Formation of the plasma mantle in the Venusian magnetosphere

ICARUS 58, 412-430 (1984)

Formation of the Plasma Mantle in the Venusian Magnetosphere O. L. VAISBERG AND L. M. ZELENY Space Research Institute, Academy o f Science,~ USSR. Prqf~'qjuznqia 84/32, Moscow I 174&5, USSR Received January 14, 1982; revised February 6, 1984 A model of the interaction of the solar wind with Venus is proposed including magnetic barrier formation, ionopause structure, plasma dynamics in the magnetic barrier, and the formation of the V e n u s i a n tail (wake). It is shown thai under stationary conditions the ionopause is practically an equipotential b o u n d a r y and its current is determined by a diamagnetic drift. The source of the plasma mantle can be provided by photoions appearing in the magnetic barrier and convecting toward the wake as a result of both magnetic pressure gradient and magnetic tension. The formation of the magnetic tail is determined by convection of magnetic barrier flux tubes in which the solar-wind plasma is replaced by ions of planetary origin. Compared to observational data the proposed model gives s o m e w h a t overestimated values of ion convective velocity and magnetic barrier thickness near the terminator and underestimated values of n u m b e r density and magnetic field strength in the tail. Accordingly this suggests the possible influence of the a n o m a l o u s ionization effects in the solar w i n d - V e n u s interaction.

I. I N T R O D U C T I O N

Detailed study of the plasma and magnetic field performed from Venera 9 and 10 and Pioneer Venus orbiter have shown that the solar-wind flow past Venus is controlled by its interaction with the ionosphere and atmosphere of the planet. Two of the most important features of the solar wind-Venus interaction are the formation of the plasma and magnetic tail (Vaisberg et al., 1976: Dolginov e t al., 1978) and the formation of the region of amplified magnetic field above the ionosphere on the sunward hemisphere of the planet which is called the magnetic barrier (Russell et al., 1979). The formation of the magnetic barrier was noticed by Lipatov (1976, 1978) in the numerical simulation of the interaction between Venus and the solar wind and was analyzed with the anisotropic hydrodynamic model of Zwan and Wolf (1976). Later this effect was discussed in detail in the magnetogasdynamic calculations of Pivovarov and Erkaev (Pivovarov, 1982). Another distinct feature of the Venusian magnetosphere is the existence of the wake, first suggested by Mariner 10 mag412 0019-1035/84 $3.00 Copyright ~5 1984by AcademicPress, Inc. All rights of reproduction in any form reserved.

netic measurements (Ness et al., 1974) and clearly demonstrated by Venera 9 and Venera 10 experiments. Orientation of the magnetic field in the wake depends on that of the interplanetary magnetic field (Dolginov et al., 1978). In addition the plasma velocity and temperature in the wake are much lower than in the surrounding flow (Vaisberg et al., 1976). The topology of the tail forming as a result of the interaction of a flowing plasma with a wax ball was also studied in the laboratory experiments of Podgorny et al. (1980). In this paper primary attention will be given to the p l a s m a m a n t l e - - t h e special plasma regime just above the ionosphere and in the near-wake region on the nightside. The plasma mantle was discovered by Venera 9 and 10 as a flux of ions of planetary origin with an energy of directed motion of 100 to 200 eV and a temperature of 1 to 10 eV, which usually fills the Venusian wake (Vaisberg et al., 1976). The electron component of this plasma mantle was also observed by the Pioneer-Venus orbiter by Spenner et al. (1980) in the region which approximately coincides with the magnetic barrier. Characteristic features of this flow

VENUSIAN PLASMA MANTLE of planetary ions were also discussed by Taylor et al. (1980) on the basis of Pioneer Venus orbiter ion mass-spectrometer measurements. A topological connection between the magnetic barrier region and the main body of the tail is suggested by observations of the electron component of the plasma mantle (Spenner et al., 1980) as well as consideration of the plasma and magnetic boundaries in the wake region (Vaisberg et al., 1976) and on the dayside of the Venus ionosphere (Russell et al., 1979). This paper presents a number of quantitative estimates concerning processes which characterize the dynamics of plasma in the plasma mantle and the associated magnetotail. The estimates are compared with the results of Venera 9 and 10 and Pioneer Venus orbiter measurements. As a first step in understanding the problem we use simple, qualitative concepts of the interaction (Johnson and Hanson, 1979), based on the Alfven model of the interaction of a nonmagnetic body with a magnetized flow (Alfven, 1957). We will not discuss here the question of magnetic field penetration into the ionosphere either in large-scale form in the case of high solarwind pressure (Elphic et al., 1980b) or in a form of localized and sporadic magnetic ropes (Russell and Elphic, 1979). We will therefore treat the boundary separating the ionospheric plasma from the region of strongly compressed magnetic field/3 = 8 nT/B 2 1, the ionopause, as a thin superconducting surface screening the ionosphere from the penetration of the magnetic field. The results of the Pioneer-Venus mission (Elphic et al., 1980b) give some grounds to treat this situation as typical at least if the solar-wind pressure is not too high (i.e., less than 10 -7 dyn/cm2). Some calculations supporting the concept of an equipotential ionopause for stationary conditions are given in Section 2. Section 3 is devoted to the formulation of the model of photoion loading of the magnetic field tubes convecting around the planet. Some estimates of the plasma mantle parameters based on this

413

model are given in Section 4. Comparison of the model with experimental results is made in Section 5. Magnetotail and plasma wake characteristics derived from the plasma mantle dynamics are discussed in Section 6. Some additional plasma processes that may also contribute to the plasma mantle formation are briefly discussed in Section 7. 2. IONOPAUSE AS AN EQUIPOTENTIAL BOUNDARY OF THE IONOSPHERE AS observations show, the boundary layer between the almost nonmagnetized ionospheric plasma (/3 ~> 1) and the magnetic field of the barrier that limits it (/3 ~ 1) is located at small zenith angles at 250-300 km altitude and has a thickness 8iv of a few tens of kilometers (Russell et al., 1979), which is comparable with the gyroradius of ionospheric ions (O +) in the magnetic field of the barrier. The presence of such strong gradients of plasma density makes it necessary to take into consideration the gradient terms in the generalized Ohm's law (Pickelner, 1966) j± = o'pE + O'H(E × b) + j l + j ~ × b where %=

hlel -~

([l~+Ha),

hlel

CrH = - ~ - (Hi - He), 1 jl = ~ (HeVPe - HiVPi), 1 j2 = - - ~ (HeVPe + HiVPi),

B

b=-~.

(1)

414

VAISBERG AND ZELENY

Pc Pet q- Pen and ui = Pie + Pin a r e frequencies of particle collisions and oJt(i is the gyrofrequency. On one hand, the transverse plasma conductivity b e c o m e s low at heights of about 250 km, where the number of collisions is relatively small. On the other hand, the strength of the current in the ionopause layer can be determined by A m p e r e ' s law from the magnetic field j u m p across the boundary. For a 50-kin-thick ionopause with a magnetic field in the bartier of the order of 60 nT this gives a current density -

-

Bb

"J

/*oSip

I0 ~ A / m z.

