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Motion of artificial ion clouds in the upper atmosphere
Planet. Space Sci. 1967. Vol. 15, pp. 1 to 18. Pergamon Press Ltd.
Printed in Northern Ireland
MOTION OF ARTIFICIAL ION CLOUDS IN THE UPPER ATMOSPHERE G. HAERENDEL, R. LUST and E. RIEGER Max-Planck Institut fiir Physik und Astrophysik, Institut fiir extraterrestrische Garching bei Milnchen
Physik,
(Received 10 June 1966) Abstract-The paper sets out to solve the equations of motion for an ionized irregularity. of finite length, and to apply it to the behaviour of a Ba+ cloud. After a number of simplifymg assumptions, an expression for the ionospheric electric field is derived in terms of (1) the magnetic field, (2) the velocities of the neutral and ionized clouds, (3) 1* (the ratio of the integrated Pedersen conductivities in the cloud and in the atmosphere), (4) K‘(= gyrofrequency for Ba+/collision frequency). The magnitude and orientation of the electric field is evaluated from the observation of six barium and strontium clouds. il* is assumed to be unity. The derived field strengths lie between 1 and 3 . 1O-s V/in. In the evening the fields are pointing southward and in the early morning release northward. 1. INTRODUCTION
Experiments with visible artifical ion clouds have been proposed to provide a means of studying the interaction processes between the interplanetary plasma and artificially injected ions, hoping that we might thus improve our understanding of the physics of ionized comet tails and of the interplanetary plasma itself. (l) In addition, ion clouds can be used to map out the distant geomagnetic field,t2) and also for measurements of electric fields in the ionosphere. ~3~) For obvious reasons the technique of releasing visible ions is most easily studied with small sounding rockets in the ionosphere. Any observed drift motions of the ion clouds should throw some light on the existing electric fields. In the course of release experiments at heights between 130 and 2000 km with barium, which seems to be at present the most suitable element for these purposes,(1*2*5)we have succeeded several times in producing easily visible ion clouds during twilight. As a basis for the understanding of the observed motions, the expansion, and the deformations, we shall briefly review the theory of the movement of ionospheric irregularities. We will show that the finite extension of any real configuration and the spatial variation of the ionospheric parameters, as for instance the conductivity, have serious consequences on the behaviour of an ion cloud. The flow of electric currents along the lines of force introduces new aspects which are missing in semi-infinite configurations which have been investigated in most of the earlier theoretical work. As the mathematical difficulties encountered in treating very realistic models are considerable, our discussion will remain rather incomplete. Finally, we shall present our first experimental data with Ba+-clouds as far as the above mentioned aspects are concerned. All other topics, especially the technical questions have been or will be discussed elsewhere.(5*6) 2. BASIC RELATIONS
We start with compiling the well-known equations on which the treatments of ambipolar diffusion and of the motions of ionospheric inhomogeneities are based. 1
1
2
G. HAERENDEL,
R. LUST and E. RIEGER
The equations of motion of the three components considered (indicesj and 1 stand for e = electrons, i = ions, n = neutral molecules) are:
where mj is the mass, nj the number density, vg the velocity, pj the pressure, g the gravitational acceleration, e, the charge, E the electric field, B the magnetic field, and yjCthe collision frequency for momentum transfer between the j-th and the I-th components (the reduced mass appearing in the momentum transfer has been included in the definition of vjl). The following simplifications of (2.1) are typical for most of the applications in the discussed context: (1) The left-hand side of (2.1) is set equal to zero. Thus all rapid changes, especially the initial expansion of a disturbance, are omitted. (2) The influence of gravity is neglected. This means that the atmospheric scale heights are considered to be large compared to the extension of the cloud, or both are infinite. (3) The magnetic field is homogeneous and constant with time. The currents flowing in the irregularities are so small that the disturbance field can be neglected. This is possible as long as the disturbance of the electron pressure pe is small compared to B2/8vr. In all our experiments, after the initial expansion, this ratio is less than about 10-5. (4) The collisions between ions and electrons are assumed to be of much less importance than the collisions with the neutral particles. For Ba+-ions this is true up to heights of about 300 km. Another consequence of this assumption is that the velocity of the neutral component, v,, can be regarded as constant with time; and usually also spatial variations (wind shears) are neglected. So, only very simplified equations of motion for the ions and electrons remain. These have to be solved together with Maxwell’s equations, an equation of state relating the pressure to the density, and the equations of continuity for ions and electrons. From Maxwell’s equations only: curl E = 0
(2.2)
has to be taken into account explicitly, which is consistent with the assumption of slow processes. All processes are considered to be isothermal: pj = n,kT;
T, = Ti = T,, = T = const.
(2.3)
Because of the smallness of the Debye-length (about 1 cm) we have to postulate charge neutrality, i.e. for singly ionized atoms: n, = n, = 12.
(2.4)
div j = 0,
(2.5)
As a consequence we have: where j = en (vi - v,) is the electric current density. Equation (2.5) is equivalent to the difference of the two equations of continuity. Thus only one of them remains, g + div (n vi) = P - L.
(2.6)
The right-hand side represents all production and loss processes, which will subsequently be neglected.
MOTION OF ARTIFICIAL
3
ION CLOUDS IN THE UPPER ATMOSPHERE
With the above mentioned simplifications we can now solve the equation of motion for the velocity, We shall work in a frame of reference where the neutral component is at rest : y.* =2 v. J 3
y *;
(2.71
j=e,i
E* = E -j- i Y, x B.
cw
With the definitions : e,=-,
B
5=-=
B
*cd
X (Vj*
Kj2eB
X eB)
(2.9)
it is negative for electrons!) we can write
(mgj is the gyrofrequency of the j-th component; v, in the following form: vj” -/-
ejB
Yin mP5,
=
Kjttj +
Kj”uj
(2.10)
X eB
with uj
=
c B
(2.11)
K, and K~ for Ba+-ions at heights between 120 and 240 km are plotted in Fig. 1. If we separate vj into its components perpendicular (yj,) and parallel (vji,>to B, we can write instead of (2.10): (2.12a) (2.12b) %I* = 'Ciujir From the difference between (2.12) for ions and electrons we find the relation for the current density : t-)
%‘.E*---6.pi-
j=
Vn
(2.13)
n
2 is the conductivity tensor and zis essentially the tensor of the difference of the diffusion coefficients. In a Cartesian coordinate have the form
system where B is parallel to the z-axis, ‘a*and x
op is the so-called Pedersen, CJ, the Hall, and ufi the direct conductivity: ---
K, 1 +
--~
'
1 +K:
2 K* 1 +
alI =
Ki Ke2
net B (Kz -
Ki"
K&
;
‘ce
I+
(2.15a)
KS2
(2.15b)
’
61,=
net 7 (Ki +
Ke)
(2.15~)
G. ~AERENDEL,
R. LUST and E. RIEGER
lo6
10
5
104
103
lo2
10'
100
10“ 120
I
I
140
1Eo
180 "&"'I
I
I
2cO
220
1 240
-
FIG. 1. WTIO, K, OF CiYROFRJZQUJ3NCYAND COLLISION FREQUENCY WITH NEUTRAL FOR Ba+-IONSAm ELECT~~~NS AT HEIOHTS BETWEEN 120 AND 240km.
PARTICLES
We have arbitrarily named the corresponding components of the z-tensor by the same subscripts as in the conductivities (note that K@ < O!). All contributions to the current perpendicular to B decrease with decreasing collision frequency, except the term 6&e, x (Vn/n) which converges for K$ > 1 towards the expression for the magnetization current in fully ionized gases. As this part of the current flows parallel to contours of constant density it is not relevant to our later considerations. Essential is the continuity of j [equation (2.5)] in the direction of Vn, which leads to the distribution of the electric field. The magnetic perturbation due to the magnetization current has already been assumed to be small. If we now consider the ambipolar diffusion and the movements of ionospheric inhomogeneities we can characterize these two idealized types of problems in the following way: (a) In ~~b~po~ar~1~~~0~the electric field is assumed to be entirely due to the polarization within the inhomogeneity because of the different mobilities of ions and electrons. Thus E* = 0 at infinity if we consider a cloud of ionized particles imbedded in an infinite weakly
MOTION OF ARTIFICIAL
ION CLOUDS IN THE UPPER ATMOSPHERE
5
ionized atmosphere. (b) For the motion of irregularities the existence of an outer electric field is essential. For the sake of simp~fication one generally neglects the diffusion terms and looks for solutions where the irregularity can move under conservation of its shape. This is only possible for semi-infinite discontinuities of the electron density,“,@ where Vn vanishes except at the boundaries. The variation of the density perpendicular to B over the extension of the cloud, i.e. the variation of the conductivities, leads to a variation of the screening of the outer electric field. Thus the forces acting on the particles inside the cloud are not constant; the cloud will be deformed. However the bulk motion should be well described by the simple, discontinuous model; particularly if the polarization field, E,, arising from the ambipolar diffusion [(cf. equation (2.1 l)] : ]E,]
=
I I=
T ;
kT1 e
(2.16)
E
is small compared to \E*/ (L is a characteristic length). Numerical values give: ]E
(2.17)
] 2,
With clouds whose width is at least 1 km, IE,j is certainly much less than the field strengths of about lo* V/m which are encountered in the ionosphere. This estimate, on the other hand, demonstrates that any changes in the shape perpendicular to B after the initial phase are more likely due to the action of an outer electric field rather than due to merely the ambipolar diffusion.(s) In section 4 we shall see that the finite extent of a cloud along the direction of the magnetic field increases the difficulties considerably. In one of the experiments described in section 5 we can see deformations developing (Fig. 8). 3. MOTION OF A CYLINDRICAL
IRREGULARITY
OF F’INITE LENGTH
The theory of the motion of ionospheric irregularities, which has been developed by Martyn, (lo) Clemmow et al.,(ll) Dungey,o) Kato(8J2) and many others, applies closely to the motion of an ion cloud in the upper atmosphere. Most of these considerations deal with irregularities that extend infinitely along the lines of force in a homogeneous medium. For a more general discussion we have to consider the case of an irregularity of finite length above the region of maximum Hall- and Pedersen-conductivities. Then, as Dougherty’@ has previously pointed out, the polarization field within the cloud can be short circuited by currents flowing along the lines of force and closing in the E- and F-regions of the ionosphere. Therefore, the jump in the electric field at the boundary of the irregularity is no longer determined by the ratio of these densities inside the cloud and outside, but by the ratio of the integral conductivities along the lines of force through the cloud and outside. A problem of this kind has been investigated in detail by BostrGm(14Jin a theory of aurora1 arcs, but these inhomogeneities have a finite width only in one dimension perpendicular to the magnetic field. The new aspect introduced by ion clouds lies in the finiteness in all three dimensions. We consider the following model sketched in Fig. 2. The ion cloud is represented by a homogeneous cylinder of finite length with an electron density which is ii times the density of the ambient atmosphere. The cloud is shorter than the atmospheric scale height, so that
6
G. HAERENDEL,
R. LUST
and E. RIEGER
we are justified in assuming constant values of K~ and K,. The currents, J, need not be continuous on a horizontal level because surface currents, J,, along the lines of force between the cloud and the lower ionosphere are allowed. The horizontal current through the cloud J,Omight exceed the current just outside by Js, but then JzE has to be smaller than JIE by the same amount. The lines of force are considered to be equipotentials, since the direct conductivity is higher than the Pedersen conductivity by at least three orders of magnitude. Even if the “surface’‘-current flows within a relatively narrow region the parallel component of E can be neglected in comparison to the perpendicular component above the bottom of the dynamo region.
