Observations of the solar-wind turbulence near the sun

OBSERVATIONS OF THE SOLAR-WIND TURBULENCE NEAR THE SUN

T h e s i s by

P h i l i p S i d n e y C a l l a h a n

I n P a r t i a l F u l f i l l m e n t of t h e R e q u i r e m e n t s f o r t h e Degree o f

D o c t o r o f P h i l o s o p h y

C a l i f o r n i a I n s t i t u t e o f Technology P a s a d e n a , C a l i f o r n i a

1974

( S u b m i t t e d F e b r u a r y 1,1974)

Acknowledgements

I have morethan t h e usual number of people t o thank f o r t h e i r a s s i s t a n c e during my s t a y a t Caltech -and f o r my s t a y i n g here a t a l l . We a l l remember t h e War, the Draft, and t h e Great D r a f t Lottery of 1969:

I l o s t t h e l o t t e r y , but ( a s most of t h e white, educated middle c l a s s d i d ) avoided t h e War. Prof. M. Cohen, m y f i r s t mentor, a s s i s t e d me i n g e t t i n g a job a t JPL. Prof. Ward Whaling has spent t h e last f o u r y e a r s bending r u l e s i n my favor so I could keep t h e job. To both

I am g r a t e f u l .

Many people a t J 7 L have helped me i n t h e course of t h i s work.

I would e s p e c i a l l y l i k e t o thank Don Trask and Pete MxcDoran f o r t h e i r s a s s i s t a n c e and encouragement.The d a t a f o r t h i s t h e s i s would not have e x i s t e d without t h e hard work of Warren Martin and A r t Zygielbaum. I a l s o thank Jack L o r e l l of t h e Mariner Mars 1971 C e l e s t i a l Mechanics Experiment f o r a s s i s t i n g me i n obtaining t h e d a t a from t h a t mission.

I am indebted t o Dorothe Horttor of JPL who has worked beyond t h e c a l l of duty typing t h e t h e s i s f o r me.

I have b e n e f i t t e d g r e a t l y from my a s s o c i a t i o n with my advisor Prof. J. R. J o k i p i i . H i s comments on t h i s manuscript were extremely valuable i n making it coherent and readable. I aFso thank Prof.

D. 0. Muhlemn f o r h i s comments. Profs. James Gunn and PeterGoldreich have done much t o s t i m u l a t e my l e a r n i n g about a s t r o p h y s i c s ; I thank them f o r t h e i r p a t i e n c e ,

Many f r i e n d s have made my s t a y a t Caltech more p l e a s a n t . I e s p e c i a l l y thank Paul Schechter f o r h i s companionship and f o r t a k i n g a d a t e t o t h e p r t y where I met my wife, Judy. She deserves s p e c i a l

c r e d i t f o r keeping me sane and happy enough t o f i n i s h t h i s endeavor.

During t h e course of my graduate study I have been supported

By a n NSF Fellowship, t u i t i o n fellowships from C a l Tech, and my job a t JPL. Computer funds were supplied by JPL. The J e t hro- p u l s i o n I a b o r a t o r y , C a l i f o r n i a I n s t i t u t e of Technology i s operated under NASA c o n t r a c t , number NAS 7-100. I a l s o acknowledge p a r t i a l support Prom NASA Grant E R 05-002-160.

ABSTRACT

The solar-wind turbulence near the sun i s investigated with d a t a obtained near t h e superior conjunctions of Mariners 6, 7, and 9.

The data a r e time h i s t o r i e s of t h e change i n t h e e l e c t r o n columnar content between t h e e a r t h and spacecraft. The d a t a were obtained with a group-phase technique which i s s e n s i t i v e only t o t h e change i n t h e columnar content. The measurement technique i s discussed. The theory of power s p e c t r a i s outlined. The r e l a t i o n s h i p between t h e temporal power spectrum of t h e columnar content data and t h e camoving wave-

number spectrum of t h e s o l a r wind i s derived. It i s found thak comoving spectrum i s well represented by a parer-law ( ~ ( v ) a v-@) of index

8 ^L 3.9 ^{Jt 0.2.} Cornpariaon of the o v e r a l l average s p e c t r a l amplitude

near t h e sun ( r ^h" 0.15 a . ~ . ) t o t h a t near 1 a , u , shows t h a t t h e turbulence declines with h e l i o c e n t r i c distance as An(r) ^a! r ^{-2. 383.11} _{9 ig-}

noring time v a r i a t i o n s . I n t h e region near t h e sun (0.07 A x 5 0 . 2 2 a. u . ) ~ n ( r ) declines more slowly. It i s suggested t h a t t h e r e i s a region of enhanced turbulence near t h e sun. The M&riner 9 s p e c t r a l amplitudes c o r r e l a t e with Zurich sunspot number. The

data a r e used t o investigrnte t h e r e h t i o n s h i p between MtMath oialcium plage regions and density enhancements i n t e r s e c t i n g t h e l i n e of s i g h t . The r e l a t i o n s h i p of the present observations t o t h e o r i e s of s o l a r wind heating and t o i n t e r p l a n e t a r y s c i n t i l l a t i o n observation8 i s discussed.

TABU2 OF CONTENTS

I. INTRODUCTION TO THE SOLAR WIND AND SUMMARY OF THE PRESENT INVESTIGATION

11. DRVID DATA: PHYSICS,IMPLEMENT!ATION, AND COLLECTION A . Fjhysics of t h e DRVID Technique

B. Implementation of t h e D R V D Technique

t'.

C o l l e c t i o n of DRVID Data 111. DRVID DATA REDUCTION

A . DRVID Records from Multiple Range Acquisitions B. Power Spectra af I n d i v i d u a l Records

C. Addition and Averaging of DRVID Spectra D. Mapping A u t o c o r r e ~ t i o n Xags t o the Sun

IV.

RELATIONSHIP OF IDRVID OBSERVATIONS TO THE SOLAR-WIND TURBULENCE

A . I n t e r p r e t a t i o n of DRVTD Observations of the S o l a r -Wind Turbulence

B. Predicted Spectra f o r D i f f e r e n t Velocity and Density Models

C . The Relation of D R V m Spectra t o

--

^{In Situ}

Spacecraft Measurements

V. DRVID 1VIEASUREMEWS OF THE SOLAR-WIND TURBULENCE A . Q u a l i t a t i v e Description of DRVID Data

B. The Average DRVID Spectrum

C. Radial V a r i a t i o n of t h e D R V m Spectra Near t h e Sun

D. Temporal V a r i a t i o n of t h e DRVID Spectra -4 E. The Existence of' S p e c t r a l Minima Near 3x10 Hz F. Summary of DWID Spectral Observations

Page

VI. THE ATTEMPT TO LOCATE DENSITY ENHANCEMENTS ALONG THE RAY PATH AND RELATE THEM TO FEATURES ON THB SUN'S SURFACE

A , Locating Density Enhancements with t h e Autocorrelation Function

B. Mapping from t h e Ray Path t o t h e S u n ' s Surface

C. Solar Surface Data

D. R e s u l t s of the Mapping of Autocorrelation Peaks

V I I

.

IMPLICATIONS QF DRVID OBSERVATIONS FOR CURREXI?

;PROBLEMS IN UNDERSTANDING T I E SOLAR WIM,

A . Turbulence and t h e Heating of t h e Solar Wind B. The Spectrum of t h e Solar-Wind Turbulence

C. Suggests f o r Future Work

REFERENCES

1

I: IMTRODUCTION TO T H E S O U R WIND AM> SUMMARY OF THE: RBSENT INVESTIGATION

Ever s i n c e Biemnann (19

51,1957)

suggested from h i s study of i o n i c comet t a i l s t h a t t h e r e was a continuous emission of p a r t i c l e s from t h e sun, t h e s o l a r wind has been t h e o b j e c t of i n c r e a s i n g study.

