SMITHSONIAN

CONTRIBUTIONS

to

ASTROPHYSICS

Smithsonian Institution

Astrophysical Observatory

Volume 8, Number 7

Meteor Geomagnetic

Effects

By Sydney Chapman

and Attia A. Ashour

Washington, D. C.

Smithsonian

Contributions to Astrophysics

VOLUME 8, NUMBER 7

METEOR GEOMAGNETIC EFFECTS

by SYDNEY CHAPMAN and ATTIA A. ASHOUR

SMITHSONIAN INSTITUTION

Washington, D.C.

1965
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Meteor Geomagnetic Effects

SYDNEY CHAPMAN1 and ATTIA A. ASHOUR2

1. Introduction

Kalashnikov (1949) reported the observation of

small changes of the geomagnetic field, which

he attributed to meteors. The record was

made using a large horizontal coil as fluxmeter;

thus it referred to the vertical magnetic component Z. Kahishnikov's evidence for the

connection with meteors was partly statistical,

but was also based on correspondences between

observed meteors (Leonids, Geminids) and

magnetic peaks on the fluxmeter record.

His first and later papers (1952) aroused

interest in the subject. Recently Ellyett and

Fraser (1963) summarized subsequent observational work in this field, carried out by

Bumba (1955), Hawkins (1958), Campbell

(1960, 1962), Jenkins, Phillips, and Maple

(I960), and Ellyett and Gillion (1963). They

state (pp. 5937-8): "Experimental work already

carried out thus gives no evidence of a magnetic

effect due to a single meteor, with the possible

exception of the first worker, Kalashnikov.

The correlation to date with showers also lacks

conviction, . . . ."

Ellyett and Fraser (1963) further investigated

the question, using a large horizontal loop near

Christchurch, New Zealand, to record magnetic

micropulsations, and radar to record meteors

(down to a zenithal magnitude of 8.2). The

sensitivity of their magnetic measures considerably exceeded that of any work previously

published; their minimum detectable signal was

50 microgammas (MY), or 5 X 10~10 gauss. Their

amplifier had a bandwidth of 1 cps centered on

1 Geophysical Institute, University of Alaska; also High Altitude Observatory, Boulder, Colo., there engaged in a research program sponsored

by the National Bureau of Standards and the Air Force Geophysical

Research Directorate.

2

 High Altitude Observatory, Boulder, Colo.; on leave from the Department of Applied Mathematics, Faculty of Science, University of

Cairo, United Arab Republic.

1.5 cps, so that the rise time was about 1 sec.

They showed by a graph the mean daily variation of the mean hourly all-sky meteor rate for

the period March 5-16, 1962; the daily mean

was about 100 meteors per hour.

"Owing to the possible occurrence of manmade pulsations in the daytime" (p. 5940),

they restricted their detailed studies to evenings.

They claim that the variation of meteor rates

for each hour, plotted through a succession

of nights, is not significantly related to the

corresponding micropulsation activity. They

examined the relation between individual

meteors and micropulsations, recording them

on the same chart. They conclude that most

individual meteors do not have any observable

associated micropulsation activity, but the

number of coincidences is greater than random.

It remains possible that some of the larger

meteors do produce magnetic effects. They

add (p. 5945) that "if the matter is to be pursued

further it will be desirable to investigate the

characteristics of the individual meteor echo

and the frequency coverage of the accompanying

micropulsation. . . . The frequency of 1.5

cps was chosen to make the results strictly

comparable with previous work, but it might

well be that this is not the best frequency for

the detection of such an effect."

Kalashnikov (1949) suggested two ways in

which a meteor might modify the geomagnetic

field: by motion of charges along the trail,

and, as a second phase, by the convective motion

of the ionized train, here called the trail. He

envisaged the possibility of studying meteor

phenomena by two stations, 80 or 100 km apart,

each equipped with 3-component fluxmeters,

to obtain the direction of the meteor magnetic

field disturbance vector at each station; this

might enable the meteor velocity and trajectory

to be determined.

181
182 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

2. General considerations

Any magnetic effect of a meteor must certainly

depend on the ionization along its trail and on

electric currents introduced or modified by this

ionization. If the whole trail were situated in

previously non-ionized air, the only way in which

current could be caused to flow would be by an

electromotive force induced by the convective

motion of the trail. Any component of this

emf along the trail would cause current to

flow; but this would also quickly set up opposite polarization charges at the two ends,

whose electric field would annul the component

emf. The current would thus flow only very

briefly. All meteors entering the atmosphere,

however, first traverse the ionosphere, where

they add to ionization already present and where

currents are already flowing. The sudden

creation of extra ionization and conductivity

will modify these currents. This modification

is equivalent to the superposition, upon the

pre-existing currents, of an additional "meteor"

current system, whose magnetic field may be

observable at the ground.

The meteor current system will be proportional to the intensity of the pre-existing currents and will depend on the location and direction of the trail in relation to those currents.

The magnetic effect recorded at a particular

observing station will depend also on the

position of the station relative to the meteor

trail. The recognition of the effect will depend

not only on its magnitude and type, but also

on the ability to distinguish it from other

changes unconnected with meteors. Thus,

quiet magnetic conditions will be the most

favorable for the investigation of meteor

magnetic effects. As magnetic disturbance

is most prevalent and intense in the higher

latitudes, especially near the auroral zone, such

localities are least suitable for the study.

In quiet magnetic conditions the main current system flowing in the ionosphere is the

Sq system associated with the quiet-day daily

magnetic variations. The direction and intensity of the Sq currents are functions of

latitude, longitude, local time, and sunspot

epoch; Sq also undergoes an unpredictable

day-to-day variation. The current is most

intense in the equatorial electrojet, which lies

nearly along the magnetic equator, where the

magnetic dip is zero. There its greatest intensity occurs at the hours around 11 a.m. local

time. Hence a station under or nearly under

the jet will be most favorable for the study of

meteor effects. The meteors most likely to

give observable magnetic records are daytime

meteors entering the atmosphere nearly horizontally, within two or three hours of 11 a.m.

local time; their mass and speed should be such

as to produce very considerable ionization.

According to McKinley and Millman (1949),

radar-detectable ionization is usually produced

only between 80 and 110 km.