(2)

If the diamagnetic currents at the ionopause are neglected and the Joule heating of the ionosphere is calculated (Elphic et al., 1980b) from the well-known standard formula j 20"p crY, + (rp

W = ,/-~/trC,,wli,g

(3)

(4)

(r~ + (rL, As we are dealing now with a one-dimensional stationary ionopause model, it is reasonable to a s s u m e it to be in a static equilibrium, at least in the v e r t i c a l (perpendicular to planetary surface) direction. Of course, in the real situation, pressure gradients in the horizontal direction produce plasma flow toward the terminator (Knudsen et al., 1980), so we have

j×b-

V(Pe + Pi)

B

1 (rnj × ben)

{5)

16)

b'cPi 8p(b')

- -

PcPi + O)lle('Otti,

8tt

I.

Although Eq. (6) resembles O h m ' s law in its conventional form, the effect o f ep(p) bec o m e s extremely important for small b'i/O9tli: u~/WH~. The same small factor now enters the expression for the Joule dissipation which, in fact, is determined by a very high conductivity along the magnetic field: W = j • E-

"/'-ev(U) O-('o,Ming

"~ J-/O'H;

~Op~

o-p~-- 4true'

the unlikely large values of the released power, W - 3 x l0 4 e V / c m 3 . sec, and of the ion heating rate, ~ ~ 1 eV/particle •sec, are obtained in the thin ionopause layer. In fact, in this layer of weakly collisional plasma, almost all of the current is produced by diamagnetic currents, and calculations of W should be made with allowance for all terms in (1):

W = (j - j l - j 2 × b)°-~ +~ o-Hj~× b

Coming back to Eq. (1) it is easy to obtain the electric field using the simplifying assumption P~ - P~:

(7)

At heights of 250 to 300 km (estimating u~ --10 sec ~: u~n "- 2 x I0 -~ sec ]: uio -- 4 x l 0 4 s e c I) w e obtain for a 60-nT magnetic field in the barrier (¢on~ - 104 sec E ~OHi 0 . 4 s e c i) ep(t,) ~ l 0 7 - 1 0 6. The true dissipation rate differs from that evaluated directly from (3) by the same ['actor 10 7_ l0 6. Recently Russell et al. (1981) came to the same conclusion about the dissipationless c h a r a c t e r of the ionopause current. Returning to (6) we can check the validity of the assumption of Johnson and Hanson (1979) about the equipotential ionopause. The electric field is actually perpendicular to the ionopause. The tangent of the angle at which the electric field lines are inclined toward the ionopause (along which the current j flows) is tan c~ - O"HEH/O'pI:?,p which is equal to about 104-103 at the assumed ionopause altitudes. Correspondingly, the estimate of the total potential drop through the entire ionopause of the planet gives very small values of the order of Aq~ -- 7rRvjo-[ 1 V. During the last decade m u c h attention has been given (Cloutier and Daniell. 1973; Daniell and Cloutier, 1977) to the cal-

VENUSIAN PLASMA MANTLE culations of current systems generated by the E0 = - C 1Vsw x B~w field in the ionosphere of Venus. In these papers estimates of the current distribution in the model ionosphere are based on the principle of minimum ohmic dissipation of this current with the usage of the simplest form of Ohm's law without drift terms. The calculated ionospheric current is localized in a layer of 4050 km thickness at a height of 150-200 km, corresponding to the maximum Cowling conductivity of the partially ionized ionospheric plasma. The Hall conductivity o-± at this height is of the order of o-± - 1 ohm 1 m-~ so the small potential drop through the entire ionosphere A + - - j • ~rRv/cr I ~ 30 V, obtained in this paper can be easily understood. As we have shown here, the allowance for the drift terms not considered in earlier papers by Cloutier and Daniell (1973) and Daniell and Cloutier (1977) also leads to a small potential drop, even for the high ionopause altitude. Although drift terms are formally taken into account in the next paper by Cloutier and Daniell (1979), this is not done self-consistently since they assumed that the current is merely the sum of gradient and ohmic parts: bxVP

j = o-E + ~

In fact, in the stationary models, where j = according to (5), the estimation of the ohmic current should be based on more accurate equations, as has been done above. Our point is that even for a poorly conducting ionospheric plasma, one may have an almost dissipationless current system within the thin ionopause layer. There are some arguments for an absorption in the ionosphere of the small fraction of surrounding flow either through charge exchange or due to finite gyroradius of magnetosheath particles. The last process can contribute to electrodynamic coupling of solar wind to ionosphere. Yet the simplified MHD ionopause model proposed here does not take into account this small secondary effect that cannot have strong influb × VP/B

415

ence on the plasma dynamics within the magnetic barrier. The simple MHD calculations performed above, could not answer, of course, the question of the nature and dynamics of the ionopause. Further development of the theory should be based on the studies of kinetic (collisionless) models similar to the self-consistent Vlasov configurations suggested by Lee and Kan (1979) for the Earth's magnetopause. From this viewpoint the Venus ionopause acts both as a current and as a charge layer. The flowing current prevents magnetic barrier field penetration below the ionopause, and the polarization of the latter prevents penetration of the convective electric field into the ionosphere. Imbalance of these two properties of the ionopause (e.g., lowering of the current layer), caused by growing instabilities or by the increasing role of dissipative terms in (6) along with a decrease in the ionopause altitude due to increased solarwind pressure, may result in the drawing of flux tubes into the ionosphere. This is one of the possible mechanisms of formation of the flux ropes, first observed by Russell and Elphic (1979). Other mechanisms proposed recently for the explanation of this phenomenon are related to finite gyroradius effects from Kelvin-Helmholz instability (Wolff e t a l . , 1980) and the instability of regions of large magnetic fields within the ionosphere (Cloutier e t a l . , 1981). 3. FORMATION OF A MAGNETIC BARRIER ON THE DAYSIDE OF THE INDUCED M A G N E T O S P H E R E AND PHOTOPLASMA PRODUCTION WITHIN IT

The formation of a magnetic barrier may be understood in the context of Alfven's model, initially proposed to explain the interaction of a comet with the solar wind (Alfven, 1957). Tubes of the field lines of the magnetic field frozen in the flowing plasma are compressed due to the deceleration of their central parts nearest to the body. The equations of motion and continu-

416

VA1SBERG AND ZELENY

ity written for the plasma propagating within a flux tube (parallel or axial coordinate Sir; tube cross-section a) are a(pa) a --Ot + ~ (pvl;a) = q(t)a ( Ov I,

P~-

Owl] _

+ vH~ /

(8)