__
.___--_c~-_c_____ -I T
y-
T
J,
'2
E-and
F-rqlon
JE
FIG. 2. MODEL OF A FINITE CYLINDRICAL IRREGULARITY WITH AXIS PARALL EL TO B IN THE IONOSPHERE. THE CURRENTS Jl.2 ARE HORIZONTAL CURRENTS, INDEX 2 REFERRING TO LINES OF FORCRPASSINGTHROUGHTHEIRREGULARITYANDINDEX1TOTHOSERBMAININGOUTSIDE. Jg~sz ELECTRONCURRENTSPARALLELTO B FLOWINGONTHESURFACEOFTHBlRREGULARlTY. THEE AND~LAYERSAREREPRESENTEDBYAFINITELAYER(INDEXE)OFHIGHhDBRSENCONDUCTIV~.
The continuity of the total current is expressed by: n . (Jlo + J,“) = II . (Jzo + J,“),
(3.1)
where n is the normal vector of the irregularity perpendicular to B and J,,, are the integrals ofj,f, along the lines of force:
J,,, = We write [cf. equation (2.13)] :
s
j& dl
J=s.E
(3.2)
(3.3)
with the two-dimensional conductivity tensor, s, which is obtained from 2 (2.14) by disregarding ull and integrating a, and au along the lines of force: Z&H = / ~P,H dl
(3.4)
From (3.1) and (3.3) we find: n.&.E,--f&.E,)=O
(3.5)
MOTION OF ARTIFICIAL
ION CLOUDS IN THE UPPER ATMOSPHERE
7
In writing (3.3) we have assumed that the neutral component of the atmosphere is at rest, Later we have to transform to a coordinate system which allows for a wind. If we introduce cylindrical coordinates (r, 8, z) with respect to the axis of the cylindrical inhomogeneity which lies parallel to B, (3.5) can be written as:
&Er, - CH,J%, - &,Er, + OH&, = 0
(3.6)
We define the ratios: A* = 1P -2, & and make use of curl E = 0, i.e. :
2 l=g
(3.7) u, (3.8)
J%, = G,
at the boundary of the cylinder.
Then (3.6) becomes:
El., = a* Ev, - (E - 1) 5 Ee,
(3.9)
With (3.9) we have reduced the problem to the case of an infinite cylinder in a homogeneous atmosphere; only the coefficients have a different meaning. Comparison with earlier work, e.g. Dungey (‘) shows that with a homogeneous electric field E, at infinity E, is also homogeneous (neglecting the small component E,,) and related to E, by: E, = 4 (A* + 1) E, - + (t - 1) 5 (Es x e& (cf. equation (9.30) in Dungeyo)).
(3.10)
We solve for E, and get: (3.11)
E, = NE,, + BE, x eB, with
cc =(1 +
2(1 + a*> n*>z + (1 - E)252’
265- 1x IR= (1 + A*)2 + (1 - E)2<2
(3.12)
A* and t are equal to il in the case of an infinite cylinder. The variation of the ionospheric conductivities with height, however, has the consequence that 1* and [ will be different. If the cloud is above 130 km (K~> 1, cf. Fig. l), its contribution to En will be less than that to & [cf. equation (2.15)]; thus 1<5<1*
(3.13)
The inequality (3.13) reduces the importance of the second term on the right-hand side of (3.10) in the determination of E, (5 G 1 according to Table 1) compared to the first term. If we know the electric field inside the cloud we can derive the velocity of the ions from (2.12a). But one can observe only the motion of the boundary U; part of the ion velocity, vi, only contributes to the current which continues through the boundary. As the surface current parallel to B is carried by the electrons and diffusion is neglected, we can claim continuity of the ion flux on a horizontal level: n . U (n) = n . (nv,)
(3.14)
((n) = n2 - nJ. We emphasize that we make the assumption that the motion of the finite cylindrical irregularity can occur without deformation or changes in the density. Later this point will be examined.
8
G. HAERENDEL,
R. Lf_.bT and E. RIEGER
The constant density inside the cloud, ns, is jl times the density, ~zr,outside at the height of the cloud. With a constant value of K~, (2.12a) and (3.14) lead to: c ?Z,n . (A& + AK~E~ X eB -
n . u nl(l - 1) = Ki
I+KFB
El -
Ki El
X
eB)
(3.15)
Replacing E, by E, with help of (3.8) and (3.9) and using the fact that (3.15) holds for all directions of n (perpendicular to B) with the constant vectors U and E,, we find that: (3.16) where :
a - a*
Ki
~___2L 1+
Ki
Ki +
g
I)
(3.17)
.
We are interested in U as a function of the field strength at infinity, E,. We introduce (3.11) into (3.16) and get: E, x B (3.18) 73
U=ac%+bc
where : a = uy -
/IS,
(3.19)
b = a6 + By.
For future application to the observations we transform (3.18) to a coordinate system in which the neutral atmosphere moves with velocity vnl perpendicular to B. We call the velocitv of the cloud in this frame of reference VI and the electric field at infinity El,. Thus:
I
’
u = v, -
E, = EL0 + A vn,_ xB
vnl,
El0 cy+v*l
VL=a
(3.20)
C
+bcT+
xeB
EL0 x B
>
(
(3.21)
(1 - b) vnl
If we solve (3.21) for EL0 we get; EL0 = T D-‘[a (V, - v,J
+ b(eB x V,) -I- (b - D) vnl x
(3.22)
eB1
with : (3.23)
D = a2 + b2.
is useful to consider an appropriate expression of (3.22) for heights above the E-layer > 1). According to (3.13) we have (5 - 1) 5 < 1 + A*. In addition A* < 1. So we get approximately : 1 2 am--, bw2 (3.24) 1 + 1* Ki 1 + a*
It
(Ki
and : l+l*B
EL0 m 2
c
A* eBxvl-t+-vnL)+~v
*
1 nl
’
eB
1
(3.25)
MOTION OF ARTIFICIAL
ION CLOUDS IN THE UPPER ATMOSPHERE
9
The equations (3.22) and (3.25) are the basis for the interpretation of the motion of an ion cloud in terms of the ambient perpendic~ar component of the electric field. We see that one has to measure, in principle, also the velocity of the neutral atmosphere and that one needs the values of K~ at the height of the cloud, and the integrated conductivities. Not only the electron density inside the cloud but also in the ionosphere must be known, as far as it contributes appreciably to the integrated perpendicular conductivities.
The polarization of a column of enhanced ionization in the ionosphere depends essentially on the ratio, il*, of the height-integrated Pedersen conductivities inside the column and in the undisturbed ionosphere. If the irregularity is above the region of maximum conductivity, i.e. if K~ > 1, a* is considerably smaller than the ratio, il, of the electron densities at the level of the irregularity. It is seen from (3.17) to (3.19) that for L* < 1 the mobility, a, of the cloud in the direction of E, is increased relative to the case of an infinite cylinder with ratio A. This means that the electric field inside the column is not very effectively shielded. So the particles have also a considerable drift velocity, bc[(I$, x B)/B2] (3.18), which, for 2* + 1, approaches the drift of a single charged particle (b -+ l), since (t - l)[ is a small number. The increase in mobility in the direction of EOis achieved by the flow of currents along the lines of force between the cloud and the regions of high Pedersen condu~tivities (E- and F-layers). The electrons which according to (2.12a) cannot follow the ions directly are removed from the rear of the cloud, and new electrons appear at the front (with respect to E,!) to neutralize the arriving ions. As the electrons can nowhere move across B in the direction of E. (the currents are closed by Pedersen currents), they accumulate in the E- and F-layers along the lines of force passing through the rear of the cloud; and a deficiency of electrons is built up in these layers along the field lines through the front of the cloud. The total number of electrons along a line of force remains of course unchanged, as long as diffusion is neglected. This problem has also been considered by Piddington(15) in a theory of spread F, and by BostrGm(14) in a model of an auroral arc. The change of the electron distribution along B, initiated by the cloud’s motion, results in changes of the integrated conductivities, since they also depend on K( and IC*(2.15), which vary greatly with height (Fig. 1). Consequently, the important assumption made in section 3, that a* is not affected by the motion of the irregularity, breaks down. The conductivity, i.e. il*, is lowered at the front, and increased at the rear of the column. Thus, different parts of the cloud move with different velocities, U; the cloud will be broadened and sheared in the sense that the rear, where a* is higher and thus E, weaker, more closely sticks to the neutral atmosphere. How serious this effect will be depends mainly on the number of electrons injected, N,,c, per unit area along a line of force. (We call the line integral of the density parallel B: N,,, and the line integral perpendicular to B : NL. The indices c, E, F refer to the cloud and to the E- and F-layers, respectively.) Even with very little change of 2 (a* = 1) due to this increase in the electron density Niicand NE might be comparable; or the latter can even be smaller. Nlis is always much higher than N,?; so 2” is not affected. As the con~ibution of the E-layer to the integral Pedersen conductivity is at least as high as that of the F-layer(26) a substantial fraction of the current Js (Fig. 2) will initially flow through the &layer until the conductivity there becomes seriously altered. The condition N,y < NjIE would mean a very serious limitation for an ion cloud