These considerations do not seem to have

been taken sufficiently into account in past

studies of meteor magnetic effects. In the

study by Ellyett and Fraser, only nighttime

meteors were examined, although the radar

data doubtless gave information about daytime

meteors. Moreover, in past discussions little

or no attention has been paid to the height of

the meteors whose passage has been correlated

with small magnetic pulsations. The only

meteors likely to give observable magnetic

effects at ordinary times are those of considerable speed and brightness that traverse the

ionosphere between about 90 and 130 km

height. Thus, statistical studies, if they are

to be convincing, must be more selective than

heretofore as to the meteor records used in

comparison with the magnetic data. For satisfactory demonstration of meteor magnetic

effects, it is really necessary to show an association between (a) particular meteors (preferably daytime meteors) fully observed as to

time, location and direction of trail, and intensity of ionization per cm along the trail, and

(b) particular magnetic changes fully recorded

in all three magnetic components at one or

more observatories not too far away. This is

a considerable undertaking. Lovell (1954)

quoted only one case where such complete

radar meteor data had been obtained up to the

time of his writing. The observations were

made by McKinley and Millman (1949), who

did not, however, give any information about

the intensity of the ionization along the trail.

(It may still be worthwhile to examine the

magnetic records of the stations nearest to the

plan location of the trail to see whether any

identification of a magnetic effect can be made.)
METEOR GEOMAGNETIC EFFECTS 183

The Harvard-Smithsonian Radio Meteor Project now makes regular determinations of the

distribution of ionization along the trails observed at its six stations.

Photographic observations of meteors, such

as were considered by Hawkins (1958) in his

study of meteor magnetic effects, are less suitable than radar studies, because of the smaller

intensity of the Sq currents in the nighttime

ionosphere; the relative disadvantage is by a

factor probably of order 5 or more. Most

photographic meteors have trails that lie too

low in the atmosphere to be promising for magnetic effects, because the Sq current intensity

probably falls off rapidly below 100 km (cf.

rocket observations of current heights [Singer,

Maple, and Bowen, 1951; Cahill, 1959]).

Magnetic pulsation measurements by horizontal coils—giving data of the kind most

considered in past discussions of this subject—are the least favorable for identification

of magnetic changes with meteors. In general,

the peak magnetic effect will be shown by the

horizontal component at places under the trail.

The peak effect on the vertical component

will be smaller and will occur some distance

away; it is smaller because of the induced

currents caused by a rapid change in the external magnetic field. Such currents tend to

increase the external change in the horizontal

force by about half and to decrease the change

in the vertical force (see sec. 5). Hence, coils

in vertical planes are preferable to horizontal

ones, though a set of three perpendicular coils

is most desirable. Kalashnikov set up such a

system at his Borok station near Moscow;

Hawkins (1958) also used three perpendicular

coils.

Identification of the magnetic effect of a fully

observed meteor and its trail requires clear

agreement in their time relations, not only as to

the beginning of the magnetic effect, but also

as to the duration of the two phenomena.

It is useful in this connection to infer as fully

as possible what is the expected nature and

magnitude of the magnetic effects of meteors

moving in specified directions at known heights

in known regions of the Sq current system. An

example of such identification between magnetic

effects of other kinds and their inferred cause is

the association of Sqa, the augmentation of the

normal Sq current system, with observed solar

flares. X-rays from the flares greatly enhance

the ionization of the D layer and thus extend

downward the ionospheric layer in which dynamo-induced Sq currents flow; the duration in

this case is of order 20 minutes to an hour. The

phenomenon is much easier to study than are

meteor magnetic effects. Because the magnetic

Sqa effects are much larger, they are easily

identified in the magnetic records, and the solar

flare can be identified visually on the sun and

also by its sudden disturbance of the ionosphere

(called an SID), as shown by ionospheric

recorders (Dellinger, 1937; Fleming, 1936;

McNish, 1937; Veldkamp, 1960; Van Sabben,

1961).

3. Formulae for meteor magnetic effects

a. Vertical trail.—The first theoretical estimation of a meteor magnetic effect was carried out

by Jenkins and DuVall (1963). They considered

a meteor descending vertically through the Sq

currents, which they took to be uniform in

horizontal direction and intensity j0, throughout

a uniformly ionized ionosphere with electric

conductivity K, bounded by horizontal planes

at heights h and h-\-d above the ground. They

took the extra meteor ionization to be uniform

through a cylinder of radius a with its axis on

the meteor trajectory, such that the previously

existing conductivity K within the cylinder was

increased to K'. They treated the current

flow as being steady in the presence of this

conductivity distribution, ignoring any rise

time and decay of the meteor current system.

All these features of their work are suitable in a

pioneer study of the problem. They estimated

only the peak magnetic effect of the meteor at

the ground, i.e., the disturbance at the point

directly below the meteor.

The modification of the uniform current flow

by the cylinder of enhanced uniform conductivity constitutes a well-known electrical problem. The mathematics is the same as that

used by Chapman (1933) in discussing the

magnetic effect of a solar eclipse, although in

that case the changed conductivity K' is less

than K, instead of being greater, as here; also,

the change is more gradual, continues longer,

covers a much larger area, and is perhaps less

uniform. The current intensity within a cylinder
184 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

of modified uniform conductivity remains uniform, but its intensity becomes 2K'j0KK+K').

The modified current distribution corresponds

to superposition, on the uniform flow with

intensity j0, of an additional current system

(fig. 1), consisting of a uniform flow of intensity

(K'—K)jo/(K+K') within the cylinder and an

equal return flow outside the cylinder, along

current lines that are circular arcs. Chapman

gave an approximate calculation of the magnetic

field of this superposed current system for different points on the ground below the cylinder.

In his case a/h is large; in the meteor case, this

ratio is small.

It is convenient to denote by J the total

excess current flowing through the cylinder; thus

J=2ad K'-K

K'+K Jo- (1)

The magnetic change at the ground caused by

the meteor is greatest at the point O where the

1/2

meteor trajectory meets the ground. The

change there (dHQ) is horizontal and transverse

to the direction of the Sq current flow; it

enhances the normal Sq magnetic vector at O.

Jenkins and DuVall give a formula for dH0,

which in the notation used here is

<

2

>

neglecting higher powers of a/h. They do not

indicate how they obtained this result.

In another paper (Ashour and Chapman, 1965)

we give a complete determination, for any

point of space, of the magnetic field of the current in a thin plane sheet, corresponding to a

thin horizontal slice of the ionosphere and the

meteor current system here indicated. By

integration with respect to height, the field of

the thick meteor current system can be obtained

from our formulae. For the point O this gives

the approximate formula

FIGURE 1.—Meteor current system for a vertically descending meteor. The current lines are straight

lines within the cylindrical trail and arcs of coaxial circles outside. They are drawn at intervals of

one-eighth of the total current flux through the cylinder.
METEOR GEOMAGNETIC EFFECTS

TTt/ i

°=2^{ h(h+d) (3)

thus replacing h2 in (2) by h(h+d). For the

eclipse case, where ajh is large, we find the true

value of dH0 to be about 5 percent greater than

the estimate made by Chapman (1933).

