have shaped my education to be solid, as it is now. I am thankful to everybody I have known at MIT for an unforgettable memory.

Table of Contents

S

Introduction... ₉

1 .1 P u rp o se ... 9

1.2 Literature Review of Publications on the M arch 1991 Event... 10

2 Large Scale Stream Structure of the 1991 CM E Event ... 12

2.1 The Trajectory of the IM P-8, U lysses, and Voyager in 1991... 12

2.2 Large Scale O bservations at IM P-8 ... 15

2.3 Large Scale Observations at U lysses ... 16

2.4 Large Scale Observations at V oyager 2... 19

2.5 Comparisons between Results from Ulysses and Voyager... 20

3 Interm ediate Scale Structure of the 1991 Event at V oyager... 23

3.1 The Reconnection Site ... 23

3.2 Region with D ouble Stream ing... 24

4 Properties of the D ouble-Stream ing Events... 26

4.1 Fits to the Spectra... 26

4.2 D ouble-Stream ing Properties in the M arch 1991 Events ... 27

4.3 Streaming Velocity Differences in Terms of Thermal and Alfven Speeds ... 29

5 D iscussion and Conclusions ... 35

5.1 Im plications for Reconnection at 35 AU ... 35

5.2 Future W ork ... 35

6 Appendix... 36

6.1 The Voyager Plasm a M easurem ents... 36

6.1.1 Sensor Geom etry and Placem ent on Spacecraft ... 36

6.1.2 Energy Channels ... 37

6.2 Error Analysis ... 38

6.3 M ATLA B Program s ... 38

6.3.1 Spectral Plots ... 38

6.3.2 D ata N um ber Conversion ... 40

6.3.3 Fitting Process ... 41

6.3.4 Junior Lab Template "fitnonlin" ... 42

6.4 Tim e Reference for D ouble-Stream ing Events... 44

6.4.1 D ay 160, A Cup... 45 6.4.2 Day 160, C Cup... 48 6.4.3 Day 161, A Cup... 49 6.4.4 Day 161, C Cup... 50 7 References... 52 8 Index ... 53

6

Figure Captions

Figure 2-1: The Trajectory of the Voyager 2 Spacecraft in Heliographic Coordinates... 12 Figure 2-2: The Trajectory of the Ulysses Spacecraft in Heliographic Coordinates - The spacecraft moved from 1.6 AU to 5.1 AU in 1991 (between Mars and Jupiter). The red

asterisk indicates the location of the Sun. ... 13

Figure 2-3: The Trajectory of the IMP-8 Spacecraft in Heliographic Coordinates - The IMP-8

spacecraft (in blue and pink) orbits the Earth (whose orbit is shown in green). In the plot, the pink dots represent the trajectory of IMP-8 spacecraft during March of 1991... 14 Figure 2-4: The Combined Plot of Trajectories of All Three Spacecraft in Inertial Heliographic Coordinates: The heliographic latitudes of all three spacecraft were small enough that we

can assume that all of them lay in the elliptic plane during this period. ... 15

Figure 2-5: The Bulk Velocity of the Solar Wind Plasma Detected by IMP-8 during March 1991

: The CME period begins with a jump in all velocity components starting on day 83 and

lasts un til d ay 9 5 ... 16

Figure 2-6: The Number Densities of Protons and Alpha Particles and the Magnetic Field

Strength by Ulysses in 1991 - The upper panel gives the plots of proton (red) and alpha

particle (blue) densities. The RTN components (r in red, t in blue, and n in green) and the

magnitude (black) of magnetic fields are shown in the lower panel. The dotted black lines

are used for comparison between peaks of the two plots... 17

Figure 2-7: Bulk Velocity Components and Proton Temperatures by SWOOPS Detector of

Ulysses over 1991 - The upper panel shows bulk velocity and the lower panel shows proton

temperatures. Note that the bulk velocity is almost entirely radial. Furthermore, the peaks

on day 84 coincide in both plots, as do other peaks... 18

Figure 2-8: Proton Number Density and Bulk Velocity Observed by Voyager 2 at CME Shock in

1991 - The upper panel is the proton density plot and the lower panel is the bulk velocity

plot in R TN coordinates ... 19

Figure 2-9: The Shock on Magnetic Field Detected by Voyager 2 in 1991 - In this plot, only the

magnitude of the magnetic field is shown. The sharp increase started on day 146 and lasted until day 177, agreeing with the shock signature in the velocity plot in the Figure 2-8... 20

Figure 2-10: The Comparison between Voyager 2 and Ulysses Plasma Data - The two spacecraft

detected very similar time profiles, even though they were on opposite sides of the Sun. The time coordinate zero corresponds to the time when the shock fronts arrived at the spacecraft. (The large blue pluses (+) represent Voyager 2's data, and the small red plusses (+) represent

tho se o f U lysses.) ... 2 1

Figure 3-1: An Overview of Plasma Events around the Reconnection Event on Day 163 - The

green dotted lines mark the region where Voyager 2 encountered the sheath structure. The orange lines show the boundary of the region of double-streaming events. The reconnection event happened on day 163 with a clear signature-the sudden reversal of the magnetic field (see the second panel where the angle 6 suddenly flipped from 30 degrees to 120 degrees).

