A search for the origin of very low electron temperatures

Planer. Spuce Sci.. Vol. 26, pp. 571 to 579. 0 Pergamon Press Ltd., 1978. Fvinted in Nathem

A SEARCH

Ireland

FOR THE ORIGIN OF VERY TEMPERATURES

LOW

ELECTRON

A. GERANIOS

Max-Planck-Institut

fiir Kernphysik,

69 Heidleberg

1, Federal Republic of Germany

(Heceiued 2 May 1977, received for publication 4 Jnnuory

197X)

Ah&net-VLET’s (Very Low Electron Temperature) are regions in the solar wind (lasting 12-30 h) in which the electron temperature is abnormally low. Because it is generally believed that the thermal conductivity parallel to the interplanetary magnetic field lines is high for electrons, i.e. the contact with the Sun should be ideal, VLET’s are surprising observations. In this work a statistical analysis of many of these events is made with respect to the dependence of this phenomenon on interplanetary plasma and field parameters. In contrast with earlier work it was found that VLET’s exist not only after a

shock front. The statistical analysis showed further that a VLET is always associated with a VLPT (Very Low Proton Temperature) event and that, whilst on average the temperature of the electrons and protons outside the low temperature regions is about the same, the mean proton temperature inside is three times lower than that of the electrons. A particular model for VLET’s is investigated in detail; the closed magnetic loop or “blob” model. By assuming: (a) pure adiabatic expansion in a radially streaming solar wind without pressure equalization across the “blob” boundary, and (b) rapid pressure equalization across the boundary, an attempt was made to quantitatively investigate the feasibility of the “blob” model in the light of olasma and field data. It can be shown that the closed magnetic loop model is unlikely to be the major ‘cause of VLET’s. INTRODUCDON

Plasma measurements made by experiments on the VELA 5, 6 and IMP 6 satellites have shown that

electron temperatures (T.) in the solar wind can be anomalously low for periods of - 1 day (Montgomery et al., 1974). The measurements indicated further that these periods seemed to follow interplanetary shock waves after 10-20 h, and are associated with a simultaneous depression in proton temperature (‘I’,). The electron heat flux had a tendency to be smaller. In addition, Gosling et al. (1973) have reported that the anomalously low values of the solar proton temperatures are observed when the solar wind velocity is high. During these periods the proton density was depressed and the HeZf/Hf ratio in the solar wind was increased. In the present work many periods of anomalously low electron and proton temperatures (VLET-Very Low Electron Temperature-and VLPT-Very Low Proton Temperature) have been identified (Fig. 1). The temperature parameters are obtained from measured two-dimensional velocity distributions (Montgomery et al., 1970; Feldman et al., 1973a). During these periods it was found that on average T. = 5.5 x 10“ K and T, = 1.5 X 104K respectively, while the usual, measured values are T. = 20 X lo4 K and ‘I, = 5 X lo4 K (Feldman et al., 1973b). Only 30% of these periods in our survey occurred after the passage of an interplanetary shock wave. The majority of the 30%

showed a proton density increase and a shock correlated He2+/Hf ratio increase. The events correlated with the presence of a shock wave also showed an increase in the interplanetary magnetic field (IMF) amplitude whereas 80% of those events not associated with a shock wave showed no increase in the LMF amplitude. A search for a possible correlation between VLET’s and Cosmic Ray (CR) decrease (at energies of about 8 GeV using measurements of the nucleonic component at the Earth) yielded the result that for 80% of all cases there was a Cosmic Ray decrease at the time of abnormally low solar electron and proton temperatures. In three cases we observed not just a CR decrease but a Forbush Decrease without, however, being able to identify a shock wave. Amongst the few cases for which we had complete data coverage of the IMF we observed one event of electron depression during which the azimuthal of the IMF reverses by 180” (Fig. 2). OBSERVATIONS

Interplanetary plasma data collected over a period of five years (23 August 1969-8 May 1974) by electrostatic hemispherical analysers on board the VELA SA, 6A, 6B and the IMPI, J and H satellites (Bame et al., 1967; Montgomery et al., 1970) are used in order to examine regions within 571

A. GERANIOS

572

ELECTRON TEMPERATURE

0.5 -

COSMIC

MINIMUM

VLET\

RAYS

N.M.DATA, 0 FIG

1.

