I N S T I T U T D ' A E R 0 N 0 M l E S P A T I A L E D E B E L G I Q U E 3 - A v e n u e C i r c u l a i r e
B • 1 1 8 0 B R U X E L L E S
A E R O N O M I C A A C T A
A - N° 253 - 1982
On the releyance of the MHD approach to study the Kelvin- Helmholtz instability of the terrestrial magnetopause
by
M. ROTH
FOREWORD
T h e paper entitled "On the relevance of the MHD approach to study the Kelvin-Helmholtz instability of the terrestrial magnetopause"
will be published in the "Bulletin de la Classe des Sciences de l'Académie Royale de Belgique".
A V A N T - P R O P O S
L'article "On the relevance of the MHD approach to study the Kelvin-Helmholtz instability of the terrestrial magnetopause" sera publié dans le "Bulletin de la Classe des Sciences de l'Académie Royale de Belgique".
VOORWOORD
Het artikel "On the relevance of the MHD approach to study the Kelvin-Helmholtz instability of the terrestrial magnetopause" zal gepubliceerd worden in het "Bulletin de la Classe des Sciences de l'Académie Royale de Belgique.
VORWORT
Das Artikel "On the relevance of the MHD approach to study
the Kelvin-Helmholtz instability of the terrestrial magnetopause" wird in
dem "Bulletin de la Classe des Sciences de l'Académie Royale de
Belgique" herausgegeben werden.
ON T H E R E L E V A N C E OF T H E MHD A P P R O A C H T O S T U D Y T H E K E L V I N - H E L M H O L T Z I N S T A B I L I T Y OF T H E T E R R E S T R I A L M A G N E T O P A U S E
b y
M. R O T H
A b s t r a c t
I t is s h o w n t h a t t h e u s u a l MHD a p p r o x i m a t i o n is n o t s u i t a b l e f o r t h e d e s c r i p t i o n o f t h e K e l v i n - H e l m h o l t z i n s t a b i l i t y o f t h e t e r r e s t r i a l m a g n e t o p a u s e . I n d e e d s u c h a d e s c r i p t i o n i m p l i e s an ideal m a g n e t o p a u s e w i t h a smooth c o n t i n u o u s v a r i a t i o n o f t h e plasma a n d f i e l d p a r a m e t e r s o c c u r i n g i n an e x t e n d e d c u r r e n t s h e e t . H o w e v e r , t h e a c t u a l m a g n e t o - pause a n d i t s a d j a c e n t plasma b o u n d a r y l a y e r a r e h i g h l y i r r e g u l a r , b o t h s p a t i a l l y a n d t e m p o r a l l y . T h e r e f o r e , f i n i t e ion L a r m o r r a d i u s e f f e c t s d o n o t r e p r e s e n t small c o r r e c t i o n s . I t is a r g u e d t h a t t h e s e s m a l l - s c a l e i n h o m o g e n e i t i e s can c h a n g e d r a s t i c a l l y t h e u s u a l l a r g e - s c a l e d e s c r i p t i o n o f t h e m a g n e t o p a u s e o s c i l l a t i o n s .
Résumé
On m o n t r e q u e l ' a p p r o x i m a t i o n h a b i t u e l l e MHD n ' e s t pas
a p p r o p r i é e a la d e s c r i p t i o n de l ' i n s t a b i l i t é de K e l v i n - H e l m h o l t z de la
m a g n é t o p a u s e t e r r e s t r e . En e f f e t , u n e t e l l e d e s c r i p t i o n i m p l i q u e u n e
m a g n é t o p a u s e idéale avec u n e v a r i a t i o n r é g u l i è r e et c o n t i n u e des
p a r a m è t r e s d u plasma e t d u champ se p r o d u i s a n t à l ' i n t é r i e u r d ' u n e
c o u c h e de c o u r a n t é t e n d u e . C e p e n d a n t , la m a g n é t o p a u s e r é e l l e et la
c o u c h e f r o n t i è r e de plasma q u i l u i e s t a d j a c e n t e s o n t f o r t e m e n t
i r r é g u l i è r e s , à la f o i s s p a t i a l e m e n t e t t e m p o r e l l e m e n t . C ' e s t p o u r q u o i les
e f f e t s d û s à l ' e x i s t e n c e d ' u n r a y o n de L a r m o r f i n i p o u r les ions ne
S a m e n v a t t i n g