10
G. HAERENDEL.
R. LUST and E. RIEGER
experiment. With numbers taken from Maeda and Ma~urnoto(l~) we would have to postulate*. N c < 7 . 1O1*cm-2. Because of the elongation of the cloud we would get: N,” < 1.5 , 10lt cm-2. If we choose for instance: NLc = 2. IO* cm-2 the photon flux from the cloud would be 5 . 10’ cm-2 se& sterad- 1.(6) During twilight conditions this is a barely detectable intensity. We can escape this difficulty, if we use only the initial period of the cloud’s motion, before the conductivities have been changed appreciably, for the interpretation in terms of the ionospheric electric field. A quantitative description of the deformation phase for a realistic model seems to be extremely difficult. The time-scale for the appearance of deformations is estimated by: 7=-
L
(4.1) UE
where L is a characteristic scale of the cloud in the direction perpendicular to B (L-l = n-l ]Vnlma.J and U, is the component of U (3.18) in the direction of I&. If we designate by U, the more easily observable drift velocity [second term on the right-hand side of (3.18)] we can express (4.1) by: bL 7=_--, a uD
(4.2)
with a and b from (3.19). A good choice for L is 1 km and for U, (see next section) 30 m see-l. If Iz* M 1 initially, (b/a) z q, and we find: 7 z 30 Ki [Set] (4.3) In order to have an observation period of about 15 min, KS should be larger than 30, i.e. the ion cloud should be produced at heights above 180 km (see Fig. 1). Since the ionospheric conductivities change considerably during twilight conditions, z:, and zn are rather delicate parameters. Consequently, we should require a* = 1. Some numbers extracted from the work of Maeda and Matsumoto(16) and BostrGm(14) (with correction for an inclination of 45’) have been gathered in Table 1 in order to indicate the TABLE
1
Local time (hours) 0
4.0
6 12 0
3:.: 0.77
0.14 0.43 1-O 0.34
16 16 16 14
range of variation and uncertainty. With a constant value for K( and the contribution of the cloud to the Pedersen conductivity by:
K#
>
1, we can express
zr Z 4. lo_11 Nile [Q-l]. Ki The postulate that iz* = 1 would mean:
(4.4)
N,f < 5 . lOlo fci [cm-2].
(4.5)
Together with the limitation for ~~ arising from (4.3) this is not a serious restriction. The ion cloud may even be optically thick along the smaller axis (for Ba+: NLc M 5 . IOx0cm-3.
MOTION
OF ARTIFICIAL
ION CLOUDS
IN THE UPPER
ATMOSPHERE
11
Of course we would like to measure electric fields with as little material as possible. So we would choose the lowest possible height, which according to (4.3) lies near 200 km (K~= 50). By (4.5) NgiO< 3 . 10” cm-2; with a typical cross-section of a cloud of 20 km2 we find that the total mass of released Bat is limited to 14 g. This is still a surprisingly low number. Even with inefficient evaporation the whole experiment would have a total weight of only a few kg. 5.
EXPERIMENTAL
DATA
In Table 2 we have gathered a few data characterizing all visible Ba+-clouds so far produced by our group. The technological aspects are left out; they will be discussed elsewhere.(6) Ba+-ions are generated in two different steps, during the initial phase with a time-scale of about 5 see and by a slower photo-ionization with a time-scale of about 100 sec.fl’) The initial ionization is particularly effective since it gives rise to well concentrated clouds with a width of a few km in the direction perpendicular to B. Later on the cloud expands only along the lines of force, until the deformations discussed in section 4 become important. TABLE 2 NO.
i i i i i
Date
Time
Site
h fkm)
M C@
m @
1 2 3 4 5
Nov. Nov. Nov. Sept. Oct.
27,64 30,64 30, 64 30, 65 2, 65
e e e m m
H H H P P
152 159 199 225 220
357 83 1965 6050 467
1.8 4.1 5.3
i 6
Nov. Nov. Nov. Nov. Nov. Apr. Apr.
18,65 18,6.5 19,65 20,65 20, 65 22, 66 22,66
e e e e e e e
H H H H H H H
167 135 194 365 415 2000 2000
330 95.5 790 200 16.108 255 291
-
i 7
i 8 i 9 i 10 ill i 12
-
-
Remarks
Bad observing conditions Very faint cloud Ba+-tail Cloud with stripes
e, evening (normally at soiar depression angle of 6”). m, morning (normally at solar depression angle of 13”). H, Hammaguir (Sahara). P, Perdasdefogu (Sardinia). h, height of release. M, mass of evaporable material. m, mass of initially generated Baf.
The mechanism leading to this initial ionization is not yet clear. The width of the ion clouds corresponds well to the product of the initial velocity of expansion times about 5 sec. It could be that the initial ionization starts from a metastable atomic level with a life-time of 5 sec. Also the subsequent slow photoionization is much faster than has been estimated previously.(6) The absorption starting from the ground level of Ba is strengthened by several auto-ionization lines below 238OA. But the oscillator strengths are far too weak to explain the observed time-scale. fr*) Also here the process might use an intermediate level (perhaps the same as in the initial ionization). The efficiency of the reactions has been evaluated quantitatively only for (il) (i2), (i3) by Liitjens.07) From these and later experiments it was apparent that the burning of Ba with CuO as oxidizer and evaporating the excess Ba is the most efficient method that we
G. HAERENDEL,
12
R. LUST and E. RIEGER
have found so far (efficiency about 5 per cent). It has been used for the clouds (i2), (i7), (is), (i9), (ill) and (i12). In this context we are interested in the evaluation of the clouds’ motions in terms of ionospheric electric fields. Cloud (i6) was too faint for a good determination of the velocity, and the visibility of cloud (W) was very poor because of suddenly developing morning fog. The high experiments (i9) to (i12) have not yet been evaluated. Also the considerations of this paper are not relevant to them. N
+
pant of &erMtlon
E
I--
&I* (144) (lh4)
I1521 1 /A
Zmln after evapcmt~m pm ,.
3
1P”
”
m
3
3
2
1 2
2
(161)
1159)
1 1153)
FIG. 3
+
1Okm H
FIGS.
3-5.
punt of
cbservut!on
Nov. 27, 196L
PROJECTIONSONAHORIZONTALPLANEOFTHEVELOCITIESOFSEVERAL Sr CLOUDS. -I-HENUMBERS IN BRACKETS GIVE THE HEIGHT IN km.
Ba+,Ba,
AND
For the derivation of an electric field strength from the observed motion of an ion cloud we have to know in addition the velocity of the neutral atmosphere [see equation (3.22)]. But as barium is so quickly ionized the neutral barium is not very apt for this purpose. So it turns out to be very fortunate that the Ba metal that we use contains always a small admixture of strontium which is not effectively ionized. Since the resonance line of Sr at 4607 A lies very near to one of the resonance lines of Ba+ (4554 A), one can photograph the Ba+- and Sr-clouds with rather narrow interference filters, in order to exclude the sky background. The separation of the clouds is easy because of their entirely different geometries (Figs. 6 and 7). (b) The ion clouds So far we have found three typical patterns of motion which are shown in Figs. 3-5. In evening releases the neutral wind velocity as well as the ion cloud velocity had generally
FlCa. 7. FIGS.
6-X.
PHOTOGKAPHS
OF SEVERAL
Ba’
(ELONGATED
SHAPES)
‘THREF SURSFQIIENT
AND
TIMES.
IUELITRAL
Sr
CLOI~IX
(SPHFKIC‘AL
SHAPFS)
,AI
FIG. 8.
MOTION OF ARTIFICIAL
1 0 7mn
after
ION CLOUDS IN THE UPPER ATMOSPHERE
13
evaporation
pod of + obserwtion
Sept
30 ,
1965
FIG. 4
strong north-easterly components (Fig. 3). During the morning twilight the motions (two cases so far) pointed south-westward (Fig. 5). Generally the neutral cloud moves faster than the ionized one. Ion cloud (i7) was peculiar in several respects. A* of the Ba+-cloud was apparently much higher than unity so that the ion cloud was forced to move with the neutral atmosphere (Fig. 5). We see it always as a sharp stripe through the center of the neutral Sr-cloud (Fig. 7). In addition to the Ba+-cloud we see the Pedersen current, which has to flow continuously through the cloud, emerging at one side of the cloud like a tail (barely detectable on the print). The invisible air ions fill up the rear of the cloud (as viewed in the direction of the
14
G. HAERENDEL,
R. Lf_hT and E. REIGER
+ porbt of observation
1 : 0.15m’n 2:2fjN”
after I,
waporatiar II
Ba+- tall ,4 t Ba I Ed. Sr
c N
+
point of
E
lOkm Nov
FIG.