... 2 3

Figure 3-2: The Overall Proton Spectra of Solar Wind Plasma on Day 160 1991 - Data from the

A, B, and C cups are presented, as the D cup barely detected any signal. The color bar is

proportional to the the logarithmic value of the distribution function, with high values

Figure 3-3: The Overall Proton Spectra of Solar Wind Plasma on Day 161 1991 - Similar to

Figure 3-2. The exact time where the feature ended is at time 09:31:19. The

double-streaming feature is probably continuous from day 160 through 0200 on day 161, but there is a data gap after hour 17.413 on day 160. Note that there is period of reoccurrence of

double-streaming, between 11: 35:46 and 12:09:04 on day 161... 25

Figure 4-1: Spectra Samples from A Cup on Day 160 - The two spectra are taken from channels

60 to 85. The blue asterisks represent the actual data and the red lines are the results from

our fit calculation. For these two data sets, the fits gives the speeds at peaks to be,

respectively, 427.6 and 490.1, and 428.8 and 484.6 kilometers per second... 26

Figure 4-2: A Sample Spectrum from A Cup on Day 161 - This spectrum has a clean

double-peaked feature. The speeds are at the peaks are 414.0 and 462.6 . ... 27

Figure 4-3: The Speed of Solar Wind Proton at Peaks during Double-Streaming - The upper

panel is the analysis results of the A cup spectra, and the lower panel the C cup spectra. These two plots classify data into three categories, as described in the text. Note that the data from the A cup are the cleanest. We can see from these plots that at about hour 12.50, the two speeds became stable. This is because double streaming started to be settled at hour

12 .4 0 ... 2 7

Figure 4-4: The Density Calculated from the Fit Results on Day 160 - The jump at around hour

12.50 is explained in Figure 4-3. The results from fitting data in both cups agree fairly well.

... 28

Figure 4-5: The Thermal Speeds as Calculated from the Fit Results on Day 160... 29 Figure 4-6: The Magnetic Field, the Alfven Speed, the Ratio of the Particle Densities, and the Speed Difference on Day 160- The resolution of the magnetic field data is hourly. The Alfven speed, high and erratic initially, dropped to between 120 and 150 kilometers per second after hour 12.50. Finally, recall the spectra in Figure 3-1 and note that before hour

12.50 the upper peak was smaller until hour 12.50, when it abruptly grew... 30

Figure 4-7: The Speed Ratios on Day 160 - The upper panel gives the ratio , or the sonic Mach

number of the speed difference. Notice that after hour 12.50, the Mach number falls between 2 to 4 (with a mean at 3.0, and the fluctuation has a standard deviation of 0.7 ).

The lower panel gives the ratio Av / vA , or the magnetohydrodynamic Mach number of the

speed difference. Post hour 12.50, this ratio is distributed around the mean 0.33 with a

standard deviation 0.04 . ... 31

Figure 4-8: Particle Densities and Thermal Speeds on Day 161 - Day 161 spectra are noisier than

those obtained on Day 160. These noisy spectra result in erratic patterns in both densities and thermal speeds. However, we can see that the upper peak started to take over the lower peak, and therefore the particle density is higher for the upper peak in this regime... 32 Figure 4-9: Magnetic Field, Alfven Velocity, Proton Density Ratio, and Speed Difference on

Day 161 - Again, we use a step magnetic field function to derive the Alfven speed. As

discussed in the last plot, the particle density in the upper peak starts to dominate that of the

lower peak. On this day, the ratio n2 /n, is distributed around 1.7 with a standard deviation

o f 1.2 ... 3 3

Figure 4-10: The Speed Ratio on Day 161 - The sonic Mach number Av/ w is distributed

around the mean 3.9 with the standard deviation 1.9. The Alfven Mach number Av /vA has

Figure 6-1: The Voyager 2 Spacecraft and Its Instruments - The PLS instrument is installed at the top of the spacecraft in this picture (shown in green). The symmetry of this instrument

9

1 Introduction

1.1 Purpose

Space weather has many effects on the environments of all planets. The Earth's

magnetosphere and the aurora borealis are examples of how space weather interacts with a

planet's magnetic system. In our solar system, interplanetary space is filled by the solar wind

plasma-a particle stream primarily consisting of electrons and protons that is ejected from the Sun's upper atmosphere due to processes going on in the million degree solar corona. The study of the solar wind can lead to an understanding of many processes which affect space weather within our solar system, such as solar flares and the coronal mass ejections (CMEs). The effects of space weather on the earth were first demonstrated by a French geophysicist Jean-Jacques d'Ortous de Mairan in 1731, who pointed out the relationship between the aurora intensity and the solar cycle.' More than one hundred year later, in 1859, the presence of the geomagnetic field was recognized by Lord Richard Carrington, who observed geomagnetic

storm in the Earth's magnetic field data after a white light flare.2 _{The first actual recognition of}

the existence of the solar wind dates from around 1950, when Ludwig Biermann, a German astrophysicist, speculated that the sun must emit a stream of particles. He based this conclusion

on the fact that comet tails were always oriented away from the Sun.3 _{The solar wind, a plasma}

steam ejected from the upper solar atmosphere, is responsible in forming the solar system's local atmosphere, or the heliosphere. The Sun's atmospheric structure plays significant roles in space weather, and its instability causes many phenomena such as sunspots and solar flares.

Among the most energetic solar atmospheric phenomena affecting space weather is the coronal mass ejection (CME). CMEs are related to solar flares and eruptive prominences, and many investigations suggest that CMES may precede the associated flares by up to thirty minutes. That is, the CMEs are driven by their own mechanism which can in turn induce associated flares. The CME process ejects material, which consists mostly of electrons and protons, from the solar corona. This coronal process enhances the electron density, which in turn scatters more electromagnetic radiation through Thompson scattering, and, hence, can be observed by coronagraphs. A coronagraph is an optical telescopes with an occulting device that blocks light from the solar photosphere. The frequency of CME occurrence is roughly periodic, with a period determined by the solar cycle, and a peak occurrence rate during solar maximum. This correspondence is due to the fact that the CME phenomenon is closely related to the sun's

magnetic processes. It is thought that the basic driving mechanism driving the explosive

expansion of CME's from the solar surface is rapid magnetic reconnection on a large scale-that is the energetics of the CMS's are due to the rapid conversion of magnetic energy density at the sun into kinetic energy of the plasma. When a CME reaches interplanetary space, it is called an

interplanetary coronal mass ejection (ICME).4

Moldwin's An Introduction to Space Weather, 2008, Chapter 1. 2 Kahler, 1992.