Er w o r d t a a n g e t o o n d d a t de g e b r u i k e l i j k e MHD b e n a d e r i n g n i e t g e s c h i k t is v o o r de b e s c h r i j v i n g v a n de K e l v i n - H e l m h o l t z o n s t a b i l i t e i t v a n de a a r d s e m a g n e t o p a u z e . Een d e r g e l i j k e b e s c h r i j v i n g v e r e i s t een ideale m a g n e t o p a u z e met een r e g e l m a t i g e en c o n t i n u e v e r a n d e r i n g d e r plasma- en v e l d p a r a m e t e r s d i e o p t r e d e n in i n w e n d i g e v a n de u i t g e b r e i d e s t r o o m l a a g . De w e r k e l i j k e m a g n e t o p a u z e en de a a n - g r e n z e n d e plasmalaag is e c h t e r h o o g s t o n r e g e l m a t i g zowel in de r u i m t e als in de t i j d . Om d i e r e d e n e n s t e l l e n de e f f e c t e n , t e w i j t e n aan h e t b e s t a a n v a n een e i n d i g e L a r m o r s t r a a l , geen v e r w a a r l o o s b a r e c o r r e c t i e s v o o r . A r g u m e n t e n w o r d e n n a a r v o o r g e b r a c h t , d i e e r o p w i j z e n d a t k l e i n e schaal i n h o m o g e n e i l e i l e n d r a s t i s c h de g e b r u i k e l i j k e g r o o t s c h a l i g e b e s c h r i j v i n g v a n de m a g n e t o p a u z e o s c i l l a t i e s k u n n e n w i j z i g e n .
Z u s a m m e n f a s s u n g
Wir z e i g e n dass d i e MHD A p p r o x i m a t i o n n i c h t g ü l t i g i s t um d i e K e l v i n - H e l m h o l t z I n s t a b i l i t ä t d e r M a g n e t o p a u z e z u b e s c h r e i b e n . I n d i e MHD B e s c h r e i b u n g i s t es e i n b e g r i f f e n dass d i e I n t e n s i t ä t des m a g n e t i s c h e s Feld u n d d i e G r a d i e n t e n i n d i e Plasma p a r a m e t e r s s i c h langsam v e r ä n d e r n ü b e r A b s t ä n d e v o n e i n i g e L a r m o r R a d i e n . Die M a g n e t o p a u z e u n d d i e n a b e i l i e g e n d e "Plasma B o u n d a r y L a y e r " s i n d s e h r u n r e g e l m ä s s i g u n d u n s t a t i o n ä r . Deswegen s i n d d i e " f i n i t e ion L a r m o r r a d i u s " E f f e k t e n n i c h t v e r n a c h l ä s s i g b a r . Wir d e n k e n dass d i e I n h o m o g e n e i t ä t e n i n d i e Plasma B o u n d a r y L a y e r u n d an d e r M a g n e t o - pauze in d i e B e s c h r e i b u n g d e r M a g n e t o p a u z e S w a n k u n g e n eine w i c h t i g e Rolle s p i e l l e n m ü s s e n .
- 2 -
1. I N T R O D U C T I O N
Most work on the stability problem of the terrestrial magneto- pause has been carried on with ideal MHD equations considering this transition as a discontinuity (see for instance Southwood, 1968). More recent work however has taken into account of the finite thickness of the magnetopause layer (Ong and Roderick, 1972; Trussoni et a l . , 1982), while retaining the MHD approximation.
It has been shown by Lerche (1966) that the growth rate for the Kelvin-Helmholtz instability of a discontinuous transition is proportional to the wave number. Therefore, for such a model, the highest growth rate occurs for the shortest wave-lengths quite in- consistently with the approximation of negligible thickness. On the other hand, it has been put forward (Trussoni et a l . , 1982) that due to the finite magnetopause thickness, finite ion Larmor radius effects can be expected to be negligible. In that case, the MHD equations should remain a suitable approximation to investigate the large-scale oscillations of the magnetopause boundary.
It is the purpose of this paper to show that the MHD approximation is actually not appropriate for the study of disturbances at the terrestrial magnetopause. Such an approximation implicitly implies that the magnetopause has an infinite parallel conductivity and a vanishingly small transverse conductivity. In that case, the electric field does not strongly differ from the convection electric field.