In considering the meteor field at a point P on

the ground elsewhere than at O, it is convenient

to take right-handed Cartesian coordinates x,

y, z, relative to O as the origin, Oy being along

the direction of the undisturbed Sq current flow;

Or, along the direction of dH0; and Oz, vertically

downward. For example, if the Sq current

flow is eastward, Oa: is northward. The corresponding components of the meteor magnetic

field will be denoted by X, Y, Z. It is also convenient to use plane polar coordinates r, <f> instead of x, y, measuring <f> clockwise from Ox

(looking down toward the ground); the corresponding meteor field components will be

denoted by R, *. Our formulae for a plane

horizontal sheet can be integrated with respect

to the height, to obtain the (accurate) results:

-(l/r)/ a (a,M,r)}cos0; (4)

h,d,r)sm<t>; (5)

Z= (2Tj/d)J3(a, h, d, r) cos<£; (6)

where the functions j are defined in terms of

integrals of Bessel functions:

A=/(l,0; -l),/ 2 =/(l , 1; -2),/,=J(l, 1; -1),

I(m,n;p)= f Jm(at)Jn(rt)e-ht(l-e-td)t^dt. Jo

(7)

In the integrand t has the dimensions of an

inverse length.

Using Luke's (1962, p. 319) formulae (26)

and (27) we obtain the following approximate

forms of R, S>, Z:

+ (3a2r

2

/8)^6(r, h, d)} cos <f>, (8)

-(a?j4)t3(r,h,d)}sin<t>, (9)

Z= (irarJ/2d)Mr, h, d)cos<f>. (10)

Here

185

(H)

In (8) and (9) terms involving \f/n are neglected

for n > 7, as ^7 is of order a8r

2

/(r2+^2)

7/2

.

Hence, to this high degree of approximation,

and

-(a2/4)+3(r,h,d)}, (8a)

Y(r)=0. (9a)

Thus the horizontal component of the meteor

field everywhere at the ground is in or almost

in the same direction as dH0, that is, perpendicular to the Sq current flow. Its magnitude

X(r) varies (over the ground) only with r; that

is, its isolines are circles. Figure 2 shows

X(r)/dH0 for points on the ground as a function

of r/h=R, when d/h=D—0.3 (e.g., for such

typical values as h=100 km and d=SO km).

It falls to about one-half when i?=0.85.

From (10) we find that

(Z sec 4>)/dH0

=R(1+D)(2+D)/[(R2+1)X

{R2+(l+D)2}]. (10a)

Thus at the ground (Z sec 4>)/dHo is a function

of R only; it has a maximum at R=Rm, given

by

i?ro=(l/V3)(l+Z?/2+Z?2/8+7Z>3/32), (10b)

ignoring D to powers of 4 or more. The points

of maximum Z on the ground along any radial

direction from O lie on a circle of radius Rm;

(Z sec <f>)/dH0 for points on the ground is shown

in figure 2 for the particular value D=0.3. The

peak ground values of Z/dHQ are about ±0.65

at i?=0.62, in directions (<£=0, <£=*•) perpendicular to the Sq current flow. If the Sq

current flow is eastward, the "meteor" vertical

component Z is downward (+) to the south of

the trail and upward (—) to the north.

b. Horizontal trajectory along Sq current.—The

problem of the meteor magnetic effect is

especially simple for an infinitely long horizontal meteor trajectory at height hr

 lying

along the direction (y) of the Sq current

flow j0. The conditions, axes, and notation in

other respects (such as h, d, a, j0, K, K.') are
186

SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

1.0

.8

X/dH,

HORIZONTAL METEOR

Z/(dHocosd>)

VERTICAL METEOR

Z/dH,

HORIZONTAL METEOR

.8 1.6 2.4 3.2 4.0

r/h , x/h1

4.8 5.6 6.4 7.2

FIGURE 2.—Variation of the meteor magnetic field at the ground with distance. Solid curves show

ZfcdH cos $) and X/dH0 for a vertically descending meteor as functions of r/h: for d/k=0.3. Broken

curves show Z/dHi and X/dHi for a horizontal meteor trail in the direction of the Sq current flow as

functions of xjh'.

taken to be the same as before, O now being

any point directly under the meteor trajectory.

If the trajectory lies in the layer previously

considered, in which current flows under the

impulse of a uniform dynamo emf because of a

uniform convection of the layer, the same emf

will act along the meteor trail, and the current

intensity within the cylindrical trail will be

K'jolK; in this case there will be no change in

the current elsewhere. Thus the effect of the

meteor is simply to produce an additional

horizontal current, of cylindrical cross section

and mean height h', with no return current.

The total additional current J£ along the trail

is given by

its magnetic effect dHx at the ground anywhere

directly beneath the meteor trajectory is given

by

(13)

As in the case of the vertical trajectory, the

direction of dHi is perpendicular to the direction of the Sq current flow; it enhances the

normal Sq field under the trail.

Elsewhere, the horizontal field of the meteor

current at the ground is a function of the x

coordinate only; the Ycomponent is zero. The

X and Z components are given by

and

= -h'x

, (14)

= -(xjh')X. (15)

Thus X steadily decreases with distance from

the plan position of the meteor trajectory,

whereas Z rises along the x direction from zero

to a peak value ±(\j2)dHl at x=

:Fh' (there

Z= ± X). Beyond this distance Z numerically

exceeds X Figure 2 shows X/dHi and Z/dHi

as functions of xjh'.

The supposed uniform Sq current intensity

j0 corresponds to the flow under the impulsion

of a dynamo-produced electric field E such

that jo=KE. Outside the Sq layer the air may

be in convective motion with a different speed;
METEOR GEOMAGNETIC EFFECTS 187

there the induced dynamo field will differ from

E. If at height h' it is E', the current J'o along

the infinitely long horizontal meteor trail will

be va

2K'E'}

 which could flow in an otherwise

insulating layer of the atmosphere below the Sq

layer. Such an infinitely long trail in insulating

air, however, falsifies nature. Owing to the

curvature of the earth and the passage of the

meteor through the ionosphere before reaching

the supposed nonconducting layer, the intensity and duration of the current flow would

depend on the end conditions of the trail.

A less crude model is a horizontal trail of

finite length 26. In this case the meteor magnetic field at the ground would be greatest at

O, the point under the center of the meteor

trajectory, and X and Z would depend on both

coordinates x, y. The meteor current system

now includes return currents outside the trail,

which reduce the magnetic effect of the current

along the trail. The mathematical problem of

the modification of uniform current flow caused

by a uniform enhancement of previously constant conductivity K to the value K' throughout a cylinder of radius a and finite length 6,

with its axis along the direction of the electric

field E, has not been solved even where the

region of flow is unbounded; the problem is

still more difficult when the region is bounded

by two horizontal planes. The current intensity within the cylinder will not be uniform,

although if b/a is large, its value at the center of

the cylinder will not be much less than K'E.