Many new techniques, including t h e one used i n t h i s i n v e s t i g a t i o n , have come i n t o use, but Brandt (1970) p o i n t s o u t t h a t s t u d i e s of comets can s t i l l provide valuable information about t h e

m

l a r

wind, p r t i c u h r l y a t l a r g e heliographic d i s t a n c e s o r h i g h latitudes.

Brandt

(1970)

provides an i n t e r e s t i n g h i s t o r y and e x p o s i t i o n of c u r r e n t i d e a s about the s o l a r wind. Much r e c e n t work and r e f e r e n c e s t o e a r l i e r work can be found i n S o l a r Wind (sonnet, ei;

--

al., eds.,

1972

) ^a

The d e s c r i p t i o n of t h e s o l a r wind (as well a s t h e term) was f i r s t given by Parker i n t h e l a t e 1950's. H i s m r k i s well summslxldzed

i n Parker (1963). The key f e a t u r e of t h e s o l a r wind, a s opposed t o other t h e o r i e s of t h e s o l a r corona c u r r e n t i n t h e late l95Ots, i s i t s continuous, supersonic expansion t o zero pressure a t i n f i n i t y . Parker reasoned t h a t such a model was necessary s i n c e t h e p r e s s u r e a t i n l ' i ~ l i i ; , ~ of s t a t i c models i s much l a r g e r than -t;hitt expectcd i n 1.ni;er-

s t e l l a r space.

P a r k e r ' s a n a l y s i s of t h e s o k r wind may be b r i e f l y summarized a s follows. The s o l a r atmosphere i s t r e a t e d a s a s i n g l e , inviscous, s p h e r i c a l l y symmetric f l u i d which must obey t h e equation of

c o n t i n u i t y ,

2 n ( r ) v ( r ) r 2 = c o n s t a n t ,

and t h e momentum equation,

where m i s t h e proton mass, T i s t h e temperature, G i s t h e gravi- P

t a t i o n a l constant, and F i s t h e sum of o t h e r f o r c e s ( i f any). Note t h a t t h e r e i s no energy equation so T ( r ) must be s p e c i f i e d . When t h e s e equations a r e solved t o g e t h e r , with F = 0 , a temperature d i s t r i - b u t i o n which f a l l s o f f l e s s r a p i d l y t h a n r-I ( t h e s o l a r wind i s

roughly isothermal), and t h e requirement of z e r o p r e s s u r e a t

r = a, a s o l u t i o n with a " c r i t i c a l point" i s found. A t t h i s p o i n t (r = r c ) t h e f l u i d v e l o c i t y , assumed t o be less t h a n t h e speed of sound o r i g i ~ l c t l l y , cxceeds t h e l o c a l sound spc:c?d; t h e wind t h a n ex- pands t o r - m w i t h supersonic speed. The behavior i c l i kc. t l t r ~ t ,

of a Lava1 nozzle i n which t h e f l u i d reaches t h e sound speed a t t h e p o i n t of minimum a r e a and then expands outward supersonically. The

s o l a r g r a v i t a t i o n a l f i e l d provides t h e " t h r o a t " f o r t h e subsonic t o supersonic t r a n s i t i o n of t h e s o l a r wind. The c r i t i c a l r a d i u s f o r t h e s o l a r wind i s r 3 R Barnes (1973) notes t h a t i f

C 49'

t h e e x t e r n a l f o r c e F i s l a r g e enough, o r i f t h e coronal temperature i s high enough ( ~ s t r k e r , 19631, t h e supersonic flow may be shut off.

3

P a r k e r ' s a n a l y s i s of t h e s o l a r wind i s important f o r s e v e r a l reasons. F i r s t , i t explains many observations made by i n t e r p l a n e t a r y s p a c e c r a f t and r a d i o astronomy techniques. Second, i t shows the importance of c r i t i c a l p o i n t s f o r understanding physical phenomena.

Such a n a l y s i s may prove very u s e f u l i n other gas dynamics problems i n a s t r o p h y s i c s such a s " g a l a c t i c winds" and t h e nuclei of a c t i v e g a l a x i e s . Third, s t e l l a r winds may have a s i g n i f i c a n t e f f e c t on t h e e v o l u t i o n of t h e sun and o t h e r s t a r s , and t h e e f f e c t can be estimated by t h e use of solar-wind models. The e f f e c t on s o l a r r o t a t i o n could be p r t i c u l a r l y important ( ~ r a n d t , 1970). Thus, t h e s o l a r wind provides a u s e f u l a s t r o p h y s i c a l Laboratory i n which t o t e s t our t h e o r e t i c a l t o o l s .

While many observations have confirmed t h e broad out l i n e s o f P a r k e r ' s model, they have turned up new and i n t r i g u i n g probl.ems a s w e l l , General-ly, t h e s t a t e of observations i s only good enough t o r a i s e quest ions, not conclusively resolve them. g o h r wind observa- t i o n s t y p i c a l l y y i e l d t h e values of various q u a n t i t i e s shown i n Table 1.1. However, a s the v a r i a t i o n s of t h e s e values show, the solar-wind flow i s not smooth but f l u c t u a t e s . The amplitudes of t h e changes may be of t h e order of t h e mean.

The f l u c t u a t i o n s a r e p a r t i c u l a r l y i n t e r e s t i n g because they a r e probably r e l a t e d t o t h e energy source which maintains t h e corona a t i t s observed temperature of 1-2 x 10 K.

6

Brandt (1970) presents a

4

Table 1.1

Observed P r o p e r t i e s of t h e Solar Wind Near 1 a.u.

Density n

-

^{5 - 8 4 +50 cm-3}

Velocity v

- 300-400

^{+250 -50 krn s -1}

E l e c t r o n Temperature T e - 1.5 x 10 5 K Proton Temperature T - 4 x 10

4 + b l o 5

P - - - 0

Magnetic F i e l d <IBI>- 5-7 y Magnetic F i e l d F l u c t u a t i o n s < 6 ~ ~ >

-

^{1-3 y}

5

schematic p i c t u r e of

-

⁵ minute ( t h e time s c a l e of t h e g r a n u l a t i o n seen i n t h e photosphere) o s c i l l a t i o n s generated i n t h e sun's convection zone propagating i n t o t h e lower corona where t h e y a r e d i s s i p a t e d and turned i n t o thermal energy. A number of o t h e r a u t h o r s (see t h e review by Barnes, 1973) have used waves a s a d i r e c t energy source f o r t h e s o l a r wind. The exact mechanisms f o r generating and d i s - s i p a t i n g t h e waves have not y e t been made c l e a r . It i s l i k e l y t h a t the f l u c t u a t i o n s observed i n t h e s o l a r wind a r e t h e remnants of t h i s turbulence which have escaped d i s s i p a t i o n because of t h e i r long wavelengths or p a r t i c u l a r wave mode ( ~ e l c h e r and Davis, 19'71).

U n f o r t u m t e l y , it i s very difficu1.t t o observe fluctuaLions nearer t o t h e sun than a few s o l a r r a d i i , Newkirk (1967) reviews t h e s t r u c t u r e of t h e corona and t h e methods used t o measure i t . New techniques have been introduced but l i t t l e progress has been made.

The inner corona and t h e r e g i o n o u t t o r - 5 R can be i n - 0

v e s t i g a t e d with e c l i p s e and coronagraph photographs, The former a r e of much higher q u a l i t y but a r e , of course, somewhat hard t o o b t a i n . Also, e c l i p s e s do not l a s t long enough t o see s i g n i f i c a n t temporal changes. Coronagraph p i c t u r e s can be obtained d a i l y but contain information only out t o r

-

^{2 R}

.

Altschuler and h r r y (1972),

0

and Perry and Altschuler (1973) have developed a technique f o r ob- t a i n i n g the three-dimensional coronal e l e c t r o n d e n s i t y f o r r

5

2 R

0 from coronagraph observations, i f t h e s t r u c t u r e i s assumed t o be s t a t i c f o r ¹⁴ days.