0

0s t (P~,0,

(9)

pressure of solar-wind plasma P~,,, to the obstacle (ionosphere or surface of the planet). The only case when the magnetic barrier would transfer the pressure is when the kinetic energy of the transverse plasma motion within it is low as compared with the energy of the magnetic field: B~

phv2

P,~, ~ 8 - - ~ ~

(11) where the symbol I[ stands for projection of V onto the direction along the magnetic When q(t) = 0 the condition (I I) is automatfield; Pgas is the gas-kinetic plasma pressure ically met owing to plasma squeezing along in a tube; q(t) is the local rate of mass profield lines. duction caused by photoionization (per cm ~ As will be shown below, the effects of per sec), charge exchange, and other promass addition (q(t) ~ 0) in the vicinity of cesses. the Venus ionopause may be regarded as Equations (8) and (9) in fact correspond adding small corrections to the general barto appropriate equations from the paper by rier structure. This conclusion is confirmed Zwan and Wolf (1976) with the additional by considerations of pressure balance near ion production term taken into account. As the ionopause (Vaisberg et al., 1980; Brace was shown by Zwan and Wolf (1976), the et al., 1980) and by direct measurements by noninertial character of the coordinate sysElphic et al. (1980b), according to which/3 tem related to the moving field tube will not ~- 8rcn(T~ + Ti)/B~ ~ ~ - 1 within the Venus introduce significant corrections. In the magnetic barrier. Thus, as to a good apcase of flow past the Earth's magnetoproximation, it can be regarded as a static sphere q(t) = 0, the plasma is squeezed tbrmation transferring all of the solar-wind along the field tube from a higher-pressure dynamic pressure to the Venus ionosphere, region in the characteristic time L/VII (L although the photoionization of heavy ions rrD/2, where D is the diameter of an obstain the magnetic barrier plays an important cle). The result is the magnetic field pileup role. As experimental data show, the inci(compression) occurring ahead of the body dent dynamic solar-wind pressure is well with the violation of frozen-in field concept. described by the quasi-Newtonian approxiAccording to Zwan and Wolf (1976), the mations: barrier thickness may be simply estimated P,w(O) = Po + pswV~w(COS2~d/)

asz

A ~ 1.5LMA ?,

(10)

where MA is the Mach number in the unperturbed solar-wind flow. In the three-dimensional case, the field line may leave the region of compressed magnetic field (the magnetic barrier) along the flanks of the obstacle. It is evident that the dynamics of field line motion in the barrier also control the magnetic field character of the magnetospheric tail. Dynamically the barrier may be considered as a magnetic cushion, transferring the normal c o m p o n e n t of the incident dynamic

(12)

(Elphic el al., 1980b). Here Po is the gaskinetic pressure of the solar wind; p~,, and V~w are its density and velocity, respectively; qJ is the solar zenith angle; and tx is the numerical coefficients of the order of unity. For our considerations it is essential to note that the ionopause altitude in the subsolar region of Venus is usually about 250 to 300 km (Elphic et al., 1980a). The basic ionization mechanism producing Venus" ionosphere is photoionization. Photoions, formed above the ionopause, mass load the shocked solar-wind plasma

VENUSIAN PLASMA MANTLE

417

flowing around the ionopause. Furthermore, this mass loading may determine the velocity of the plasma convection around the ionopause within the magnetic barrier. We will try to determine below the parameters of the photoion flux convecting around the ionopause and to assess whether the classical photoionization mechanism explains the described observations of the plasma mantle in Venus' magnetosphere. The neutral atmosphere at ionopause altitudes is optically thin; thus the local mass production rate q(t) at the point r = R is roughly (Bauer, 1973)

charge exchange can be neglected in the study of the mantle formation. The dynamics of the neutral atmosphere above the ionopause should also be estimated from self-consistent equations which take into consideration loss processes such as ion recombination, their convection, etc. (e.g., Cloutier and Daniell, 1979). Here, however, we shall assume, to a first approximation, a uniform model of the neutral atmosphere:

(13)

which allows us to take into account a strong decrease of neutral particle density with altitude (Ho2 - 30 km, HHe -- 200 km, according to Niemann et al. (1979)). As mentioned above, the plasma pressure in the barrier appears low compared with the magnetic pressure (/3 < 1), so that the magnetic field strength in the barrier is assumed to be a given quantity and in the first approximation is determined by expression (11). On the other hand, the effect of squeezing along field lines may be neglected for photoplasma ions. This is attributed to the relatively short period of time the field tubes loaded with plasma spend within the barrier. The relative significance of photoplasma production and its depletion along the magnetic field line tube during the convection around the ionopause is easily assessed by comparison of the second term with the third one in Eq. (8). For the case of low photoion production rate q(t) ~ O, such as may exist near the boundary of the magnetic barrier for small neutral scale height, H0, the characteristic time of plasma mass variation in the field tube ~-± is

q(t) = ( i N i ( R ) M i ,

where (; is the photoionization rate coefficient; Mi and N i ( R ) are the mass and density of neutral atoms of species i. For oxygen and helium atoms prevailing at heights of the magnetic barrier, the photoionization coefficients at a distance of 0.7 AU from the Sun under average solar cycle conditions are: (02 ~ 4 X 1 0 - 7 s e c -1 and ( H e ~ 2 × l 0 - 7 s e c - ' , respectively (Bauer, 1973). An additional term in the mass loading is associated with the charge exchange between solar-wind ions and neutral atmosphere. The mass addition rate q~(t) due to charge exchange is q ±(t) ~-- nswNi(R)Mio'ov,

where v is the flow velocity and or0 is the charge-exchange cross section. The value of o-0 for the most important process H + + O --> H + O + is close to resonance o-0 3 x 10 -15 cm z. The relative significance of charge exchange is determined by the ratio q±(t)/q(t) = nswO'0V • (6~-

It will be shown below that the typical flow velocity within a magnetic barrier is of the order 30 km sec -~. Taking into account the strong depletion of the solar-wind plasma in the magnetic barrier, we can estimate on the average nsw - 3 cm -3. Then q±(t)/q(t) is about -<0.1. So the role of

1 (R N i ( R ) = Noi exp{ - Hi

R0)t, (14)

//

~'± ~ L/vrl < (iN----~/

Here the role of photoions in loading flux tube appears negligibly small, and plasma density in it is controlled by balance o f two effects: convection in

(15) the the the the

418

VAISBERG AND ZELENY

direction across the field and plasma depletion along it. In the barrier region nearest to the ionopause, with the increasing N~, the photoplasma production in the tube dominates the plasma depletion, thus n

7~

,~iNi <- L/vil"

(16)

Below, an estimate is made of how well justified such a supposition is. The limit (16) corresponds to an assumption of very long flux tubes and, with another simplifying assumption, these tubes are supposed to be straight. That is, we shall consider the flow around a cylinder, its axis being parallel to

the interplanetary magnetic field, rather than around a sphere. This simple model shown in Fig. 1 yields an estimate of the velocity with which the convection of field tubes around the planet occurs. Besides neglecting the effects of longitudinal plasma squeezing, we will make another simplification by taking into account only the transverse gradient of magnetic pressure, and by neglecting the tension associated with the stretching of the field lines in the pressure balance of the flux tube. The accuracy of this assumption was discussed by Zwan and Wolf (1976), where it was shown that the maximum error this as-

Exosph

Atmos~

FIG. 1. Simplified two-dimensional model of flux tube molion around the Vcnusian ionopause I solid line is the cross-section of two-dimensional body). White flux tubes ure fillcd by solar-wind plasma. Their motion is s h o w n by while arrows. Depleted flux tube in the magnetic barrier is filled by lhe photoions originating in oxygen planelary e x o s p h e r e (dolsl. Halched tlux tubes are flux tubes loaded by photoplasma. Their motion is s h o w n by black arrows.