3 Lang, 1995.

10

The speed of CME propagation can range up to 1000 km/s and beyond. Thus, CMEs can travel faster than the Alfven speed of approximately 100 km/s, creating shocks in the solar wind. Energetic particles associated with the CME may disrupt the Earth's magnetosphere and cause catastrophic damage to astronauts or satellites, and may as well cause deterioration in radio

communications. Fast CMEs trigger large, non-recurrent geomagnetic storms-disturbances

usually occurring when the interplanetary magnetic field turns southward for a long period of time and the cause of rapid injections of magnetic and particle energy into the Earth's magnetosphere.5

In this thesis we are interested in studying the properties of a particular CME that occurred in March 1991, as it propagates into the outer heliosphere to the location of Voyager 2 at about 35 AU. We are particularly interested in any evidence of magnetic reconnection in the

CME plasma as observed at Voyager 2, as the survival of such processes to this great distance

has the potential to reveal much about the energy sources driving the reconnection. We in fact do observe what we interpret as a magnetic reconnection site at a magnetic sector reversal in the Voyager 2 data. In addition, our major interest here is in the properties of a double-streaming signature in the solar wind protons in a near-by region, in which the measured proton distribution function exhibits a two-beam distribution. Our speculation is that the free energy driving the kinetic processes responsible for double-streaming is somehow related to the reconnection process, although the exact relationship remains unknown. Our data primarily come from the Voyager 2 spacecraft, with data also from Ulysses and IMP-8.

1.2 Literature Review of Publications on the March 1991 Event

McDonald et al. (1994) gives a broad summary of intense solar activities in 1991. The data come from five spacecraft: IMP-8, Voyager 1, Voyager 2, Pioneer 10, and Pioneer 11. There were two extraordinarily active periods in that year: in March and again in June. The March events resulted from activities in the Sun's southern hemisphere, but in June, the Sun's northern hemisphere was responsible for most events. All five spacecraft saw a sudden increase in ion and electron distribution functions. This paper emphasizes mostly results from Voyager 1 and Voyager 2. There is a noticeable drop of the counting rate of galactic cosmic rays at each

ICME event, which was observed by both Voyager 1 and Voyager 2.

Ulysses observed five plasma wave events around two successive shocks in the end of March 1991, as discussed in Tsurutani et al., 1991. Tsurutani mentions two plasma wave modes which were generated by instabilities and possibly ion anisotropies. The first wave mode he observes is a mirror mode, which can be formed via the diamagnetism of hot plasmas. The second is a magnetosonic mode with whistler precursors. His observation supports Parker's idea that microflares and nanoflares are the engine of CMEs.

In the work of Neidu et al., 1992, the proton distribution function from Ulysses's Energetic Particle Composition Experiment (EPAC) is analyzed. Neidu pays the most attention to the energy spectra from channels 3 to 7. He points out the anisotropy for protons during three interplanetary shocks in March 1991. The agreement between this observation and the numerical

11

simulation strongly suggests that the diffusive shock acceleration may be taking place at the

CME shocks.

Proton anisotropies are also discussed in Sanderson et al., 1992. In this paper, data from Cosmic Ray and Solar Particle Investigation (COSPIN) instrument on the Ulysses spacecraft are analyzed. Sanderson observes two shocks which corresponded to two ICMEs. The first shock arriving at 0342 UT on March 24 was probably moving with the CME, and, hence, exhibited considerable enhancement of trapped particles with high energy. The second arriving at 0552

UT on March 25 carried bi-directional particle anisotropies. This shock led to a slight increase

in low-energy particles. Lastly, Ulysses entered the decay phase of the CME, which also showed bi-directional proton anisotropies. This region was possibly a magnetic cloud as the magnetic field slowly rotated.

In addition to two observed ICMEs in the aforementioned work, Phillips et al., 1992, also postulated the existence of a third ICME at 0800 UT on March 26, as recorded by the Ulysses solar wind plasma experiment. Phillips associates each ICME event with a electron counter streaming halo event. However, the start of the third counter streaming event is ambiguous, and this unclear signature leads to three alternate interpretations: (1) there were two ICMEs with two shocks; (2) there were three ICMEs with three shocks; and (3) there were three ICMEs with two shocks (no shock from the middle ICME).

Of course, in addition to the 1991 events, there have been many publications about CMIEs

occurring in other years. Reames et al., 1996, examined data from IMP-8, 1, and Helios-2 during CMEs in 1979. This author gave an explanation of how intensity-time variations during a shock correspond to how the observer is located with respect to the CME. Linsay et al., 1999, discovered a linear correspondence between a CME's coronal speed and its interplanetary speed. The data come from the Pioneer Venus Orbiter and the Helios-1 spacecraft over the years from

1979 until 1988. More recently, Malandraki et al., 2003, comment on the Ulysses magnetic field

data during an ICME in July 2000. Malandraki's observation of electron flux depletion during the commencement phase may be caused by topological features of the magnetic field such as magnetic loops or magnetic mirrors near the Sun.

2 Large Scale Stream Structure of the 1991 CME Event

2.1 The Trajectory of the IMP-8, Ulysses, and Voyager in 1991

The Voyager 1 and Voyager 2 spacecraft were launched in 1977 on September 5 and on August 20, respectively, to visit the solar system's outer planets: Jupiter, Saturn, Uranus, and

Neptune. The two spacecraft took different paths but both reached Jupiter in 1979. In 1980,

Voyager 1 approached Saturn and continued its journey to the interstellar medium without any more planetary encounters. However, Voyager 2 encountered Saturn in 1981, Uranus in 1987, and Neptune in 1989.