12 24 12 24 12 15 -17 MAY 1972 TIME, UT

CHARKTERISTIC

EXAMPLES

OF

97

I 1

0

I

% I

1

12 24 12 20-22 NOV. 1973

I

I

24 12 TIME, UT

I

24

VLET’s

VLPT’S, la.

Shock associated.

the solar wind which are characterised by an anomalously large electron temperature depression. TO define such regions from the 3 h average values of electron and proton temperatures the following criteria were chosen: (a) The temperature depression must occur simultaneously both for protons and electrons. (b) The minimum electron temperature 7” inside the VLET must be either one half of the temperature outside, or T, 5 6 x lo4 K.

lb.

Shock not associated.

(c) The minimum proton temperature T, inside the VLPT must be either one third of the temperature outside, or T, I 2 x lo4 K. The selection of these events was not restricted to time periods following the passage of interplanetary shock fronts past the detector (Table 1). As a whole 32 events have been identified and their main characteristics are presented in Table 2 (id. number of event, year-date-hour of onset, period of duration, minimum temperature of electrons,

Search for the origin of VLET’s

TOSUN

18

FIG.

2.

PROJECTION DURING

m-m

VLET

00

06

ECJXX EVENT

12 UT 23 - 21 JUNE 1971 PLANE

ON

OF

IMF

VE~OR

24 JUNE 1971.

minimum temperature of protons, shock identification, observation of an increase in the interplanetary magnetic field (B), the proton density and the He’+/H+ ratio, and finally observation of cosmic ray flux decreases at neutron monitor energies). Events l-15 are identified by VELA and 16-32 by IMP satellites. Because the quality of the BELA data is worse than that of the IMP satellites, both the onset time and the duration of the identified events are estimated only roughly for events 1-15. Shocks are identified by an abrupt increase of the solar wind velocity and an associated Storm Sudden Commencement, and are considered to be, possibly, related to the VLET if they are observed 10-20 h before the onset of the VLET (SGD, 1969-1974). An interplanetary magnetic field (IMF) intensity increase is defined when the field amplitude B exceeds a value of 6y (1-y = lo-’ Gauss), a proton density increase if q exceeds 5 particles cmm3. An increase in the He”/H’ ratio above 12% occurs generally only during events associated with an interplanetary shock (the ratio He2+/H+ is available only for the IMP satellites during the period 19 April 1971-8 May 1974). CR decreases of an amplitude more than 2% recorded by neutron monitors have also been included to see if there is any correlation with VLET’s Two representative samples of interplanetary measurements during the occurrence of a VLET are shown in Figs la and b. Figure la shows a VLET which is associated with an interplanetary shock (id. No. 25, see Table 2) and Fig. lb shows an example of a VLET without an associated shock (id. No. 31). The event of Fig. la shows very clearly from the solar wind velocity plot that a shock front passed the satellite about