VENUSIAN PLASMA MANTLE sumption could introduce would be a factor of - 1 . 2 which is quite permissible for our semiquantitative model. It should be mentioned, however, that if both the additional acceleration due to field line stretching and the plasma density decreases in the tube due to squeezing are neglected, this will underestimate the velocity and overestimate the density of the photoion flux. Hence, our calculations provide the upper limit for the density and the lower boundary for the velocity of plasma in the mantle. 4. THEORETICAL MODEL OF THE PHOTOION CONVECTION IN THE VENUSIAN MAGNETOSPHERE We now turn to the calculations of the motion of photoions around the ionopause in the plane transverse to the magnetic field using the cylinder-type model described above. We use a continuity equation in the form (8), with the second term (depletion) deleted. The equation of transverse motion may be written analogously to that of Zwan and Wolf (1976) according to the previous assumption that the main force responsible for plasma motion in the barrier is the magnetic pressure gradient: dvi P dt

-

O B2 as8~

(17)

where s is the coordinate along the stream line. The equations of motion and continuity for photoions are one-dimensional in the proposed approximation. Thus all quantities depend on either the distance along the ionopause from the subsolar point to the point of observation or equivalently on the azimuthal angle, which is even more convenient for calculations. Taking into account the flux tube cross-section a - B we finally have 0

=

q(t) B

, /R2(to) + (oR(to)'l

\ ato ! = f i

(18)

419

a Ov a+

-

O+ 87r - f 2

(19)

where R(to) is the distance to the streamline in the polar coordinates and ds = X/R2(+) + (OR/ato) 2 is the streamline length element. In the case of an equipotential ionopause within a thin region (as compared with the radius of the boundary), the streamlines of the flowing plasma closely follow the boundary of the ionopause. The shape of the streamline may be specified from the available experimental data. Accordingly, we chose the ionopause altitude lying between 250 and 300 km with a relatively weak dependence on the azimuth angle up to 30 ° zenith angle, and between 30 and 65 ° the ionopause altitude increases with tO up to 450-500 km, after which it remains at a nearly constant altitude all the way to the terminator (Elphic et al., 1980a; Vaisberg et al., 1980; Knudsen et al., 1982). Denoting the right-hand sites of Eqs. (18) and (19) asfl a n d S , respectively, we get an equation for the ion density p(to) - -

=

O.

(20)

Since it is not expedient to derive a precise solution of the approximate equation (18) by numerical methods in the context of the semiquantitative model, one more simplifying approximation is made to allow an analytical solution of (20). Oxygen photoions are supposed to load a convecting flux tube only for sufficiently small angles to < too 50 °. When to > too the ionopause altitude increases, a streamline enters the region where the density of neutral oxygen, rapidly decreasing with altitude, is low and photoion production becomes small. This is not, of course, the case for helium atoms and photoloading occurs up to the terminator, too - ~r/2. Thus, the region of most effective production of oxygen photoions corresponds to a limited interval of to where B ( t ) ~ const - Bb and lies within not too large distance AR = R(to) - Rip(0) from the ionopause.

420

VAISBERG AND ZELENY

The production rate q(t) in such a simple model m a y be a p p r o x i m a t e d by a step function: q(t) = ( N o ( R ) M ,

t~ < too and AR < H,, = 0,

* > Oo and AR > tt,,.

(21)

The thickness of a gaseous sphere H,, where the appreciable photoloading of the plasma flow occurs is determined below (condition (28)). To simplify calculation we have replaced the real distribution of atoms around the ionopause with a uniform gaseous sphere (radius ~' ~ R i p ( 0 ) , thickness tt,,. and density N , , ( R ) . The model under consideration is shown in Fig. 1. Finally. for #~ < +0 we obtain

__.1~

,, , ~ pp,+ + BZf ~ ( p , )

linear approximationf~U)(0) ~ , is not very good, and although it enables us to solve Eq. (23) analytically, it is used below only for c o m p a r i s o n with (24). Expressions for photoion flow parameters can be easily derived in both cases o v e r the r e g i o n , < too. The first solution that is of interest to us is obtained after specifying initial conditions at the point where the streamline enters the gaseous envelope ( , = *i~, P = po, v - v0): _ _ -* *in + ~//:2~//in~-- 1 ¢T 2

P0

P0

(~)

=

0

P0

.. UM

instead of (20). It is possible to reduce the nonlinear differential Eq. (22) to a linear differential equation for the inverse function dKp): O,),,

0.

P B2f~

(23)

Equation (23) is solved by using two model functions f,(O). In the first approach a constant magnetic pressure gradient averaged o v e r the entire barrier is assumed P~w(0)R -

/'?)

•

-

12

P~(0) K 77 .2

K ....

V

2--3,

(24)

where 1 is the distance from the subsolar point to the terminator measured along the streamline in the plane o r t h o g o n a l t o the interplanetary magnetic field, and R is the average ionopause radius. In the second a p p r o a c h the.f2 function is obtained directly from Eq. (12) with g ~ 1: f~")

p~,~V ~w ~ sin 2*

(25)

where, if 0 < O( < 1, only the first term in the Taylor expansion of f~u)(*) is taken into account. For reasonable values of*0 such a

Y = ~,

VM

~ K72 "'

P,~,.(O)/K~NoMR.

(26)

In (26) we assumed Vo ~ V,,~ \'~Oi~/K which may be easily obtained from Eq. (17) with the use of the a p p r o x i m a t e form (24). It differs from the usually assumed linear dependence u0 ~- * (see, e.g., Zwan and Wolf, 1976). The difference, however, is insignificant as the mantle plasma is accelerated up to V~' ~ VII. The important p a r a m e t e r is the velocity VM which, in fact, determines the characteristic velocity of the photoplasma flow. The simplest solution of Eqs. (26) may be obtained in the interval *i~ < * < KY~ U/U M ~

(20/Ky:)":

(27)

where the plasma flow appears to be undisturbed by photoion addition, in the case Ky: tb0 ~ 1 regime (27) holds o v e r the whole region of p h o t o p l a s m a production, 0 < ~b < • 0. The criteria for the importance of photoionization in the convection within the magnetic barrier can be easily shown from (27) to be VM/V~,,. -~ ~v/*o/K. Hence, it is not difficult to estimate the condition of the minimum neutral gas density required lbr considerable photoion loading of the flow

VENUSIAN PLASMA MANTLE Mi psw(0) -- > No(R) mp %/KtOomp Vsw

(28)

The condition (28), in fact, determines the size of the neutral gas shell Hn which interacts with the IMF flux tube depleted from the solar-wind plasma. The specific numerical value of Hn for various gaseous components of the neutral atmosphere (H, He, O) may be estimated from well-known models of Venus' neutral atmosphere. Let us now consider the case where photoion production strongly affects the interaction: tO~n< KY2 < too. In this limit simple iterations give estimates for photoion density and velocity:

_% /

tO

(29a)

p(tO)/po ~ K'y2 // l n K'y2e

+ ~f~,

(29b)

where e = 2.718. And finally simple expressions can be obtained in the last case Ky2 < tO~. < tO: (to -

v(tO) - v0.