The Trajectory of the Voyager H Spacecraft between 1990 and 1992 in Heliographic Coordinate System

7,", I I- (' ~I-L 0 --4 6 -- -1 -12 -14 -16-4-I -20... . -.. 36 150 -5 0 40-AU Sphere 130-AU Sphere 20-AU Sphere 10-AU Sphere The Sun -1990 Trajectory -- 1991 Trajectory --1992 Trajectory 7

Li

0 -5 YHE (AU) ACHEL (AU)

Figure 2-1: The Trajectory of the Voyager 2 Spacecraft in Heliographic Coordinates

Since the solar wind plasma travels with radial speeds ranging from 400 km/s to

800 km/s, the solar wind plasma in March 1991 required from 70 to 140 days from to move from

1 AU to the position of the Voyager 2 spacecraft. Hence, any CME signature should be observed between June (day 150) and August (day 220) of 1991, when the spacecraft was near

35 AU.

The trajectory data of Voyager 2 are in the short Supplemental Experimental Data Record (short SEDR) format that can be accessed by FORTRAN commands. The original data are in

ecliptic (ECL50) coordinate system. The coordinate transformations from ECL50 to Heliographic coordinates are given in the Appendix section.

The Trajectory of Ulysses in 1991 in the Non-Rotating Heliospheric Coordinate

<0.. 3 (AU)LT 1.1.4 42. 0.5 Xm (AU) 0

Figure 2-2: The Trajectory of the Ulysses Spacecraft in Heliographic Coordinates - The spacecraft

moved from 1.6 AU to 5.1 AU in 1991 (between Mars and Jupiter). The red asterisk indicates the location of the Sun.

Launched on October 6, 1990, the Ulysses spacecraft orbits the sun at a high inclination to the ecliptic plane. The spacecraft moves back and forth between the orbit of Earth and that of Jupiter. With this inclination, Ulysses was the first spacecraft to observe the Sun from high latitudes and returned extremely valuable information about the 3D structure of the heliosphere.

Fortunately, Ulysses was at low solar latitudes at the time the 1991 CME occurred. Nevertheless, Ulysses was on the same side of the Sun as Voyager 2 during the phenomena, and hence, we may be able to find more correlation between Ulysses data and those of Voyager 2, than with the data from the IMP-8 spacecraft (discussed below).

The trajectory data for Ulysses were taken from lttp://ulvsses.ipl.nasa.gov/ , which is its

official website. We are especially interested in the plasma data, and hence mostly analyze the data collected by the instrument whose acronym is SWOOPS, which stands for Solar Wind Observations over the Poles of the Sun.

The Trajectory of the Imp-8 Spacecraft in 1991 in the Non-Rotating Heliocentric Coordinate System 0.1 0 -11 -0.8 -0.5 -NI 0.9

V

0.7 0.5 /0 3 -0.1 -0.3 -0.2 0 I 0.4 0,7 -0.9 XHEL (ALJ) -. -0.5 0.7 YBEL (AU)

Figure 2-3: The Trajectory of the IMP-8 Spacecraft in Heliographic Coordinates - The IMP-8

spacecraft (in blue and ) orbits the Earth (whose orbit is shown in green). In the plot, the pink dots represent the trajectory of IMP-8 spacecraft during March of 1991.

The Interplanetary Monitoring Platform (IMP) project is dedicated to the investigation of interplanetary plasma and magnetic fields. It has launched a number of probes, including IMP-8

(IMP-J), which was the last of the ten IMP probes. Launched on October 26, 1973, the

spacecraft orbits around the Earth with period of 12.5 days (with an average radius of 35Re, where R, is the Earth's radius). Since IMP-8 spends only two-thirds of its orbital time in the solar wind, the data from the spacecraft are not always taken in the solar wind.

The trajectory data of IMP-8 may be roughly estimated by the Earth's orbit. The National Aeronautics and Space Administration (NASA) provides this data under the following link: http: /coho\web. sFc.nasa. gov /helios/hel i-html. We chose the inertial heliographic mode with time resolution of 1 day for our trajectory plot.

We also show in Figure 2-4 a combined plot of the trajectory of all three spacecraft. In this plot, we see that during March 1991, IMP-8, Voyager 2, and Ulysses were observing the solar wind plasma at completely different angles. However, all of them detect solar wind at and below the ecliptic plane (and, therefore, they are more likely to observe only the plasma ejected from the southern hemisphere of the Sun, as the Sun's obliquity to the ecliptic plane is only

7.25 ). 2

-10 0

-5

-15

The Trajectories of the Voyager 2, the Ulysses, and the Imp-8 Spacecrafts around the Year 1991 in the Non-Rotating Heliospheric Coordinates

The Orbit of Ulysses In the Year 1991

The Orbit of Jmp-l

-(Green patch represents the trajectory during March andApril of 1991.)

Voyager 2's T7ajectory in 1991

/--35 -30 -25 -20 -15

Xl (AU)

0 5

Figure 2-4: The Combined Plot of Trajectories of All Three Spacecraft in Inertial Heliographic Coordinates: The heliographic latitudes of all three spacecraft were small enough that we can assume

that all of them lay in the elliptic plane during this period.

2.2 Large Scale Observations at IMP-8

Large scale parameters observed by IMP-8 include the proton density, the magnetic field strength, and the plasma bulk velocity. As mentioned earlier, IMP-8 does not spend all of its orbital time in the solar wind. Although not shown here, the proton number density and magnetic field data do not show drastic changes in March 1991.

Although the sudden increase in the particle bulk speed is not very high compared to the surrounding speed, we can identify the drastic jump around day 85 of year 1991 as coincident with the arrival of the CME (see Figure 2-5). Unfortunately, this jump occurred slightly before the time when the spacecraft entered the Earth's magneto-tail, and thus, we cannot see a continuous pattern of the shock until four day thereafter. We can see that the shock front traveled with speed approximately 700 km/s.

i

i I

5F

Solar Wind Plasma Velocity (Imp-8, 1991): Blue-Radial, Red-Tangential, Green-Normal I I I I 4P

I

aft

0--1

:1 900 K 800 700

.9

API

,~ 4 ~*

l~1

60 65 70 75 80 85 90 Day of Year 1991 I I I I 95 too 105 110 115

Figure 2-5: The Bulk Velocity of the Solar Wind Plasma Detected by IMP-8 during

The CME period begins with a jump in all velocity components starting on day 83 and

95.

