plots of 1.28-s averages of the magnetic field (B(t), O(t), ½(t))

VOL. 82, NO. 22 JOURNAL OF GEOPHYSICAL RESEARCH AUGUST 1, 1977

Interplanetary Current Sheets at 1 AU

L. F. BURLAGA

NASA Goddard Space Flight Center, Laboratory for Extraterrestrial Physics, Greenbelt, Maryland 20771

J. F. LEMAIRE

Institut d'Aeronomie Spatiale, B-I ISO Brussels, Belgium

J. M. TURNER

,Department of Physics, Morehouse College, Atlanta, Georgia 30314

We have determined the structure and nature of 'discontinuities' in the interplanetary magnetic field at I AU in the period March 18 to April 9, 1971, by using high-resolution magnetic field measurements from Explorer 43. The discontinuities that were selected for this analysis occurred under a variety of inter- planetary conditions at an average rate of 0.5/hour. This set does not include all discontinuities that were present, but the sample is large, and it is probably representative. Both tangential and rotational discontinuities were identified. Tangential discontinuities were observed every day, even among Alfvfinic fluctuations. In particular, on one day during which Alfvfinic fluctuations were intense and persistent in a high-speed stream, tangential discontinuities (TD's) were seen throughout the day at an average rate of 0.5/hour; rotational discontinuities (RD's) were also observed during this day at a higher than usual rate, the ratio of TD's to RD's being approximately one. The structure of most of the current sheets was simple and ordered; i.e., the magnetic field usually changed smoothly and monotonically from one side of the current sheet to the other. The thickness distributions of the TD's and RD's with very smooth current sheets were similar. The average thickness of the RD's was 1200 km (13 proton Larmor radii), and the average thickness of the TD's was 1300 km (12 proton Larmor radii).

1. INTRODUCTION

The nature and structure of interplanetary discontinuities have been the subject of several investigations and much de- bate. Siscoe et al. [1968] used a minimum variance method to cxarninc thc structurc of boundary layers whose width ranged from 10 to 100 s, and they concluded that 80% seemed to be tangential discontinuities (TD's); however, the method that they used is not appropriate for studying rotational discontinuities (RD's), and they could not rule out a sub- stantial contribution of RD's. Burlaga [1971] showed that during an 8-day period (when there were no pronounced high- speed streams), less than 25% of the directional discontinuities were RD's, and he concluded that those discontinuities were predominantly TD's. The predominance of TD's in quiet low- speed regions has been confirmed by Martin et al. [1973] and Solodyna et al. [1977]. Belcher and Solodyna [1975] showed that the condition

days, or 3/day), he selected only exceptionally broad current sheets, and he did not consider plasma data.

The Explorer 43 magnetic field measurements that we use in this paper clearly resolve the structure of even the thinnest boundary layers, and the measurement errors are small enough that we can determine the nature of most of the associated discontinuities using a minimum variance method.

This is done in section 3. Since we have plasma data for the period considered, we can also examine the relation between these discontinuities and Alfv•nic fluctuations, and we do this in section 4. Finally, since the structure of the current sheets is resolved in the Explorer 43 data, we can determine the distri- bution of thickness for all events with a well-defined beginning and end; we present those results in section 5.

The plasma and magnetic field instruments are described briefly by Burlaga and Ogih)ie [1973] and Fairfield [1974], respectively.

bV = +(V/B)bB (l)

is nearly satisfied across discontinuities that occur among A lf- v•nic fluctuations in high-speed regions, and this led them to the opinion that such discontinuities are predominantly rota- tional. Martin et al. [1973] arrived at the same opinion in the same way. However, (1) is not a sufficient condition for an RD. Indeed, Denskat and Burlaga [1977] have shown, using plasma and magnetic field observations from two spacecraft, that there do exist TD's across which (1) is satisfied. Thus in order to identify the nature of the discontinuities in 'Alfv•nic' high-speed regions one must do more than test for (1). Smith [ 1973a] examined the structure of some discontinuities, and he found a distribution consistent with the presence of both TD's and RD's. However, he considered only a small fraction of the discontinuities that were present (118 discontinuities in 39

Copyright ¸ 1977 by the American Geophysical Union.

2. SELECTION OF DISCONTINUITIES

The discontinuities were selected subjectively by looking at

plots of 1.28-s averages of the magnetic field (B(t), O(t), ½(t))

on a scale of • 1 hour/508 mm. Essentially, events were se- lected because they looked like abrupt changes in the time profile of the magnetic field direction; i.e., the direction changed from one nearly uniform state to another in less than •30 s.