573

I2 h before the onset of the VLET. This shock front is also responsible for the increase in the electron and proton temperature as well as the proton density prior to the VLET. In this same plot it can be seen that the nucleonic component of the CR is affected by the shock passage, showing a Forbush Decrease inside which there is a second but less pronounced decrease, which coincides with the VLET event. The time of the shock front observations by the IMP I satellite and the time minimum T. and T, are indicated by broken lines. The event shown in Fig. lb, which is not associated with a shock, does not differ very much from the event shown in Fig. la except, of course, that the shock associated features are missing. It can be seen from Fig. lb that the nucleonic component of the CR intensity is decreased during the time of the VLET, just like the second decrease shown in Fig. la. Since no examples were found (when simultaneous proton and electron data were available) where the criterion “b” for the selection of VLET events did not simultaneously also yield a VLPT event and vice versa, criterion “a” (which demanded such simultaneous observations) was relaxed so that four events (3 VLET and 1 VLPT), where simultaneous proton and electron data was not available could be included in the analysis. A temperature distribution for all VLET and VLPT events is shown in Fig. 3. The upper part concerns the temperature distribution of protons and the lower of electrons. The continous histogram corresponds to minimum temperatures inside the depressed temperatures regions and the broken line histogram to averaged temperatures just outside the depressed region. It can be seen that the mean proton and electron temperature outside the VLPT-VLET domain is roughly the same (- 16 x 104K) and that the temperature reduction inside (relative to the value measured outside) is about a factor 10 for protons and a factor 3 for electrons. TABLE

1.

SUMMARY

OF EVENTS

574

A. GERANIOS TABLE2. MAINCHARACrERISrKS OF EVENTS DURATION ONSET

EVENT

YEAR

1

1969 1969 1969 1969 1970 1970 1970 1970 1970 1970 1970 1970 1970 1970 1970

23 15 29 5 11 21 19 2 18 4 31 13 17 20 15

1971 1971 1971 1971 1972 1972 1972 1972 1972 1972 1972 1973 1973 1973 1973 1974

29 17 24 6 18 7 24 25 16 3 25 1 14 21 21 8

i 4 5 7” 0 9 :s, 12 13 14 15 16 17 1,” 20 21 22 :: 25 26 27 28 29 30 ::

1971

19

Te. xlo4K

HOURS

Aug. Sept. Sept. act. Jan. Apr. May June June July July Sept. Sept. Oct. NOV. Apr.-m Apr.-m May -17 June-cm July-08 Feb.-c-a Mar.-15 Apr.-08 Apr.-19 May -04 Oct.-00 Dec.-a3 Apr.-15 Apr.-l4 June -Nov.-18 May03

::: 6.8 4.5 6.5 7.5 4.5 3.3 5.0 6.0

fi:: 6.6 5.0 6.1 5.8

1; 24 30 20

li

1.4 4.4

18

::: 6.3 4.6

:7’ 12

DENSITY

;:s

Y=S

no

no

Es

no

Ye*

no

Yes

Ye*

Ye* Ye*

Ye*

no

no

Ye*

1.8 3.7 3.0 2.0 0.3 1.5 2.0 1.8 1.0 0.8 1.0 0.8 1.6 1.3 0.8 0.8 0.8 3.1 1.3 1.3 2.5 1.7 1.6 2.1

::: 5.0

6 12 13 10

B

Ye*

Yes no no

no no no no

Ye*

;:s ff:.

Ye* Y=S

Ye* Y=S

no no

Y=S

no no

no no

Ye* no

no

Ye* no no

no

no no

Yes Ye* Yes

yes Ye* Yes no

no no no no

yes Yes

Ye* Ye*

&

*cl

no

no

Ye* Yes

Ye* Ye* Yes Ye* Ye= Ye* Ye*

ye* no

yes no no

$2, no no

no

Ye*

no

Ye* no

Yes

parallel to the field right down to the corona. The radial development of the T, and T, in such a region is then determined purely by the adiabatic expansion of this region through the radial outward convection by the solar wind. Figure 4 shows two possible magnetic field configurations which are disconnected from the coronal heat source. Evidence of the CR intensity decreases which were found to be associated with the VLET and

INTERP~TATION

One theoretical model which might explain the anomalously low temperature regions in the solar wind assumes that the regions where a VLET occurs is not connected magnetically to the sun, and that the temperature decrease for the electrons and protons is therefore a result of the lack of thermal connection-normally very high (for electrons)

PROTONS

ELECTRONS

0’