March 1991 :

lasts until day

2.3 Large Scale Observations at Ulysses

The SWOOPS instrument on Ulysses offers a broader range of plasma data as compared to

IMP-8. The observed plasma parameters include the proton and alpha particle densities, the bulk

velocity components, the plasma temperature, and the magnetic field. All of the data can be

found in the official website of Ulysses mentioned above.

The hourly-averaged magnetic field data are observed with the Vector Helium

Magnetometer (VHM). It is interesting that the fluctuation level in the magnetic field became

smaller as the spacecraft moved further away from the Sun. It is unclear what process would

cause the decay of the magnetic field fluctuation level over such small change in distance. In

addition, the magnetic field shows an ambiguous change near day 85, which might not be

related to the CME.

The proton and alpha particle densities are detected with the Solar Wind Ion Composition

Spectrometer (SWICS). The alpha particle density is generally less than eight percent of the

proton number density. Both densities did not show significant changes during the CME.

However, the densities did seem to be correlated with the magnetic field.

A

A

600 500 400 300 200 100 0 -100 -200 -300 -400 r

SI

120

20 Is 16 50 15

10-5~

~0o 150

JV

A

\

-6 & -y o 200 R4d Dots: Protoou

B uw Dois: Alphta Parsios

vsA~AJ

250 300

K

14 12 10 4 2 350 *~- r-Componen* -t-Conmponenl * * n-Cmponkn 0 50 100 150 100 250 300 350 Day of Year 1991

Figure 2-6: The Number Densities of Protons and Alpha Particles and the Magnetic Field Strength by Ulysses in 1991 - The upper panel gives the plots of proton (red) and alpha particle

(blue) densities. The RTN components (r in red, t in blue, and n in green) and the magnitude (black) of magnetic fields are shown in the lower panel. The dotted black lines are used for comparison between peaks of the two plots.

The SWOOPS instrument gives both electron and ion data. We primarily use ion data in our analysis. Apart from the bulk velocity, the instrument also measures the plasma temperature

(consisting of two components: T and T ). We see in Figure 2-7 below that both bulk

velocity components and plasma temperature demonstrate large jumps around day 85 of year

1991, corresponding to the passage of the CME events.

;C ZLLJ 0 -0

I

t NA '

-Solar Wind Velocity Components (Ulysses 1991)

1000

800-

600-R d Do ts: V k al 'inponot>

BVe Dots Tangenfial Component)

400

-w rena Dos N \ar CDomponlti

200-0

84 845 85 86 86. 87

Day of Y=a 1991

Proton T mperature in Solar Wind Plasma (tlyssej 1991) 2-1.8 ~Bkte Do&-TAg RedDo T' 1.6 -1.4 -12 S0.6 0A 0.2-83.5 84 84.5 8-85.5 86 86.5 87 Day of Year 1991

Figure 2-7: Bulk Velocity Components and Proton Temperatures by SWOOPS Detector of Ulysses over 1991 - The upper panel shows bulk velocity and the lower panel shows proton temperatures. Note that the bulk velocity is almost entirely radial. Furthermore, the peaks on day 84 coincide in both plots, as do other peaks.

2.4 Large Scale Observations at Voyager 2

The Voyager 2 plasma instrument provides bulk velocity, proton number density, and proton thermal speed. We also use the magnetic data from Voyager 2's magnetometer. The magnetic data set is available online at the address Ittp://inssdftp.asft.nasa.gov/spacecraft data/ vovager/vo\ager2/. .06 0. 0.C 00 00 05-04 -2 -JO I ~ ~ 130 100 160 1~l~00 Cb

Vy~

t2A~A~

N.U~

~~00

Y

₃

I

U~~~~~~~~ ~ ~ R, --- ' -.--~ ~ ~ IF 4 f +- - . I 0 *f. ..- , Y 170 ISO A K I, 190 Dary of Yeur 1991

Figure 2-8: Proton Number Density and Bulk Velocity Observed by Voyager 2 at CME Shock in 1991 - The upper panel is the proton density plot and the lower panel is the bulk velocity plot in RTN coordinates. S₀ 0~ 308 200 100 0. -V- I IN 140 150 20U

The data when the CME shock wave arrived at the spacecraft is striking. Note that on day138 there is a drastic increase in proton number density. This could be a foreshock region,

which preceded the real shock by eight or nine days. Furthermore, since the shock occurred on

day 147 as detected by Voyager 2, while Ulysses had seen the shock on day 85. Since they were

approximately 33 AU apart, we deduce that the shock wave traveled with the speed of roughly

670 km/s between Voyager 2 and Ulysses (or 2.6 days per AU).

I .1 P. *t. * ~. ~ ~1.~ 0.5 0.45 0.4 0.35- 0.3-o .25- 0.2- <0.15-

0.05-,v.

Y30 135 140 145 150 155 Day of Year 1991 160 165 10 175 180

Figure 2-9: The Shock on Magnetic Field Detected by Voyager 2 in 1991 - In this plot, only the

magnitude of the magnetic field is shown. The sharp increase started on day 146 and lasted until day 177, agreeing with the shock signature in the velocity plot in the Figure 2-8.

2.5 Comparisons between Results from Ulysses and Voyager

The exact time when Ulysses observed the first shock is the day 82.8467 0.0054 of 1991 on March 23. Correspondingly, the time when Voyager 2 detected this shock occurred on day 146.042 0.042 on May 26. In Figure 2-10, we combine results from both spacecraft by using the shock arrival time as a common zero-time marker. The combined plots contained the proton densities, the bulk velocity components, and the magnetic fields.

An obvious observation is that the particle density n decrease as 1/ r2 , where r is the distance of the spacecraft from the sun. A less trivial fact is that the magnetic field falls as 1/ r. Thus, in Figure 2-10, we compare n-r2 and B-r between Voyager 2 data and Ulysses data.