The selection was made independently by four people (L. Bur- laga, J. Chao, D. Fairfield, and N. Ness), and there was gen- eral agreement as to which events were to be chosen.

Examples of the kinds of discontinuities that were selected for this study are shown in Figures 1 and 2. Figure 1 shows a discontinuity where the change in direction co is relatively large (co = 75 ø) and where the discontinuity stands alone in a 10-min interval; this event satisfies the definition of a directional dis- continuity introduced by Burlaga [1969]. Figure 2 shows sev-

Paper number 7A0293. 3191

3192 BURLAGA ET ALl INTERPLANETARY CURRENT SHEETS AT I A U

EXPLORER 4•

25

i i i i i i i i

IBI (7')

o 360

90 0

-90

0 2 4 6 8

TIME (MIN) HOUR I0

DAY 95 APRIL 6, 1971

Fig. 1. Example of a discontinuity. In this case the direction of the magnetic field changed by 75 ø , somewhat larger than the average (60ø). This satisfies the definition for a directional discontinuity in- troduced by Burlaga [1969].

eral discontinuities where the change in direction is small and where the discontinuities are clustered in a 5-rain interval;

events such as these do not satisfy the definition of directional discontinuities, but we included them initially because they can be readily identified in the high-resolution Explorer 43 data.

Our selection procedure gave 287 discontinuities for this study from 430 hours during which plasma measurements were made in the period March 18 to April 9, 1971. Thus the rate of occurrence is 0.7/hour. This may be compared with the occurrence rate for directional discontinuities that was found in other studies [see Siscoe, 1974; Burlaga, 1972], viz.,

• l/hour. Our selection procedure did not identify all of the directional discontinuities that were present. Conversely, 31%

of the events that we selected were not directional discontin-

uities in the sense that the angle w between the field B• on one side of the discontinuity and the field B•. on the other side was less than 30 ¸ (w < 30 ¸). In other words, although we did not select all discontinuities, we do have a large and representative sample of discontinuities.

The distribution of o• for the discontinuities that were se- lected is shown in Figure 3. One can see that there were 95 events with o• < 30 ¸. The number of events with o• > 30 ¸ falls

off exponentially with o• •', as is shown by the curve in Figure 3.

This is the same curve that Burlaga [1969] obtained for direc- tional discontinuities in the Pioneer 6 data; viz., N = const X exp (-o•/75 ¸)•'. It describes the Explorer 43 results rather well, as it should if the discontinuities are representative of direc- tional discontinuities.

The number of discontinuities per day is shown as a func- tion of time in Figure 4. The rate of occurrence varies from 5/day to 45/day. These are minimum rates of occurrence, since we did not select all discontinuities. The important point demonstrated by Figure 4 is that we were observing discontin- uities under a variety of interplanetary conditions: there were two kinds of shock flows [Ogilvie and Burlaga, 1974], at least three fast streams with well-defined interfaces [Burlaga, 1974], and 'Alfv•nic' fluctuations [Burlaga and Turner, 1976]. The quantity o in Figure 4 is the correlation coefficient between the fluctuations in the speed and the radial component of the magnetic field. A value of o > 0.6 is taken as an indication of the presence of Alfv•nic fluctuations as discussed by Burlaga and Turner [1976]. It is interesting to note that the discontin- uities were most numerous (45) on the day (April 6) that Alfv•nic fluctuations were most prominent.

3. NATURE OF THE DISCONTINUITIES

The 'discontinuities' that we have been discussing are not truly discontinuous of course; they only appear to be so at low time resolution or when the field is averaged over 30 s or so. In general, there is a current sheet (boundary layer) in which the magnetic field direction changes continuously from one side of the 'discontinuity' to the other, as is illustrated in Figure 5. If the 'discontinuity' is tangential, all of the magnetic field vec- tors in the current sheet are parallel to the surface of the discontinuity, as drawn in Figure 5. If the 'discontinuity' is rotational, then one component changes as in Figure 5, and there is another component which is constant and normal to

IBl(r)

9o ø

EXPLORER 43 25

- I I I I I I I I I I I I I I i I I I I I. I I I I I I

25

I•l(r)

5 I0 15 20 2 5 30

360 ø

9½

- • • i i I i i i i I i i I i I •

35 40 45

360 ø

-90 • • • I I • • • I I • I • -

30 50 55 60

TIME (MIN) HOUR 5 DAY 95, APRIL 6, 1971

Fig. 2. Examples of other discontinuities that were selected. The events shown here do not satisfy the definition of a directional discontinuity because the change in direction co is small and/or the discontinuities are too close together. They were included in the initial selection because the changes appear to be nearly discontinuous.