.2

.3

FIG. 3. ?-HEINSIDE

’ ) ’ I I’

.5

1

AND OUTSIDE

”

I

“1

2-3

RAYS

no

Yes no no

COSMIC

;:s

no

Yes no

He++/Ii+

Yes

Yes no

DECREASE

INCREASE

104K 0.8 2.5 3.5 2.0 0.8 4.0 1.2

5.0

I

SHOCK

Tp, x

I

J”..’ ‘I”~(“‘~‘~~~~~~~~~I~~~~!~~~~I”

TEMPERATURE

5

30 50 10 20 TEMPERATURE x10’ K’

DISTRIBUTION

OF

VLET’s AND

vLm.9.

575

Search for the origin of VLET’s A, B: possible a, b: time

configurations.

during

which

a

VLET VLPT PROTON DENSITYHe/H

An Ideal

possible

disconnected

configuration

with

IDEALPOSSIEZLE

VLPT events, points to configuration A, (isolated magnetic “blobs”. Originally the expression “blob” was used by Barouch and Burlaga, 1975, for a region in which the IMF intensity is high) as being the more likely configuration and therefore we shall consider the physical processes occurring during the expansion of such “blobs” and compare the model with the results of the plasma measurements (on a statisticasl basis). Electron and proton data is investigated separately and the temporal (and therefore also spatial evolution of the inside temperatures during the solar wind expansion) is compared with that given by standard solar wind models (Hartle and Barnes, 1970; Hundhausen, 1972b) for the outside temperatures (Fig. 5). The point (radial position) where the two temperatures are equal (at least on the basis of the models used) must be the point where the particles “inside” have been decoupled thermally from the corona, i.e. this point defines the origin of the “blob”-if such “blobs” are indeed the major cause of VLET’s and VLPT’s. Furthermore, the model assumes that this point is the same for both protons and electrons so that by treating the two particle components separately we can obtain an independent check on the validity of the “blob” model. We assume that “blobs” expand with the solar wind and that they contain a constant number of particles. Inside this volume the following conditions exist: y=5/3

Piq = qiKLT,

where Pi is the V, is the r is the qi is the K is the

DECREASE

are

characterized.

magnetic

AND

regions

from the Sun.

FIG.4. AN

Pi vi’ = const.

two closed

INCREASE

C.R

pressure volume temperature mol-number of particles Bolzmann constant

IMF CONFIGURATION.

L is the Loschmidt constant qiL is the total number of particles (subscript i indicates inside the “blob”). From equations (1) and (2) we obtain

v-’ (l/r)

T VT-’ = const.

(3)

dTJdt+T,(d/dt)w-‘=O

(4)

dTJdt = -F

E)

(5)

I

Model 1

We assume that “blobs” expand adiabatically. This implies that the rate of pressure equalization across the boundary of the “blob” (l/r& is much smaller than the rate of the adiabatic expansion

(I)

103L

ia

IO'

IO0

DISTANCE

FIG.5.

THE ELECTRON

AND

102

IO3

FROM THE SUN, R.

PROTON

~ONRADIALLYFROMTHESUNACCORDINGTO

B-MODEL.

TEMPERATURE VARIA-

HARTLEAIW

576

A. GERANIOS

(l/7,& i.e. l/rP~~ 11~. We then have for the volume changes of the “blob”, s,Vdvlat=2,rdr,dt,

(6)

where r is the radial distance from the Sun. Equation (6) is derived assuming a constant solar wind radial velocity. From equations (5) and (6) we obtain: d’ltJY&= - 2(y - 1) dr/r,

(P. “P,). The procedure here to derive the distance r, has to take into account not only the condition of adiabatic expansion but also pressure equ&y across the boundary of the “blob” everywhere (Pi = P,, actually Pi = P, = Q*KT* + B2/811, Spitzer 1962, but the magnetic pressure term inside the “blob” is almost the same, q* being number density). Analogues to equation (6) were obtained for the above model (see appendix)

or (l,~dV,d~=(a+2~,~l/,dr,d~,

?; = T*(r,r,f-2’Y-“.