6

Radio o b s e r v a t i o n s - - s c i n t i l h t i o n s , two-frequency i n t e r f e r m e t r y , s p a c e c r a f t t r a c k i n g , Faraday r o t a t ion, pulsar timing--are l i m i t e d by t h e large phase changes introduced by f l u c t u a t i o n s i n t h e e l e c t r o n d e n s i t y near t h e sun. The very turbulence which one wishes t o observe proves t o be a n o b s t a c l e . Observations near r ⁼ 1.4 R have been made

0

by James (1970) using r a d a r b a c k s c a t t e r , but t h e d a t a a r e d i f f i c u l t t o i n t e r p r e t . Useful r a d i o data g e n e r a l l y e x i s t only f o r r

2

5 R

0' S u f f i c i e n t phase s t a b i l i t y t o measure t h e turbulence we11 occurs f o r

r 2

^LO R

.

The d a t a presented here have t h e point of the r a y

€3

p a t h ' s c l o s e s t approach t o t h e sun i n t h e range

14

R 4 r

5

46 ^R 0" 0' T h e o r e t i c a l s t u d i e s have shown t h a t waves a r e probably a n i m - p o r t a n t source of energy f o r t h e s o l a r wind and corona. I n order t o have a complete understanding of t h e s o l a r wind we m u s t l e a r n more about the temporal and s p a t i a l d i s t r i b u t i o n of wave energy. Since one cannot probe t h e convection zone and it i s d i f f i c u l t t o observe t h e inner corona, one would l i k e t o understand t h e f h c t - a t i o n s in t h e s o l a r wind: What i s t h e i r r e l a t i o n s h i p t o t h e underlying average s o l a r

wind7 How a r e they r e l a t e d t o t h e sun o r f e a t u r e s i n t h e lower corona?

What i s t h e i r amplitude and frequency d i s t r i b u t i o n with h e l i o c e n t r i c d i s t a n c e ? I n t h i s study new information which w i l l h e l p i n answering t h e s e questions i s presented, and i t s r e l a t i o n s h i p t o t h e s e questions i s discussed.

7

The data c o n s i s t of records of t h e change i n the i n t e g r a t e d e l e c t r o n columnar content, bI = J A n ( 8 ) d s , where An(s) i s t h e change i n t h e e l e c t r o n d e n s i t y a t point s

,

along t h e l i n e of s i g h t t o Mariners 6, 7, and 9. The d a t a from Mariners 6 and 7, t h e Mariner Mars 1969 ( h e r e a f t e r , m69)! s p a c e c r a f t , were obtained i n 1970 M R ~ through July. The d a t a from Mariner 9, t h e Mariner Mars 1971 (MM71) s p a c e c r a f t , were obtained i n 1972 August through October. The d a t a were obtained when the r a y paths went near t h e sun. This geometry probed regions of t h e s o l a r wind which a r e u s u a l l y a c c e s s i b l e only t o l e s s d i r e c t methods of observation ( r a d i o source s c i n t i l l a t i o n s ) .

Here we present a b r i e f summary of t h e o b s e r v a t i o n a l f i n d i w s nf t h i s study. The observations a r e presented i n d e t a i l i n Chapter V . A prelimjnary a n a l y s i s of the ~ ~ d a t a 6 9was published i n Callakmn e t al. (1972). The present work r e v i s e s and extends t h a t a n a l y s i s .

The data give t h e s c a l e s i z e of the d e n s i t y f l u c t u a t i o n s r a t h e r d i r e c t l y . It i s found t n a t t h e t y p i c a l size for a l a r g e change i n d e n s i t y i s L -1.5-3.0 x 10 6 km, i n agreement with previous s p a c e c r a f t observations ( ~ n t r i l i g a t o r and Wolfe, 1970).

The d e n s i t y f l u c t u a t i o n s were a l s o i n v e s t i g a t e d with power s p e c t r a l a n a l y s i s . The power spectrum gives the mean squared amplitude per u n i t frequency a t a given frequency. Since denaity f l u c t u a t i o n s a r e

approximately frozen i n t o the s o l a r wind ( t h e convection v e l a c i t y i s much l a r g e r t h a n the propagation speeds of any waves), frequency and s i z e a r e r e l a t e d by L - vSM/". Power s p e c t r a a r e t h a n a conven- i e n t way of c h a r a c t e r i z i n g t h e amplitudes of t h e f l u c t u a t i o n s t h a t occur

on various s c a l e s . It has been found t h a t a power l a w ( ~ ( v ) a v - $ 1

i s a good r e p r e s e n t a t i o n of t h e low frequency v

5

10'~ HZ) power spectrum of t h e solar-wind d e n s i t y , v e l o c i t y , and magnetic f i e l d . A power law f i t s t h e observations presented here i f p = 3.9

-

+ 0.2, a value c o n s i s t e n t with both s p a c e c r a f t and r a d i o s c i n t i l l a t i o n observations.

The data provide important information about t h e r a d i a l dependence of t h e amplitude of t h e low frequency d e n s i t y f l u c t u a t i o n s . Infor- mation i s obtained both by comparing t h e o v e r a l l average of the ob-

s e r v a t i o n s near t h e sun t o s p a c e c r a f t d a t a near 1 a , u , and by comprl.ng t h e amplitudes of small groups of t h e observations. By comparing t h e observations near t h e sun t o t h e r e s u l t s of I n t r i l i g a t o r and Wolf'e

(1970) it i s found t h a t t h e d e n s i t y f l u c t u a t i o n s decrease a s

r -2'381-0*11

-

between r = 0.15 and r = 1 a . u . , i f long-term time vari- a t i o n s a r e unimportant. I f t h e o v e r a l l f l u c t u a t i o n amplitudes a r e approximately p r o p o r t i o n a l t o sunspot number ( s e e below), which

changed about of f a c t o r of

4

between t h e I n t r i l i g a t o r and Wolfe measurements and t h e ~ ~ and 6 W l 9 measurements, t h e n t h e r a d i a l decrease of the f l u c t u a t i o n s i s about r -2

.

Anderson e t a l . (1972) using ~ ~ 6 9 d a t a and Anderson and I a u (1973) using MM71 d a t a found

-2.O+0.2 that thelarge-scale v a r i a t i o n o f t h e s o l a r d n d d e n s i t y i s r

- .

9

The r a d i a l v a r i a t i o n of t h e f l u c t u a t i o n s near t h e sun i s d i f f e r e n t f o r t h e m 6 9 and t h e MM71 observations. The r a d i a l d e c l i n e f o r t h e

MN69

d a t a i s not w e l l determined, b u t it i s approximately r-2 t o r ^-2.5 For t h e bM71 d a t a the d e c l i n e i s r -1'5f0'2,

-

f o r 0.07 r _C 0.22 a . u . , considerably slower than t h e large-scale r a d i a l dependence of t h e d e n s i t y f l u c t u a t i o n s . The

~ ~

observations a r e a l s o c o n s i s t e n t

6 9

w i t h t h e near-sun r a d i a l f a l l - o f f being l e s s s t e e p t h a n t h e large-scale r a d i a l d e c l i n e . These observations suggest a region of enhanced turbulence near t h e sun.

It i s found t h a t t h e amplitude of t h e s p e c t r a v a r i e s on a time s c a l e of weeks i n t h e MM71 d a t a . However, t h e amplitudes of t h e ~ 6 9 and MM7l d a t a taken 2 y e a r s a w r t agree f a i r l y well. The short-term v a r i a t i o n s a r e c o r r e l a t e d with Zurich sunspot number and 2.8 GHz r a d i o f l u x . The v a r i a t i o n i n t h e sunspot number between t h e MM09 and MM71 observations i s only about 3%. The s p e c t r a l amplitudes

change by roughly t h e same amount, but no f i r m conclusion on t h e f l u c t u a t i o n amplitude-sunspot r e h t ionship can be drawn from theee d a t a . The s p e c t r a l amplitudes do not depend on heliographic Latitude.