0 ø

BURLAGA ET AL.: INTERPLANETARY CURRENT SHEETS AT I AU 3193

ioo

8o

• •o

40

20

00o

EXPLORER 43

DISCONTINUITIES MARCH 18-APRIL 9

197 I

=

120 ø 180 ø

Fig. 3. Distribution of to, the change in direction of the magnetic field, across the discontinuities that were selected. For 31% of the discontinuities, to < 30 ø . The curve for to > 30 ø is N = No exp (_co/75 o)2, which is the same function that Burlaga [1969] found for the to distribution of directional discontinuities in Pioneer 6 data.

the plane of the discontinuity. Thus, in principle, one can distinguish between a TD and an RD by analyzing the struc- ture of the current sheet.

Sonnerup and Cahill [1967] introduced a technique for ana- lyzing the structure of a current sheet; this is illustrated in Figure 6. Basically, the procedure is as follows: (1) determine the average of the magnetic field vectors in the current sheet, (Bi); (2) for each vector Bi in the current sheet, compute the difference ABt --- Bt - (Bb; (3) find the plane which best fits the set of vectors AB• (the minimum variance plane); and (4) determine the average component of Bi normal to that plane.

For a TD the AB, are all parallel to the surface of the discon- tinuity, since the B• themselves are parallel to that surface.

Thus there is no component of B normal to the minimum variance surface of ABt for a TD, as is illustrated on the right side of Figure 6. For an RD the vectors B• rotate on the surface of a cone, as is shown on the left side of Figure 6, and the surface of the discontinuity is the base of the cone. In this case there is a nonzero component of B• normal to the base of the cone (B,,), and the other component of Bt rotates parallel to this surface. For an RD, one eliminates B,, by taking the difference ABt = B• - (Bi), and the minimum variance surface

SHOCK

of ABt is the surface of the discontinuity. For an RD, one

should find that B,• = <lB,l> = (•/N) IB,.l is nonzero

(where N is the number of vectors in the current sheet and g is the normal to the minimum variance plane of the ABe).

In principle, the Sonnerup-Cahill technique determines the surface of the discontinuity, and one can distinguish between an RD and a TD by determining whether or not there is an average component of B normal to that surface. In practice, the technique can give misleading results if not used judi- ciously, since it can be very sensitive to experimental errors.

The problem arises because the minimum variance plane and its normal can be determined only if the experimental errors in AB• are small enough that the AB• lie close to the plane.

The digitization error in the Explorer 43 magnetic field measurements is • +0.06 'y, and the rms sensor noise in each component is 0.03-0.05 'y. Thus the uncertainty in determining each component of the field is •0.07 'y. Now consider the size of the quantities to be measured, viz., ABi. (See the base of the cone in Figure 6.) Suppose, for the purpose of illustration, that B,• = 2 'y, B• = B2 = 5 'y, and co = 30 ø. The length of the chord AB in Figure 6 is then 1.3 'y. The component of AB• in the

direction along the arc of the circle (•) is of the order of 0.65

A more thorough error analysis by K. Behannon and R. P.

Lepping (private communication, 1977) (based on simulations of current sheets) showed that when co >• 60 ø, the uncertainties in B,• are •<0.5 'y. For co close to but greater than 30 ø the un- certainties in B,• are •<2 'y. For co < 30 ø the error in B,• can be very large, and the Sonnerup-Cahill method cannot be used.

Similar conclusions are obtained by using the error analysis of Sonnerup [ 1971 ].

We selected the Explorer 43 discontinuities with co > 30 ø (there were 192 of them), and we applied Sonnerup's technique to each of the current sheets. Typically, there were 100 values of AB• in each current sheet. In most cases the surface of the discontinuity was satisfactorily determined. This is shown in

STREAM STREAM STREAM

INTERFACE INTERFACE INTERFACE

I I

I S HOCK I

5OO V (krn/sec)

1.0 :500

/0 0.6

0 40 DISCONTINUITIES

PER DAY 20 0

18 19 20 21 22 23 24 25 26 27 28 29 30 31 I 2 3 4 5 6 7 8 9

MARCH APRIL

1971

Fig. 4. (Top) Flow configuration in the period that is considered in this paper, (middle) correlation o between speed and the radial component of the magnetic field, which indicates the presence of Alfv•nic fluctuations when it is large (>0.6), and (bottom) number of discontinuities per day as a function of time. The main point is that the discontinuities that we selected are found under a wide variety of interplanetary conditions.