Therefore, the contributions due to the Hall effect, the pressure
gradient, the temporal dependence and the effect of a finite resistivity
are neglected in this MHD framework. These contributions could actually
be neglected if the magnetopause were an ideal transition with smooth
continuous variations occuring in an extended current sheet. However,
t h e a c t u a l m a g r i e t o p a u s e a n d i t s a d j a c e n t plasma b o u n d a r y l a y e r a r e h i g h l y i r r e g u l a r , b o t h s p a t i a l l y a n d t e m p o r a l l y . I n d e e d , h i g h s p a t i a l a n d t e m p o r a l v a r i a t i o n s o f plasma a n d f i e l d p a r a m e t e r s i n s i d e t h e m a g n e t o p a u s e l a y e r ( M P L ) a n d pi asma b o u n d a r y l a y e r ( P B L ) h a v e b e e n d e m o n s t r a t e d b y many o b s e r v a t i o n s (see f o r e x a m p l e Eastman a n d H o n e s , 1 9 7 9 ) . F o l l o w i n g Eastman, t h e MPL is t h e c u r r e n t l a y e r t h r o u g h w h i c h t h e m a g n e t i c f i e l d s h i f t s i n d i r e c t i o n . T h i s c u r r e n t l a y e r ( t h e m a g n e t o p a u s e ) is o f t e n r e s o l v e d w i t h b o t h plasma a n d f i e l d p a r a m e t e r s a n d m u s t be d i s t i n g u i s h e d f r o m t h e PBL w h i c h d e n o t e s t h e l a y e r o f m a g n e t o s h e a t h - l i k e plasma o b s e r v e d e a r t h w a r d o f t h e MPL ( E a s t m a n , 1 9 7 9 ) .
From t h e s e i n s i t u o b s e r v a t i o n s , i t has been e s t a b l i s h e d t h a t t h e t h i c k n e s s o f t h e m a g n e t o p a u s e l a y e r ( M P L ) is m u c h smaller t h a n t h e t h i c k n e s s o f t h e plasma b o u n d a r y l a y e r ( P B L ) . A l t h o u g h h i g h l y v a r i a b l e , a t y p i c a l t h i c k n e s s o f t h e PBL is *v> 0 . 4 R ^ , w h i l e t h e m a g n e t o - pause t h i c k n e s s r a n g e s b e t w e e n 140 km a n d 700 k m , i . e . 1 - 5 ion L a r m o r r a d i i ( R . ) of 140 k m . A l t h o u g h t h e m a g n e t i c f i e l d v a r i a t i o n t a k e s place t h r o u g h t h e M P L , most of t h e plasma v a r i a t i o n s , i n c l u d i n g t h e v e l o c i t y s h e a r , t a k e place i n s i d e t h e PBL a n d at i t s i n n e r e d g e . H o w e v e r , scale l e n g t h ( L ) f o r s i g n i f i c a n t v a r i a t i o n s ( g r e a t e r t h a n a f a c t o r o f f o u r ) i n plasma p a r a m e t e r s w i t h i n t h e PBL r a n g e s b e t w e e n 10 km a n d 1000 km ( E a s t m a n , 1 9 7 9 ) . In s u c h a s i t u a t i o n , i t is c l e a r t h a t f i n i t e L a r m o r r a d i u s e f f e c t s d u e t o t h e s e s h a r p v a r i a t i o n s c a n n o t be n e g l e c t e d s i n c e t h e r a t i o ( L / R . ) r a n g e s b e t w e e n 0 . 0 7 a n d 7 w i t h t h e a b o v e o b s e r v e d v a l u e s o f L a n d o f t h e ion L a r m o r r a d i u s ( R j ) .
S e c t i o n 2 g i v e s t h e basic MHD e q u a t i o n s of an i n c o m p r e s s i b l e f l u i d . T h e s e e q u a t i o n s a r e u s u a l l y p e r t u r b e d f o r t h e s t u d y of t h e K e l v i n - H e l m h o l t z i n s t a b i l i t y . In s e c t i o n 3 , i t is s h o w n t h a t t h e a s s u m p t i o n o f t h e " f r o z e n f i e l d " is i r r e l e v a n t f o r b o t h t h e MPL a n d P B L . I n d e e d , t e r m s u s u a l l y n e g l e c t e d i n t h e g e n e r a l i z e d Ohm's law a r e s h o w n t o be c o m p a r a b l e t o t h e c o n v e c t i o n t e r m d u e t o t h e e l e c t r i c f i e l d .
- 4 -
Finally, the relevance of the MHD framework to study the physical processes involved at the magnetopause surface is critically analysed in section 4.