Also, no c o r r e l a t i o n with solar-wind v e l o c i t y measurements or s o h r x-ray f l u x i s found.

10

Chapter V I I d i s c u s s e s t h e r e l a t i o n s h i p of t h e s e f i n d i n g s t o previous observations of t h e s o l a r wind and t o c u r r e n t i d e a s about t h e h e a t i n g and a c c e l e r a t i o n of t h e s o l a r wind. The

p i c t u r e of t h e t u r b u l e n c e suggested i n Chapter V I I i s r e p r e s e n t e d schematically i n Figure 1.1. Short wavelength waves h e a t t h e lower corona, h e l p t o a c c e l e r a t e t h e s o l a r wind, and f e e d t h e longer wavelength t u r b u l e n c e very near t h e sun, 0 . 0 1

5

^r

5

0.2 a.u.

(1 a . u . = 216 R )

.

A h i g h l y t u r b u l e n t r e g i o n i s formed o u t t o about 0

r

-

^{45 R}

.

Since most of t h e remaining energy i s i n t h e longer wave- 0

l e n g t h waves, t h e t u r b u l e n c e i s only slowly d i s s i p a t e d and reduced by expansion ( r -2 ) as it propagates t o 1 a . u . The d e t a i l e d mechanisms of t h i s p l a u s i b l e p i c t u r e a r e d i f f i c u l t t o f i l l i n . More o b s e r v a t i o n s l i k e those r e p o r t e d h e r e and o t h e r s nearer t h e sun would be a g r e a t h e l p i n understanding t h e processes a t work.

I n Chapter VT a n o t h e r a t t e m p t i s made t o r e l a t e t h e obacrva- t i o n s t o t h e sun. Because t h e measurements of t h e columnar c o n t e n t change a r e made by a s i g n a l propagating t o and from t h e space- c r a f t , it i s p o s s i b l e t o l o c a t e d e n s i t y enhancements a l o n g t h e r a y path. The suspected d e n s i t y enhancements d e t e c t e d a r e mapped t o t h e sun a l o n g Archimedian s p i r a l s ( t h e apparent t r a j e c t o r y of t h e r a d i a l l y moving plasma a s seen from t h e r o t a t i n g s u n ) . The p o i n t s on t h e sun a r e compared t o t h e l o c a t i o n s of Mclvlath calcium p l a g e r e g i o n s t o s e e if dense streams o r i g i n a t e i n s o l a r a c t i v e r e g i o n s . The c:onclusion of t h e i n v e s t i g a t i o n i s that ^{Lhe originu 1} d a t a r e c o r d s a r e not Long enough t o g i v e r e l i a b l e detection of' s tremns

.

F i g u r e 1.1. Schematic p i c t u r e of s o l a r - w i n d t u r b u l e n c e . Turbulence i s enhanced i n t h e r e g i o n

1-64 5%.

S p i r a l l i n g o f magnetic f i e l d L i n e s because of s o l a r r o t a t i o n i s a l s o shown ( n o t

.

R a d i a l s c a l e i s Logarithmic i n u n i t s o f 1 a . u . = 216 Ro

1 .

12

The o r g a n i z a t i o n of t h i s work i s a s follows. Chapter I1 d e a l s with t h e d a t a a c q u i s i t i o n equipment and procedures. Chapter 1 x 1 d e s c r i b e s t h e d a t a r e d u c t i o n used. The theory of power s p e c t r a i s presented. The computer programs used a r e described. Chapter IV i s a formal development of t h e r e l a t i o n s h i p between t h e t h r e e - dimensional wavenumber power spectrum or" t h e s o l a r wind and t h e temporal power spectrum of t h e s p a c e c r a f t d a t a . Chapter V g i v e s t h e r e s u l t s of t h e d a t a a n a l y s i s . The r a d i a l and temporal v a r i a t i o n s of t h e s p e c t r a a r e discussed. The r e s u l t s a r e summarized a t t h e end of Chapter V . Chapter V I d i s c u s s e s t h e f i n d i n g of d e n s i t y enhancements and mapping t o t h e s u n ' s s u r f a c e . Chapter V I I d i s c u s s e s previous observations, t h e o r e t i c a l f i n d i n g s , and t h e information provided by t h e p r e s e n t work about t h e solar-wind turbulence.

13

11. DRVID DATA : PHYSICS, IM-NATION, AND COWTION

Differenced

-

^Range

-

^Versus

- -

I n t e g r a t e d Doppler

-

(DRvID) i s a group-phase technique developed a t JPL t o measure changes i n t h e e l e c t r o n columnar content between t h e e a r t h and a d i s t a n t space- c r a f t . The o r i g i n a l purpose of t h e technique was t o c o r r e c t Dop- p l e r radio-tracking d a t a f o r columnar content changes. The f i r s t s e c t i o n of t h i s chapter d i s c u s s e s t h e physics of t h e group-phase technique. The advantages and disadvantages of t h i s method of columnar content measurement a r e pointed o u t . I n t h e second

s e c t i o n t h e hardware used t o implement t h e DRVID technique i s des- cribed. I n t h e f i n a l s e c t i o n t h e o p e r a t i o n a l c o n s t r a i n t s on obtain- ing DRVID d a t a near t h e s u p e r i o r conjunction of MM71 a r e discuesed.

A . PHYSICS OF THEDRVID TECHNIQUE

DRVID i s a group-phase technique f o r measuring t h e change i n e l e c t r o n columnar content. The technique was f i r s t discussed by Muhleman and Johnston (1966). The discussion here follows MacDoran

( 1970

It can e a s i l y be shown from Maxwell's equations t h a t t h e d i s - persion r e l a t i o n f o r a tenuous plasma i s given by

14

where w i s t h e plasma frequency, w2 = 4 m e 2 /m

,

and ne i s t h e

P P e e

number d e n s i t y of e l e c t r o n s .

The phase v e l o c i t y of a n electromagnetic wave i s v ⁼ w/k, o r P

from equation (2 . l )

The l a t t e r expression holds i f w >> ^tu a s i s t h e case f o r space- P

'

c r a f t cammunications i n t h e s o l a r wind. The group v e l o c i t y , v ⁼ dcu/dk, i s given by

g

I n t r a c k i n g s p a c e c r a f t two types of d a t a a r e obtained--"rangen and " ~ o p p l e r " . Range d a t a a r e measurements of t h e time-of-flight

f o r a r a d i o signal from t h e e a r t h t o t h e s p a c e c r a f t and back. The d i s t a n c e (range) t o t h e s p a c e c r a f t i s deduced by multiplying t h e measured time by t h e speed of l i g h t .

Doppler d a t a c o n s i s t of measurements of t h e s p a c e c r a f t ' s l i n e - o f - s i g h t v e l o c i t y taken a t frequent i n t e r v a l s . The data a r e obtained by t r a n s m i t t i n g a known frequency from t h e e a r t h t o a phase-locked transponder aboard t h e s p a c e c r a f t . When t h e s i g n a l i s received back a t t h e e a r t h another phase-locked r e c e i v e r counts t h e zero crossings of t h e d i f f e r e n c e between t h e received and t r a n s m i t t e d

frequencies. The count i s accumulated over some i n t e r v a l ; t h e Doppler frequency f o r t h a t i n t e r v a l i s t h e c y c l e count divided by t h e time span.

It i s c l e a r from t h e above explanation t h a t range d a t a a r e a s s o c i a t e d with t h e group v e l o c i t y , Doppler, with t h e phase v e l o c i t y . S i n c e t h e d i f f e r e n c e i n t h e v e l o c i t i e s i s p r o p o r t i o n a l t o t h e e l e c t r o n d e n s i t y , comparison of range and Doppler d a t a should given i n f o r - mation about t h e e l e c t r o n d e n s i t y d i s t r i b u t i o n .