3194 BURLAGA ET AL.: INTERPLANETARY CURRENT SHEETS AT 1 AU

SURFACE 2

SURFACE

BOUNDARY LAYER

Fig. 5. The transition between the two sides of a 'discontinuity' is actually a continuous one and is called a boundary layer or current sheet. For a TD the magnetic field vector rotates in the boundary layer from one state to another, always remaining parallel to the surface of the 'discontinuity,' as shown here. For an RD, one component of B rotates as shown here, and in addition, there is a component of B perpendicular to the surface of the 'discontinuity.'

60-

50'

40 co > 30 ø ,

re -

ß 30-

2o

io

v i i i i i i i i I i i i i i i i I

o 4 e i• 16 2o 24 2•

Fig. 7. Distribution of the ratio of the intermediate eigenvalue X• to the minimum eigenvalue X8 from the minimum variance analysis of the ABe. This quantity must be large if one is to determine accurately the minimum variance plane of ABe. One sees that it is large for most of

the discontinuities with co > 30 ø.

Figure 7, which gives the distribution of X2/Xs, where X8 is the minimum eigenvalue obtained by diagonalizing the matrix Mtt

= (B•B•) - (Bt)(Bt) as described by Sonnerup and Cahill and is the intermediate eigenvalue. The most probable value of X•/Xa is -•3, and the average is higher, 6.5, because the distri- bution is highly skewed.

The distribution of the average normal component B, --

([ B•[) is shown in Figure 8. There is a strong peak at B, = 0

exp -(([ B•[)/1.25) •', is a Gaussian fit to the population near

<l&l> = o. This gives a a = 0.9 • for the variance, which is of

• TD

MINIMUM VARIANCE PLANE

FOR A •i-- •i- < õi >

MINIMUM VARIANCE PLANE

FOR A •i = •i - < '•i >

Fig. 6. For an RD (left) the magnetic field rotates on the surface of a cone, while for a TD (right) it rotates in a plane. The Sonnerup- Cahill method determines the plane which contains ABt = Bt - (Bt).

For an RD there is a nonzero component of B normal to this plane, while for a TD there is no component of B normal to this plane. The determination of the plane containing ABt is uncertain when co is small because some of the ABt are too small to measure accurately in this

case.

The number of events with B• > 3 • is 43, and the num- ber of events with B• < 2 -y is 122. If our sample of dis- continuities (which probably contains one half to one third of all discontinuities with co > 30 ø) is representative, then the ratio of TD's to RD's defined in this way is 2.8. In other words, those results suggest that the ratio of TD's to RD's was typically 2.8 to I in the interval that we are considering. Since events with B, < 2 -y might include some RD's and since discontinuities with small co were excluded, the ratio of 2.8 to 1 is not an unambiguous determination of the ratio of TD's to RD's. The results indicate a predominance of TD's, but the

actual ratio of TD's to RD's cannot be determined.

The distributions of the normals of TD's and RD's have been discussed in several papers (see the reviews by Burlaga [1972]

and Siscoe [1974] and the papers by Siscoe et al. [1968], Burlaga [1969], Smith [1973], Turner [1973], and Turner and Siscoe [1971]). The general result is that the normals of TD's tend to be perpendicular to the spiral average magnetic field direction and close to but somewhat out of the ecliptic plane, while the

•. I I I I I I I I I I

• EXPLORER 43

5 0 i!•.•,. co ^{54.1 e} -(<lazl>/ •'25 )2 >30 ø -

u• 40

•- iIii,••ALL EVENTS (N" 192 )

z

tu 30 EVENTS WITH /3 > 0.6 -

o

n- • (N-'lOg)

,'n 20

2 4 6 8 I0

< IBzl> (7)

Fig. 8. Distribution of <lB, I>, the component of B normal to the minimum variance plane of AB,. Only discontinuities with co > 30 ø are considered, so that the minimum variance plane is well determined.

The peak is at <1B,l> -- 0, and there is a population of events with <lB, l>

< 2 •, consistent with TD's. There is another population with (I B,I) >

3 •, consistent with RD's. The ratio of TD's to RD's obtained in this way is 2.8 to 1. One obtains essentially the same distribution when only Alfvfnic (p > 0.6) periods are considered.