2. B A S I C MHD EQUATIONS
The basic equations usually adopted for the Kelvin-Helmholtz instability problem are the MHD equations of an incompressible fluid, i . e . , in MKSA units (Trussoni et a l . , 1982).
(1)
(2)
(3)
(4)
(5)
(6)
where p is the mass density and u the bulk velocity of the plasma, p is the pressure, J is the current density and B the magnetic field.
Equation (1) is the equation of continuity while equation (2) is the hydrodynamic equation of motion. Equation (3) accounts for the in- compressibility of the flow. If the plasma is infinitely conducting along the field lines and infinitely resistive across them, then the magnetic field is "frozen" into the plasma and is "carried out" along at the velocity u as described by equation ( 4 ) . Equation ( 5 ) is the Maxwell
+ V. (p u) = 0
p + p (u.V) u = - V p + J A B
V . u = 0
| | = V A (u A B)
V A B = - o -
|JJ
V . B = 0
equation for the curl of B for which the displacement c u r r e n t is neglected, (j
qbeing the vacuum permittivity. T h e divergenceless character of B is given by equation ( 6 ) .
A perturbation technique is usually applied to these equations. Linearized perturbed equations are then used to derive a dispersion relation from which unstable modes can be deduced. In this paper however we only want to check the relevance of these basic equations for the study of the hydromagnetic stability of the t e r r e s t r i a l magnetopause.
T h e f i r s t three equations are similar in form with the original hydrodynamic equations of an incompressible fluid. However in a collisionless magnetized plasma, the pressure tensor does not remain iso- tropic and therefore equation ( 2 ) assumes the smallness of the aniso- t r o p y .
T h e MHD approximation comes from equation ( 4 ) and it is interesting to recall from which assumptions this equation is derived.
To derive equation ( 4 ) , it is f i r s t assumed that the electric field ( E ) is zero along the lines of force, i . e . ,
E . B = 0 (7)
T h i s implies also that the magnetic field B is steady or slowly v a r y i n g . Secondly, it is also assumed that all the particles d r i f t with the electric drift velocity which therefore is identical with the bulk velocity u.
u = t A J (8)
B
From ( 7 ) and ( 8 ) , the electric field is
E = - u A B (9)
Using the Maxwell equation
(10)
with E given by ( 9 ) , it follows that equation ( 4 ) is reproduced. T h i s is the usual form of the "frozen" field approximation. In this approxima- tion, the electric drift ( 8 ) is the principal motion of the plasma. T h i s means that gradient drifts have been left out. T h i s is satisfactory providing
where R. is the ion g y r o r a d i u s and L is the scale length for spatial variations of the field (and associated plasma parameters).
3. ON T H E R E L E V A N C E OF T H E " F R O Z E N " F I E L D A P P R O X I M A T I O N
implies an infinite parallel conductivity (CT^ = while the assumption ( 8 ) of the same common drift for all particles is not compatible with any transverse conductivity. In that case, the t r a n s v e r s e Pedersen conductiv- ity of the plasma must be zero (a
x= 0 ) . However, the existence of
(R./L) « 1 (11)
T h e assumption ( 7 ) that the parallel electric field vanishes
large potential drops along field lines linking the magnetopause to the polar ionosphere is undoubtedly admitted from observations of precipitated electron fluxes (Arnoldy et a l . , 1974; Croley et a l . , 1978).
Therefore, the relevance of (7) is questionable at the magnetopause. On the other hand, the finite value of a cannot be neglected, not only because of the internal resistance of the medium resulting from local wave-particle interactions, but also because of the finite integrated Pedersen conductivity ( I . ) of current systems linking the magnetopause •L to the ionosphere.
As shown in section 2, the "frozen" field approximation ( 4 ) is derived from the fact that the electric field reduces to the convection electric field ( 9 ) . However, the actual electric field results from the generalized Ohm's law which can be written (see for instance, Seshadri, 1973) :
2
| i = — V . lb + — ( E + u A B ) - — ( J A B )
at m
eZe m
e- - - m
e— -
- % , j (11) m = — e
In this equation, itj<
eis the electron kinetic pressure dyad, n is the number density, e is the magnitude of the electron charge, m
gis the electron mass and Tip is the dyadic resistivity.