21 ~I2 I -~ 4 - ++ 40 -20 -- ' + + II 800 - +-400 4444 444.4 1 1 2 3 4 5 a 7 8 9 10 4+444H+44 *6+44+ F+ 4%j,+ #++ 4- 4* 100 . -100 -s 200-100 00t 2 3 4 5

T'ime afer the Shock (days)

+ va W, 2 +4 _ + 31

-1

2 I4 5 6 7 f 9 14 Is.1 0 1 2 3 4 4 6 7 0 3 1 20 -+ 41 1+- -*t 4 --* + . .... 1 0 1 2 3 4 5 6 7 a 9 10 10- _-2 L+ +4+ +- 4,~43~ 9~4*'~ ,~ 1'~+ 0 . 57a1 4+ 20 _____+_+ 1 0 + +4 +*4 ~ ~ ~ 4 '~ I+ + I,;; * * 'IH IH ++ 8 1 4 a

Tim after the Shock (days)

Figure 2-10: The Comparison between Voyager 2 and Ulysses Plasma Data - The two spacecraft

detected very similar time profiles, even though they were on opposite sides of the Sun. The time coordinate zero corresponds to the time when the shock fronts arrived at the spacecraft. (The large blue

pluses (+) represent Voyager 2's data, and the small red plusses (+) represent those of Ulysses.)

7*6 1 0 1 2 3 4 5 0 7 a 9 to 3 1 2 3 4 6 4 7 a a 10 144 i i [ + EO - 4 *4. 44,4. 5 3 S7 9 10 I I . .1 6 7 8 9 to

I

I

+.++++fP+

22

An interesting feature of these spacecraft observations is that they both have good agreement on features magnetic field and the bulk speed data. To illustrate this, consider the turbulence of the plasma prior to the sixth day after the shock. The peaks of the magnetic field radial component between days 4 and 5 almost occurred simultaneously on the two spacecraft, with the decay mode starting after day 6. This shows the common features of the event at both spacecraft, even observed at such widely separate locations, in both radius and longitude.

3 Intermediate Scale Structure of the 1991 Event at Voyager

3.1 The Reconnection Site

Prior to the shock on day 146, the Voyager 2 spacecraft observed a typical plasma with the

bulk speed roughly 370 km/s, a proton density n =0.003 cm-3, and a magnetic field strength of

0.1 nT. After the spacecraft experienced the shock on day 146. 1, it observed a sheath structure

in which the proton density was compressed to 0.007 cm-3 along with the magnetic field to 0.3

nT. The sheath passage lasted until day 152.2. The sheath is normal interplanetary plasma which has been overtaken and swept up before the CME driving plasma, in a "snow plow" effect.

Plasma Data around the Reconnection Event at 34 AU, Day 163, 1991

I I I I 14 -03 -140 145 150 155 140 165 170 175 140 185 190 195 20 ISO 150-20L 00- -4 s d n !4ipped155 16, 165 170 175 180 so 15 0 195 200 --Nt0 15 150 155 e b - a 175 160 eg0 1 da s 6o 195 1d 200

Feiure th1:Anvriwo lsmvnsaon the Reconnection Event ossnhwinodi roiigfe eDeay 163 -The

grbe-teaboundar oeifa the asto dultre amin tevet.rh reconnection eventtw happened obsnv daya16

Ntic th atietc th double-streaming ro on days t60 and 161ocre aybfr h

mantcrcneto7eetwsosre.Athuhtetoeet0aentcicdnw

There is also a magnetic cloud structure observed from day 163 until day 183.

magnetic field gradually rotated over this time period. The bulk speed slowly decreased

530 km/s to 400 km/s. The density profile remained low during this time (usually less

0.001 cm3).

The from than

3.2 Region with Double Streaming

After the CME shock front arrived at the Voyager 2 spacecraft, there was one and only one

period exhibiting double-streaming event, the interval between days 160 and 161. During this

period, the spacecraft was at distance between 34.74 AU and 34.75 AU. The double streaming

feature during this time interval is clearly shown in spectral data from the A cup and C cup of the

Voyager sensor cluster, as illustrated in Figure 3-2 and 3-3. See Appendix 6.1 for a description

of the Voyager sensor geometry.

Solar Wind's Soectra on Day 160. 1991

~.) ~o 4: 0~ Q 5~ 3 - 2 4 5 7.2 i. 6 12 13 14 15 16 1 Hour on Day 160, 1991

Figure 3-2: The Overall Proton Spectra of Solar Wind Plasma on Day 160 1991 - Data from the A, B, and C cups are presented, as the D cup barely detected any signal. The color bar is proportional to the

logarithmic value of the distribution function, with high values lighter. The exact time where the feature started is at time 12: 23: 46.

On day 160, the double streaming event occurred most prominently from hour 12.5, while on day 161, the event lasted until hour 10. The peak bulk speeds are approximately 425

25

and 480 kilometers per second. A more accurate analysis will be given in the next section, where we use a two-Maxwellian functions to fit the individual spectra.

Solar Wind's Spectra on Day 161, 1991

M. 7 --2 4 6 : 10 12 14 16 550 50 -43 4t -- 352 Hour n Da 161 199 12:H9:ur on ay 161. 19

4 Properties of the Double-Streaming Events

4.1 Fits to the Spectra

To carry out our fits in the double-streaming region, we convert all data numbers into currents and evaluate the proton distribution function. The instrumentation and the conversion information are discussed in the Appendix 6.1. We mainly analyze spectra from time around hour 12.40 on day 160 until roughly hour 9.52 on day 161, as the double-streaming occurred most prominently in this interval

The fitting equation we use is a double-Maxwellian function:

I 2 2%

ni (V -vI)_ n2 (v-v2

f(v):= 1 exp- 2 + 2 expr~ 2 +fo, (1)

where

fo

is a constant offset, ni and n2 are the proton densities, w and w2 are thermal speeds,

and v' and v' the mean bulk speed component along a given sensor normal. We always use index 1 to correspond to the lower peak, and the index 2 the upper peak (or equivalently,

v > v'₂). The error distribution of each variable is discussed in Appendix 6.3.