BURLAGA ET AL.: INTFnPI,ANETARY CURRENT SHEETS AT 1 AU 3195

9O'

60'

2 6 I0 14

NUMBER

I0 6 2 2 6 I0

• o'

/ \ ß

150ø I 210

90 ø

/ 60 ø

/ /

io

NUMBER

:50 20 I0 I0 20 :50

I I I I I I I

'4o'

18o'

ROTATIONAL DISCONTINUITIES TANGENTIAL DISCONTINUITIES

Fig. 9. Distribution of the normals to the surfaces ot'TD's and RD's. Both tend to be above the ecliptic plane. The TD normals tend to be normal to the spiral field, whereas the RD normals are more isotropically distributed.

normals of RD's are more randomly scattered. Figure 9 gives

the distribution of normals for TD's and RD's in our data set.

For this purpose we identify those discontinuities with B,• < 2 '• as TD's and those with B,• > 3 '• as RD's. One sees that the distributions show the same general patterns that were sug- gested by the earlier work.

4. DISCONTINUITIES IN THE PRESENCE OF ALFV!•NIC FLUCTUATIONS

It has been suggested that discontinuities are predominantly rotational when there is a high correlation between bV and particularly when the speed is high and decreasing in a stream.

We now consider whether or not this is in fact the case.

Let p be the correlation coefficient between the radial com- ponent of B and V during an hour interval, as discussed by Burlaga and Turner [1976]. Considering the experimental un- certainties, p > 0.6 is also consistent with p = 1 as required for Alfv•nic fluctuations [Burlaga and Turner, 1976], so we shall take p > 0.6 as an indication of Alfv•nic fluctuations. A similar definition was used by Belcher and Davis [1971], Bel- cher and Solodyna [1975], and Martin et al. [1973].

The distribution of (IBI> for discontinuities that occurred

than half of the discontinuities that we chose between March

15 and April 9 occurred under this condition (109 among 192).

The distribution of (I Bz[) for these discontinuities is very much

with (I Bz[) < 2 '•. In other words, our results are consistent

fluctuations.

Now let us consider a 24-hour interval during which Alfv6- nic fluctuations (0 > 0.6) were present throughout the day, viz., April 6, 1971. At this time the spacecraft was in a well- defined stream; the speed was high and decreasing, as is shown

in Figure 10. The speed and radial magnetic field profiles in Figure 10 are very much like those in Figure 1 of Belcher and Davis [1971] and in Figure 1 of Belcher and Solodyna [1975];

those authors interpreted the variations as Alfv•nic fluctua- tions. The Alfv•nic nature of the fluctuations in Figure 10 is indicated by the high correlation between V and B,• (p > 0.6)

and by the relatively small fluctuations in I BI and in the

found that o• > 30 ø for 37 of them.

The left panel of Figure 11 shows an example of a TD that was observed among the Alfv•nic fluctuations on April 6. The components are shown in the minimum variance system: œ is the minimum variance direction, • is normal to œ and in the plane containing the average field and œ, and • completes the right-hand coordinate system. For this event, o• = 91.8 ø, and the ratio of the intermediate to minimum eigenvalue obtained by using Sonnerup's method is X2/X• = 6.5, so the minimum variance plane was well determined. The average component of normal to this plane is B,• = 0.16 'y, so the discontinuity is clearly a TD. This boundary layer happens to be rather smooth. A less regular boundary layer which occurred at 1450 on April 6 is shown in the right panel of Figure 11. In this case, o• = 97.6 ø, X2/X• = 17.1, indicating a well-defined minimum variance plane, and B,• = 0.58 'y, which is consistent with zero.

Thus this too is apparently a TD among Alfv•nic fluctuations.

Table 1 summarizes the properties of 12 boundary layers with B,• < 1 '• that occurred on April 6 (note that B,• < 0.5 '• for half of these). They are all consistent with being TD's, and all occur in the presence of Alfv•nic fluctuations. Their relation to these fluctuations is shown by the vertical lines in Figure 10.

Examples of RD's on April 6 are shown in Figure 12. For the event at 0357 UT, shown in the right panel of Figure 12, the change in angle was small (o• = 37 ø), but the minimum variance plane was well determined (X•/X• = 10.6). The com- ponent of B normal to this plane was 4.4 'y in an average field of 5 'y. The event of 0239 UT, shown in the left panel of Figure

3196 BURLAGA ET AL.: INTERPLANETARY CURRENT SHEETS AT 1 A U

EXPLORER 43

0 650

.,x_.,.p-•••••• •_ • 450

IO

-

-15 25

25 O

n(cm -3) _ .