16,
1965
5.
current) and proceed very slowly because of the low field strength inside the cloud. We interpret the relatively sharp boundary at the rear of the Ba+-cloud as the transition from air ions to ionized barium inside the electron cloud. An equal amount of Ba+ ions is leaving at the front and moving with the unperturbed velocity of ions in the surrounding ionosphere. The propagation of the tail’s end is plotted in Fig. 5. A much better frame of reference for an understanding of the motions is oriented with respect to the magnetic field. Table 3 contains the velocity components, v,,, parallel to B, the magnitudes of the perpendicular components, 1V,l, and the angle, v, between V, and vnl (p’ > 0, if V,, vni and B are right-handed). We expect: veil = vill. This is almost fulfilled in four of six cases. The strong deviation in experiment (i4) has probably the following reason: The velocity of the neutral cloud was determined from the first 4 min after release; afterwards the neutral
MOTION OF ARTIFICIAL
ION CLOUDS IN THE UPPER ATMOSPHERE
1.5
TABLE3
No. il i2 i3 i4 i7 it3
U/I
1~11
Element
(m/s=)
(m/W
Ba+ Sr, Ba Ba+ Sr, Ba Ba+ Sr, Ba Ba+ Sr, Ba Ba+-tail Sr, Ba, Ba+ Ba+ Sr, Ba
35.1 17.8 22.4 26.8 63.7 64.9 27.7 62.9 -39.0 -41.1 21.7 19.5
22.6 73.0 47.6 75.0 53.9 117 39.7 113.5 90.7 47.1 28.1 54.5
VJ -t5” +3.4” - 14.2” +28” +25” -8”
clouds were too faint. During this time interval the neutral clouds are falling rapidly. A substantial part of this vertical velocity is due to the action of gravity. The sedimentation of neutral gas clouds has been investigated by Haerendel .(lg) Its velocity increases with molecular weight, and decreases with time. The observed velocity is in good agreement with the predictions of the theory. As the ions are less affected because of the inclination of the magnetic field, we see that the actual neutral atmospheric wind component parallel to B should have been appreciably smaller than V,, of the neutral clouds. For experiment (il) we are not able to give a definite reason for the discrepancy. It might be due to the observed wind shears in the atmosphere (see below), which make the definition of the cloud’s center a bit difficult. The most striking result concerning the velocity components perpendicular to B is that, in five out of six cases, that of the neutral component is higher than that of the ion cloud by a factor between 15 and 3.0. Only in experiment (i7) this factor was 0.5. The angle, v, between the velocity vectors was always smaller than 30”, in four cases less than 15”. It is interesting to compare (i2) and (i3), because these clouds were generated during the same flight. Although the neutral gas velocities were very different, we found about equal V,. A few remarks should be added concerning three of the clouds. From the brightness of the tail coming out of cloud (i7) (Fig. 7) one could measure the ionospheric electron density. It should be very nearly equal to the Ba+ density within the tail, since the ratio of Ba+ to air ions is very great inside the cloud where the tail originates. In Fig. 6 we have three photographs from our first ion cloud (il). Two features are of interest here: (1) The light-bridge between the Ba+- and the Sr-clouds is a result of the photo-ionization after the initial phase showing the path of the neutral Ba-cloud. Its brightness agrees well with the expectations from photoionization with a time scale of 100 sec. (2) The distortion of the ion cloud is interpreted as due to a shear of the mainly horizontal atmospheric wind. As ~~for this experiment was near 7 and, as we shall estimate below, il* might not have been very near to unity, V, was sensitive to changes in v,~. This would explain the deviation of the long axis of the Ba+-cloud from the direction of the magnetic field (cf. Fig. 3) and the widening of the lower end (in real space!) of the ion cloud (Fig. 6), since there is always a diffusion along the lines of force superimposed. (All other ion clouds were oriented parallel to B). In addition we expect the deformations that have been discussed in section 4 to take place after a few minutes. Also the ambipolar diffusion might contribute to the broadening.@)
The stripes that appear 15 min after release of cloud (is) (Fig. 8) are very remarkabk. A deformation of the cloud becomes noticeable only after about 8 min. We regard this as a manifestation of the same effect, namely the modi~~ation of the ionospheric co~ducti~ities I; due to the presence of the cloud. As K~ for this experiment was near 30 we expect the deformations to develop with a time-scale about of 15 min (4.3), but it is not clear what causes the stripes instead of a more homogeneous deformation. The finite width oE the cloud and the recombination in the E-layer might be partially responsible. In other cases we found the width of the ion clouds essentia~y constant. In (27) it has even a slight tendency to decrease, which is expected from the entering of air ions into the electron cloud. The time-scale 7-(4-2)of deformation is very long for this doud in spite of K~RS2, The high Ammakes the relative drift, U,, with respect to the neutral cloud unobservably small, and consequently also U’
The interpretation of the measured velocities perpendicular to 3 (TabIe 3) in terms of ionospheric field strengths suffers mainly from the unbrtainty about the actual value of 1”. The amount of Ba* produced during the phase of initial ionization has been evaluated so far for clouds (il) to (i3) With an integrated ionospheric Pedersen conductivity of 2 !G@(an intermediate value according to Table 4) we find values of ;1* that deviate subs~ntially from unity (Table 4). The numbers in Table 4 serve only for demonstration purposes. The
1-1i@f 2.5IO= 3.2IO=
30.0
o-68 f-18 0.43
f-34 1-6 1-22
is so uncertain that any correction for a* r 1 according to actual value of x:plonoerph* formula (3.25) is impossible. Also among the later experiments the situation is not better, For (~7) we know from its motion that a* > 1. From the amount of theoretically evaporizable material and with typical efficiencies for the difIerent types of reactions we expect only for the very faint cloud (S) that a* is very near to unity. So we reduce our data with ir* = I, i.e. o = K~ (1 -t_ Q)-Xand b = 1 and emphasize that we do not get true electric fields. How strong the corm&ions are, to which these field strengths are to be subjected, might be estimated from d* of Table 4. The most important correction would stem from the last term in equation (3.25); it tends to reduce the magnisince the tude of E*. The application of (3.25) with A* = 1 is only correct for the tail in (a”‘?} perturbation of the ionospheric electric field by the presence of the cloud should be negligible at some distance from the cloud’s axis. Figure 9 shows the magnitudes and orientations of the “measured” electric fields. The generai pattern at least should be real. During the four experiments carried out in the evening at a magnetic latitude of about 33”N, the -fields were generahy directed southward. In experiment fi4), a morning launching, at a magnetic latitude of about 40”N the geld pointed to the north. So far we cannot decide whether this reversal in direction indicates essentially a morning-evening elect or whether it is partly due to the diEerence in magnetic latitude.
MOTION
OF ARTIFICIAL
ION CLOUDS
IN THE UPPER
ATMOSPHERE
17
The field strengths were between 1 and 3 . 1O-3 V/m. This is of the same order of magnitude as is to be expected from the strength of the &-current system. From the magnetic observations at Fiirstenfeldbruck (Germany) (private communication) there is no indication of any significant disturbances during the experiments listed in Fig. 9.
FIG.~.POLARDIAGRAMOFELECTRICFIELDSINAPLANEPERPENDICULARTOTHEMAGNETICFIELD As DETERMINED FROM THE MOTION OF ION CLOUDS. THE NUMBERS IN BRACKETS REFER TO THE EXPERIMENTS LISTEDINTABLE 2.
6. CONCLUDING
REMARKS
The experiments so far carried out led for the first time to well observable ion clouds. But they should be regarded only as preliminary. Nevertheless they have demonstrated that one can use this method to investigate phenomena of the upper atmosphere and particularly to determine electric fields if a suitable amount of barium is released at an altitude of about 200 km. Further experiments are planned at different geographical locations to investigate the electrical fields under different conditions more thoroughly. Other experiments shall be carried out at much higher altitudes to study the earth’s magnetic field, and finally the interplanetary plasma. It has just been demonstrated that the method works also at higher altitudes by producing two ionized barium clouds at a height of about 2000 km on April 22, 1966. The two clouds extended along the lines of force over an angle of about 80 degrees which corresponds to a length of more than 2000 km. The clouds were visible for about half an hour and from locations at the earth which were separated by more than 3000 km. Detailed results about this experiment will be published later. Acknowledgements-The
experimentsin Nov.
the help of the French authorities. 2
1964, Nov. 1965, and April 1966 have been carried out with We would like to thank them and particularly the “Centre National
18
G. ~~REN~EL,
R. L@YlYand E. REEGER
d’Etudes Spatiaks” (CNES) and Prof. Bfamont for alI their support. For the experiments in September 1965 faciIities were provided by the “European Space Research Ur~~sa~on*’ (ESROf. We thank afi the stti members who he&d us in these experiments. Last but not Ieast we are most thar&fuI to our caIIeques who were invoked in these experiments, particuIarly Messrs. EL FappI, L. Baser, J. LoidI, P. Lritjens, F. M&zner, B. Meyer and H. Neuss. 1. L. BIE~NN, R. L&T, m, LilsT and H. U. SCXM~T,2. A&+@~$. 53,226 (1961). 2. E. R. HARRISON, Geo@ys. J. 6,462 (1962). 3, E. W. HONES,JR., On the use of eie&risaI ion sources for iOn tracer experiments in the ~~~~t~p~~, UniversilJi of Iowa Report 65-31@%). 4. C. 0. Hms, Spcrf? Sci. && 3,342 (1964). 5. H. FSPPL, G. -EL, J. MIDL, R. L&T, F. MELZNBR, B. MEYER,H, NEU~~and E. RIIZGER, PTanLlt, Space Sci. X3,95 (1965). Submitted to Planet, 6. H. F~PPL et nl. Artificial strontium and barium clouds in the upper a~osphe~. space sci. (1966).
10. D. F. MARTYN,Phil. Trans. R. Sot. A246,306 (1953). 11. P. C. CLEMMOW, M. A. JOHNSON and K. WEEKES, A note on the motion of a cylindrical irregularity in an ionized medium, Proc, Zonoykexe Conf pp. 136-139 Physical Society, Landon (1955). 12. S. KATO,PIazet. @ace Sci, I& 823 (1%3). 13. J. P. I~o~c+&~zRTY, b. geupkys. Res. 64,2215 (1959). 14. R. Bosfffijhl, J. geopkp Res. 69,4983 (19&Q. $5. J. H. P~D~QToN, Planet. S@~ceScf. Z&l27 (1964). 16. K. MAEDA and H. M~Tsu~o+ro, Rep. fonosph. and Space Res in Japan X6,1 (1962& 17. P. L~TJENS,Messung der ~~pf~chte an ~stlich~ Met~ld~pfwoI~en in der Ionosph&e mit photo~aph~en Methoden, ~iplomar~it, Univ. Munich (1966). 18. R. I). HUDSON, Private ~mrnuni~tio~ (1965). (1966). 19. G. HAEREPJIIEX., Sedimentation of arthieal gas clouds in the upper atmosphere* fn lotion ~~~~~~~T~~
aTog CTZITIII-3~t-%TCSiL&WA0 p??KIWTIaypaBEeKER @E-XeKES% &XK ~eHK3~~~~aK~O~ ReO@iO~~~HoCTSi ~Pe~e~bH~~~~~K~,~ flPMJIOIKEITbTa~~B~eKnOBe_ ~eazia o6naKa Ba*. Bcjre~saqe~rb~~p~~Ao~ ynpo~aro~arcnpe~nocbIJro~,~aaolrtt;rrcK sbIpaK@Kae gnK ~o~ac@ep~oro axexTpsfYecKOr0 nons wa OCBOBBHHU (1) MarntZTBora IIOJIK,(2) CHopOCTeltfr Ht?iTpaJlbIiJJX EI KOEm?HpOBaHIibIX OlinaKOB, (3) I* (OTltrQux?Hm? nATerpHposaHm&x ne~epceaoacK~x npoBv~uMocTefi B o6aaKe I aTMoctpepe), (a} K# (= rzpasac+roTa ASIR YacToTu Ba~~~oy~apeK~e~. B+XKRYXH~ a opxewrxpowa axe=pasecxoro no~llii ~~e~~a~T~K ~3 zr362xiogerisiK me6TEc o6~1azio13 6apws x c~pos~m. iipaccnnaTp~rsae~cR~tza~e~3ee~knmqM. C~~bIfiOJXK,xaaoKassntaeTER,RcuncarK~T~ ~e?wy I H 3,10+Vjnf. Bevepoiw IIOZR ;yxaabrxwjT KalrparrjIeKKea c~opo~y rora,a paIiHKM yTpOM OHX p3306~3~TCXB ~TO~oKyCeEep3.