It is seen that terms of the generalized Ohm's law (11) neglected in the MHD approximation (9) include
%. J, —
w—
n am,
- ' ne J A B . - - —' ne «1» ie and —„ zrr ne M at
T h e role of the f i r s t term J h a s a l r e a d y be d i s c u s s e d at the b e g i n n i n g of this section. T h e s i g n i f i c a n c e of the other terms neglected in equation ( 9 ) can be evaluated in terms of the scale length L for spatial v a r i a t i o n s of the plasma a n d field parameters a n d in terms of the characteristic velocity u of the plasma ( E a s t m a n , 1979).
C o n s i d e r i n g that
u> = ^ (12) ce m„ e
2 ne^
(i o \
U) = (13) pe m e
r
e o
B v
MJ L (14)
r
o
( w h e r e ui and w are respectively the g y r o f r e q u e n c y a n d the plasma ce pe
f r e q u e n c y for the electrons while e
Qand p
Qare the v a c u u m permittivity and permeability r e s p e c t i v e l y ) we can evaluate the ratios X , Y , Z of the electric field due to convection | u A B | to the other c o n t r i b u t i o n s to the electric field neglected in equation ( 9 ) , i . e . ,
r J A B |, . J j - n d f f
e ne
r e s p e c t i v e l y . It is f o u n d
I . , g . ' j s L (15,
w c
where c is the velocity of light in v a c u u m
v i i u w m
E ' * r »
B« «
I = e I
ewhere k T
gis the electron thermal e n e r g y
(m"
2) uB / J f i Y
L' .. iff i u j (")
T a k i n g into account of the following typical v a l u e s a c r o s s the M P L ( E a s t m a n , 1979)
- 3 n ^ 10 cm B 30 nT u ~ 150 km/s T 100. eV e
for which
u) ^ 5 . 3 ks ce u) ~ 178 ks pe - 1 - 1
and
x
j- ^ 10 m , " I
^ 4.5 x 10~
5m"
1~ 3.5 x 1 0 "
7m~
2L
- 1 0 -
i t can be seen f r o m ( 1 5 ) , ( 1 6 ) a n d ( 1 7 ) t h a t t h e c o n t r i b u t i o n s t o t h e e l e c t r i c f i e l d n e g l e c t e d i n e q u a t i o n ( 9 ) become c o m p a r a b l e ( o r g r e a t e r ) t o ( t h a n ) t h e c o n v e c t i o n e l e c t r i c f i e l d ( i . e . , X = Y = Z ^ 1) f o r scale l e n g t h s of t h e o r d e r ( o r s m a l l e r ) o f ( t h a n ) 100 km f o r t h e Hall t e r m , 22 km f o r t h e p r e s s u r e g r a d i e n t t e r m a n d 1 . 7 km f o r t h e t i m e d e p e n d i n g t e r m . S u c h scale l e n g t h s f o r plasma a n d f i e l d v a r i a t i o n s a r e o f t e n o b s e r v e d w i t h i n t h e MPL whose mean t h i c k n e s s is o n l y a f e w h u n d r e d k i l o m e t e r s . I n d e e d , scale l e n g t h s f o r s i g n i f i c a n t v a r i a t i o n s ( g r e a t e r t h a n a f a c t o r of f o u r ) i n plasma a n d f i e l d p a r a m e t e r s , as d e t e r m i n e d f r o m h i g h t i m e r e s o l u t i o n m a g n e t i c f i e l d d a t a , may be as small as 10 km ( E a s t m a n , 1 9 7 9 ) . T h e s e i r r e g u l a r i t i e s a r e a l w a y s p r e s e n t a n d well d o c u m e n t e d b y o b s e r v a t i o n s w i t h h i g h t i m e r e s o l u t i o n ( s e e also Eastman a n d H o n e s , 1979; F r a n k e t a l . , 1 9 7 8 ) . T h e y s h o u l d n o t be smoothed o u t f o r c o n v e n i e n c e a n d c a n n o t be n e g l e c t e d , e v e n in a f i r s t a p p r o x i m a t i o n , because o f t h e i r l a r g e a m p l i t u d e . T h e r e f o r e , a t t h e m a g n e t o p a u s e , w h e r e t h e s e i r r e g u l a r i t i e s a r e p r e s e n t , t e r m s u s u a l l y n e g l e c t e d in t h e g e n e r a l i z e d Ohm's law become c o m p a r a b l e t o t h e c o n v e c t i o n t e r m d u e t o t h e e l e c t r i c f i e l d . C l e a r l y t h i s i n v a l i d a t e s t h e MHD a p p r o a c h .