3 6 9 12 15 18 21 24

TIME (HRS) DAY 95,APRIL 6, 1971

V (kin/s)

Fig. 10. An Alfv6nic period. The fluctuations in V and Bx are highly correlated (the correlation coefficient p being greater than 0.6 throughout the day), and the density and magnetic field intensity are relatively constant, indicating Alfv6nic fluctuations. Forty-five discontinuities were observed during this day, shown by the vertical lines in the top panel.

Several of these were tangential discontinuities, indicated by the vertical lines extending through all of the panels.

12, was somewhat broader, the angular change was larger (w = 70.3 ø), and the minimum variance plane was less well defined (X2/X3 = 2.2), but again we find a large normal, B,, = 4.0'7 in a 5-'7 field. Thus there is little doubt that RD's can also occur among Alfv6nic fluctuations.

The general character of the discontinuities with w > 30 ø on April 6 is summarized in Figure 13, which shows the distribu-

tion of B,, -- (I B•l) for this day. There were 37 discontinuities,

1.5/hour. There is a peak in the B,, distribution at B,, = 0, consistent with the presence of TD's. For 16 events (43%),

IO

Bx (r) o

-IO IO

By (7') o

-IO IO

Bz(r) o

-IO

20

io o o

• ß 92' Bn = 0.2 7'

Bx()

.

By(7

Bz(7'

B(r)

• ß 98' Bn ß 0.6 7'

I I I I I , I I I I I I I I

I0 20 30 SEC 20 50 40 50 60

APRIL 6, 1971 APRIL 6, 1971

1625 1450

Fig. 11. Structure of two TD's. In both cases the magnetic field intensity is nearly const0ot, and the field vector rotates in a plane. The component normal to this plane (Bz) is consistent with zero in both cases, indicatingthat the discontinuities are tangential.

BURLAGA ET AL.' INTERPLANETARY CURRENT SHEETS AT I AU 3197

TABLE 1. Tangential Discontinuities on April 6, 1971

UT (Bz), 7 co, deg

0408 -0.19 30.4 2.0

0525 -0.78 53.4 13.5

1004 0.32 78.9 4.3

1450 0.54 97.6 17.1

1621 0.16 91.8 6.5

1638 0.25 167.7 3.6

1714 0.34 35.3 7.8

1716 0.21 61.9 8.6

1827 0.62 30.0 1.9

1838 0.65 81.9 7.5

2022 0.85 106.0 6.4

2347 0.52 78.4 3.4

< 2 3'; these events are probably TD's, since the uncertainties are approximately 1 or 2 3'. In addition, there is a second peak in the Bn distribution between 3.5 and 4 3'. For 17 events (46%), Bn > 3 'y, and these events are probably RD's. Thus during this Alfv6nic period the B, distribution is atypical (in comparison with that in Figure 8), being bimodal with roughly equal numbers of TD's and RD's.

We conclude that ( 1 ) TD's can coexist with Alfv6nic fluctua- tions and (2) RD's are not necessarily predominant in the presence of Alfv6nic fluctuations, but (3) RD's occur preferen- tially with Alfv6nic fluctuations in high-speed streams. The association of RD's with Alfv6nic fluctuations is not surpris- ing, since RD's themselves satisfy the conditions for an Alfv6- nic wave.

5. THICKNESS OF LAMINAR BOUNDARY LAYERS

Sestero [1964] and Lemaire and Burlaga [1976] developed a theory for the structure of 'laminar' boundary layers, i.e., those in which the magnetic field varies smoothly in the cur- rent sheet. Their results predict that the thickness of such a

current sheet should be of the order of a few to several proton Larmor radii, depending on the details of the distribution function in the current sheet and on the conditions on both sides of the sheet. To compare this theory with observations, we selected the subset of current sheets for which (1) the magnetic field changed very smoothly in the layer, (2) there was a well-defined beginning and end of the layer, and (3) plasma data are available.

The current sheets are convected with the solar wind past the spacecraft. Let the interval during which a layer moves past the spacecraft be denoted by ¾. The thickness •/of a cur- rent sheet is related to T, the solar wind speed V, and the radial component of the unit vector normal to the discontinuity

surface Inrl by the formula

(2)

The 'thickness' distributions for TD's (defined by B, < 2 3') are shown in Figure 14. The most probable duration is 2.5 q- 0.5 s, and the average is 4.7 s. Seventy percent of the durations were less than 10 s, and 98% were less than 15 s. The shortest duration was 0.6 s. The thickness ranged from 158 to 8000 km;

in terms of proton gyroradii (RL) the thickness ranged from 1.5RL to 82R•. The average thickness of the TD's was 1300 km and 12R•.