(7)

la Electrons. Outside the “blob” in the “normal” solar wind we use the model of Hartle and Barnes (1970) to define the radial dependence of the solar wind electron temperature (Fig. 5), this yields TAT0 = (r/r,}-’

for

2% I‘~I

TJT, = (r/ro)s-2(7-1’.

TJT, = (r/r,)-“,

(16)

TJT 0 = (r/r 0)~--(s+2)(r-‘)‘y, for

2% 5 r c 38%. (17)

TJT, = (r/r )@+(**2xY--l)tr , for *

38% zzr
DATA ANALYSIS

for

2&=r<38%

(lo)

38%sr
(11)

Q = 0.349. TL/T, = (r/rJ8,

(15)

2b Protons. Because the total pressure and, therefore, the radial development of the “blobs” is controlled by the electrons we follow the same procedure as in 2a, using the proton temperature model (Ha&e and Barnes, 1970). Equation (15) becomes with equations (10) and (11)

(9)

again the Hartle and Barnes model, for protons (Fig. 51, we

or

(8) becomes finally

‘&= T~(r,ro)-~(2+~~‘-1)/V~~.

(8)

where T, is the temperature outside the “blob”, R,, is the radius of the Sun and T, is the (reference) temperature at r = r,. Assuming that at r = r,, where the “blob” is formed (according to the above arguments) the temperature inside the “blob” is the same as that outside we have from equation (7) and (8).

for

@= 1.272, and equation

with which equation

(14)

(5) and (14) we have

dT,/1; = -(~+2)(y-l)/~dr/r, Ti = To(r,r~)-(Y-1)(*+2)‘y,

1000%

E = 0.316,

lb Protons. Using (1970) temperature have

2a EZectrons. From equations

l/~~>>l,~,+

(7) becomes

T,,T, = (r,rJ”-2”-1’,

for

2R,,sr<38%,

TJT, = (r,r,)8-2’y-“,

for

38% 5 r< lOOO&,.

(12) (13) Model 2 In this model the rate of pressure equalization across the boundary of the “blob” is assumed to be much greater than the rate of the adiabatic expansion (1,~~ >>l/7&. The dominant part of the solar wind thermal pressure is that due to the electrons, because their number density is the same as that of the protons (charge neutrality) but their temperature is greater.

The

temperatures prior to (T,) and just after (T,‘) a VLET or VLPT event are generally not equal, we used both values for our estimates of the “outside” temperature and thus determined two radial distances from the Sun, r, and r,‘, for each event within which the “blobs” may be formed. Thus by substituting the measured data for r = 214% into equation (9) for electrons and (12) or (13) for protons (Model l), we obtain two ranges r, -to’ in which the “blobs’” must be formed (one for electrons, one for protons) for each event. (For Model 2, equations (16), (17) and (18) are used.) As described in the Interpretation section, the radial distance range within which the data place the formation point of a “blob” is calculated separately for electrons and protons in order to check whether or not both ranges overlap. A substantial overlap is a necessary criterion for the “blob” hypothesis to be valid. For Model 1 (adiabatic expansion) we use equation (9) for electrons and solve for TdT,--measured values at r =214&. This yields r, and r,’ for a T, and T,‘. Similarly, for

577

Search for the origin of VLET’s

100

20 -g 18

70 Lz-

G

6

80

16

5

6 2

60

14 12

3 w

2 L

40

8

2.

6

0

4

E

2

x

10 f

9 g

20

8 0

10-l

10’

100 DISTANCE

Od

102

FROM

THE

SUN,

R.