Examples of the data and our fits to the spectra are given in Figures 4-1 and 4-2. We classify the spectra that exhibit the double-streaming feature into three classes: probable,

convincing, and certain. The probable spectra contain two clear peaks, but there are small peaks

in between or considerable noise. The convincing spectra do not have much noise, but the shape of each peak may not look like a Maxwellian distribution. The certain spectra have at least two easily identified Maxwellian peaks.

Hour 12.334 _{lioor 14_,-6V}

ft- d 9.v

Figure 4-1: Spectra Samples from A Cup on Day 160 - The two spectra are taken from channels 60 to

85. The blue astenisks represent the actual data and the red lines are the results from our fit calculation.

For these two data sets, the fits gives the speeds at peaks to be, respectively, 427.6 and 490.1, and

Figure 4-2: A Sample Spectrum from A Cup on Day 161 - This spectrum has a feature. The speeds are at the peaks are 414.0 and 462.6.

4.2 Double-Streaming Properties in the March 1991 Events

clean double-peaked

Protqn Averitge Speeds tit Double-Streaming Events, A Cup

500

150-40 2 13 1 4 11 1

~~17

Hour on Da\ 1(0, 1991

Proton Average Speeds at Double-Streamning Events. C Cup

4. 4. 4. 4. 4. 4.4.44. 4. '4... S .. .* 4. 1) 3 13 14 Homt on DaN 160, 1991 . Probabie. Low ?robabie. High Convincing. Low Convincing, High + Certain, Low Certarn, High I1 7 18

Figure 4-3: The Speed of Solar Wind Proton at Peaks during Double-Streaming - The upper panel is

the analysis results of the A cup spectra, and the lower panel the C cup spectra. These two plots classify data into three categories, as described in the text. Note that the data from the A cup are the cleanest. We

*1 \

/ \ , II / \ I' \ I' \ I \ *4/ I, 490- 480470 - 460-450 - 440- 430-ill 4. .4. 4. 4.894 10 1Iur SO - - I . o I 8 41 9 41 .2 15

can see from these plots that at about hour 12.50, the two speeds became stable. This is because double streaming started to be settled at hour 12.40.

With the fit analysis discussed above, we can easily determine the speed at each peak for every spectrum that exhibits double streaming. Figure 4-3 gives a plot of these speeds during

day 160, for the A and the B cup. We also give in Figure 4-4 plots of the densities of the two

peaks, there thermal speeds, the total density, and the average thermal speed, for each of the cups

A and C.

Note that the difference in speed obtained by subtracting our two speeds obtained from the fit in a given cup is not the real proton speed difference, but the difference of the projection of the proton true velocity difference along the cup normal direction. However we can estimate the true magnitude of the speed difference if we assume that any difference in velocity is aligned

with the field, as it must be. If the angle between the cup normal and the magnetic field is (0

(we will call this the correction angle) then the corrected proton speed difference is given by (2)

Av =V2 V. cos((P)

404- Densitv Plot: Double Streaming, Day 160, 1991, A Cup

3.4- + '- + ++4 45 +- + + 4 + 2 1+ + 4-+ + + + 3 + - + + + + +++ -1,5 +-+ + ++ F 4 + + -++ + 4 + + + 4 +, + - + ++.4 +# + + - +4 +~ +1 + 9S 10 12 13 14 15 14- 17 Ho u7

5410-4 Densit.' Plot: Do)uble SreauiiisT Day 1601, 1991, C Cup 4

5 X 35 -- 4 4

3 -

+

+

-

+

+-

+-

+1

2.5 -- + ++ 4- F- ++ +- ++++ + + + + ++ 4 4-44 F- + + + 4 4-4 4 4- ++ + + ++ 4 + + + + 44 + 44 + F X 10' 45 3 - --5 10

Figure 4-4: The Density Calculated from the Fit Results on Day 160 - The jump at around hour 12.50 is explained in Figure 4-3. The results from fitting data in both cups agree fairly well.

3

10

Thermal Speed Plot: Double Streaming, Day 160, 1991. A Cup 40

35

-Thema 0See P Dobl -ot Stemn Dy1 19oQ91, C Cu0p1~ 0.

30 3 0 -OP 1 o 0 Q? 1 Cb. 000 Oft 0 o 0 0 0 ~ 3 5 *0 00 0 00 01 0 0 0 ID 0 9 10 11 12 14 14 15 Is 17 18 Hom

Thergm al Speed Plot Double Srea min , Nr m 160, 19F1 i ea 1C0

33 r y a 3 0 -0 0 .00 0 ~0 0 0 - 301 3 o 30 0 s 7: -30, 05 0 0 30 1 0 0-10 11 12 13 1415618

Figure 4-5: The Thermal Speeds as Calculated from the Fit Results on Day 160

4.3 Streaming Velocity Differences in Terms of Thermal and Alfven Speeds

To get a clearer idea of the physical meaning of the speed differences seen in Figure 4-3, we compare them with other characteristic speeds in the plasma. We want to compare the speed difference Av defined in equation (2) with the average thermal speed of the two distributions,

W = (+ vv2) / 2, and also with the other characteristic speed in our plasma, Alfven velocity VA,

where

B BTX cn l2 3

V B

(21.812

km/s) (3)

p0nm "I nT cm

where B is the magnetic field strength, to is the magnetic permeability in a vacuum, n is the

particle density. In our analysis, n = n + n2.

In Figure 4-6, we plot these characteristics speeds and the velocity difference, along with the magnitude of the field. Unfortunately, we only have hourly averages of the magnetic field strength. It is worth remarking that the hourly average magnetic field reached a local minimum at the hour where double streaming started. There may be a connection between the magnetic field strength and the kinetic process that feeds double streaming. A

The thermal speed w in this analysis is not a true representation of the real thermal speed. In our analysis, we disregard any angular correction of the thermal speed as it is given by the pressure tensor, which is second-rank, and therefore, the correction formula is fairly complicated.