Over the region tO > tOo where photoion pick-up may be neglected, the frozen-in condition is fulfilled, and it is easy to obtain the expression for plasma flow parameters:

v(tO) =

2P~w v2(tO°) + Kp(tOo----5

dtO

]"

f~0 (COSZtO + B~erm/B~)l/2J

"

(32)

Here Bterm/Bb is the ratio of magnetic fields near the terminator and at the subsolar point of the magnetic barrier. Hence, one immediately obtains the values of the photoplasma flow velocity and density near the terminator,

tOo

Oterm ~ VM(ln 2 K,y2

2 ln(2BdBt¢~ - ln(tOo/Ky2e)]'/2 + (33a) tOo/K~/2 /

tO v(tO) _ In tO VM ~ -- l n l n -Ky2e

tOi.)

P(tO)/Po - ~ i , / ~ y

421

2

tOO l Pterrn = P0 K,y2 In tOo/KT2e

Bterm

B/~ " (33b)

It is evident that, until tOo/Ky2 > I, the velocity increase is small over the region of additional acceleration tO > too and the parameter VM is a characteristic scale of the velocity of the photoions.

(30) (31)

Thus the calculations made with our first model f~i) (tO) (averaged gradient) predict a weak, almost logarithmic growth of velocity with tO and a rapid, almost linear density increase. In contrast, the second version forf~ m - tOin the photoion pick-up region tO < tOo yields a rapid velocity rise v(tO) - tO/ In(tO/tO0 and a slow density increase p(tO) ln2(tO/tOj) where tOl = VO/VM. As shown below, even the first model with a slower increase of photoion velocity overestimates the convection velocity value within the barrier as compared with the observations within the plasma mantle. Nevertheless we will concentrate on the model described by Eqs. (28) to (31), using it as a lower limit estimation.

5. COMPARISON OF THE PHOTO1ON LOADING MODEL WITH OBSERVATIONS

Let us compare the plasma flow parameters estimated above with those measured onboard the Venera 9 and l0 spacecrafts. Figures 2a and b show characteristic ion energy distributions observed in Venus' tail. Figures 2a correspond to a "low-latit u d e " crossing, that is, to that mantle area where the plasma from the barrier region flows into the tail along the field lines draping the planet. It can be seen that the plasma is detected in a thin layer of tail. Figure 2b corresponds to a "high-latitude" part of the mantle where the plasma moves across the direction of the magnetic field lines and drives with it the flux tubes into the tail. In the last case the plasma layer in the tail is thick and the concentration and

422

VAISBERG AND ZELENY

N, counts, sec-1

100

10

\

couN~.sec_l 100[ ~X

®

.I3 ~I4 -Is

ole

o

0[6 ~I7

~17

0 ~" 10 " ~

®

",//!/~13

~./'~",

10 0

,///

10

/

~%,~

/

~

,~ \

o

\

o f,o 100

;'~,,,\~

lOO

~o _~fi,°,,,i

,o 0 1000

~''..

100

mo 2o;

-A?~

10 11000#,, i10 t~~

0

0.1

1.0

10

0

E/Q, kev

0.1

1.0

10

E/Q,kev

@

B FIG. 2. Variations of ion spectra along two orbits of Venera 10 when it was moving from the planetary shadow. (a) Low magnetic latitude crossing of the interaction region and (b) high magnetic latitude crossing. Different marks show the measurements made by different electrostatic analyzers of RIEP plasma spectrometer (13-17): their orientations relative to Sun direction (top) are shown by arrows. Upper low-energy spectra ( 1 and 2 for a and 1-4 for b correspond to the mantle plasma in the tail, wide spectra, to the shocked solar wind. Undisturbed solar wind lowest spectrum in a. (c) Schematic of the convection of field lines around the planet and the cross-section of the plasma tail of planetary origin in the plane perpendicular to solar-wind flow. White arrows show the projections of respective spacecraft trajectories on the same plane.

temperature in the given region are higher. It is this situation that is considered in the model. The characteristic parameters of the ion c o m p o n e n t of the mantle in the tail at a distance - 1 Rv behind the terminator are: drift energy e0 - 150 eV, Ti - 1 to 10 eV.

Since the plasma spectrometer with which the mantle parameters were determined measures the number flux, it is necessary to know the type of ions to derive the number density. Characteristics of mantle ions suggest that these ions are of

VENUSIAN PLASMA MANTLE T i,ev 100

423 b

Vot

Vos

50 0 V,km/sec 40O 3O0 20O 100 0

!

I

2

13141

5

TM

7=5/3;M=6"5;MA=6"75 ; H / r 0 = 0 " 0 1

Xse(103km)

15

10

~

e

.

Jrl0

5

0

--5

103 k

-10

m

~

--15

FiG. 3. Direction of solar-wind plasma flow (solid arrows) and tail plasma (mantle) flow (open arrows) as observed by RIEP plasma spectrometer on October 29, 1975. Thin solid lines show the direction of flow, shock, and ionopause, according to the hydrodynamic (HD) model of Spreiter et al. (1968). (a) The variation of ion temperature and flow velocity along the orbit (solid lines) compared to the HD model (solid circles, solar wind plasma; open circles, tail flow). Time scale corresponds to Moscow time, (b) Vector diagram of velocities of two components near the boundary of the tail: Vo, undisturbed velocities; Vc, cross-tail plasma velocity, subscripts t and s are for the tail plasma and solar plasma, respectively.

planetary origin (Vaisberg et al., 1976). The mass of these ions may be estimated from the experiment. Figure 3a shows the results of measurements of plasma flow direction in the region o f solar-wind interaction with Venus (Vaisberg et al., 1976). Here two plasma components were recorded in the tail near its boundary: a weak flux of ions with characteristics similar to those of the ionosheath solar plasma flux, and a major flux of low-energy ions of the mantle. The measured energies of the drift of the two components and the angle between the vectors of their velocities may be used to estimate the mass of the mantle ions (Fig. 3b). Since the deflection angle of external flow

particles (protons) entering the tail cannot be determined from observations with reasonable accuracy, a relatively crude estimate is obtained for the mass of low-energy particles in the tail. The ratio of mass of the tail ions to that of external flow ions is therefore Mt Wt sin2(a + al) M---~= W----~" sin2al ,

(34)

where W is the energy of convective motion in the tail, subscript t is for the tail and subscript s holds for external flow (see Fig. 3b). Data obtained just below the tail boundary on N o v e m b e r 29, 1975, give W~ = 470 eV, Wt = 170 eV, and a ~ 25 °. Ifa~ lies