Printed in Northern Ireland
MOTION OF ARTIFICIAL ION CLOUDS IN THE UPPER ATMOSPHERE G. HAERENDEL, R. LUST and E. RIEGER Max-Planck Institut fiir Physik und Astrophysik, Institut fiir extraterrestrische Garching bei Milnchen
Physik,
(Received 10 June 1966) Abstract-The paper sets out to solve the equations of motion for an ionized irregularity. of finite length, and to apply it to the behaviour of a Ba+ cloud. After a number of simplifymg assumptions, an expression for the ionospheric electric field is derived in terms of (1) the magnetic field, (2) the velocities of the neutral and ionized clouds, (3) 1* (the ratio of the integrated Pedersen conductivities in the cloud and in the atmosphere), (4) K‘(= gyrofrequency for Ba+/collision frequency). The magnitude and orientation of the electric field is evaluated from the observation of six barium and strontium clouds. il* is assumed to be unity. The derived field strengths lie between 1 and 3 . 1O-s V/in. In the evening the fields are pointing southward and in the early morning release northward. 1. INTRODUCTION
Experiments with visible artifical ion clouds have been proposed to provide a means of studying the interaction processes between the interplanetary plasma and artificially injected ions, hoping that we might thus improve our understanding of the physics of ionized comet tails and of the interplanetary plasma itself. (l) In addition, ion clouds can be used to map out the distant geomagnetic field,t2) and also for measurements of electric fields in the ionosphere. ~3~) For obvious reasons the technique of releasing visible ions is most easily studied with small sounding rockets in the ionosphere. Any observed drift motions of the ion clouds should throw some light on the existing electric fields. In the course of release experiments at heights between 130 and 2000 km with barium, which seems to be at present the most suitable element for these purposes,(1*2*5)we have succeeded several times in producing easily visible ion clouds during twilight. As a basis for the understanding of the observed motions, the expansion, and the deformations, we shall briefly review the theory of the movement of ionospheric irregularities. We will show that the finite extension of any real configuration and the spatial variation of the ionospheric parameters, as for instance the conductivity, have serious consequences on the behaviour of an ion cloud. The flow of electric currents along the lines of force introduces new aspects which are missing in semi-infinite configurations which have been investigated in most of the earlier theoretical work. As the mathematical difficulties encountered in treating very realistic models are considerable, our discussion will remain rather incomplete. Finally, we shall present our first experimental data with Ba+-clouds as far as the above mentioned aspects are concerned. All other topics, especially the technical questions have been or will be discussed elsewhere.(5*6) 2. BASIC RELATIONS
We start with compiling the well-known equations on which the treatments of ambipolar diffusion and of the motions of ionospheric inhomogeneities are based. 1
1
2
G. HAERENDEL,
R. LUST and E. RIEGER
The equations of motion of the three components considered (indicesj and 1 stand for e = electrons, i = ions, n = neutral molecules) are:
where mj is the mass, nj the number density, vg the velocity, pj the pressure, g the gravitational acceleration, e, the charge, E the electric field, B the magnetic field, and yjCthe collision frequency for momentum transfer between the j-th and the I-th components (the reduced mass appearing in the momentum transfer has been included in the definition of vjl). The following simplifications of (2.1) are typical for most of the applications in the discussed context: (1) The left-hand side of (2.1) is set equal to zero. Thus all rapid changes, especially the initial expansion of a disturbance, are omitted. (2) The influence of gravity is neglected. This means that the atmospheric scale heights are considered to be large compared to the extension of the cloud, or both are infinite. (3) The magnetic field is homogeneous and constant with time. The currents flowing in the irregularities are so small that the disturbance field can be neglected. This is possible as long as the disturbance of the electron pressure pe is small compared to B2/8vr. In all our experiments, after the initial expansion, this ratio is less than about 10-5. (4) The collisions between ions and electrons are assumed to be of much less importance than the collisions with the neutral particles. For Ba+-ions this is true up to heights of about 300 km. Another consequence of this assumption is that the velocity of the neutral component, v,, can be regarded as constant with time; and usually also spatial variations (wind shears) are neglected. So, only very simplified equations of motion for the ions and electrons remain. These have to be solved together with Maxwell’s equations, an equation of state relating the pressure to the density, and the equations of continuity for ions and electrons. From Maxwell’s equations only: curl E = 0
(2.2)
has to be taken into account explicitly, which is consistent with the assumption of slow processes. All processes are considered to be isothermal: pj = n,kT;
T, = Ti = T,, = T = const.
(2.3)
Because of the smallness of the Debye-length (about 1 cm) we have to postulate charge neutrality, i.e. for singly ionized atoms: n, = n, = 12.
(2.4)
div j = 0,
(2.5)
As a consequence we have: where j = en (vi - v,) is the electric current density. Equation (2.5) is equivalent to the difference of the two equations of continuity. Thus only one of them remains, g + div (n vi) = P - L.
(2.6)
The right-hand side represents all production and loss processes, which will subsequently be neglected.
MOTION OF ARTIFICIAL
3
ION CLOUDS IN THE UPPER ATMOSPHERE
With the above mentioned simplifications we can now solve the equation of motion for the velocity, We shall work in a frame of reference where the neutral component is at rest : y.* =2 v. J 3
y *;
(2.71
j=e,i
E* = E -j- i Y, x B.
cw
With the definitions : e,=-,
B
5=-=
B
*cd
X (Vj*
Kj2eB
X eB)
(2.9)
it is negative for electrons!) we can write
(mgj is the gyrofrequency of the j-th component; v, in the following form: vj” -/-
ejB
Yin mP5,
=
Kjttj +
Kj”uj
(2.10)
X eB
with uj
=
c B
(2.11)
K, and K~ for Ba+-ions at heights between 120 and 240 km are plotted in Fig. 1. If we separate vj into its components perpendicular (yj,) and parallel (vji,>to B, we can write instead of (2.10): (2.12a) (2.12b) %I* = 'Ciujir From the difference between (2.12) for ions and electrons we find the relation for the current density : t-)
%‘.E*---6.pi-
j=
Vn
(2.13)
n
2 is the conductivity tensor and zis essentially the tensor of the difference of the diffusion coefficients. In a Cartesian coordinate have the form
system where B is parallel to the z-axis, ‘a*and x
op is the so-called Pedersen, CJ, the Hall, and ufi the direct conductivity: ---
K, 1 +
--~
'
1 +K:
2 K* 1 +
alI =
Ki Ke2
net B (Kz -
Ki"
K&
;
‘ce
I+
(2.15a)
KS2
(2.15b)
’
61,=
net 7 (Ki +
Ke)
(2.15~)
G. ~AERENDEL,
R. LUST and E. RIEGER
lo6
10
5
104
103
lo2
10'
100
10“ 120
I
I
140
1Eo
180 "&"'I
I
I
2cO
220
1 240
-
FIG. 1. WTIO, K, OF CiYROFRJZQUJ3NCYAND COLLISION FREQUENCY WITH NEUTRAL FOR Ba+-IONSAm ELECT~~~NS AT HEIOHTS BETWEEN 120 AND 240km.
PARTICLES
We have arbitrarily named the corresponding components of the z-tensor by the same subscripts as in the conductivities (note that K@ < O!). All contributions to the current perpendicular to B decrease with decreasing collision frequency, except the term 6&e, x (Vn/n) which converges for K$ > 1 towards the expression for the magnetization current in fully ionized gases. As this part of the current flows parallel to contours of constant density it is not relevant to our later considerations. Essential is the continuity of j [equation (2.5)] in the direction of Vn, which leads to the distribution of the electric field. The magnetic perturbation due to the magnetization current has already been assumed to be small. If we now consider the ambipolar diffusion and the movements of ionospheric inhomogeneities we can characterize these two idealized types of problems in the following way: (a) In ~~b~po~ar~1~~~0~the electric field is assumed to be entirely due to the polarization within the inhomogeneity because of the different mobilities of ions and electrons. Thus E* = 0 at infinity if we consider a cloud of ionized particles imbedded in an infinite weakly
MOTION OF ARTIFICIAL
ION CLOUDS IN THE UPPER ATMOSPHERE
5
ionized atmosphere. (b) For the motion of irregularities the existence of an outer electric field is essential. For the sake of simp~fication one generally neglects the diffusion terms and looks for solutions where the irregularity can move under conservation of its shape. This is only possible for semi-infinite discontinuities of the electron density,“,@ where Vn vanishes except at the boundaries. The variation of the density perpendicular to B over the extension of the cloud, i.e. the variation of the conductivities, leads to a variation of the screening of the outer electric field. Thus the forces acting on the particles inside the cloud are not constant; the cloud will be deformed. However the bulk motion should be well described by the simple, discontinuous model; particularly if the polarization field, E,, arising from the ambipolar diffusion [(cf. equation (2.1 l)] : ]E,]
=
I I=
T ;
kT1 e
(2.16)
E
is small compared to \E*/ (L is a characteristic length). Numerical values give: ]E
(2.17)
] 2,
With clouds whose width is at least 1 km, IE,j is certainly much less than the field strengths of about lo* V/m which are encountered in the ionosphere. This estimate, on the other hand, demonstrates that any changes in the shape perpendicular to B after the initial phase are more likely due to the action of an outer electric field rather than due to merely the ambipolar diffusion.(s) In section 4 we shall see that the finite extent of a cloud along the direction of the magnetic field increases the difficulties considerably. In one of the experiments described in section 5 we can see deformations developing (Fig. 8). 3. MOTION OF A CYLINDRICAL
IRREGULARITY
OF F’INITE LENGTH
The theory of the motion of ionospheric irregularities, which has been developed by Martyn, (lo) Clemmow et al.,(ll) Dungey,o) Kato(8J2) and many others, applies closely to the motion of an ion cloud in the upper atmosphere. Most of these considerations deal with irregularities that extend infinitely along the lines of force in a homogeneous medium. For a more general discussion we have to consider the case of an irregularity of finite length above the region of maximum Hall- and Pedersen-conductivities. Then, as Dougherty’@ has previously pointed out, the polarization field within the cloud can be short circuited by currents flowing along the lines of force and closing in the E- and F-regions of the ionosphere. Therefore, the jump in the electric field at the boundary of the irregularity is no longer determined by the ratio of these densities inside the cloud and outside, but by the ratio of the integral conductivities along the lines of force through the cloud and outside. A problem of this kind has been investigated in detail by BostrGm(14Jin a theory of aurora1 arcs, but these inhomogeneities have a finite width only in one dimension perpendicular to the magnetic field. The new aspect introduced by ion clouds lies in the finiteness in all three dimensions. We consider the following model sketched in Fig. 2. The ion cloud is represented by a homogeneous cylinder of finite length with an electron density which is ii times the density of the ambient atmosphere. The cloud is shorter than the atmospheric scale height, so that
6
G. HAERENDEL,
R. LUST
and E. RIEGER
we are justified in assuming constant values of K~ and K,. The currents, J, need not be continuous on a horizontal level because surface currents, J,, along the lines of force between the cloud and the lower ionosphere are allowed. The horizontal current through the cloud J,Omight exceed the current just outside by Js, but then JzE has to be smaller than JIE by the same amount. The lines of force are considered to be equipotentials, since the direct conductivity is higher than the Pedersen conductivity by at least three orders of magnitude. Even if the “surface’‘-current flows within a relatively narrow region the parallel component of E can be neglected in comparison to the perpendicular component above the bottom of the dynamo region.