If as an approximation the intensity were

taken to have the value K'E everywhere

inside the cylinder, the field at O on the ground,

under the center of the cylinder, would be

partly caused by this flow within the cylinder,

reduced by the field of the return currents.

The part resulting from the idealized uniform

current within the cylinder, which may be

calculated as if the current Jo were concentrated

along the axis, would be

bdHiJ(b2+hn)X. (16)

If b/a is large, this will be a good approximation

to the field at O caused by the current within

the cylinder. It is more difficult to estimate

the field of the return currents, whether the

ionosphere is taken to be unbounded or of

finite thickness.

74G-362—65 2

The problem becomes somewhat simpler,

mathematically, for an unbounded ionosphere,

if the meteor trail of finite length is taken to

create extra uniform ionization in a prolate

spheroid with a long horizontal axis of length

26 and a short axis of length 2a. In this case

(whatever the ratio b/a) the modification of

the uniform current flow is known (for example,

see Smythe (1950), p. 208, problem 82). The

magnetic field of the modified current system

has not, however, been determined, so far as

we are aware; it is probably a difficult problem.

It is, however, possible to infer from Ampere's

theorem the meteor magnetic field at any point

in the vertical diametral plane. In that plane

the field lines are circles about C, the center of

the spheroid. At distance r from the axis, we

have

2vrdH= UwjdS=8ri fjrdr. (17)

Within the cylinder (hence from r=0 to r=a)

the extra "meteor" uniform current density,

when b/a is very large, is very nearly

(K'—K)joK; beyond r=a the current is reversed, and its density, when b/a is very large,

is approximately

where

(18)

Hence from (17) we infer that at distance

r=h from the axis of the spheroid, the "meteor"

magnetic intensity is

(2J'0/h){ l -

where

/a)}, (19)

(20)

This model current system associated with a

spheroidal meteor trail differs, however, from

the more realistic case of such a trail lying in

the bounded ionosphere. Even if the trail lies

at the middle level of the thick ionospheric

layer, there will no longer be axial symmetry of

the current distribution. So far as we know,

the distribution for such a layer has not been

determined, and the above method of determining dH in the diametral plane is not applicable.

The return current of the meteor current system
188 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

lies wholly in the ionospheric layer, but the

magnetic field lines will not be confined to this

layer; there will be a magnetic field at the

ground. Its value at O will be less than that

given by (19), but perhaps only moderately less,

if a is small compared with d and h'.

The mathematical problems involved in an

exact determination of the meteor magnetic

field for a horizontal meteor trail of finite length,

whether cylindrical or spheroidal, are so complex that it would seem simpler to determine

the field experimentally in the laboratory. The

uniform current flow might be created in a

large rectangular vessel full of brine, with a

small body of the shape of the trail suspended

in it, and composed of metal or other material

suitably more conducting than the brine of the

concentration used. The magnetic field of the

uniform flow in the absence of the inserted

body could be neutralized, in the "ground"

plane over which the distribution of the

"meteor" magnetic field was to be explored,

by an opposite current flow in a metal sheet

between the vessel and the ground plane.

Then the "meteor" field could be directly

determined over the ground plane.

Of course a uniform horizontal trail of finite

length does not truly simulate nature; it is

merely a mathematical idealization of the

reality. For a long trail, the curvature of the

level surfaces in the ionosphere and the consequently changing inclination of the meteor

trajectory along its length, whatever its direction, may need to be taken into account, as

well as the variation of the ionospheric conductivity with height. Such calculations as

are made here are intended only to indicate the

order of magnitude of the meteor magnetic

effect.

c. Horizontal trajectory normal to Sq current.—

When the meteor trail is horizontal, infinitely

long, and perpendicular to the (y) direction of

the Sq current flow, the problem is mathematically two-dimensional, in that all the dependent

variables are functions of y and z only, provided

that the uniform ionosphere is bounded, if at

all, by horizontal planes. The meteor-modified

current lines, and those of the meteor current

system, will lie in planes of constant x. At any

point P the magnetic field of the meteor current

system is given by an integral of the form

diXr

where di denotes an element of the volumedistributed current. The integrand has the

form

V

di3

z

because di has no x component. The j and k

components of the field of the meteor current

system are zero, because in the integrals

involving xdi3 and — xdii, x takes all positive

and negative values. Thus the meteor magnetic field (here denoted by X') is purely in the

x direction, that is, parallel to the lines of

force of the Sq field.

If the ionosphere is unbounded in the vertical

as well as in the horizontal direction, the

current lines of the meteor current system are

as shown in figure 1 (p. 184), but now they lie in

the vertical planes where x is constant. The

magnetic field of a thin vertical section of the

meteor current system has been calculated by

Ashour and Chapman (1965) and must be

integrated with respect to x to obtain X'.

Thus:

X =4*aj0 K'+K

J

«oo /»oo

t/i(aO«7i(«p)e~lx<ft dx cos <t>

— wjo

C OS <f>,

(22)

in terms of the polar coordinates p, <f> in the

vertical current plane relative to the center

C of the current system.

Hence, according to Luke's formulae (1962,

equation 24, p. 318), X' for points outside the

meteor trail (P>a) is given by

_2

= 4 x — j0 cos

(23)

For a point P on the ground, at x, y, —h', the

cylindrical coordinate p is (y2-\-hr2)

1/2

; as

<f> denotes the angle made by OP with the
METEOR GEOMAGNETIC EFFECTS 189

vertical, cos <f>—hf/p. Hence the meteor

magnetic intensity is (X1, 0, 0), where

v A a2fl'

 K ' ~ K

 •

Expressed in terms of dH\, the field intensity

on the ground vertically below a similar meteor

trail, at the same height h', directed along

the Sq current flow, is

y/

h

fi

K'+K hfi+y2

dH,. (25)

This result for an infinitely long meteor

trail in a completely unbounded ionosphere is

not accurate for the magnetic field set up by

a trail of finite length in an ionosphere bounded

by horizontal planes above and below. But if

the length of the trail is comparable with h',

equation (25) probably gives the order of

magnitude of the meteor magnetic field at

the point directly below the central point of

the trail. Elsewhere, the field will have y

and z components as well as X'. Since to

work out the meteor field exactly in this case

would involve much complexity, we do not

attempt it here, particularly because it seems

likely that an actual trail that could appreciably

modify the Sq field if it were directed along

the Sq current flow would have a very much

smaller magnetic effect if it were perpendicular

to the flow (see sec. 5c.)