However, as the correction angle does not deviate too far from 180 degrees (for each main cup, this angle is fluctuating around 150 to 160 degrees), the thermal speed as computed from the fits in the A and C cups is close to the thermal speed parallel to the magnetic field.

039

2 38

D 37

2 36

035

Iagnetic Field Plot: Double Stremming, Day 161, 1991

0331 I~ 1

3 10 11 12 13 14 1 16 17 18

Homt

Alfvoen Speed Plot: Double Streaming, Dix 160, 191Q

450 400 350 2U 300 300 250 200 150 100 111 1 10 11 12 13 14 15 16 17 18 H.,m

Particle Denity Ratio: Dulble Streaming, Day 160, 1991

I 2 + ++ + + +, + 4 cup + -12 -~ - ~ -~ 1 - C cup

Speed Difference: Double Streaming, 160, 1991

1SO I I I 140- 120- 100-50 + 4 + ++ 40-20 10 17

Figure 4-6: The Magnetic Field, the Alfven Speed, the Ratio of the Particle Densities, and the Speed Difference on Day 160- The resolution of the magnetic field data is hourly. The Alfven speed, high and

erratic initially, dropped to between 120 and 150 kilometers per second after hour 12.50. Finally, recall the spectra in Figure 3-1 and note that before hour 12.50 the upper peak was smaller until hour 12.50, when it abruptly grew.

I Cup C Cup ++ + + + ' H I H ' i + Z 8 3 12 14 I5 10

Speed Difference versus Thermal Speed: Double Streaming, Day 160, 1991 18 16 14 12 10 4 1-9 10 +4..-+t-4 4--' 13 Howr 14 16 17 11 12

Speed Difference versus Alfven Speed: Double Streaming, Day 160, 1991

I I I 5 - 44' - -+4-- S + -3 -* ---2-j 9 10 11 12 13 14 15 16 17 Hour

Figure 4-7: The Speed Ratios on Day 160 - The upper panel gives the ratio , or the sonic Mach number of the speed difference. Notice that after hour 12.50, the Mach number falls between 2 to 4 (with a mean at 3.0, and the fluctuation has a standard deviation of 0.7 ). The lower panel gives the ratio Av / vA , or the magnetohydrodynamic Mach number of the speed difference. Post hour 12.50, this ratio is distributed around the mean 0.33 with a standard deviation 0.04.

In Figure 4-7 we plot the difference in streaming speeds divided by our two characteristic speeds in the plasma. The remarkable feature of these ratios is that the streaming difference is supersonic with respect to the thermal speeds, with an average greater than mach 2, but sub-Alfvenic, with an Alfven mach number of around 0.4.

Figures 4-8 through 4-10 are similar plots for day 161, and show similar features. Note that initially the number density in the lower peak was larger than the number density in the higher peak. As time progresses, the number density of the higher speed peak increases, until it dominates in the later part of the event on day 161. The impression is of two interpenetrating

streams, with the lower peak gradually being replaced by the upper peak, but no intermixing

between the streams.

0 0 0 -4 , -+ t + + 15 8

Density Plot: Double Streaming, Day 161, 1991, A Cup

in--1 4 5 7

How

Density Plot: Double Streaming, Day 16

.5 -+ [ + 2 - + -+ + + 4: + 4 3.5 -I 0 11 9 9 111 12 1, 1991, C Cup

Thermal Speed Plot: Double Streaming, Day 161, 1991, A Cup

I I

I

-2 3 4

HoWt

Thermal Speed Plot: Double Streaming, Da

3 10 11 y 161, 1991, C Cup 50 1 I 45 40 05 20 15 107 Hou[ .

Figure 4-8: Particle Densities and Thermal Speeds on Day 161 - Day

those obtained on Day 160. These noisy spectra result in erratic patterns speeds. However, we can see that the upper peak started to take over the I particle density is higher for the upper peak in this regime.

161 spectra are noisier than

in both densities and thermal ower peak, and therefore the

2 0.5 30 25 20 15 10 12 1234 0 i II a-123 I 10, 3F-- I I I + I I I 3 10 11 12 2 I I I I 5L

Magnetic Field Plot: Double Streaming, Day 161, 1991 7I I 3 42 -0415 0 41 0.405 0 39S 038 -03B4 ₈ 9 10 11 12

Alfven Speed Plot: Double Streaming, Day 161, 1991

I + A Cup 0 Cup F--- ++ + + 4 + 4 2 3 4 5 6 7 8 9 10 11 12 Hour

Particle Density Ratio: Double Streaming, Day 161, 1991

I I I I

I I I I I I I

23 4 5 6 7 0 3 10 11 12

C 2up Speed Difference: Double Streaming, Day 161, 1991

I5C - I - I I I T

-3 9 0 11 12

Figure 4-9: Magnetic Field, Alfven Velocity, Proton Density Ratio, and Speed Difference on Day 161 - Again, we use a step magnetic field function to derive the Alfven speed. As discussed in the last plot, the particle density in the upper peak starts to dominate that of the lower peak. On this day, the ratio

n2 / n is distributed around 1.7 with a standard deviation of 1.2.

- 3 4 5 7 How* 4- -1 1--4+ 4 -4-+ 4- --- +- +- -300 250 200 150 100 50 2 3 4 5 6 7 Hour I I JU ' -T I F-p + 1+ I I 1 7 -4 '14 3 I I

f-Speed Difference versus Thermal f-Speed: Double Streaming, Day 161, 1991 2 --4-.- +-2 3 4 5 7 3 3 10 1 12 Hour C -p

Speed Difference versus Alfven Speed: Double Streaming, Day 161, 1991

0+ I 05- 03--!321 2 3 4 3 9 10 11 12 Hour

Figure 4-10: The Speed Ratio on Day 161 - The sonic Mach number Av I w is distributed around the

mean 3.9 with the standard deviation 1.9. The Alfven Mach number Av / vA has a mean of 0.38 with a