The apparent one-way range t o t h e s p c e c r a f t i s

ds

-

g 2

-

^v

-

² J d s +

r a y p a t h

2 2

where again it i s assumed t h a t ^w /co << 1. This may be w r i t t e n as P

where R i s the t r u e d i s t a n c e t o t h e s p a c e c r a f t , t i s reception time a t t h e e a r t h ,

n ( s , t ) i s t h e e l e c t r o n d e n s i t y a t p o s i t i o n s along t h e raypath, w = 2vf, f being t h e r a d i o frequency, and

2 7

A = e /&me = 2 . 0 2 x 10 i n cgs u n i t s .

~ ( t ) i s the e l e c t r o n columnar content. Since t h e plasma e f f e c t i s q u i t e small, t h e i n t e g r a l i n equation (2.5) i s c a r r i e d out along the s t r a i g h t l i n e path from t h e e a r t h t o t h e s p a c e c r a f t .

The v e l o c i t y i n f e r r e d from a Doppler measurement i n t h e presence of a changing columnar content i s e a s i l y shown t o be

where a dot denotes time d i f f e r e n t i a t i o n . I f t h e range d i f f e r e n c e between times t, and t i s computed by i n t e g r a t i n g t h e v e l o c i t y of

V

equation (2.6), t h e r e s u l t i s

The range d i f f e r e n c e batween t h e s e times can also be obtained from equation (2.4) :

17

Eqs. ( 2 . 7 ) and (2.8) have opposite s i g n s on t h e terms involving t h e columnar content. From Eqs. (2.7) and (2.8) one can form Differenced R r nge minus (versus) I n t e g r a t e d Doppler t o e x p l i c i t l y e x h i b i t t h e columnar content e f f e c t

This expression r e l a t e s one-way DRVID d a t a t o round t r i p columnar content changes. Thus, DRVID d.ata give the c o l u ~ s content a t

time t o f f s e t by the unknown content a t to.

In p r a c t i c e t h e expression f o r DRVID i s somewhat more compli- c a t e d t h a n equation (2.9) i n d i c a t e s because of a frequency m u l t i - p l i c a t i o n i n t h e s p a c e c r a r t transponder. I n order t o f u l l y s e p a r a t e transmission t o and from t h e s p a c e c r a f t , t h e transponder coherently m u l t i p l i e s t h e received frequency by b ^E 2401221 b e f o r e rebroad- c a s t i n g it. A similar s c a l i n g i s done t o the reference frequency a t t h e earth-based r e c e i v e r s o t h a t the c o r r e c t Doppler c y c l e count

is obtained. Because t h e e f f e c t of t h e plasma on the s i g n a l pro- pagation i s p r o p o r t i o n a l t o f-', t h e expression f o r DRVID i s modi- fied t o be ( ~ a c ~ o s a n , 1970)

where t h e s u b s c r i p t s r e f e r t o t h e transmission t o ("u") and from ( "d" ) t h e s p a c e c r a f t . I f it i s assumed t h a t AIU = &Id = h1(t)/2, one o b t a i n s

The v a l i d i t y of t h e assumption AIU ⁼

hid

^{i s} somewhat questionable f o r long r a y p t t h s that p a s s near t h e sun. However, t h e d a t a contain no way t o s e p a r a t e &IU from

Aid,

so t h e approximation w i l l be used.

The r e s u l t i n g e r r o r should always be l e s s than @ s i n c e t h e bracketed q u a n t i t y i s equation (2.11) is n e a r l y 1.

A s equation (2.11) stands it r e l a t e s t h e round t r i p columnar content change b 1 ( t ) i n u n i t s of cmm2 t o t h e value of D R V I D ( ~ ) (one-

way)

i n c m . Actually, D H v I D ( ~ ) i s measured j.n round t r i p time u n i t s (usually microseconds). Equation (2.11) gives f o r t h e columnar

-

content change

where t h e u n i t s of quantitiehs a r e i n square brackets, c i s t h e speed of l i g h t , and DRVID(t) is t h e value output by t h e equipment described

i n t h e next s e c t i o n . F i n a l l y , t h e q u a n t i t y of primary i n t e r e s t i s t h e one-way columnar content change, d 1 ( t ) / 2 ^r A I ~ ~ ( ~ ) . The numerical r e s u l t r e l a t i n g DRVID(~)' t o AILW(t) i s

x D R v I D ( ~ ) [observed, ~ s e c ]

.

While t h e DRVID method does not give t h e t o t a l column c o n t e n t , it has some advantages over o t h e r charged-particle measuring tech- niques which do not involve d i f f e r e n c i n g ( ~ s c ~ o r a n , 1970) or a round t r i p measurement. F i r s t , any r e a l motion of t h e spacecraft i s cancelled. The method i s not s e n s i t i v e t o o r b i t determinati-on e r r o r s or s p a c e c r a f t a t t i t u d e c o n t r o l motions as range or Doppler r e s i d u a l s a r e . Second, any propagation e f f e c t which a f f e c t s both phase and group v e l o c i t i e s i n t h e same way, e.g., t h e e a r t h ' s troposphere o r g e n e r a l r e l a t i v i s t i c delay, w i l l not e n t e r t h e mea- surement of ( t )

.

Third, any equipment delays which a r e common

t o both t h e range and Doppler systems w i l l be removed by d i f f e r e n c i n g . F i n a l l y , it w i l l be shown i n Chapter VI t h a t t h e round t r i p n a t u r e of t h e DRVID measurements presents t h e p o s s i b i l i t y of d e t e c t i q : where l o c a l i z e d e l e c t r o n d e n s i t y disturbances a r e along t h e r a y path.

Equation (2.9) and i t s d e r i v a t i o n make c l e a r t h e two p r i n c i p a l t h e o r e t i c a l l i m i t a t i o n s of DRVID d a t a . F i r s t , DRVID d a t a record only t h e changes i n t h e columnar content from t h e i n i t i a l , unknown value. DRVID d a t a cannot r e v e a l t h e average p r o p e r t i e s of t h e medium through which t h e r a d i o s i g n a l propagates. Second, a continuous count of Doppler c y c l e s i s necessary s o t h a t ~ ( t ' ) i s known a t every i n s t a n t , and t h e i n t e g r a l i n equation (2.7) can be c a r r i e d o u t . . I f t h e Doppler count i s l o s t , t h e DRVID d a t a w i l l have some a d d i t i o n a l (and unknown) o f f s e t b e s i d e s I ( t o ) . I n p r a c t i c e t h i s

l i m i t a t i o n i s not q u i t e s o severe a s it seems because t h e slope of a ( t ) i s preserved a c r o s s a Doppler d i s c o n t i n u i t y , and the data on e i t h e r s i d e can b e a d j u s t e d t o match t h e s l o p e s , However, t h e r e a r e p r a c t i c a l l i m i t a t i o n s t o t h e accuracy of such adjustments

,

^and

one would hope t o make as few of them as p o s s i b l e .

In addition t o these t h e n r e t i c a l lhi+atictns there i s aae major p r a c t i c a l l i m i t a t i o n t o the DRVID method--the d i f f i c u l t y i n measuring d i s t a n c e s of t h e order of 1.5 x 1013 cm with accuracy and s t a b i l i t y . Equation (2.8) makes no allowances f o r drifts i n t h e equipment o r f o r e r r o r s of measurement. D r i f t s show up a s spurious a d d i t i o n s t o ~ ( t ) . E r r o r s of measurement i n ~ ( t ) mask any r e a l v a r i a t i o n s of ~ ( t ) . These l i m i t a t i o n s

kll

be discussed f u r t h e r i n t h e next s e c t i o n .

B

.