FIG. 6. FREQUENCY DISTRIBIJTIONSOF THE FORMATION DISTANCE OF mm’s AND VLET’s AND FOR MODELS 1 AND 2.

protons we use equations (12) or (13) as the case may be. For Model 2 (instantaneous pressure equilibrium across the boundary of the “blob”) we use equations (16)-(18) to determine r, and r,,’ for electrons and protons respectively. Using all available data we obtain (for each Model) two histograms of the formation distance of “blob”, one derived from electron data, the other from proton data (Fig. 6). For Model 1 the most probable distance for protons (VLPT-events) is about 8% while for electrons (VLET-events) it is approximately 80%. For Model 2, the corresponding values are about 0.5% and approximately 40% respectively. Reference to Fig. 6 shows that there is virtually no overlap between the two corresponding

electron and proton histograms. This leads to the conclusion that “blobs” i.e. isolated regions of solar wind plasma cannot be the cause of VLET’s. In order to test whether the observed histograms differ if we separate out shock associated events from those where no interplanetary shocks were found the histogram of the corresponding sub-sets of data were computed and compared (Figs. 7 and 8). The comparison showed no measurable difference except of a shift of about 20% toward the sun of the maxima of the electron histograms for shock associated cases and for both Models, and we must conclude therefore that regardless of the “blob” propagation picture (Model 1 or Model 2) and regardless of shock association our statistical analysis shows that magnetically isolated regions (disconnected from the corona) cannot be responsible for the formation of VLET’s or VLPT’s which are observed at 1 a.u. 10-Z

I P ::

34 30

D

70 a= *’

22

2

‘4

v 5

18

E 10 6 2 10-l

100 DISTANCE

10' FROM

102 THE

SUN,

R.

FIG. 8. FREQUENCY DLSTRIBIJTIONS OF THE FORMATION DISTANCE

OF VLPT’S

AND

VLET’s

AND SHOCK CONNECTED

FOR SHOCK

EVENTS

DISCONNECTED

FOR MODEL

2.

DISCUSSION

20 2

16

12

8

OL

100

’ ’ ’ I

I1I1’

IO'

’ ’ ’

DISTANCE

FIG.

7.

TANCE

FREQUENCY OF vL+pT’S

FROM

DISTRIBUTIONS AND

102

THE

’ ’ J

SUN,

R.

OF THE FORMATION

VLET’s MR

AND SHOCK CONNECTED

““”

SHOCK

DIS-

DISCONNECIED

EVEN-l-S FOR MODEL

1.

The phenomenon that huge electron temperature depression appear to follow some interplanetary shock waves was discussed by Montgomery et al. (1974) who suggested that a magnetic merging may produce a closed magnetic structure and thus isolate the electrons from their coronal heat source. Gosling et al. (1973) suggested that adiabatic cooling of solar wind protons and electrons does proceed many interplanetary shocks precisely because the thermal connection with the solar corona is broken by a closed magnetic configuration. This picture is to some extent corroborated by anisotropy observations of protons with energies 0.29 < Er, < 0.5 MeV and electrons with energies Ee >0.22 MeV (Krimigis et al., 1976); in most instances there are Sunward flows which were preceded or followed by sustained anti-Sunward flows