424

VAISBERG AND ZELENY

in the range 3 to 6 ° reasonable and consistent with observations the ratio Mt/M, is between 30 and 9. This suggests that the main candidates for tail ions are O ~ ions. In this case the measured flow p a r a m e t e r s correspond to a velocity --45 km s e c t and to a n u m b e r density - 0 . 5 cm ~ To c o m p a r e these values with model values, the experimental data obtained in the tail must be normalized to the terminator. H o w e v e r , an acceleration of the plasma between the terminator region and the region of o b s e r v a t i o n s in the tail (1 Rv downstream) will o c c u r (see below). As to the n u m b e r density the main effect is the increase of the cross-section of the flow during expansion from the thin barrier layer into the tail. This expansion will diminish the n u m b e r density by about an order of magnitude (see Eq. 6). Thus n u m b e r density values estimated from m e a s u r e m e n t s should be multiplied by I0 for comparison with the model. Let us consider what we obtain with the model. Substituting values P,,, :- 4 × 10 s d y n c m : , K = 2.5, R = 6 . 3 × l0 s c m , ~ - 4 ~< 10 7 sec ~, and N 106cm ~(for oxygen) into (26) we obtain VM -- 25 km sec ~. When ~0 = 1, y = 10 i, and BjBt,:,-rn "- 3. Eqs. (33a) and (33b) yield an O ' photoion velocity at the terminator in the barrier region v~,m ~ 92 km sec 1 and n, ..... - 4.8 cm

.

The velocity value is about two times higher than those recorded in the tail. The value of the concentration is in reasonable agreement with that o b s e r v e d in the tail if the expansion of flow from the barrier to the tail is taken into account. The model data for the velocity of He ~ ions strongly exceeds the o b s e r v e d values. So, despite the fact that in our calculations all simplifications have led to an underestimation of the ion flow velocity, Vte~m, the theoretical value appreciably exceeds the experimental one. In our opinion the only conclusion this contradiction implies is that photoionization is not the only source of plasma mantle ions.

6. P L A S M A

MANTLE

AND MAGNETIC

TAll.

FORMATION

An interesting feature of the Venus interaction with the solar wind is the formation of a plasma tail and a magnetic tail. Although, topologically (opposite directions of the field in the " n o r t h e r n " and "southe r n " lobes of the tail), this formation resembles the geomagnetic tail of the E a r t h ' s magnetosphere, at Venus it is associated with the interplanetary magnetic field frozen in the solar wind. That results in a more complicated tail configuration and greater variability of its properties. Magnetic observations show that the topology of the magnetic field in the tail is determined by draping of the magnetic field lines of the interplanetary magnetic field (Dolginov et a/., 1978, 1981 ). If we restrict ourselves to the simple case of BIMF ± V~,, discussed in the paper, the formation of the tail is explained as follows. To be more definite we assume V~,, ii e, IBJM~ I[ e,, where e,,,.: are unit vectors in the planetocentric solar-ecliptic coordinates. Field lines in a thin strip with thickness A~,~ located near the s y m m e t r y plane, XY. parallel to the IMF, are associated with those streamlines in the equatorial plane, XZ, which enter the magnetic barrier and then the neutral gas shell where they are additionally loaded with ions while moving around the planet (Fig.4). The velocity of convection of the " ' h e a v y " central parts of those lines around the ionopause strongly decreases while the velocity of their ends frozen in the free solar wind remains unperturbed. Thus, the tail is a set of field lines " ' h o o k e d " by the planet, whose central parts are involved in convection around it. In this context the notion of " b o u n d a r y of the tail" is rather conventional since the perturbation of a field line, resulting fl'om the interaction with the planet, decreases monotonically with increasing distance of this line from the X Y plane and from the axis of the tail. The boundary of the tail is easily identified by the change of plasma

VENUSIAN PLASMA MANTLE

425

BOW SHOCK

IONOPAUSE /

/ ~

f

Z

Z0

_~'~

~IL~--"~'~-,,,~_~J

~

TAIL FLOW

HOTOIONS

IONOPAUSE

FIG. 4. Model of solar wind-Venus interaction. Subsequent locations of magnetic flux tube (white arrows) entering the interaction region at the distance Z0 from the symmetry axis are shown. Spirals show the parts of flux tubes loaded by photoions in the magnetic barrier on the dayside; near the terminator and subsequently in the tail. Two "ends" of the flux tube are moving along the dashed trajectories located in the surrounding flow and within the tail. The Venusian plasma mantle appearing as the thick tail flow at the "high magnetic latitudes" and the thin plasma layer at the "low magnetic latitudes" is marked by arrows.

flow regime from the shocked solar-wind flow to low-energy flow in the tail (Vaisberg et al., 1976; R o m a n o v et al., 1978) (see also Fig. 2). In this context the formation of the mantle is inseparable from the formation of the tail. Thus with the velocity of the mantle plasma known, we may estimate how the central parts of the curved field lines follow behind their ends during the convection, and that can give us the characteristics of the tail. We see that the parameter

lidS )

(~/2 dtO ao

U~)

(35)

which is the time of mantle photoion convection around the ionopause, becomes important. The total magnetic field flux in each of the tail lobes at the given distance l0 down the tail may be estimated as

@ = BswV~wA~w rB

Rv + 1o ) V~w + rio ,

(36)

where Ti0 is the time of motion of the " t o p " (central part) of the flux tube from the terminator over the distance of observation,/0, in the tail, and A~w ~ Rv is the thickness of the strong-interaction region, which will be defined as that distance such that for all field lines with ]z0] < A~w/2 the convection time is more than twice that in the undisturbed flow, and so the field lines are appreciably curved due to the loading of their central parts by photoions. With A~w so determined, we implicitly use the equipotentiality of the ionopause, proven above. Equation (36) allows for three groups of the field lines (positions 3-5 in Fig. 2) that have to be considered when we discuss the tail, each one is represented by a term in the brackets of Eq. (36). Term rB applies to

426

VAISBERG AND ZELENY

field lines that are connected to the magnetic barrier (lines 3 and 4), except for those that did not convect planetary ions to the distance l0 (line 3 of Fig. 2) and the term (Rv + lo)/V~,~ allows for these. Other field lines in the tail (line 5 of Fig. 2) are from unclosed magnetic loops that completely passed the planet, but have their tops between the terminator and the distance of observation 10; term r;0 allows for these field lines (see Fig. 5). If the value qb is given, it is possible to evaluate the field in the tail: 2 Bt~61 ~

- 7rg~ail

planet in the undisturbed flow where this line is parallel to the X axis. Within the interaction region near the ionopause the lines of flow may be considered as approximately parallel to the ionopause surface (see Section 3), that is, close to the direction e:, when the angle 0 is small. If r(0) is the distance of the streamline from the center of the planet for the given 0 - =/R, then the condition of conservation of the number of field lines transported between the two adjacent lines of flow (at a distance d Z , from each other) yields v~wB~,dZo = v(d~)Bh(O)dr.