T h i s c o n c l u s i o n is e v e n r e i n f o r c e d i f we c o n s i d e r t h e i n n e r edge o f t h e PBL l a y e r w i t h t h e f o l l o w i n g t y p i c a l v a l u e s ( E a s t m a n , 1979)
.. - 3 n ~ 1 cm u ^ 50 km/s B ~ 40 nT T ^ 150 eV
e
f o r w h i c h
, - 1 u) *v< 7 k s
C e
- 1
u) 56 k s pe
a n d
y - 7 - 1
£ * 2.5 x 10 m
p 1.3 x 1 0 "
5m"
1~ 3.5 x 1 0 "
8m"
2L
Indeed, in t h i s case the c o n t r i b u t i o n s to the electric field neglected in equation ( 9 ) become comparable ( o r g r e a t e r ) to ( t h a n ) the convection electric field ( i . e . , X = Y = Z ^ 1 ) for scale l e n g t h s of the o r d e r ( o r smaller) of ( t h a n ) 4000 km for the Hall term, 75 km f o r the p r e s s u r e g r a d i e n t term and 5 km for the time d e p e n d i n g term.
Remembering that typical scale l e n g t h s for s i g n i f i c a n t v a r i a t i o n s in plasma and field parameters ( g r e a t e r than a factor of f o u r ) within the P B L r a n g e s between 10 km and 1000 km ( E a s t m a n , 1979), it can be concluded that the M H D approximation is even much less a p p r o p r i a t e within the P B L than it is within the M P L layer.
4. I S A N M H D A P P R O A C H R E L E V A N T T O S T U D Y T H E S T A B I L I T Y O F T H E T E R R E S T R I A L M A G N E T O P A U S E ?
In section 3, it has been s h o w n that terms u s u a l l y neglected in the generalized O h m ' s law became comparable to the convection term due to the electric field for r e g i o n s both inside the M P L and P B L . T h i s is due to the presence of large amplitude i r r e g u l a r i t i e s whose scale l e n g t h s r a n g e between 10 km and 1000 km. A t the s h a r p b o u n d a r i e s of
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these i r r e g u l a r i t i e s , finite Larmor r a d i u s effects do not r e p r e s e n t small c o r r e c t i o n s a n d the inequality ( 1 1 ) is certainly not c h e c k e d . C l e a r l y this invalidates the M H D a s s u m p t i o n of " f r o z e n " field as d e s c r i b e d b y equation ( 4 ) . T h e r e f o r e it is not relevant to u s e an M H D a p p r o a c h to s t u d y the p h y s i c a l p r o c e s s e s o c c u r i n g at the terrestrial magnetopause and in particular to s t u d y its stability.
Most p r e v i o u s w o r k on the magnetopause stability was performed before h i g h time resolution o b s e r v a t i o n s become available and this fact e x p l a i n s w h y ideal M H D was so f r e q u e n t l y assumed in these early s t u d i e s . However as it has been demonstrated in this p a p e r , the relevance of a c o n t i n u i n g M H D a p p r o a c h becomes h a r d l y justifiable.
A c t u a l l y , the small-scale inhomogeneities p r e s e n t inside the M P L and P B L can c h a n g e drastically the usual large-scale d e s c r i p t i o n of magneto- pause oscillations somewhat like in h y d r o d y n a m i c s when t u r b u l e n t eddies p r e s e n t in an otherwise laminar flow can c h a n g e the c h a r a c t e r i s t i c s and the stability of the layer s u r r o u n d i n g this flow.
A n o t h e r point to be criticized in the M H D t h e o r y of the Kelvin-Helmholtz instability is the assumption of incompressible p e r t u r b a - tions of the magnetopause layer. I n d e e d , it may be s u r p r i s i n g that, in s u c h a h i g h l y spatial and temporal v a r y i n g layer, the plasma inside the magnetopause b e h a v e s like an ideal incompressible f l u i d .
It is also important to note that the layer o v e r which the
plasma b u l k velocity c h a n g e s s i g n i f i c a n t l y has a l a r g e r t h i c k n e s s t h a n
the layer o v e r which the magnetic field variation takes place. A s
demonstrated b y o b s e r v a t i o n s (Eastman and H o n e s , 1979), the plasma
velocity variation does not so much take place at the magnetopause (as
the magnetic field d o e s ) , but the largest velocity s h e a r o c c u r s at the
so-called plasma b o u n d a r y layer ( P B L ) . How can then the K e l v i n -
Helmholtz modes be unstable when the plasma velocity a p p e a r s nearly
u n c h a n g e d a c r o s s the magnetopause?