578

A. GERANIOS

suggesting a close loop-type structure in the interplanetary magnetic field. However, no real conclusive evidence has been presented as yet, so that the model of closed magnetic loops remains no more than a suggestion at the present time. In order to improve that situation multi-spacecraft measurements of the IMF must be correlated with solar wind properties, in particular measurements of the plasma temperature as well as the galactic and solar energetic particles modulations and anisotropies. In the present analysis we have investigated a large number of VLET and VLPT events, both those associated with shocks and those without any obvious interplanetary shock connections. Assuming a mean solar wind velocity of 400 km s-l, we obtain a size for the VLET (see Table 2) which varies between 0.06-0.5 a.u. From the available interplanetary magnetic field we found only one or possibly two cases in which the direction of the field shows the required signature of closed configurations (f. ex. Fig. 2). Measurements also show that satistically CR decreases are associated not only with those VLET’s, which follow a shock wave, but also with VLET’s not connected with any intense interplanetary perturbation. (Fig. lb). Analysis of those examples where the He’+/H+ ratio was available shows a clear correlation between a He*+/H+ increase and the presence of an interplanetary shock wave (Table 2) in agreement with Gosling et al. (1973). According to the experimentally measured proton temperatures at 1 a.u. just before and after the VLPT’s they are on the average the same as these for electrons (T, = T, ~1.6~ 105K, Fig. 3). This value is characteristic for the one-fluid model (Hundhausen, 1972a) and is about 4 times greater than the value predicted by the two-fluid model of Hartle and Barnes (1970). According to a statistical analysis of Bame et al. (1969) they found that for disturbed interplanetary periods (solar wind speed greater than 370 km s-l) the mean proton and electron temperatures are the same. In fact nearly all the analyzed VLET periods of the solar wind velocity exceeded this value. Strong er al. (1966) claimed that proton temperatures can rise above 1O’K at 1 a.u. and Sturrock ef al. (1966) in the connected theoretical work mentioned that these temperatures can extend even to 106K, that the relative energy source must be nonthermal and probably not close to the Sun. Several authors proposed that proton heating in the region r>25% takes place by means of internally generated unstable waves (Hundhausen, 1968; Forslund, 1970; Hollweg et al., 1970). Our opinion is that

I Oo

/ I I I I I, I I 20’ 40 60 80 100 OUTSIDE

VLET

I

/

120

I I 140

x 10”

FIG. 9. Tusr OFPRESSUREEOUALITYINSIDEANDOUTSIDE OF VLET’s.

protons are heated by electrons by means of waves, but there is yet no exact and concrete explanation for this process. In this work we have examined the feasibility of the closed magnetic loop or “blob” model, and have concluded that it is unlikely to be correct. In Model 2 of our analysis we assumed rapid pressure equilization across the boundary of the “blob” and can check this model requirement using available data. The results are presented in Fig. 9 which shows inside and outside pressure for all VLET’s where complete data was available. Our final remark, however, is that irrespective of the propagation model used, our present analysis does not support the closed magnetic field or “blob” model. Acknowledgements-I would like to express my gratitude to G. E. Morfill for the usefull discussions and suggestions on this work as well as for the corrections of the manuscript, H. J. V61k for the invitation to the Heidelberg Max-Planck-Institut fiir Kemphysik and suggesting the above research work. I am also grateful to N. J. Martinic for the several fruitful discussions and computing assistance and to M. D. Montgomery for the availability of the VELA and IMP satellites plasma data. REFERENCES

Bame, S. J., Asbridge, J. R., Felthauser, H. E., Hones E. W. and Strong, I, B. (1967). Characteristics of the Plasma Sheet in the Earth’s Magnetotail. J. geophys. Res. 72, 113. Bame, S. J., Asbridge, J. R., Hundhausen, A. J. and Montgomery, M. D. (1969). Electron and proton temperatures in the disturbed Solar Wind (abstract). Trans. AGU, SO, 301. Barouch, E. and Burlaga, L. (1975). Causes of Forbush Decreases and other Cosmic Ray variations. J. geophys. Res. 80, 449. Feldman, W. C., Asbridge, J. R., Bame, S. J. and Montgomery, M. D. (1973a). Double ion streams in the Solar Wind. J. geophys. Res. 78, 2017.