__
.___--_c~-_c_____ -I T
y-
T
J,
'2
E-and
F-rqlon
JE
FIG. 2. MODEL OF A FINITE CYLINDRICAL IRREGULARITY WITH AXIS PARALL EL TO B IN THE IONOSPHERE. THE CURRENTS Jl.2 ARE HORIZONTAL CURRENTS, INDEX 2 REFERRING TO LINES OF FORCRPASSINGTHROUGHTHEIRREGULARITYANDINDEX1TOTHOSERBMAININGOUTSIDE. Jg~sz ELECTRONCURRENTSPARALLELTO B FLOWINGONTHESURFACEOFTHBlRREGULARlTY. THEE AND~LAYERSAREREPRESENTEDBYAFINITELAYER(INDEXE)OFHIGHhDBRSENCONDUCTIV~.
The continuity of the total current is expressed by: n . (Jlo + J,“) = II . (Jzo + J,“),
(3.1)
where n is the normal vector of the irregularity perpendicular to B and J,,, are the integrals ofj,f, along the lines of force:
J,,, = We write [cf. equation (2.13)] :
s
j& dl
J=s.E
(3.2)
(3.3)
with the two-dimensional conductivity tensor, s, which is obtained from 2 (2.14) by disregarding ull and integrating a, and au along the lines of force: Z&H = / ~P,H dl
(3.4)
From (3.1) and (3.3) we find: n.&.E,--f&.E,)=O
(3.5)
MOTION OF ARTIFICIAL
ION CLOUDS IN THE UPPER ATMOSPHERE
7
In writing (3.3) we have assumed that the neutral component of the atmosphere is at rest, Later we have to transform to a coordinate system which allows for a wind. If we introduce cylindrical coordinates (r, 8, z) with respect to the axis of the cylindrical inhomogeneity which lies parallel to B, (3.5) can be written as:
&Er, - CH,J%, - &,Er, + OH&, = 0
(3.6)
We define the ratios: A* = 1P -2, & and make use of curl E = 0, i.e. :
2 l=g
(3.7) u, (3.8)
J%, = G,
at the boundary of the cylinder.
Then (3.6) becomes:
El., = a* Ev, - (E - 1) 5 Ee,
(3.9)
With (3.9) we have reduced the problem to the case of an infinite cylinder in a homogeneous atmosphere; only the coefficients have a different meaning. Comparison with earlier work, e.g. Dungey (‘) shows that with a homogeneous electric field E, at infinity E, is also homogeneous (neglecting the small component E,,) and related to E, by: E, = 4 (A* + 1) E, - + (t - 1) 5 (Es x e& (cf. equation (9.30) in Dungeyo)).
(3.10)
We solve for E, and get: (3.11)
E, = NE,, + BE, x eB, with
cc =(1 +
2(1 + a*> n*>z + (1 - E)252’
265- 1x IR= (1 + A*)2 + (1 - E)2<2
(3.12)
A* and t are equal to il in the case of an infinite cylinder. The variation of the ionospheric conductivities with height, however, has the consequence that 1* and [ will be different. If the cloud is above 130 km (K~> 1, cf. Fig. l), its contribution to En will be less than that to & [cf. equation (2.15)]; thus 1<5<1*
(3.13)
The inequality (3.13) reduces the importance of the second term on the right-hand side of (3.10) in the determination of E, (5 G 1 according to Table 1) compared to the first term. If we know the electric field inside the cloud we can derive the velocity of the ions from (2.12a). But one can observe only the motion of the boundary U; part of the ion velocity, vi, only contributes to the current which continues through the boundary. As the surface current parallel to B is carried by the electrons and diffusion is neglected, we can claim continuity of the ion flux on a horizontal level: n . U (n) = n . (nv,)
(3.14)
((n) = n2 - nJ. We emphasize that we make the assumption that the motion of the finite cylindrical irregularity can occur without deformation or changes in the density. Later this point will be examined.
8
G. HAERENDEL,
R. Lf_.bT and E. RIEGER
The constant density inside the cloud, ns, is jl times the density, ~zr,outside at the height of the cloud. With a constant value of K~, (2.12a) and (3.14) lead to: c ?Z,n . (A& + AK~E~ X eB -
n . u nl(l - 1) = Ki
I+KFB
El -
Ki El
X
eB)
(3.15)
Replacing E, by E, with help of (3.8) and (3.9) and using the fact that (3.15) holds for all directions of n (perpendicular to B) with the constant vectors U and E,, we find that: (3.16) where :
a - a*
Ki
~___2L 1+
Ki
Ki +
g
I)
(3.17)
.
We are interested in U as a function of the field strength at infinity, E,. We introduce (3.11) into (3.16) and get: E, x B (3.18) 73
U=ac%+bc
where : a = uy -
/IS,
(3.19)
b = a6 + By.
For future application to the observations we transform (3.18) to a coordinate system in which the neutral atmosphere moves with velocity vnl perpendicular to B. We call the velocitv of the cloud in this frame of reference VI and the electric field at infinity El,. Thus:
I
’
u = v, -
E, = EL0 + A vn,_ xB
vnl,
El0 cy+v*l
VL=a
(3.20)
C
+bcT+
xeB
EL0 x B
>
(
(3.21)
(1 - b) vnl
If we solve (3.21) for EL0 we get; EL0 = T D-‘[a (V, - v,J
+ b(eB x V,) -I- (b - D) vnl x
(3.22)
eB1
with : (3.23)
D = a2 + b2.
is useful to consider an appropriate expression of (3.22) for heights above the E-layer > 1). According to (3.13) we have (5 - 1) 5 < 1 + A*. In addition A* < 1. So we get approximately : 1 2 am--, bw2 (3.24) 1 + 1* Ki 1 + a*
It
(Ki
and : l+l*B
EL0 m 2
c
A* eBxvl-t+-vnL)+~v
*
1 nl
’
eB
1
(3.25)
MOTION OF ARTIFICIAL
ION CLOUDS IN THE UPPER ATMOSPHERE
9
The equations (3.22) and (3.25) are the basis for the interpretation of the motion of an ion cloud in terms of the ambient perpendic~ar component of the electric field. We see that one has to measure, in principle, also the velocity of the neutral atmosphere and that one needs the values of K~ at the height of the cloud, and the integrated conductivities. Not only the electron density inside the cloud but also in the ionosphere must be known, as far as it contributes appreciably to the integrated perpendicular conductivities.
The polarization of a column of enhanced ionization in the ionosphere depends essentially on the ratio, il*, of the height-integrated Pedersen conductivities inside the column and in the undisturbed ionosphere. If the irregularity is above the region of maximum conductivity, i.e. if K~ > 1, a* is considerably smaller than the ratio, il, of the electron densities at the level of the irregularity. It is seen from (3.17) to (3.19) that for L* < 1 the mobility, a, of the cloud in the direction of E, is increased relative to the case of an infinite cylinder with ratio A. This means that the electric field inside the column is not very effectively shielded. So the particles have also a considerable drift velocity, bc[(I$, x B)/B2] (3.18), which, for 2* + 1, approaches the drift of a single charged particle (b -+ l), since (t - l)[ is a small number. The increase in mobility in the direction of EOis achieved by the flow of currents along the lines of force between the cloud and the regions of high Pedersen condu~tivities (E- and F-layers). The electrons which according to (2.12a) cannot follow the ions directly are removed from the rear of the cloud, and new electrons appear at the front (with respect to E,!) to neutralize the arriving ions. As the electrons can nowhere move across B in the direction of E. (the currents are closed by Pedersen currents), they accumulate in the E- and F-layers along the lines of force passing through the rear of the cloud; and a deficiency of electrons is built up in these layers along the field lines through the front of the cloud. The total number of electrons along a line of force remains of course unchanged, as long as diffusion is neglected. This problem has also been considered by Piddington(15) in a theory of spread F, and by BostrGm(14) in a model of an auroral arc. The change of the electron distribution along B, initiated by the cloud’s motion, results in changes of the integrated conductivities, since they also depend on K( and IC*(2.15), which vary greatly with height (Fig. 1). Consequently, the important assumption made in section 3, that a* is not affected by the motion of the irregularity, breaks down. The conductivity, i.e. il*, is lowered at the front, and increased at the rear of the column. Thus, different parts of the cloud move with different velocities, U; the cloud will be broadened and sheared in the sense that the rear, where a* is higher and thus E, weaker, more closely sticks to the neutral atmosphere. How serious this effect will be depends mainly on the number of electrons injected, N,,c, per unit area along a line of force. (We call the line integral of the density parallel B: N,,, and the line integral perpendicular to B : NL. The indices c, E, F refer to the cloud and to the E- and F-layers, respectively.) Even with very little change of 2 (a* = 1) due to this increase in the electron density Niicand NE might be comparable; or the latter can even be smaller. Nlis is always much higher than N,?; so 2” is not affected. As the con~ibution of the E-layer to the integral Pedersen conductivity is at least as high as that of the F-layer(26) a substantial fraction of the current Js (Fig. 2) will initially flow through the &layer until the conductivity there becomes seriously altered. The condition N,y < NjIE would mean a very serious limitation for an ion cloud