4. Meteor ionization and meteor currents

The formulae for meteor magnetic effects

involve the meteor trail radius a and the

electrical conductivities K,K'. In the ionosphere the electrical conductivity is anisotropic because of the presence of the geomagnetic

field and the insulating boundary below. K

refers to the effective conductivity in the

direction of the Sq current flow. The conductivity K' for the same direction, enhanced

by the presence of the meteor trail, is n'eK/ne,

where ne, n'e denote the normal electron density

and the density enhanced by the meteor

ionization. (A complication ignored in previous

calculations of meteor magnetic effect is that

the modified current flow is not uniform in

direction, so that its distribution will depend

also on the conductivity in directions other

than that of Sq.)

Radar workers, in discussing meteor ionization, refer to a, the meteor "line" electron

density per cm length of trail. This is given by

a=ira2{n't—ne). (26)

Let /3 be the corresponding normal electron line

density per cm length of trail, so that

Then

and

(27)

(28)

(29)

Hence the field dHQ for a vertical meteor trajectory, to the first approximation (see equation

(3)), can be thus expressed

dH0=ira2j0djh(h+d)(l+2p/a). (30)

Likewise, the field dHi immediately below an

infinitely long horizontal meteor trail (see equation (13)) can be expressed as

dHl=2ajQ/neh', (31)

if the trail is directed along the Sq current flow;

if it is perpendicular to the current flow, the

maximum meteor magnetic field immediately

below the trail (y=0) is X', given (see equation

(25)) by

X

f

dH( ) (32)

The results for the meteor magnetic field, in

the various cases considered here, will next be

evaluated numerically.

5. Numerical discussion

a. Vertically descending meteor.—Jenkins and

DuVall (1963), in calculating the numerical

magnitude of the magnetic effect of a vertically

descending meteor, from their formula (2),

adopted the following values:

&=100km;<Z=30km, JD(33)

j0=10-10amp/cm2=10-n emu, JD(34)

K'IK=3, JD(35)

a=3X104cm=300m. JD(36)

Here JD signifies that the values in (33)

through (36) are those used by Jenkins and

DuVall. The value of a is quoted from Opik

(1958, p. 22), who also estimates n'e as varying
190 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

from 3X104 to 3X105/cc. In the E layer n,

(at noon in low and middle latitudes) is of order

105/cc, so that JD(30) corresponds to Opik's

upper limit for n'e.

The uniform horizontal magnetic field on

either side of a current distribution of uniform

density j0 in a horizontally unbounded layer of

thickness d is 2irj0 gauss if jQ is expressed in

emu. The values (33) and (34) give the field

intensity as 6TT(=19)T; allowing for an additional earth-current field of about half this

magnitude, the field at the earth's surface

would be about 30-y. This is of the right order

of magnitude for Sq(H) at sunspot maximum

over a considerable range of latitude (cf.

Chapman and Bartels, 1940, p. 233, where the

daily peak value is given as 2Oy for the sunspot

minimum year 1902). At Huancayo under the

equatorial electrojet, however, Sq(fl) can be

seven times as great (Chapman and Bartels,

1940, p. 243, fig. 25, July 24, 1928). Thus it is

possible to take

io=7XlO-n emu (37)

for the epoch around 11 a.m. at Huancayo for

a sunspot maximum year on a quiet day of

large Sq range.

Jenkins and DuVall evaluate dH0 from (2)

using the values (33) through (36) as about

IOOMT; but the result seems instead to be

42/ry. The correction of h2 in (2) to h(h+d)

further reduces this to 32^7.

Their values of a and n'e correspond to

a=5.7X10u/cm, JD(38)

and for the same value of a, taking n,= 105/cc,

/3=2.8X1014/cm. JD(39)

Radar workers refer to values of a up to

1016/cm; e.g., Greenhow and Lovell (1960,

p. 545) quote 1018/cm as an average value of

a for a bright meteor at height 80 km. This

corresponds to

#7^=36.3 (for a=300 m). (40)

Supposing this value of a to apply in the E

layer, in the Sq current layer, substitution

in the first term of (3) from (37) and (40)

gives 424 ny as the value of dH0, valid for

a place such as Huancayo, near noon, at

sunspot maximum. The factor of increase

between the two values of dH0, 32 fiy, and 424

ny, is less than twice the ratio 7 of (37) to (34).

This is because the factor (K'—E)/(K'+K)

is increased only from 0.5 (JD) to 0.95; it

can at most only be doubled, even if Kf/K

were infinite.

The value of a used by Jenkins and DuVall

much exceeds the values mentioned in discussions of meteor trails by some writers;

e.g., Greenhow and Lovell (1960, p. 562)

refer to "the large initial radius of the ionized

column" in connection with values of the

radius comparable with the wavelengths, such

as 8 and 17 meters, used in radar meteor

studies. They infer initial trail radii of 1 m

at 90 km height and 3 m at 115 km. Cook,

Hawkins and Stienon (1962) observed the

optical width of meteor trails during the

Geminid shower of 1957. Their results indicate

that the trail width is usually of the order of

1 m, although in individual cases the width

may be as much as 6 m. Hawkins (1963)

states: "It is difficult to see how the initial

ionization column can be any larger in diameter

than the measured optical values, i.e., of the

order of 1.0 meter over the normal range of

meteor heights from 90 to 105 km."

The initial radius of the trail depends on

the distance of penetration of the ionizing

agent associated with the passage of the

meteor. Later the trail radius increases, owing

to molecular and eddy diffusion, but at the

same time a decreases because of attachment

and recombination of the electrons. At 100

km the coefficient of diffusion is of order 108

cm2/sec, indicating that in 1000 sec (or about

% hour) diffusion would enlarge a to about

100 m. At this height, however, and in this

time, n\ might have been greatly reduced by

attachment and recombination. It is worth

remembering, however, that in the daytime,

when meteor magnetic effects are likely to

be most easily measurable, the effect of attachment will be reduced by photodetachment.

Opik (1958, p. 22) treats the positive ions

in the meteor trail as being mainly O^" and NJ,

ionized by photons from high temperature

gas close to the meteor; he estimates the

range of penetration of the photons to be
METEOR GEOMAGNETIC EFFECTS 191

300 m. Greenhow and Lovell (1960, p. 546)

consider that the bulk of the ions are those

of meteor atoms, such as Ca+, Fe+, Mg+ and

Si+; they state that if the ions were molecular,

the electron density would decay (in the E

layer, by dissociative recombination) more

rapidly than is observed. The penetration

range of such meteor atoms is of order 10 to

20 times the mean free path, giving an initial

radius at 100 km height of a few meters at the

most. It may be that different authors are

quoting values of a at different epochs in the

life of the trail, or are referring to meteors at

different levels and of different sizes.