The thickness distributions for RD's (defined by B• > 3 3') are shown in Figure 15. They are similar to the distributions for TD's. The most probable duration for the RD's is 5 q- 1 s.

The average is 5.4 s, and the range is from 1.1 to 14.7 s. The average thickness is 1200 km (13R•), and the range is from 250 km (2.2R•) to 2500 km (43RL).

The thickness distributions of the observed TD's and RD's overlap the thicknesses found for the theoretical current sheets that Lemaire and Burlaga considered. The average observed

io

Bx (y) 0

-I0

I0

By (y) 0

-I0

I0

Bz (y) o

-io

2o

B (7')

I0

•- 70 ø B n ß 4.0 7'

I0

Bx (7') 0

-I0

I0

By (7') 0

- I0

IO-

Bz (y) o

-IO -

2:0-

B (y) -

IO-

•J-37 ø Bn-4.4 Y

I I I I

I I I I

0 I I I ! I I I I I I

io 2:0 30 50 o i0

APRIL 6,1971 APRIL 6, 1971

0239 0357- 0358

Fig. 12. Structure of two RD's. The magnetic field intensity is constant, and the magnetic field rotates on a cone. The component B normal to the base of the cone is large in both cases, indicating that the discontinuities are rotational.

3198 BURLAGA ET AL.: INTERPLANETARY CURRENT SHEETS AT 1 A U

EXPLORER 45

APRIL 6, 1971

- CO > 30 ø •;• -

N=37 -

7

7 -

I 2 3 4 5

Fig. 13. Distribution of ( Bz ) for the discontinuities on April 6. It is bimodal and suggests equal numbers of TD's and RD's.

thickness is higher than that which was found for most of the

theoretical current sheets, but this might simply be due to the boundary conditions chosen for the theoretical study. There

based on a realistic distribution of discontinuities, i.e., a distri- bution with the observed changes in magnetic intensity and field direction across discontinuities. Special attention should be given to the theory of discontinuities with no change in I BI.

6. SUMMARY

We have examined the nature and characteristics of discon-

tinuities in the interplanetary magnetic field during the period March 18 to April 9, 1971. This period contained a variety of interplanetary conditions: simple and compound streams,

which we identified visually in plots of 1.28-s averages of the

TANGENTIAL DISCONTINUITIES

EXPLORER 43

(• >50 ø

5 I0 15 >15

THICKNESS (SEC)

8

I0 •o

THICKNESS (100KM)

30 >30 o io

Fig. 14. Thickness distributions for TD's.

20

THICKNESS (R L)

30 >30

BURLA•A ET AL.' INTERPLANETARY CURRENT SHEETS AT 1 AU 3199

ROTATIONAL DISCONTINUITIES EXPLORER 45

• >50 ø

02 4 6 8 I0 12 14 16 THICKNESS (SEC)

of relative abundance of RD's and TD's in regions of high and decreasing speeds, where Alfv•nic fluctuations are most pro- nounced. We found that TD's do indeed occur in such periods.

In fact, we showed that during one interval lasting 24 hours, TD's occurred at the rate of at least 0.5?hour. On the other hand, we also found that the Bn distribution was bimodal in this interval with roughly equal numbers of TD's and RD's, suggesting that RD's preferentially occur in such intervals.

The structure of the boundary layer was clearly resolved in every case that we considered. Considering the subset of very regular boundary layers with well-defined beginning and end we found that the average thickness of TD's was 1300 km (12RL) and that the average thickness of RD's was 1200 km (13RL). The Larmor radius was somewhat larger on average in the intervals containing TD's than in the intervals containing

RD's.

Acknowledgments. The results of this paper are based on the aCcu- rate high-resolution magnetic field data from the GSFC magnetometer on Explorer 43; we are indebted to N. F. Ness and D. Fairfield i for allowing us to use these data for our investigation. The plasma data were obtained from the GSFC plasma experiment on Explorer 43, and we are likewise indebted to K. W. Ogilvie. We acknowledge important discussions with K. Behannon, J. W. Belcher, and R. P. Lepping. P.

Harris assisted in the programing. One of us (J.L.) was supported by the NAS/NRC during part of this work.

The Editor thanks J. W. Belcher and J. V. Hollweg for their assis- tance in evaluating this paper.

REFERENCES

I0 20 30 40 I0 20

THICKNESS (100KM) THICKNESS (R L)

Fig. 15. Thickness distributions for RD's.

4O

This is a minimum rate, for we did not attempt to include all discontinuities present. Discontinuities with a small change in the magnetic field direction were discarded, giving a rate of 0.5/hour for the discontinuities that were analyzed in detail.