10
G. HAERENDEL.
R. LUST and E. RIEGER
experiment. With numbers taken from Maeda and Ma~urnoto(l~) we would have to postulate*. N c < 7 . 1O1*cm-2. Because of the elongation of the cloud we would get: N,” < 1.5 , 10lt cm-2. If we choose for instance: NLc = 2. IO* cm-2 the photon flux from the cloud would be 5 . 10’ cm-2 se& sterad- 1.(6) During twilight conditions this is a barely detectable intensity. We can escape this difficulty, if we use only the initial period of the cloud’s motion, before the conductivities have been changed appreciably, for the interpretation in terms of the ionospheric electric field. A quantitative description of the deformation phase for a realistic model seems to be extremely difficult. The time-scale for the appearance of deformations is estimated by: 7=-
L
(4.1) UE
where L is a characteristic scale of the cloud in the direction perpendicular to B (L-l = n-l ]Vnlma.J and U, is the component of U (3.18) in the direction of I&. If we designate by U, the more easily observable drift velocity [second term on the right-hand side of (3.18)] we can express (4.1) by: bL 7=_--, a uD
(4.2)
with a and b from (3.19). A good choice for L is 1 km and for U, (see next section) 30 m see-l. If Iz* M 1 initially, (b/a) z q, and we find: 7 z 30 Ki [Set] (4.3) In order to have an observation period of about 15 min, KS should be larger than 30, i.e. the ion cloud should be produced at heights above 180 km (see Fig. 1). Since the ionospheric conductivities change considerably during twilight conditions, z:, and zn are rather delicate parameters. Consequently, we should require a* = 1. Some numbers extracted from the work of Maeda and Matsumoto(16) and BostrGm(14) (with correction for an inclination of 45’) have been gathered in Table 1 in order to indicate the TABLE
1
Local time (hours) 0
4.0
6 12 0
3:.: 0.77
0.14 0.43 1-O 0.34
16 16 16 14
range of variation and uncertainty. With a constant value for K( and the contribution of the cloud to the Pedersen conductivity by:
K#
>
1, we can express
zr Z 4. lo_11 Nile [Q-l]. Ki The postulate that iz* = 1 would mean:
(4.4)
N,f < 5 . lOlo fci [cm-2].
(4.5)
Together with the limitation for ~~ arising from (4.3) this is not a serious restriction. The ion cloud may even be optically thick along the smaller axis (for Ba+: NLc M 5 . IOx0cm-3.
MOTION
OF ARTIFICIAL
ION CLOUDS
IN THE UPPER
ATMOSPHERE
11
Of course we would like to measure electric fields with as little material as possible. So we would choose the lowest possible height, which according to (4.3) lies near 200 km (K~= 50). By (4.5) NgiO< 3 . 10” cm-2; with a typical cross-section of a cloud of 20 km2 we find that the total mass of released Bat is limited to 14 g. This is still a surprisingly low number. Even with inefficient evaporation the whole experiment would have a total weight of only a few kg. 5.
EXPERIMENTAL
DATA
In Table 2 we have gathered a few data characterizing all visible Ba+-clouds so far produced by our group. The technological aspects are left out; they will be discussed elsewhere.(6) Ba+-ions are generated in two different steps, during the initial phase with a time-scale of about 5 see and by a slower photo-ionization with a time-scale of about 100 sec.fl’) The initial ionization is particularly effective since it gives rise to well concentrated clouds with a width of a few km in the direction perpendicular to B. Later on the cloud expands only along the lines of force, until the deformations discussed in section 4 become important. TABLE 2 NO.
i i i i i
Date
Time
Site
h fkm)
M C@
m @
1 2 3 4 5
Nov. Nov. Nov. Sept. Oct.
27,64 30,64 30, 64 30, 65 2, 65
e e e m m
H H H P P
152 159 199 225 220
357 83 1965 6050 467
1.8 4.1 5.3
i 6
Nov. Nov. Nov. Nov. Nov. Apr. Apr.
18,65 18,6.5 19,65 20,65 20, 65 22, 66 22,66
e e e e e e e
H H H H H H H
167 135 194 365 415 2000 2000
330 95.5 790 200 16.108 255 291
-
i 7
i 8 i 9 i 10 ill i 12
-
-
Remarks
Bad observing conditions Very faint cloud Ba+-tail Cloud with stripes
e, evening (normally at soiar depression angle of 6”). m, morning (normally at solar depression angle of 13”). H, Hammaguir (Sahara). P, Perdasdefogu (Sardinia). h, height of release. M, mass of evaporable material. m, mass of initially generated Baf.
The mechanism leading to this initial ionization is not yet clear. The width of the ion clouds corresponds well to the product of the initial velocity of expansion times about 5 sec. It could be that the initial ionization starts from a metastable atomic level with a life-time of 5 sec. Also the subsequent slow photoionization is much faster than has been estimated previously.(6) The absorption starting from the ground level of Ba is strengthened by several auto-ionization lines below 238OA. But the oscillator strengths are far too weak to explain the observed time-scale. fr*) Also here the process might use an intermediate level (perhaps the same as in the initial ionization). The efficiency of the reactions has been evaluated quantitatively only for (il) (i2), (i3) by Liitjens.07) From these and later experiments it was apparent that the burning of Ba with CuO as oxidizer and evaporating the excess Ba is the most efficient method that we
G. HAERENDEL,
12
R. LUST and E. RIEGER
have found so far (efficiency about 5 per cent). It has been used for the clouds (i2), (i7), (is), (i9), (ill) and (i12). In this context we are interested in the evaluation of the clouds’ motions in terms of ionospheric electric fields. Cloud (i6) was too faint for a good determination of the velocity, and the visibility of cloud (W) was very poor because of suddenly developing morning fog. The high experiments (i9) to (i12) have not yet been evaluated. Also the considerations of this paper are not relevant to them. N
+
pant of &erMtlon
E
I--
&I* (144) (lh4)
I1521 1 /A
Zmln after evapcmt~m pm ,.
3
1P”
”
m
3
3
2
1 2
2
(161)
1159)
1 1153)
FIG. 3
+
1Okm H
FIGS.
3-5.
punt of
cbservut!on
Nov. 27, 196L
PROJECTIONSONAHORIZONTALPLANEOFTHEVELOCITIESOFSEVERAL Sr CLOUDS. -I-HENUMBERS IN BRACKETS GIVE THE HEIGHT IN km.
Ba+,Ba,
AND
For the derivation of an electric field strength from the observed motion of an ion cloud we have to know in addition the velocity of the neutral atmosphere [see equation (3.22)]. But as barium is so quickly ionized the neutral barium is not very apt for this purpose. So it turns out to be very fortunate that the Ba metal that we use contains always a small admixture of strontium which is not effectively ionized. Since the resonance line of Sr at 4607 A lies very near to one of the resonance lines of Ba+ (4554 A), one can photograph the Ba+- and Sr-clouds with rather narrow interference filters, in order to exclude the sky background. The separation of the clouds is easy because of their entirely different geometries (Figs. 6 and 7). (b) The ion clouds So far we have found three typical patterns of motion which are shown in Figs. 3-5. In evening releases the neutral wind velocity as well as the ion cloud velocity had generally
FlCa. 7. FIGS.
6-X.
PHOTOGKAPHS
OF SEVERAL
Ba’
(ELONGATED
SHAPES)
‘THREF SURSFQIIENT
AND
TIMES.
IUELITRAL
Sr
CLOI~IX
(SPHFKIC‘AL
SHAPFS)
,AI
FIG. 8.
MOTION OF ARTIFICIAL
1 0 7mn
after
ION CLOUDS IN THE UPPER ATMOSPHERE
13
evaporation
pod of + obserwtion
Sept
30 ,
1965
FIG. 4
strong north-easterly components (Fig. 3). During the morning twilight the motions (two cases so far) pointed south-westward (Fig. 5). Generally the neutral cloud moves faster than the ionized one. Ion cloud (i7) was peculiar in several respects. A* of the Ba+-cloud was apparently much higher than unity so that the ion cloud was forced to move with the neutral atmosphere (Fig. 5). We see it always as a sharp stripe through the center of the neutral Sr-cloud (Fig. 7). In addition to the Ba+-cloud we see the Pedersen current, which has to flow continuously through the cloud, emerging at one side of the cloud like a tail (barely detectable on the print). The invisible air ions fill up the rear of the cloud (as viewed in the direction of the
14
G. HAERENDEL,
R. Lf_hT and E. REIGER
+ porbt of observation
1 : 0.15m’n 2:2fjN”
after I,
waporatiar II
Ba+- tall ,4 t Ba I Ed. Sr
c N
+
point of
E
lOkm Nov
FIG.