If, however, the appropriate value of a

should be of order 1 m instead of 300 m, the

above estimates of dH0 would have to be

reduced by a factor of about 100,000. In

that case the magnetic effect of a vertically

descending meteor would be only a fraction of

.01 ny at most, even directly under the meteor

trajectory; elsewhere it would be still less

in H, and less again for Z.

b. Horizontal trajectory along Sq current.—

Meteors with horizontal (or nearly horizontal)

trails are likely to have a larger magnetic effect,

ceteris paribus, than those that descend vertically. A reduction of a from 300 mtol m does

not affect dHl} the magnetic change in Himmediately under the midpoint of a horizontal trail

along the Sq current flow, for a given value of

a (see equation (31)). Thus, for a=1018/cm,

j 0=7X10- " emu, h'=115 km, and 7ie=105/cc,

(31) gives dHi= 120,000 y.y, or 0.12 7. As we

have stated above, however, the value of dHx

given by (31), valid for an infinitely long horizontal trail in an unbounded horizontally uniform ionosphere with uniform Sq electric

currents, is an overestimate of the actual dH\

for a trail of finite length, because it takes no

account of a return current in the superposed

"meteor" electric current distribution.

For a prolate spheroidal trail with short and

long semiaxes a,b, in an ionosphere with no

upper and lower boundary, equation (19) gives

dHi, taking the return current into account.

The result is practically independent of the

value of a, so long as we can ignore a?/b2 in (19);

this is certainly the case when a is 300 m or

less and b is 50 km or more. The following

table shows the values of dHx for a few values

of b, taking the same values of a, j0, and hr as

before:

b (km) 50 100 200

26(km): trail length 100 200 400

dHiiixy) 26,800 58,900 99,106.

Comparing these values with 120,000 ny, for

b infinite, it is clear that the finite length of the

trail and the return current do not greatly

reduce dH\ when the ionosphere is unbounded.

The effect of the vertical limitation of the actual

ionosphere is difficult to calculate mathematically and may be best found by experiment, as

suggested above (sec. 36). The return current

will spread out laterally from the trail more in

the horizontal than the vertical direction.

The lack of axial symmetry in the current and

field distribution precludes the application of

the above simple "Ampere" method of calculating dH\. But it seems not unlikely that the

change of dHx caused by the limitation of the

ionosphere will be moderate, by only a small

factor. If so, it should easily be possible to

measure the magnetic effect dHx for a horizontal

trail along the direction of the Sq current flow,

if a=1016/cm at a time when j0 is given by

(37); indeed, aj0 could be less by a factor of 100

and dHi should still be rather easily measurable.

There is perhaps some doubt whether a trail

of line density as large as 10lfl/cm could be

formed at a height of 115 km. Greenhow

(1963, p. 7) gives a diagram showing the level

of the mean height of maximum electron line

density a for meteors of different speeds and

different values of amftX; for amax=l018/cm the

greatest height shown is 90 km. At this level

j0 may perhaps at times be not less than a

hundredth of the value (37). However, during

a solar flare (sec. 2) the Sq layer is extended

downward, and at such a time j0 at 90 km may

approach the value (37) under the electrojet.

In that case a trail for which a=1016/cm should

give a magnetic effect, near 11 a.m., of some

tens of thousands of ny; a less intensely ionized

trail should easily be detectable, e.g., one for

which a=l015cm.

We should also remark that a will vary along

the trail, whereas our calculations have supposed it to be constant; thus if am&x is 1018/cm,

the average value of a will be less; this would

need to be taken into account in any attempt
192 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

to connect a meteor trail with a measured

coincident magnetic change. Such a variation

of a along the trail could be taken into account

in the suggested experimental determination of

the effect of the return current (sec. 36).

c. Horizontal trajectory perpendicular to Sq current.—The maximum meteor magnetic intensity

(Xif) at the ground owing to an infinitely long

horizontal trail normal to the direction of the Sq

current flow is shown by (32) to be 2/3/(a+0)

times the value of dHx for a physically similar

horizontal trail along the current flow. If n/

exceeds ne only by a factor of 2 or 3, as in

the case considered by Jenkins and DuVall,

(Xi') will be only moderately less than dHt.

But if a is of order 1 m and a of order 1016/cm—

in which case dHx appears readily observable,

if the trail occurs at a suitable place and time—

then /8 is very small compared with a, and

(Xi) may well be below the level of detection.

d. Trail in general direction.—The meteor current system is more complicated when the trail is

neither vertical nor horizontal. Let 0 denote

its azimuth relative to the direction of the

Sq current flow and e its inclination to the horizontal; its direction cosines relative to i, j , k

are sin 0 cos «, cos 0 cos e, sin e. Suppose that

the extra ionization along such an inclined

trail is uniform throughout a cylinder of radius

a with the meteor trajectory as axis. The

horizontal sections of the cylinder are ellipses

with axes inclined to i, j at the angle 0. In

successive layers traversed by the meteor the

ellipses are progressively displaced. If each

thin horizontal layer of the ionosphere were

insulated from its neighbors, the current distribution in each layer, resulting from the uniform excess conductivity within the elliptic

section, is determinable mathematically from

known results. But the magnetic field of such

a sheet-current distribution is not known in

mathematical terms. As the ionospheric layers

are not insulated from one another, and as the

electric potential varies over each, the displacement of the current pattern from layer to layer

involves the existence of vertical electric fields.

Hence the current flow will no longer be in

horizontal planes. In this case the mathematical problem of the magnetic field of the

meteor current system is complex. Experiment (sec. 3b) seems to offer the only presently

available means of determining the meteor

magnetic field. But it seems not unlikely that

the peak field intensity at the ground, especially

when a is small and a//3 is large, is of the same

order as the peak intensity dHi for a phj^sically

similar horizontal trail at the mean height of

the Sq currents, in a uniform current flow

parallel to the trail but less intense than that

of the Sq currents by a factor of cos 0.

6. Meteor magnetic field as modified by induced earth currents

The varying magnetic field of the meteor

current system in the atmosphere will induce

currents in the sea or land below the earth's

surface (2=0). The meteor magnetic effect

observed anywhere at this surface is the sum

of the direct field X, Y, Z generated in the

atmosphere and the induced field X', Y', Z'

generated in the earth.

The induced field is determined by the

variation of the direct meteor magnetic field

and its space distribution and by the distribution of electric conductivity k below the

earth's surface. The calculation involves the

determination of the induced current distribution and of its magnetic field at the surface.