IMPLEMENTAT I O N OF THE BRV _{ID TECHNIQUE}

The implementation of t h e DRVID technique r e q u i r e s a s o p h i s t i - c a t e d range measuring system which has t h e s t a b i l i t y and accuracy needed t o make meaningful columnar content measurements. Such a system was developed by W. L. l h r t i n of JPL _(Martin, 1969a, lg@b, 1970). It i s t h e Binary-Coded S e q u e n t i a l Acquisition Ranging System, more canmonly known a s t h e "Mu system" o r "Mu machine". The device was f i r s t i n s t a l l e d on t h e

64

rn antenna (DSS 14) a t Goldstone,

C a l i f o r n i a i n 1969, September. It was used on a research and development b a s i s during t h e

m69

Extended Mission and throughout

t h e MM71 mission.

A block diagram of t h e Mu-system taken from MacDoran and Martin (1970) i s shown i n Figure 2.1. Only t h e b a r e s t e s s e n t i a l s of t h e system a r e discussed here; d e t a i l s may be found i n MacDoran and Martin (i970), and % r t i n (1969a, t).

The key t o the system i s "Doppler r a t e aiding", a scheme

whereby the received Doppler frequency i s used i n generating a model of t h e received range code. The r a t e - a i d i n g allows t h e ranging code components t o be s e n t s e q u e n t i a l l y . ('The r e s t of t h e Mu system's name comes from t h e f a c t t h a t t h e period of t h e nth camponent i s Pn = 2" x 64/fs, where f s i s a r e f e r e n c e frequency i n t h e r a d i o t r a c k i n g system. ) However, it has another property with r e s p e c t t o DRVID measurements: Since t h e range code model i s generated using

F i g u r e 2.1. Block diagram of t h e Binary-Coded S e q u e n t i a l A c q u i s i t i o n (MU) Ranging System. Block num- b e r s a r e r e f e r r e d t o i n t h e t e x t . ( ~ r o m M a c b r a n and arti in,

1970.

)

23

t h e received Doppler frequency (blocks (1-5) of Figure 2.1)

,

^{t h e}

repeated measurement of a s i n g l e range code cmponent shows only t h e e f f e c t s of a changing columnar content.

The range measurement i s made by comparing t h e phase (block (6) ⁾ of a received range code cmponent t o t h e phase of t h e code model.

J u s t b e f o r e t h e measurement i s begun ( t ) t h e model code i s syn-

0

chronized (switch (9)) with t h e t r a n s m i t t e d code (block ( l o ) ). The i n i t i a l phase d i f f e r e n c e between t h e received code and t h e model i ~ a

a measure of t h e range t o t h e s p a c e c r a f t . I n t h e absence of colurnmr content changes t h e r a t e - a i d i n g system (blocks (2-4) ) w i l l cause t h e same phase t o be measured a t any f u t u r e time. Phase o f f s e t s a r e a measure of changes i n t h e columnar content. Suppose t h e columnar

content i s i n c r e a s i n g . Equation (2.6) shows that t h e received Doppler frequency w i l l decrease; t h e model code w i l l have i t s phase retardedk as time goes on. The received range code w i l l be delayed by the increased columnar content and i t s phase advanced. Thus a

phase measurement a t some Later time w i l l show a p o n i t i v e o f f s e t r e l a t i v e t o t h e i n i t i a l determination, i n d i c a t i n g an increasing columnar content

.

During a range measurement ( " a c q u i s i t i o n " ) t h e Mu machine sends a s e r i e s of code components ( t y p i c a l l y 6-10, up t o a maximum of 18) beginning with t h e highest frequency one. When it ^has c m -

p l e t e d t h e transmission of t h e lower frequency components, it re- t u r n s t o t h e high frequency one and reestimates i t s phase a t

i n t e r v a l s determined by t h e operator. These reestimations a r e t h e DRVID d a t a .

The Mu system automatically provides DRVU) observations. To s e e i f they a r e meaningful measurements of AI(t) t h e s t a b i l i t y and accuracy of t h e system must be investigated. Such t e s t s were performed by k t i n (1970) during t h e e a r l y part of t h e MM69 Extended Mission, 1969 September through 1970 January.

I n a bench t e s t of t h e Mu system i t s e l f t h e s t a b i l i t y was

measured t o be b e t t e r than 10 psec h r - l . A f t e r t h e Mu system was i n s t a l l e d a t DSS 14, t e s t s were made of t h e t o t a l ground r a d i o system delay, and i t s short- and long-term s t a b i l i t y . From 1969 November 22 t o 1970 January 24 Martin (1970) found an average t o t a l system delay o f 3.34 psec with a standard deviation of 26 nsec.

A l i n e a r f i t showed a slope of -15 nsec month -1

.

Short term s t a b i l i t y t e s t s were done on 1969 November 4 f o r 8 h r and 1969 December 6 f o r 3.5 ^hr. Peak d r i f t r a t e s of 2.9 nsec h r -1 a n d 3 . 7 nsec hr-'were found. Peak v a r i a t i o n s were 7.6 nsec and 9.2 nsec, r e s p e c t i v e l y . The t o t a l system delay was found not t o vary s i g n i f i c a n t l y with received ranging power. ( ~ e l a y i n t h e

spacecraf't transponder does depend on t h e received s i g n a l l e v e l , but no s i g n i f i c a n t power v a r i a t i o n s should occur i n one day. )

F i n a l l y , a Cest of t h e r e a c q u i s i t i o n accuracy of t h e ground system was made on 1$9 November 12 f o r one hour ; t h e received s i g n a l

2 5

l e v e l was a l s o varied. A systematic d r i f t with peak t o peak amplitude of 3 nsec was found. No completely s a t i s f a c t o r y ex- p l a n a t i o n f o r t h e d r i f t was found, but i t should be noted t h a t i t i s not i n c o n s i s t e n t with o t h e r measurements reported above, Thus t h e s h o r t term system s t a b i l i t y and r e a c q u i s i t i o n accuracy would allow one-way columnar content changes bILW

2

9 x 10l2 cm-2 t o be measured over periods of a few hours. Unfortunately t h i s i s n o t t h e only l i m i t on t h e accuracy of DRVU) d a t a .

The c h i e f c o n s t r a i n t on t h e accuracy of DRVID d a t a i s f l u c t u - a t i o n s of t h e measured phase caused by noise on t h e received ranging

s i g n a l . Figure ^2.2 i s a p l o t of t h e c a l c u l a t e d ( k r t i n , 1971) standard d e v i a t i o n (a) of t h e range observations a s a f u n c t i o n of received s i g n a l l e v e l and i n t e g r a t i o n (averaging) time on each r e e s t i m a t i o n of t h e high frequency code. Near t h e nuperior con- j unctions of ~ ~and 6 MM71 9 t h e received ranf4ing power was i n t h e

range -185 t o -200 dbm. To o b t a i n a u s e f u l number of DRVID p o i n t s during a t r a c k i n g pass a n i n t e g r a t i o n time near 100 sec ( t y p i c a l l y 60 or 120 s e c ) was used. Thus t h e expected standard d e v i a t i o n of t h e d a t a i s i n t h e range 50 t o 100 nsec, f a r g r e a t e r than t h e mea- sured equipnent d r i f t s . I n f a c t observations near s u p e r i o r con- junction showed t h e noise t o be worse, o f t e n by a f a c t o r of 2 , than c a l c u l a t e d . P a r t of t h i s e f f e c t may be due t o t h e increasing system temperature as t h e antenna i s pointed toward t h e sun. ^Wow-

F i g u r e 2 . 2 . Mu r a n g i n g system p h a s e J i t t e r ( RMS o f p o i n t s f r ~ m t h e i r a v e r a g e ) a s a f u n c t i o n o f r e c e i v e d s i g n a l

power and i n t e g r a t i o n t i m e f o r an assumed system n o i s e t e m p e r a t u r e o f 30 K . Values of p a r a m e t e r s t h a t o b t a i n e d d u r i n g DRVID o b s e r v a t i o n s a r e i n

t h e boxed r e g i o n . J i t t e r n e a r t h e Sun was g e n e r a l l y found t o be l a r g e r t h a n t h e s e p r e d i c t i o n s .