B~wV~wA~, r;, + r/0

R v + 10). V~,,

(37)

Integral (35) is calculated with the expressions for the velocity obtained in the previous section. It is convenient to divide 7~ into two parts: r, is the time of motion in the region (tPin, too) and ~'2 is the time of motion in the region (too, ~r/2). Under the assumptions made in Section 4 we have J]/ v(to) = dp(to)/dto for the first region, from which one immediately obtains r, = -R p(too) - p(to~n) ~iNiMR ROo

VM In

(toO/KT2e)"

(38)

The field Bh(to) in the central part of the barrier may be assumed constant. Besides, since the value B~wV~,,. is conserved when the streamline crosses the bow shock we can use the undisturbed parameters for this quantity. Equations (27) readily yield an estimate of velocity for small (h, where the plasma is not yet depleted and photoion loading is not yet significant (i.e., p - p0), v(to) = V~,~ X/2-to/K. As mentioned above. our model of the averaged gradient yields a somewhat unusual square-root dependence of v0(0) (instead of a linear one as in the paper of Zwan and Wolf (1976)); however, since the value too -< 1 this only slightly affects the specific numerical results. Integration of (40) gives

The time "r2 is also easily estimated by integration of Eq 32: z2 =

~ - too VM In

(to0/KT2) '

(39)

We have already specified in Eq. (28) how we can estimate the characteristic size H , of the gaseous planetary shell which is responsible for a flux tube of considerable deceleration by the photoion pick-up. Let us now derive the characteristic thickness A~w of the strong-interaction region in the solar-wind flow which encloses stream lines carrying those flux tubes. Let Z0 be the distance from the symmetry axis (X axis) to a streamline upstream of the

(40)

Ms,,,

r ( t o ) - R = Zo ~

F--

;K ~/~-~

(41)

where R - Rip(0) is the ionopause radius at small zenith angles. Now, taking into account that r(t~) ~- R + H , and tO = toi, at the place where the gaseous shell is entered, by streamline the relationship between z0 and

tom is z0 - ~

H,~

.

(42)

As all plasma flow deceleration ceases at the boundary of the plasma shell thin ~> th0 the reasonable estimate of (toi,).... is 0o/2. This through Eq. (41) immediately gives the

VENUSIAN PLASMA MANTLE estimate o f (Z0)ma x and correspondingly Asw = 2(Z0)max

nb

Asw --~ 2~-~w Hn

Ilt~-~ •

(43)

Now we may calculate the characteristic values ~ , Btail, 7B, Asw predicted by the photoionization theory of the mantle. It is also convenient to calculate the dream-value, which is the characteristic thickness of the mantle at the terminator easily determined from the same condition of a stationary plasma flow in the mantle, as used above dterm-

A~w B~V~w 2 VtermBt~rm"

(44)

The comparison of values (37) and (44) with those observed in the experiment again shows that the photoionization theory of the mantle is not entirely adequate• In fact, convection times from (38) and (39) are estimated as rl = 73 sec and r2 = 69 sec, the total convection time rB = 142 sec. The thickness o f the plasma mantle, according to (44), is estimated a s dterm - 270 km. The observations allow dterm to be determined as a height difference between the lower boundary o f the solar plasma flow at the terminator ( - 9 0 0 km, according to Romanov et al. (1978)) and the mean upper boundary of the ionosphere (~700 km) (Knudsen et al., 1982)• To compare the model values of magnetic field in the tail with observations (according to E r o s h e n k o (1979) the longitudinal c o m p o n e n t of the magnetic field in the tail at the distance - 1 . 5 Rv behind the terminator is - 1 2 nT) it is necessary to allow for acceleration of the mantle plasma from the terminator o v e r the distance of observation. This acceleration dotail /]tail-

dt

.2 t r ( ' ) UA/L'tail

(45)

where VA is the Alfven velocity in the tail and L~l ~ rBV~,~

(46)

427

is the length of the part of the tail connected to the magnetic barrier. The Alfven velocity in the tail is - 1 0 0 km sec -l and Lla!j - 10 Rv which gives/]tail ~ 0.1 km sec 2. It is easy to estimate the velocity of the plasma and the time of propagation of the " t o p " of the magnetic field line loop to this distance rt0 60 sec for the model value vterm - 90 km sec -j. Substituting these obtained values in Eq. (37) we have a model estimation of the magnetic field strength in the tail at the distance ~ 1.5 Rv behind the terminator, Btail - 5 . 7 nT. Thus, the photoionization theory which gives overestimated (by about a factor of 1.5-2) values of Uterm and dterm and underestimated values of rB and Btail should evidently be corrected by introduction of additional ionization mechanisms (or by additional sources of ions)• It is interesting to estimate roughly the total length of the Venusian tail in the model as a location where tail ions are accelerated up to the solar-wind velocity L(M) tail

V~w- WswUtail •

(47)

Utail

that gives L, tailr(M) ~1.5 X 106 km or -102 diameters of an obstacle• 7. ROLE OF P L A S M A P R O C E S S E S IN THE F O R M A T I O N OF T H E P L A S M A M A N T L E IN T H E M A G N E T O S P H E R E OF V E N U S

We have tried to develop a purely "classical" model of solar wind-Venus interaction employing only photoionization. A certain inconsistency of the available experimental plasma data with theoretical estimates derived from the model implies, however, that other mass loading plasma processes may be important. These processes provide an additional source of ions to the flow, resulting in a net deceleration of the flow. One mechanism of such additional plasma production, anomalous ionization, or Alfven mechanism, has been recently

et al.

t Recent measurements by Nagy (1981) showed the existence of a nonthermal neutral oxygen component that may be an additional source of photoions.

428

VAISBERG AND ZELENY

discussed in relation to the problem of ionization of c o m e t a r y a t m o s p h e r e s (Formisano e t a l . , 1982). The a n o m a l o u s ionization process is maintained by electron heating due to d e v e l o p m e n t of plasma instabilities associated with relative motion of ~'new" ions with respect to plasma electrons. The important p a r a m e t e r of this interaction, ~, is the fraction of energy which is transferred in the course of the development of the instability to the electrons through the electrostatic plasma waves from the reservoir of free energy (the kinetic energy of counter streaming between the ambient plasma and the newly formed ions). The value of "O appears to be small if the ratio of the time of ionization by electron impact (~'i) to the gyroperiod of ions is high, 7~oni > 1. Under the conditions within the Venusian m a g n e t o s p h e r e this last criterion is met, so that we may use for ~O the estimate "O ~ ~.-2~, (using the data of Formisano e t al. (1981) for evaluation o f ~ ) . This estimate does not contradict the experimental results of Brenning (1981). With an exact value of ~ taken into account, it is necessary to modify the well-known necessary condition for anomalous ionization discharge (Formisano e t a l . , 1982) U .~> U~, ~