The mathematical solution is rarely simple,

even for the surface of the sea, for which k

may be considered known (4X10~n emu) and

effectively uniform. On land the problem is

simplest for desert areas under which there is

no ground water; there k may be taken as

uniformly 10~15 emu, down to a considerable

depth. Where there is a moist surface layer,

k for the layer is much greater (e.g., 10~13 emu).

Deeper down, k increases to such an extent that

the material below about 800 km is shielded

from external field changes.

The simplest type of direct meteor magnetic

field is that for an infinitely long horizontal

trail along the direction of the Sq current

flow. In this case the field is that of an infinitely long horizontal current at height h'

above the surface. The time variation of

this current is considered in sec. 8. For the

present purpose of estimating the order of

magnitude of the induced field it is convenient

to treat the variation as periodic, so that the

linear current is taken to be

JQ j cos pt.
METEOR GEOMAGNETIC EFFECTS 193

In this case

v 2j'oh' cos pt v 2JQX COS pt

Price (1950, equation 10.7) has determined the

induced field for such a varying line current, at

a height h' above a uniform medium of conductivity k filling all space below the surface

2=0. In our notation his result is

+ {2J'oa sin pt) { -2 1 Vf2+ . . .} . (42)

Here

. (43)

This result is valid for large |f|. This condition is fulfilled if the medium is sea water and

the period is one second; then a=5.6X10~5; if

h' is 100 km, |f | at the ground is at least 560,

and the terms in 1/f2 are negligible. Hence, to

this order of approximation

X'=X,Z' = - (44)

Thus the induced field doubles the horizontal

component of the direct field and annuls the

vertical component. Even if the period of

variation is as large as a minute, ah' is 75, and

again 1/f2 is negligible, and the same remarks

apply. To a good degree of approximation, the

induced field is that of an image line current

at depth h'.

As the ocean is not infinitely deep, these

results need to be examined to see at what

depth the induced currents become negligible;

if this is less than the depth of the ocean considered, the finite depth of the ocean will not

appreciably affect the result. From Price's

result (1950, equation 10.3) it is not difficult to

show that for the above values of ah' (560 and

75), the rate of decay of the currents with

depth is approximately as exp (—az/21'

2

). This

is the same rate as in the ordinary case of the

"skin effect." For sea water and a period of

1 second, the currents at a depth of 1.16 km

are reduced in intensity by a factor of 100.

Thus for this period the induced field is of

image character, as above. For a period of a

minute the reduction of the current intensity

is by a factor of 10 at a depth of 4.5 km, so

that again the image field is a good approximation for an ocean of this or greater depth.

If the depth is 4.5 km and the period is an

hour or more, the ocean does not fully shield

the region below from the varying external field,

and the problem becomes more complicated.

On land, in places where the conductivity

may be taken to be of order 10"15 emu down

to 100 km or so, ah' is 2.8 for a field varying

with a period of a second. In this case the

field penetrates to a much greater depth before

the induced currents shield the region below.

The induced field at the surface is reduced in

intensity, so that the direct horizontal field

is less enhanced and the direct vertical field is

less reduced. Price (1950, equations 10.8-

10.11) gives expressions for this particular surface-induced field and numerical tables of the

functions involved. Figures 3 and 4 have

been calculated from his formulae and tables

for the case A'=2.8; they show on the same

scale the horizontal and vertical components,

both direct and induced, and the total field in

each case.

7. Time relations

The preceding sections have discussed in various

cases the magnitude of the maximum magnetic

VERTICAL COMPONENT

Z /cos pt

2 4 6 8 10

FIGURE 3.—Effect of induction in the earth, in a desert area,

on the magnetic field of an infinitely long horizontal meteor

trail along the direction of the Sq current flow. Vertical

component: of the inducing field=Z; of the induced

field=Zi+Z2; of the total field= Z+Z2 . Components are

all drawn as functions of xjh'.
194 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

effect of a meteor on the horizontal and vertical

components of magnetic force at ground level

and also the variation of the magnetic effect

with position on the ground relative to the

meteor trail. In determining the best instrumental means of detecting and identifying

meteor magnetic effects, it is necessary also to

consider how the effects are likely to vary with

time.

Three rates of change are especially involved:

(1) the rate at which the meteor travels along

i.o

.8

.6

.4

.2

- . 2

HORIZONTAL COMPONENT

X2 /sin pt

8 10

FIGURE 4.—Effect of induction in the earth, in a desert area,

on the magnetic field of an infinitely long horizontal meteor

trail along the direction of the Sq current flow. Horizontal

component: of the inducing field=X; of the induced

field=Zi+Xi; of the total fit&d=X+Xt. Components are

all drawn as functions of xjh'.

its trajectory, creating or increasing the

ionization there;

(2) the rate at which the ionospheric electric

currents adjust themselves to the changed

distribution of ionization and conductivity;

(3) the rate at which the pre-existing distribution of the electric currents is restored by

the decay of the excess ionization produced by the meteor, thus terminating the

duration of the meteor magnetic effect.

a. Development of ionized trail.—Meteor

speeds of entry into the atmosphere range from

10 to 72 km/sec (Greenhow and Lovell, 1960, p.

516). There is not much retardation in the

course of the passage of the meteor along its

trajectory during the period in which it is partly

evaporated, emitting atoms that are themselves

ionized and may also ionize atmospheric atoms

and molecules. Hence a vertically descending

meteor would take from 3 to 0.4 sec to develop

its ionized trail in the thickness of the ionospheric layer in which the Sq currents mainly

flow—taking this layer to be between 100 and

130 km height (Jenkins and DuVall, 1963).

The smaller value, 0.4 sec, corresponding to a

high entry speed, seems the more relevant here,

as it is the more likely to give a large line density

of ionization along the trail and an appreciable

magnetic effect. However, vertically descending meteors are relatively ineffective magnetically.

For a horizontal meteor trail, even one of a

meteor of high entry speed, the corresponding

time would be greater. This is because the

magnetic effect at a ground point P immediately

under the trail would depend on the length 2s

of the trail within a distance s on either side of

the zenith of P on the trail. For magnetic

observability of the meteor current system, s

may be taken to be of the same order as the

height h' of the trail, or preferably rather more.

Thus 2s may be at least 200 km, requiring a

travel time of about 3 sec or more. Hence the

most easily detectable meteor magnetic effects,

those of a long horizontal trail at a suitable

height and along or nearly along the direction

of Sq current flow, would be likely to have a rise

time of order 1 second or more.