2 7

e v e r , even looking i n t h e a n t i s o l a r d i r e c t i o n t h e curves of

Figure 2.2 proved t o be o p t i m i s t i c . The Doppler observations i n - troduce e s s e n t i a l l y no n o i s e i n t o t h e DRVID data.

C. COUCTION OF D R V D DATA

The DRVID d a t a used i n t h i s study were obtained during t h e

~ ~ and 6 W1 9 Extended Missions. The ~ ~ 6 9 data were obtained by P. F. MacDoran. A s a member of t h e C e l e s t i a l Mechanics Experiment, Team, I a s s i s t e d with t h e c o l l e c t i o n of d a t a during t h e MM71 mission.

Near t h e superior conjunction of W l 33 days of usuable D R V D d a t a were obtained. Seventeen days of data were c o l l e c t e d during t h e m69 mission. Table 2 . 1 l i s t s a l l t h e d a t a used i n t h i s stugy.

The columns of t h e t a b l e give ( I ) t h e GlvlT d a t e on which t h e pass

began; ( 2 ) t h e GM!I! hour i n which t h e p a s s began; (3) t h e length oL' the DRVID record; (It) t h e number of r e a c q u i s i t i o n s during t h e pass;

(5) t h e l e n g t h of t h e longest segment; (6) t h e t o t a l number of d a t a p o i n t s obtained during t h e pass ; (7) t h e standard d e v i a t i o n of t h e d a t a about i t s mean; and (8) t h e d i s t a n c e of c l o s e s t approach of t h e r a y path t o t h e sun ( q ) .

Near t h e s u p e r i o r conjunction of MM71 t h e r e were two competi- t o r s f o r the use of t h e Mu system: a group attempting t o d i f f e r - e n t i a t e among r e l a t i v i s t i c t h e o r i e s of g r a v i t y on t h e b a s i s of t h e time delay of t h e r a d i o s i g n a l as it passed near t h e sun and m y

experiment i n v e s t i g a t i n g the s o l a r wind near t h e sun. The r e l a t i v i t y experiment had p r i o r i t y . The team's s t r a t e g y f o r c o l l e c t i n g d a t a

2 8

was t h e opposite of mine: They wished t o make m n y independent range measurements during a day and t o make a s few reestimations of each value a s possible. I d e s i r e d a s i n g l e a c q u i s i t i o n with a s many reestimations a s p o s s i b l e . I n a d d i t i o n t o t h i s c o n f l i c t t h e r e were o t h e r c o n s t r a i n t s : Commands had t o b e s e n t t o t h e s p a c e c r a f t . DSS 14, t h e only s t a t i o n with a Mu system, was wanted f o r other t a s k s . The high power t r a n s m i t t e r (20-400 k ~ ) malfunctioned.

During c e r t a i n periods t h e spacecraft was occulted by Mars. Other experimenters d e s i r e d t h a t no ranging s i g n a l be s e n t . For ray paths very near t h e sun t h e phase-locked r e c e i v e r on t h e ground could not maintain phase-lock.

In s p i t e of t h e s e problems both t h e r e l a t i v i t y and DRVID _ex- p e r i m n t s have produced worthwhile r e s u l t s . Much of t h e c r e d i t belongs t o A . I. Zygielbaum of JPL who wrote a s p e c i a l program

f o r t h e Mu system which allowed it t o produce n maximum of data i n t h e time a v a i l a b l e . Because of t h e l a r g e amount of d a t a produced t h e DRVID experiment was given approximately t h r e e long (4-6 hr) uninterrupted segments of reestimation per week; on those days about 12 independent range values were acquired a l t o g e t h e r . On o t h e r t r a c k i n g days t h e d a t a were taken as t h e r e l a t i v i t y team wished but with t h e s t i p u l a t i o n t h a t a t l e a s t two and, ^{i f} p o s s i b l e f o u r or more reestimations of each value be made. On t h e s e days from 12 t o as many as 60 range values were obtained.

TABLE 2.1

Swnmary of a l l DRVID Data Used i n Study

(1) (2) (3) (4) (5 (6) (7) (8)

Date Hour Length

#

Reacgui- Longest Total Std. Dev. q ( w ) ( w ) ours) s i t i o n s Segment Points ()I sec)(a.u.)

TABLE

2.1 (cont.)

TABLE 2.1 (cont.)

32

111. DRVID DATA REDUCTION

To make a q u a n t i t a t i v e i n v e s t i g a t i o n of t h e s o l a r wind using DRVID d a t a extensive d a t a processing was necessary. Figure 3 . 1

i s a block diagram of the w e r a l l data reduction scheme. The e l e - ments of t h a t scheme w i l l be discussed i n t h i s chapter. F i r s t , a cgnputer program was needed t o use Doppler cycle counts t o make t h e range r e a c q u i s i t i o n s from a pass i n t o a continuous DRVm record.

Second, t h e a u t o c o r r e l a t i o n function and power spectrum of each record of ~ ( t ) were computed, Third, a program added together

i n d i v i d u a l power s p e c t r a t o produce s p e c t r a with increased s t a t i s - t i c a l r e l i a b i l i t y . The program a l s o computed t h e earth-Sun-

s p a c e c r a f t geometry s o t h a t v a r i a t i o n s of t h e averaged s p e c t r a with h e l i o c e n t r i c d i s t a n c e and o t h e r parameters could be i n v e s t i g a t e d q u a n t i t a t i v e l y . F i n a l l y , a program t o map p o i n t s along t h e e a r t h - s p a c e c r a f t r a y p t h t o t h e Sun's surface was used t o i n v e s t i s t e t h e r e b t i o n s h i p between f e a t u r e a on t h e Sun's s u r f a c e and disturbances

located along t h e r a y path. ( s e e Chapter V I f o r d i s c u s s i o n of t h e technique used t o l o c a t e t h e disturbances.)

These programs were coded i n FORTRAN V f o r t h e Univac 1108 computer a t JPL. Computer funds were supplied by t h e Deep Space Network and t h e C e l e s t i a l Mechanics Experiment of the W l mission.

Figure 3.1. Block diagram of d a t a reduction acheme.

34

None of t h e d a t a used i n t h i s study were c o r r e c t e d f o r t h e co1um.- nar content of t h e e a r t h ' s ionosphere. The t o t a l change i n t h e

ionospheric colwnnar content from z e n i t h t o near t h e horizon i s 13 -2

about 7 x 10 cm

,

l e s s than t h e noise on most DRVID records.

F'urthermore, when t h e s m c e c r a f t is near superior conjunction, t h e p a t t e r n of t r a c k i n g tends t o reduce t h e ionospheric columnar

content change during a day. Thus, it d i d not seem necessary t o remove t h i s e f f e c t from t h e d a t a .

A . DRVID DATA RECORDS FlROM IUnnTIPW RANGE ACQUISITIONS

Much of t h e DRVID d a t a from t h e W l mission was obtained i n very s h o r t segments ( s e e Table 2.1.). I n order t o make a continuous record of A I ( ~ ) it was necessary t o use Doppler cycle counts t o r e l a t e t h e segments. The technique i a simply a mechanization of t h e d e f i n i t i o n of DRVID.

The Doppler c y c l e count a t t h e beginning of each range a c q u i s i - tion was used t o f i n d t h e range c h a w e t h a t had occurred s i n c e t h e first a c q u i s i t i o n :

where DC (T. ) is t h e Doppler count a t T, and A i s t h e r a d i o wave-

1 1

l e n g t h ,

-

^{13 cm.}

%i

was t h e n reduced by t h e l a r g e s t i n t e g r a l number of range a n b i g u i t y u n i t s p o s s i b l e . The range ambiguity i s

due t o t h e f i n i t e length of t h e range code. The ambiguity i n t e r v a l i s f a r l a r g e r t h a n any conceivtzble columnar content change. The reduced value of ARDi i s t h e e f f e c t i v e i n t e g r a t e d Doppler range c h n g e from t h e beginning of t h e DRVID record t o time Ti.