16,
1965
5.
current) and proceed very slowly because of the low field strength inside the cloud. We interpret the relatively sharp boundary at the rear of the Ba+-cloud as the transition from air ions to ionized barium inside the electron cloud. An equal amount of Ba+ ions is leaving at the front and moving with the unperturbed velocity of ions in the surrounding ionosphere. The propagation of the tail’s end is plotted in Fig. 5. A much better frame of reference for an understanding of the motions is oriented with respect to the magnetic field. Table 3 contains the velocity components, v,,, parallel to B, the magnitudes of the perpendicular components, 1V,l, and the angle, v, between V, and vnl (p’ > 0, if V,, vni and B are right-handed). We expect: veil = vill. This is almost fulfilled in four of six cases. The strong deviation in experiment (i4) has probably the following reason: The velocity of the neutral cloud was determined from the first 4 min after release; afterwards the neutral
MOTION OF ARTIFICIAL
ION CLOUDS IN THE UPPER ATMOSPHERE
1.5
TABLE3
No. il i2 i3 i4 i7 it3
U/I
1~11
Element
(m/s=)
(m/W
Ba+ Sr, Ba Ba+ Sr, Ba Ba+ Sr, Ba Ba+ Sr, Ba Ba+-tail Sr, Ba, Ba+ Ba+ Sr, Ba
35.1 17.8 22.4 26.8 63.7 64.9 27.7 62.9 -39.0 -41.1 21.7 19.5
22.6 73.0 47.6 75.0 53.9 117 39.7 113.5 90.7 47.1 28.1 54.5
VJ -t5” +3.4” - 14.2” +28” +25” -8”
clouds were too faint. During this time interval the neutral clouds are falling rapidly. A substantial part of this vertical velocity is due to the action of gravity. The sedimentation of neutral gas clouds has been investigated by Haerendel .(lg) Its velocity increases with molecular weight, and decreases with time. The observed velocity is in good agreement with the predictions of the theory. As the ions are less affected because of the inclination of the magnetic field, we see that the actual neutral atmospheric wind component parallel to B should have been appreciably smaller than V,, of the neutral clouds. For experiment (il) we are not able to give a definite reason for the discrepancy. It might be due to the observed wind shears in the atmosphere (see below), which make the definition of the cloud’s center a bit difficult. The most striking result concerning the velocity components perpendicular to B is that, in five out of six cases, that of the neutral component is higher than that of the ion cloud by a factor between 15 and 3.0. Only in experiment (i7) this factor was 0.5. The angle, v, between the velocity vectors was always smaller than 30”, in four cases less than 15”. It is interesting to compare (i2) and (i3), because these clouds were generated during the same flight. Although the neutral gas velocities were very different, we found about equal V,. A few remarks should be added concerning three of the clouds. From the brightness of the tail coming out of cloud (i7) (Fig. 7) one could measure the ionospheric electron density. It should be very nearly equal to the Ba+ density within the tail, since the ratio of Ba+ to air ions is very great inside the cloud where the tail originates. In Fig. 6 we have three photographs from our first ion cloud (il). Two features are of interest here: (1) The light-bridge between the Ba+- and the Sr-clouds is a result of the photo-ionization after the initial phase showing the path of the neutral Ba-cloud. Its brightness agrees well with the expectations from photoionization with a time scale of 100 sec. (2) The distortion of the ion cloud is interpreted as due to a shear of the mainly horizontal atmospheric wind. As ~~for this experiment was near 7 and, as we shall estimate below, il* might not have been very near to unity, V, was sensitive to changes in v,~. This would explain the deviation of the long axis of the Ba+-cloud from the direction of the magnetic field (cf. Fig. 3) and the widening of the lower end (in real space!) of the ion cloud (Fig. 6), since there is always a diffusion along the lines of force superimposed. (All other ion clouds were oriented parallel to B). In addition we expect the deformations that have been discussed in section 4 to take place after a few minutes. Also the ambipolar diffusion might contribute to the broadening.@)
The stripes that appear 15 min after release of cloud (is) (Fig. 8) are very remarkabk. A deformation of the cloud becomes noticeable only after about 8 min. We regard this as a manifestation of the same effect, namely the modi~~ation of the ionospheric co~ducti~ities I; due to the presence of the cloud. As K~ for this experiment was near 30 we expect the deformations to develop with a time-scale about of 15 min (4.3), but it is not clear what causes the stripes instead of a more homogeneous deformation. The finite width oE the cloud and the recombination in the E-layer might be partially responsible. In other cases we found the width of the ion clouds essentia~y constant. In (27) it has even a slight tendency to decrease, which is expected from the entering of air ions into the electron cloud. The time-scale 7-(4-2)of deformation is very long for this doud in spite of K~RS2, The high Ammakes the relative drift, U,, with respect to the neutral cloud unobservably small, and consequently also U’
The interpretation of the measured velocities perpendicular to 3 (TabIe 3) in terms of ionospheric field strengths suffers mainly from the unbrtainty about the actual value of 1”. The amount of Ba* produced during the phase of initial ionization has been evaluated so far for clouds (il) to (i3) With an integrated ionospheric Pedersen conductivity of 2 !G@(an intermediate value according to Table 4) we find values of ;1* that deviate subs~ntially from unity (Table 4). The numbers in Table 4 serve only for demonstration purposes. The
1-1i@f 2.5IO= 3.2IO=
30.0
o-68 f-18 0.43
f-34 1-6 1-22
is so uncertain that any correction for a* r 1 according to actual value of x:plonoerph* formula (3.25) is impossible. Also among the later experiments the situation is not better, For (~7) we know from its motion that a* > 1. From the amount of theoretically evaporizable material and with typical efficiencies for the difIerent types of reactions we expect only for the very faint cloud (S) that a* is very near to unity. So we reduce our data with ir* = I, i.e. o = K~ (1 -t_ Q)-Xand b = 1 and emphasize that we do not get true electric fields. How strong the corm&ions are, to which these field strengths are to be subjected, might be estimated from d* of Table 4. The most important correction would stem from the last term in equation (3.25); it tends to reduce the magnisince the tude of E*. The application of (3.25) with A* = 1 is only correct for the tail in (a”‘?} perturbation of the ionospheric electric field by the presence of the cloud should be negligible at some distance from the cloud’s axis. Figure 9 shows the magnitudes and orientations of the “measured” electric fields. The generai pattern at least should be real. During the four experiments carried out in the evening at a magnetic latitude of about 33”N, the -fields were generahy directed southward. In experiment fi4), a morning launching, at a magnetic latitude of about 40”N the geld pointed to the north. So far we cannot decide whether this reversal in direction indicates essentially a morning-evening elect or whether it is partly due to the diEerence in magnetic latitude.
MOTION
OF ARTIFICIAL
ION CLOUDS
IN THE UPPER
ATMOSPHERE
17
The field strengths were between 1 and 3 . 1O-3 V/m. This is of the same order of magnitude as is to be expected from the strength of the &-current system. From the magnetic observations at Fiirstenfeldbruck (Germany) (private communication) there is no indication of any significant disturbances during the experiments listed in Fig. 9.
FIG.~.POLARDIAGRAMOFELECTRICFIELDSINAPLANEPERPENDICULARTOTHEMAGNETICFIELD As DETERMINED FROM THE MOTION OF ION CLOUDS. THE NUMBERS IN BRACKETS REFER TO THE EXPERIMENTS LISTEDINTABLE 2.
6. CONCLUDING
REMARKS
The experiments so far carried out led for the first time to well observable ion clouds. But they should be regarded only as preliminary. Nevertheless they have demonstrated that one can use this method to investigate phenomena of the upper atmosphere and particularly to determine electric fields if a suitable amount of barium is released at an altitude of about 200 km. Further experiments are planned at different geographical locations to investigate the electrical fields under different conditions more thoroughly. Other experiments shall be carried out at much higher altitudes to study the earth’s magnetic field, and finally the interplanetary plasma. It has just been demonstrated that the method works also at higher altitudes by producing two ionized barium clouds at a height of about 2000 km on April 22, 1966. The two clouds extended along the lines of force over an angle of about 80 degrees which corresponds to a length of more than 2000 km. The clouds were visible for about half an hour and from locations at the earth which were separated by more than 3000 km. Detailed results about this experiment will be published later. Acknowledgements-The
experimentsin Nov.
the help of the French authorities. 2
1964, Nov. 1965, and April 1966 have been carried out with We would like to thank them and particularly the “Centre National
18
G. ~~REN~EL,
R. L@YlYand E. REEGER
d’Etudes Spatiaks” (CNES) and Prof. Bfamont for alI their support. For the experiments in September 1965 faciIities were provided by the “European Space Research Ur~~sa~on*’ (ESROf. We thank afi the stti members who he&d us in these experiments. Last but not Ieast we are most thar&fuI to our caIIeques who were invoked in these experiments, particuIarly Messrs. EL FappI, L. Baser, J. LoidI, P. Lritjens, F. M&zner, B. Meyer and H. Neuss. 1. L. BIE~NN, R. L&T, m, LilsT and H. U. SCXM~T,2. A&+@~$. 53,226 (1961). 2. E. R. HARRISON, Geo@ys. J. 6,462 (1962). 3, E. W. HONES,JR., On the use of eie&risaI ion sources for iOn tracer experiments in the ~~~~t~p~~, UniversilJi of Iowa Report 65-31@%). 4. C. 0. Hms, Spcrf? Sci. && 3,342 (1964). 5. H. FSPPL, G. -EL, J. MIDL, R. L&T, F. MELZNBR, B. MEYER,H, NEU~~and E. RIIZGER, PTanLlt, Space Sci. X3,95 (1965). Submitted to Planet, 6. H. F~PPL et nl. Artificial strontium and barium clouds in the upper a~osphe~. space sci. (1966).
10. D. F. MARTYN,Phil. Trans. R. Sot. A246,306 (1953). 11. P. C. CLEMMOW, M. A. JOHNSON and K. WEEKES, A note on the motion of a cylindrical irregularity in an ionized medium, Proc, Zonoykexe Conf pp. 136-139 Physical Society, Landon (1955). 12. S. KATO,PIazet. @ace Sci, I& 823 (1%3). 13. J. P. I~o~c+&~zRTY, b. geupkys. Res. 64,2215 (1959). 14. R. Bosfffijhl, J. geopkp Res. 69,4983 (19&Q. $5. J. H. P~D~QToN, Planet. S@~ceScf. Z&l27 (1964). 16. K. MAEDA and H. M~Tsu~o+ro, Rep. fonosph. and Space Res in Japan X6,1 (1962& 17. P. L~TJENS,Messung der ~~pf~chte an ~stlich~ Met~ld~pfwoI~en in der Ionosph&e mit photo~aph~en Methoden, ~iplomar~it, Univ. Munich (1966). 18. R. I). HUDSON, Private ~mrnuni~tio~ (1965). (1966). 19. G. HAEREPJIIEX., Sedimentation of arthieal gas clouds in the upper atmosphere* fn lotion ~~~~~~~T~~
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