579

Search for the origin of VLET’s Feldman, W. C., Asbridge, J. R., Bame, S. J. and Montgomery, M. D. (1973b) Solar Wind heat transport in the vicinity of the Earth’s bow shock. J. geophys. Res. 78, 3697. Forslund, D. W. (1970) Instabilities associated with heat conduction in the Solar Wind and their consequences. .I. geophys. Res. 75, 17. Gosling, J. T. Pizza, V. and Bame, S. J. (1973) Anomalously low proton temperatures in the Solar Wind following interplanetary shock waves, evidence for magnetic bottles? J. geophys. Res. 78, 2001. Gosling, J. T. and Roelof, E. C. (1974). A comment on the detection of closed magnetic structures in the Solar Wind. Solar Phys. 39, 405. Hartle, R. E. and Barnes, A. (1970). Nonthermal heating in the two-fluid Solar Wind model. J. geophys. Res. 75, 6915. Hollweg, J. V. and Vijlk, H. J. (1970). Two new plasma instabilities in the Solar Wind. Nature, Land. 225,441. Hundhausen, A. J. (1968) Direct observations of Solar Wind particles. Space Sci. Rev. 8, 690. Hundhausen, A. J. (1972a), Coronal expansion and the Solar..Wind, in Physics and Chemistry in Space. Vol. 5, p. 53. Springer, New York. Hundhausen, A. J. (1972b). Coronal expansion and the Solar Wind, in Physics and Chemistry in Space. Vol. 5, p. 63. Springer, New York. Krirnigis, S. M., Sarris, E. T. and Armstrong, T. P. (1976). Evidence for closed magnetic loop structures in the interplanetary medium (abstract). Trans. AGU, 57, 304. Montgomery, M. D., Asbridge, J. R. and Bame, S. J. (1970). Vela 4 Plasma observations near the Earth’s bow shock. J. geophys. Res. 75, 1217. Montgomery, M. D., Asbridge, J. R., Bame, S. J. and Feldman, W. C. (1974). Solar Wind electron temperature depression following some interplanetary shock waves: evidence for magnetic merging? J. geophys. Res. 79, 3103. S.G.D., Department of Commerce. National Oceanic and Atmospheric Administration Environmental Data Service, 1969-1974. Spitzer, L. (1962). Physics of Fully Ionized Gases. Interscience, New York. Strong, I. B., Asbridge, J. R. Bame, S. J., Heckman H. H. and Hundhausen, A. J. (1966). Measurements of proton temperatures in the Solar Wind. Phys. Rev. Letts 16, 631. Sturrock, P. A. and Hartle, R. E. (1966). Two-fluid model of the Solar Wind. Phys. Rev. L&s 16, 628.

APPENDIX The following properties of the solar wind and the model assumptions listed were used, to arrive at the final form of equation (14) 1. Radial dependence of q* is given by: 7)0*/q,,* = (r/r&’

(Sturrock et ai.. 1966)

q* = the number density. 2. Conservation of the number “blob” yields:

of particles

in the

q,*v, = qi*vi. 3. Assuming the same number density inside and outside the “blob” at the “formation point” r = r, we have * * qi.0 = qo.0. 4. Equations P, = rl,*KT,, P, = qo*KT,, Li = qi * vi, from equations (1) and (2) we have K = (P;‘YVJq&L)qY-‘)‘y, P,, V, being the initial pressure and volume of the “blob” or T =(P~“V~qi*KVi)[q~*KT,rY-‘)‘y. Pi =(qi*KP~“V~q,*Kvi)[q~*(r/r~~-zK7~~~-1)~ qa*KT, = (q,*KT,)“‘V~V,[q~*(rIr,)-ZKT,1’ -“y q,*(r/r,)-‘KT,

= (q~*KT,)“‘V~V,[q~*(r/r~)-ZKT,3 X[q~*(r/r,)-zKT,]-“v

VJV, = (T~Ta)“y(r/rO)z’Y. and with equation (8) from the main text, Vi/V, = (r/r )(E+2)‘~ l/V0(dVi!dr)=(e~2)ly

l/r(r/r0)(ef2)‘~,

l/V,(dV,/dr) = (E +2)lyll,VilV,, l/Vi(dVi/dr) = (E +2)lyl/r. This yields finally l/V,(dV,/dt)

= (E +2)/r l/r(dr/dt).