The range d i f f e r e n c e f o r Ti was computed by s u b t r a c t i n g t h e i n i t i a l value of t h e f i r s t range a c q u i s i t i o n from t h e i n i t i a l value o f t h e a c q u i s i t i o n a t t i m e Ti. F i n a l l y , t h e d i f f e r e n c e of t h e range d i f f e r e n c e and t h e reduced value of M$,i give t h e DRVBD value a t t h e beginning of t h e segment. Other p o i n t s i n t h e segment are ccanputed by s u b t r a c t i n g t h e i n i t i a l range value f o r t h e segment from the value i n question and then adding t h e DRVID value f o r t h e beginning- of t h e segment. OF course, a t t h e beginning of t h e first segment t h e DRVID value i s zero. Figure 3.2a. shows a sample output o f t h e computer program which c a r r i e d out t h e prescription j u s t described.

Occasionally t h e Doppler cycle count was r e s e t during t h e day.

This introduced a n o f f s e t between t h e DRVID d a t a on e i t h e r s i d e of t h e r e s e t . O f f s e t s were e a s i l y d e t e c t a b l e and u s u a l l y f a i r l y easy t o r e p a i r t o within t h e data noise. A b e s t estimate of t h e jump3 based on both t h e values and t h e slope at t h e break, was a p p l i e d t o all1 d a t a p a s t t h e break. Data with many r e s e t s o r f o r which a r e -

c o n s t r u c t i o n was very d i f f i c u l t o r ambiguous were discarded, If t h e r e c o n s t r u c t i o n was somewhat d i f f i c u l t , s e v e r a l reasonable one8 were made; it was found t h a t t h e f i n a l power spectrum did not depend s i g n i f i c a n t l y on which of them was used,

DRV 1 D D A T A VS T I MEr W l T H POLYNOM l AL

F

I T

f l * IB

Figure 3.2a. An example of segmented DRVID data without the gaps filled.

The values are in microseconds and are twice the round trip range change. The solid line is a least-squares polynomial fit to the data points. At the top of the frame is infor- mation output by the plotting routine.

37

DQVIfJ D A T A VS T I M E , V l T H POLYNOMIAL F I T 7 - 7

1 a. m.

'igure 3.2b. The same DRVID d a t a a s i n Figure 3.2a b u t w i t h t h e gaps f i l l e d . Note t h a t t h e r e a r e now 442 p o i n t s a s opposed t o t h e a r i g i n a l

361.

_The s t a t i s t i c s of t h e p o i n t s a r e not recomputed a f t e r f i l l i n g t h e g a p s .

3 8

Several of t h e DRVID records show extremely l a r g e r a t e s of columnar content change. During such high r a t e s of change it i s l i k e l y that t h e Doppler counter w i l l l o s e phase lock and g i v e a n i n c o r r e c t cycle count. However, a l l t h e r e c o n s t r u c t i o n s used i n t h i s study a r e believed t o be e s s e n t i a l l y c o r r e c t : They do not contain e r r o r s due t o l o s s of phase lock i n t h e Doppler counter o r t o r e s e t s of t h e counter. A l l have been checked a g a i n s t range r e s i d u a l s and have t h e c o r r e c t sense of v a r i a t i o n and amplitude,

The program nornaa1l.y used t o perform t h e a u t o c o r r e l a t i o n and spectrum amlysis r e q u i r e s e q u a l l y spaced ( i n time) d a t a p o i n t s . It was t h e r e f o r e necessary t o f i l l t h e gaps between t h e segments, This was done by passing a low order polynomial through t h e seg- ments. The polynomial was t h e n evaluated a t equally spaced i n t e r - v a l s i n t h e gaps. The standard d e v i a t i o n of t h e real. d a t a fram t h e f i t was m u l t i p l i e d by a Gausaianly d i s t r i b u t e d pseudorandom number and added t o each point t o simulate d a t a noise. Figure 3.2b.

shows t h e r e s u l t s of f i l l i n g t h e gaps i n t h e data of Figure 3.2a.

A check was made t o be s u r e t h a t t h e g a p - f i l l i n g procedure d i d n o t a f f e c t t h e s p e c t r a of t h e DRVID records. The power spectrum program was modified t o accept data with gaps. (only those p o i n t s which matched with o t h e r r e a l p o i n t s were counted i n computing t h e a u t o c o r r e h t i o n function.) The r e s u l t i n g s p e c t r a of a l l t h e d a t a

l i s t e d i n Table 2 . 1 were e s s e n t i a l l y t h e same as t h e s p e c t r a of t h e equally s p c e d d a t a i n t h e Requency range 1 x

lom4

t o l x

lom3

Hz.

The c h i e f d i f f e r e n c e between t h e two s e t s of s p e c t r a was t h a t sane o f t h e s p e c t r a of t h e unequally spaced d a t a had peaks i n t h e f r e - quency range 1 t o 3 x

lo9

Hz. These peaks r e s u l t e d from t h e p e r i o d i c way i n which t h e range segments were acquired.

I n t h e discussion of t h e s p e c t r a i n Chapter V t h e s p e c t r a of t h e equally spaced d a t a w i l l be used. They a r e used because t h e peaks i n t h e s p e c t r a of t h e unequally spaced data i n t e r f e r e with t h e adding together of s p e c t r a . This averaging of t h e s p e c t r a was used

t o remove t h e high frequency noise and t o i n v e s t i g a t e t h e v a r i a t i o n of t h e s p e c t r a with d i s t a n c e f r a n t h e sun,

B, P o r n SFECTRA OF INDIVIDUAL RECORDS

DRVID data record t h e change i n t h e e l e c t r o n columnar content as a f u n c t i o n of time. This q u a n t i t y does not change i n anJr d e t e r - m i n i s t i c way and s o may be c l a s s i f i e d a s a random v a r i a b l e . The DRVID record shown i n Figure 3.2b i s a textbook example o f a sample

of a random v a r i a b l e .

A random v a r i a b l e , x ( t ) , m y be s p e c i f i e d by i t s moments

R N

given by

endat at

and P i e r s o l , 1966)

where t h e angular b r a c k e t s denote a n ensemble average. An ensemble average i s t a k e n over M i d e n t i c a l systems, measured a t t h e s p e c i f i e d arguments a s M tends t o i n f i n i t y . If t h e random v a r i a b l e i s

ergodic, t h e ensemble average may be replaced by a n average over t h e independent argument of any sample of t h e random v a r i a b l e ; i . e . , t h e q u a n t i t i e s

a r e a l l equal

endat at

and P i e r s o l , 1966), and we m y t a k e R N =

\.

If R defined i n equation (3.2) does not depend on t h e i n i t i a l value N

of t h e independent argument, t h e random v a r i a b l e i s s a i d t o be s t a t i o n a r y . Since i n p r a c t i c e one d e a l s almost exclusively with ergodic processes, a more u s e f u l concept i s s e l f - s t a t i o n a r i t y

endat at

and P i e r s o l , 1966) : The moments Rk of equation ( 3 . 3 ) do not depend on to when T i s reasonably l a r g e ,

It i s assumed t h a t t h e DRVUl records a r e samples from a n ergodic, s e l f - s t a t i o n a r y process. These assumptions a r e ueually t r u e of r e a l , p h y s i c a l l y i n t e r e s t i n g processes.

The two most important moments f o r c h a r a c t e r i z i n g data a r e R1 and Rg--the average value and t h e a u t o c o r r e l a t i o n function. For

DRVID data t h e average value has l i t t l e p h y s i c a l s i g n i f i c a n c e s i n c e DRVID data only record changes i n the columnar con