Ucr.A X T~ I/2

(48) Here ~l is the ionization potential of a neutral atom, m~, is its mass, e, is electron charge, v~,A = v ~ l n = I is the well-known Alfven critical ionization velocity. Recently Brenning (1981) has shown in experiments with plasma in weak magnetic fields (~on~ < to w = (4¢rneZ/m~) ~/~-) that the transfer coefficient ~ is really very small (of the order of a few percent). Although Brenning (1981) had interpreted this as the disappearance of the a n o m a l o u s ionization p h e n o m e n o n , actually this effect m a y be associated with a strong increase of the critical ionization velocity according to Eq. (48). With these results it is reasonable to discuss briefly the possible c o n s e q u e n c e s of

a n o m a l o u s ionization discharge for the formation of the Venusian plasma mantle despite the fact that full agreement between the theoretical (Formisano e t a l . . 1982: Raady, 1978) and experimental (Brenning, 1981; Piel e t a l . , 1980) studies does not yet exist. The ionization potentials for the gases we are interested in are 24.6 eV for He and 13.6 for O. We can evaluate critical velocities for these c o m p o n e n t s under the condition of a rarefied Venus atmosphere. Thus we 0~ findvcr =40-50kmsec , f o r O ~ a n d v ~ ~•, 80 to 100 km s e c - ' for He, respectively. From these values we can also estimate the mantle plasma density. Thus, it is obvious that the plasma should reach velocities of the order of the Alfven velocity (VA ~- B/X/4~'niMi) as a result of its acceleration by magnetic pressure. At the same time if the mechanism of the anomalous ionization is really important, the flow velocity must be s o m e w h e r e near its threshold value, v~ (but a little above it!). Equating the velocity of (48) to the AIfvenic velocity yields nH~ - no, -- 10-15 cm This estimate of velocity agrees very well with the experimental results as well as with the n u m b e r density after allowing for dilution of the flow in the tail. The result of this analysis suggests that the anomalous ionization may be at least as important as the usual photoionization in the formation of the mantle/tail s y s t e m of the Venusian magnetosphere. In the photoionization model developed above, the role of the helium c o m p o n e n t appears to be negligible, and the theoretical model predicts the oxygen mantle. The estimation of the role of the anomalous ionization implies that the helium c o m p o n e n t of the Venusian a t m o s p h e r e may also conlribute to the formation of a mantle. SUMMARY

A semiquantitative model of the formation of the plasma mantle and magnetic tail

VENUSIAN PLASMA MANTLE in the Venusian magnetosphere has been developed in this paper. In the theoretical estimates only one mechanism of ionization, namely, photoionization, has been taken into account. The reasons for the neglect of the charge-exchange process are discussed. Comparison of theoretical estimates for the plasma mantle velocity and density and for the value of the tail magnetic field with experimental results obtained by the Venera 9 and 10 spacecrafts indicates that photoionization cannot be the only source of plasma mantle ions. An additional mechanism related to the anomalous ionization discharge was mentioned in this context. One important auxiliary result may be used when considering the plasma flow past Venus and the nature of ionopause currents. The strong density gradients within the ionopause results in the almost dissipationless character of ionopause currents. This justifies the important simplifying representation of the ionopause a s an equipotential surface. A number of serious simplifications have been made in order to look, from a single point of view, at the different plasma regimes within the Venusian magnetosphere--plasma mantle, magnetic barrier, and magnetotail, with special emphasis on their topological relationships. Future developments of such global models must take into account more realistic magnetic field geometries and plasma distributions, as well as treat additional ionization mechanisms and consider nonstationary solarwind conditions. ACKNOWLEDGMENTS Authors are indebted to A. A. Galeev and V. N. Smirnov for useful discussions and advice and to both referees for many helpful suggestions which improved the model. REFERENCES ALFVEN, H. (1957). On the theory of comet tails. Tellus 9, 92-96. BAUER, S. (1973). Physics o f the Planetary Ionospheres. Springer-Verlag, New York/Berlin.

429

BRACE, L. H., R. F. THEIS, W. R. HOEGY, J. H. WOLFE, J. D. MICHALOV, C. T. RUSSELL, R. C. ELPHIC, AND A. F. NAGY (1980). The dynamic behavior of the Venus ionosphere in response to solar wind interactions. J. Geophys. Res. 85, 7663-7678. BRENNING, N. (1981). Experiments on the critical ionization velocity interaction in weak magnetic field. Plasma Phys. 23, 967-978. CLOUTIER, P. A., AND R. E. DANIELL, JR. (1973). Ionospheric currents induced by solar wind interactions with planetary atmospheres. Planet. Space Sci. 21, 463-474. CLOUTIER, P. A., AND R. E. DANIELL, JR. (1979). An electrodynamic model of the solar wind interaction with the ionosphere of Mars and Venus. Planet. Space Sci. 27(8), 111-122. CLOUTIER, P. A., T. F. TASCIONE, AND R. E. DANIELL, JR. (1981). An electrodynamic model of electric currents and magnetic fields in the dayside ionosphere of Venus. Planet. Space Sci. 29(6), 635-652. DANIELL, R. E., JR., AND P. A. CLOUTIER(1977). Distribution of ionospheric currents induced by the solar wind interaction with Venus. Planet. Space Sci. 25, 621-628. DOLGINOV, SH. SH., E. M. DUBININ, E. G. EROSHENKO, P. L. ISRAILEVICH, 1. M. PODGORNY, AND S. I. SHKOLmKOVA(1981). On the field configuration in the magnetic wake of Venus. Kosm. lssled. 19(4), 624-633. [in Russian] DOLGINOV, SH. SH., L. N. ZHUZGOV, V. A. SHAROVA, AND V. B. BUSIN (1978). Magnetic field and magnetosphere of planet. Venus. Kosm. lssled. 16, 827-863. [in Russian] DUBININ, E. M., I. M. PODGORNY, Y. N. POTANIN, AND S. I. SHKOLNIKOVA(1978). On the possibility of the determination of the Venus magnetic moment by the magnetic measurements in the tail. Kosm. Issled. 16, 870-876. [in Russian] ELPHIC, R. C., C. T. RUSSELL, J. G. LUHMANN, F. L. SCARF, AND L. H. BRACE (1981). The Venus ionopause current sheet: thickness, lengthscale and controlling factors. J. Geophys. Res. 86, 11430-11438. ELPHIC, R. C., C. T. RUSSELL, J. A. SLAVIN, L. H. BRACE, A. F. NAGY (1980a). The location of the dayside ionopause of Venus: Pioneer Venus Orbiter magnetometer observations. Geophys. Res. Lett. 7, 561-564. ELPHIC, R. C., C. T. RUSSELL, J. A. SLAVlN, AND L. H. BRACE (1980b). Observations of the dayside ionopause and ionosphere of Venus. J. Geophys. Res. 85, 7679-7996. EgOSHENKO, E. P. (1979). Effects of unipolar induction in the magnetic wake of Venus. Kosm. lssled. 17(1), 92-105. FORMISANO, B., A. m. GALEEV, AND R. Z. SAGDEEV (1982). The role of critical ionization velocity in the production of inner coma cometary plasma. Planet. Space Sci. 30, 491-497.

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