The total rate of discontinuities may be 2 or 3 times that which we observed, but our sample is probably representative of discontinuities with co > 30ø; in any case, it is an order of magnitude larger than samples which have been used in the past to study the nature and internal structure of discontin- uities.

The Explorer 43 observations were quite accurate, and the sampling rates were such that typically 100 vector measure- ments were made in the current sheet associated with a discon- tinuity. Thus we were able in most cases to apply Sonnerup's minimum variance method to determine the orientation of the surface associated with a discontinuity and the component of B normal to this surface (B,•). Our analysis was restricted to discontinuities across which the change in the direction of B was greater than 30 ø in order to eliminate events for which the orientation of the surface was not accurately determined. The

distribution of B,• is peaked at B,• = 0, and the distribution

We have examined the issu• of whether or not TD's can occur in the presence of Alfvfinic fluctuations and the question

Belcher, J. W., and L. Davis, Jr., Large amplitude Alfv•n waves in the interplanetary medium, J. Geophys. Res., 76, 3534, 1971.

Belcher, J. W., and C. V. Solodyna, Alfv•n waves and directional discontinuities in the interplanetary medium, J. Geophys. Res., 80,

181, 1975.

Burlaga, L. F., Directional discontinuities in the interplanetary mag- netic field, Solar Phys., 7, 54, 1969.

Burlaga, L. F., On the nature and origin of directional discontinuities, J. Geophys. Res., 76, 4360, 1971.

Burlaga, L. F., Microstructure of the interplanetary medium, Solar Wind, NASA Spec. Publ., 308, 309, 1972.

Burlaga, L. F., Interplanetary stream interfaces, J. Geophys. Res., 79, 3717, 1974.

Burlaga, L. F., and K. W. Ogilvie, Solar wind temperature and speed, J. Geophys. Res., 78, 2028, 1973.

Burlaga, L. F., and J. M. Turner, Alfv•n waves in the solar wind, J.

Geophys. Res., 81, 73, 1976.

Denskat, J., and L. F. Burlaga, M ultispacecraft observations of micro- scale fluctuations in the solar wind, J. Geophys. Res., 82, 2693,

1977.

Fairfield, D., Whistler waves observed upstream from collisionless shocks, J. Geophys. Res., 79, 1368, 1974.

Lemaire, J., and L. F. Burlaga, Diamagnetic boundary layers in the solar wind: A kinetic theory, Astrophys. Space Sci., 45, 303, 1976.

Martin, R. N., J. W. Belcher, and A. J. Lazarus, Observations and analysis of abrupt changes in the interplanetary velocity and mag- netic field, J. Geophys. Res., 78, 3653, 1973.

Ogilvie, K. W., and L. F. Burlaga, A discussion of interplanetary postshock flows with two examples, J. Geophys. Res., 79, 2324,

1974.

Sestero, A., Structure of plasma sheaths, Phys. Fluids, 7, 44, 1964.

Siscoe, G. L., Discontinuities in the solar wind, in Solar Wind Three, edited by C. T. Russell, p. 150, University of California Press, Los Angeles, 1974.

Siscoe, G. L., L. Davis, Jr., P. J. Coleman, Jr., E. J. Smith, and D.C.

Jones, Power spectra and discontinuities of the interplanetary mag- netic field: Mariner 4, J. Geophys. Res., 73, 61, 1968.

Smith, E. J., Identification of interplanetary tangential and rotational discontinuities, J. Geophys. Res., 78, 2054, 1973.

Solodyna, C. V., J. W. Sari, and J. W. Belcher, Plasma field character- istics of directional discontinuities in the interplanetary medium, d.

Geophys. Res., 82, 10, 1977.

3200 ]]URLAGA ET AL.: INTERPLANETARY CURRENT SHEETS AT I A U

Sonnerup, B. U. O., Magnetopause structure during the magnetic storm of September 24, 1961, J. Geophys. Res., 76, 6717, 1971.

Sonnerup, B. U. O., and L. J. Cahill, Jr., Magnetopause structure and attitt•de from Explorer 12 observations, J. Geophys. Res., 72, 171,

1967.

Turner, J. M., On the relation between solar wind structure and solar wind rotational and tangential discontinuities, J. Geophys. Res., 78, 59, 1973.

Turner, J. M., and G. L. Siscoe, Orientations of rotational and tan- gential discontinuities in the solar wind, J. Geophys. Res., 76, 1816,

1971.

(Received October 26, 1976;

accepted March 25, 1977.)