6. Modification of electric currents.—As the

meteor creates a trail of increased ionization, the
METEOR GEOMAGNETIC EFFECTS 195

electric currents driven by pre-existing and continuing electromotive forces will adjust themselves to the new distribution of conductivity;

this adjustment may be viewed as the formation

of a superposed meteor current system.

The preceding estimates of the meteor magnetic effect have been made as if the meteor

current system were steady and permanent.

The mathematical determination of its actual

mode and rate of growth would be very difficult,

and we have not attempted it. Perhaps the

order of magnitude of the growth time may be

estimated as follows. In a simple circuit of

resistance R and self-induction L, to which an

emf is suddenly applied and thereafter kept

constant, the development of the current is

proportional to \—exp(—Rt/L). The growth

time for the current to attain 90 percent of its

steady final intensity is (L/R) In 10, or 2.3 L/R.

We apply this formula to our problem, substituting for the actual distribution of the meteor

current system that of a toroidal current, with

cross-sectional radius r and mean distance

6 from its axis. Then Z,=47r6{ln (85/r)—7/4}

and i?=(2ir&/7rr2)o-, where a denotes the resistivity of the toroid material. As extreme

cases we take the combinations r=10 m,

6=100 km, o-=1014 emu, and r=300 m, 6=30

km, o-=1014/3 emu. The corresponding values

of 2.3 L/R are 1.4 X10"7 sec and 1.9X10"3 sec.

These times are very small compared with those

considered in the previous section. This suggests that the meteor currents may be taken to

appear without significant delay as the meteor

develops ionization along the trail.

c. Decay of meteor currents and magnetic field.—

The ionized trail formed by the meteor decays

and diffuses; it may also be distorted by nonuniform winds or turbulence. These processes

have been much discussed by the radio physicists who have made radar observations of

meteor trails; this is because such observations

depend essentially on the ionization along the

trail. The duration of the radar echoes is

determined by the distribution of the excess

ionization, as well as by its total line density a;

the peak magnetic effect of the meteor, however, at least in the ideal case of an infinitely

long horizontal trail in the direction of the Sq

current flow, is directly proportional to a

(see equation 31). Thus the influence of diffusion on the radar echoes may somewhat modify

the parallelism that would otherwise be expected between their variation and that of

dHi in this ideal case. It is probable, however,

that the time scale of the meteor magnetic

field, after the peak value is reached, will be

similar to that of the decay of the radar echoes.

This time scale has a considerable range of

values, up to some minutes. Apparatus designed to measure and identify meteor magnetic

effects should be able to cope with such differences of time scale.

8. Conclusions

The present discussion of meteor magnetic

effects leads to conclusions that may be summarized as follows:

(1) Past statistical studies of correlations

between radar or other observations of meteors

and small concurrent magnetic variations have

not been well adapted to determine whether

observable meteor magnetic effects occur.

(2) The sensitivity of the magnetic recorders

used in some of the past studies would seem

to be amply adequate to detect meteor magnetic

effects in favorable cases, but the time scale

of the magnetic recorders should allow for time

scales of magnetic variation ranging from a few

seconds to minutes.

(3) As proposed by Jenkins and DuVall, the

meteor magnetic effects are likely to result from

modifications of the Sq ionospheric currents.

(4) Because these currents are much stronger

by day than by night, the meteor magnetic

effects are likely to share this characteristic;

hence they should be investigated by daytime

radar meteor observations during quiet magnetic periods (to avoid confusion with disturbances caused by the impact of solar plasma on

the geomagnetic field).

(5) The Sq currents being strongest under

the equatorial electrojet at hours around 11

a.m., this location and time offer the best

likelihood of observable meteor magnetic effects;

the current flow then being eastward, a parallel

meteor trail is likely to enhance the northward

deviation of the horizontal magnetic component

from its nighttime value. At other locations

in the daytime, the Sq currents have other

directions, and the meteor effect will involve
196 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

the magnetic declination as well as the horizontal intensity.

(6) The meteor magnetic effect will depend

on the inclination of the meteor trajectory, on

the angle it makes with the direction of the Sq

current flow, and on the height of the trajectory;

favorable circumstances include a high meteor

electron line density a, e.g., 1015 or 1016/cm, and

a height near that of the level of maximum Sq

current intensity—probably about 110 or 120

km. These two requirements may be conflicting; the greatest values of a may occur below

the level of the peak Sq current intensity imax.

Meteors that give the greatest value of the

product aimax and have nearly horizontal trails

lying along or nearly along the direction of

im&x should give the most easily observable

magnetic effect. Solar flares, accompanied by

an SID and a magnetic Sqa (temporary augmentation of the Sq variation), extend appreciable ionization downward into the D layer

and should, therefore, enhance the magnetic

effect of meteors at that level.

(7) The effect on the horizontal component

at the ground is greatest directly under the

meteor trail and is increased by earth currents

induced by the direct field of the varying meteor

current system. The effect decreases to a small

fraction of the maximum value at distances

from the ground plan of the trail that are

comparable with the height of the trail.

(8) The vertical component at the ground is

less affected by the trail, and its peak value is

reached at a distance from the ground plan of

the trail comparable to the height of the trail;

the direct meteor effect on this component is

reduced by earth currents. Hence if coils are

used to record the magnetic changes, those in

a vertical plane containing the direction of the

Sq current are best, and horizontal coils will

have smaller meteor changes to record.

(9) The growth of the meteor magnetic effect

is determined mainly by the speed of the

meteor, which governs the rate of formation

of the trail. The decline of the meteor magnetic effect may be expected to resemble that

of the radar echoes from the trail.

(10) To establish the occurrence and magnitude of meteor magnetic effects, it is desirable

to have radar measurements of individual

strongly ionized trails that are of the right

height and low inclination, and that lie nearly

along the direction of the Sq current at the

time and place of the observations during a

time of low magnetic activity.

Ackno wledgm ents

We gratefully acknowledge support, facilities

and help accorded to us in this research by the

Institute of Science and Technology of the

University of Michigan and by the School of

Physics of the University of Minnesota, where

part of this work was done.

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Abstract

Past studies of magnetic effects ascribed to the passage of meteors through the ionosphere are reviewed, and

the expected effects are estimated for different levels, inclinations, azimuths and electron line densities of the meteor

trails, at different times and geographical locations. The most favorable circumstances for the identification and

measurement of meteor magnetic effects are inferred. The conclusion is that they should be easily measurable during times of low magnetic disturbance, when strongly ionized trails are formed in the daytime at or near the level of

maximum intensity of the Sq ionospheric currents, along or nearly along or opposite to the direction of these currents.

The effects should be greatest under the equatorial electrojet, especially at times of strong solar flares.

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