H o w e v e r , a salient feature of many satellite t r a v e r s a l s is that the magnetopause a p p e a r s to be c r o s s e d repeatedly in a s i n g l e p a s s (multiple c r o s s i n g s ) . It has therefore been s u g g e s t e d that the magneto- p a u s e is f r e q u e n t l y in motion ( A u b r y et a l . , 1971; L e p p i n g a n d B u r l a g a , 1979). T h e s e i n f e r r e d magnetopause motions h a v e also been interpreted as magnetopause oscillations c o n s i s t e n t with ripples on the magnetopause s u r f a c e , a l t h o u g h d e d u c t i o n s about the temporal s t r u c t u r e of the magnetopause are h a r d to formulate from a s i n g l e satellite t r a v e r s a l . R e c e n t l y , the pair of I S E E satellites h a v e detected some detached s t r u c t u r e s of magnetosheath - l i k e plasma well inside the magnetopause (Eastman and F r a n k , 1982). S u c h m a g n e t o s h e a t h - l i k e s t r u c t u r e s have also been detected inside the P B L b y the P r o g n o z - 7 satellite ( L u n d i n a n d A p a r i c i o , 1982). T h e s e m a g n e t o s h e a t h - l i k e r e g i o n s are u s u a l l y associated with s t r o n g flow of solar wind ions ( H
+a n d H e
+ +) and the presence of terrestrial 0
+ions a n d can be classified r o u g h l y as " n e w l y injected" or " s t a g n a n t " ( L u n d i n a n d A p a r i c i o , 1982).
A non stationary indentation mechanism cannot explain the s t a g n a n t magnetosheath-like e v e n t s with s t r o n g 0
+f l u x e s inside the s t r u c t u r e s . O n the other h a n d , the t h e o r y of impulsive penetration of solar wind i r r e g u l a r i t i e s into the magnetosphere f i r s t p r o p o s e d b y Lemaire a n d Roth (Lemaire and R o t h , 1978) can account for these o b s e r v a t i o n s . It is likely that some magnetosheath-like plasma i r r e g u l a r i t i e s h a v e been o b s e r v e d in the past d u r i n g single satellites t r a v e r s a l s but have been u n d e r s t o o d as magnetopause oscillations.
F u r t h e r m o r e , the role of the interplanetary magnetic field orientation with respect to the e a r t h ' s dipole field is k n o w n to be important for the interaction p r o c e s s e s between the solar wind a n d the magnetosphere ( S c k o p k e et a l . , 1976). In an M H D f r a m e w o r k , the importance of this factor does not appear a s i g n i f i c a n t one ( T r u s s o n i et al., 1982). H o w e v e r , in the impulsive penetration t h e o r y of Lemaire and R o t h , it is s h o w n that the interplanetary magnetic field direction controls the capture of plasma i r r e g u l a r i t i e s into the m a g n e t o s p h e r e (Lemaire et al., 1979).
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In c o n c l u s i o n , g r e a t e r theoretical i n s i g h t into the p h y s i c a l p r o c e s s e s o c c u r i n g at the terrestrial magnetopause must come from s t u d i e s of the s e l f - c o n s i s t e n t plasma and field e q u a t i o n s , allowing f o r the p r e s e n c e of the i n t e r p l a n e t a r y magnetic field. T h i s r e q u i r e s the reformulation of the problem in the kinetic domain.' T h i s is however a v e r y difficult problem but it r e s u l t s from o b s e r v a t i o n s that there is no other alternative. F u r t h e r m o r e , observational evidence of large potential d r o p s along p o l a r - c u s p field lines indicates the need for f u r t h e r efforts to determine the a p p r o p r i a t e b o u n d a r y conditions at the magnetopause (Willis, 1975).
In this context, a c o n t i n u i n g M H D a p p r o a c h would hamper the
p r o g r e s s to be e n c o u r a g e d along the line of more a p p r o p r i a t e kinetic
a p p r o a c h e s . I n d e e d , it would g i v e the false impression that the M H D
framework can p r o v i d e a satifactory " E r s a t z " to s t u d y the p h y s i c a l
p r o c e s s e s i n v o l v e d at the magnetopause.
R E F E R E N C E S
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