TRITA-EPP-72-07

POTENTIAL DOUBLE LAYERS

IN THE IONOSPHERE

Lats P. Block

•

April 1972

Ihié report i* submitted for publicationin COsmic Electrodynamics, volume 3. Itreplaces the earlier report TRITA-ÉPP-71-14

Author's address:Department of Plasma Physicsox Department of MechanicsRoyal Institute of TechnologyS-100 44 Stockholm, Sweden

POTENTIAL DOUBLE LAYERS IN THE IONOSPHERE

Abstract.

In this paper Langmuir's old theory of double layers

is reviewed and extended to ionospheric conditions, including

effects of gravity ard expansion in diverging geomagnetic

flux tubes. Bohm's self-consistency condition is refined by

including the temperature of "the beam particles. Chances

for stable sheath? are greatest at 1000 - 3000 km altitude

on closed field lines, or higher on open plasma sheet field

lines, and near \he F-region maximum for upward currents,

according to observations. Randomly arising and disappearing

double layers may cause anomalous resistivity in regions

vhere the plasma is subject to rarefaction instabilities,

namely in the polar wind for upward currents, below the

F-region maximum for downward currents, and in the topside

ionosphere in a limited region at perhaps 1000 - 5000 km

altitude. When double layers occur plasma is accelerated

upwards, and the topside electron density may be reduced

considerably within minutes. At the same time the electric

fields in the double layers accelerate large fluxes of

particles, both downwards as precipitation, and upwards as

energetic particles, preferably, observed in the midnight

sector, e.g. at synchronous altitude. However, in spite of

the very large fluxes there is no particle depletion problem,

since current systems are always closed. Electrostatic

parallel electric fields can also be constructed, such that

both electrons and protons precipitate at the same place.

2.

!• Introduction.

experiments with gaseou- discharges in the laboratory

have shown that the current carrying capacity of a plasma is

limited (Langmuir, 1929; Tonks, 1937; Schönhuber, 1958;

Torvén, 1968; Andersson et.al., 1969). If the current density

exceeds a certain critical value the plasma breaks down and a

thin potential double layer appears, where quasi-neutrality is

not valid.

Double layers are often referred to as sheaths, in parti-

cular in caseous discharge physics. The characteristics of

uoubJe layers are:

a) The charged particle density is much lower than in the

surrounding plasma.

b) There is a substantial deviation from quasi-neutrality.

c) The total net space charge integrated over the double

layer volume is very small or negligible.

d) The thickness of the double layer is much less than a

mean free path of the charged particles (transverse to the

current the layer may extend over many mean free paths). Usu-

ally the thickness is of the order of one or several Debye

lengths.

e) The electric field within the double layer is very much

stronger than any fields that can possibly exist in the un-

disturbed plasma. It is directed along the smallest dimension

(the thickness) of the layer.

f) The potential difference across the layer is of the order

of kT/e or larger, T being the temperature of the plasma.

Double layers must not necessarily be associated with a

high current. They may also occur as boundaries between

plasmas with different temperatures and densities, where they

prevent a current that would otherwise flow between the two

plasmas, due to their different diffusion rates.

In space several sharp boundary regions between different

types of plasmas are known: the shock front separating the

solar wind from the magnetosheath, the magneto pause,. the

inner bondary of the plasma sheet, and the plasmapause.

Calvert (1966) has discovered very steep horizontal electron

3.

density gradients in the topside ionosphere. Drawing from

laboratory experience it may be concurred that a sharp

boundary, in the form of a double layer, may also separate

the cold ionospheric plasma from tho sometimes extremely hot

plasma sheet. In fact, it was suggested long ago by Alfven

(1958) that "a plasma sheath may be situated very high up in

the ionosphere, or perhaps in space far above the ionosphere,

and from this sheath the ionosphere will be bombarded by

positive ions and electrons".

A double layer of the kind proposed here is perpendicul

to the magnetic field, in contrast to the boundary regions

known before (magnetopause, etc.).

Jacobsen and Carlqvist (1964) proposed that solar flares

may be caused by circuit interruptions giving rise to extrem-

ely strong double layers with potential drops of the order of

10 - 10 volts for great flares. A similar mechanism was

proposed as an explanation of the explosive phase of an

auroral substorm (Akasofu, 1969). See also Mcllwain (196 ).

Many recent observations of auroral particle spectra have

indicated acceleration processes associated with parallel

electric fields. (For a review, see Block, 1972.) It is possible

that these fields are concentrated in double layers, as is in

fact the most likely explanation of the observations by Albert

and Lindström (1970).

In the present paper the most pertr.nent parts of the

double layer theory is reviewed, extended in some respects,

and applied to ionospheric conditions.

2. Qualitative structure of a sheath

The first self-consistent but very simplified theory of

a double layer was given by Langmuir (1929), To give some

feeling for the nature of a double layer before the more

detailed study of it in the following sections Langmuir's

theory will be outlined here. It is assumed that the layer

is infinitely extended in the x- and y-directions, that the

plasmas on both sides are cold, and that the layer is confined

between the planes 2 = 0 and z = z. > 0 . Because of

the negligible plasma temperatures, these planes

4.

are infinitely sharp divisions between plasma and double

layer.

If a current flows through the layer in the positive

z-direction, 2 ~ 0 is a source of ions with negligible

initial velocity, plasma electrons from z < 0 , being

reflected there by the layer electric field. At 2 = 2

the same occurs with the roles of ions and electrons being

reversed.

Flux and energy conservation require

n . u. ~ n u = o .1 1 0 0 1

n u = n u = oe e 1.1

2m. u. / v

" V 1 = e(vo - v)2

m ue e = e V

where V is the potential at 2 = 0 and V = 0 at 2 = 2

The meaning of the other symbols is obvious.

The Poisson equation together with the requirement of

zero electric field at 2 = z may be integrated once to

give

(1)

where E is the electric field and

.2 2= —-\/2e m (la)

(lb)

If E = 0 at V = VQ (z = 0) , equation (l) shows that

<j> = u<p. , which is the Langmuir condition (Cf section 6).

Equation (l) may be integrated numerically once more to

give V as a function of 2 • Fig. 1 illustrates qualitativ-

ely the result. At small V the two square-roots containing

V nearly cancel, and it is then found that

V -4/3 2/3 1/3

e e(lc)

which is equivalent to the famous Child* s law for c. diode

(See e.g. Hemenway et.al., 1967, p 109). Similarly, when

V « V,

(V - V) ~4/3 2/3 1/3 (Id)

Thus, a double layer may be described as approximately

equivalent to two simple diodes in series, one electron and

one ion diode (with an ion emitting anode instead of an

electron emitting cathode) or one more complex diode with an

electron emitting cathode and an ion emitting anode. Due to

the Langmuir condition cp. m. = <p m equations (lc) and (id)

are symmetric.

Note that the particle emission powers of the diode

electrodes or plasma boundaries are assumed to be infinite in

the theory, the current being limited by space charge effects.

3. Basic equations of field-aligned currents.

It is expected that ionospheric double layers usually

exist in the presence of field-aligned currents in the auroral

zones. A reasonably complete study of double layers should

include the transition (in time and space) from the plasma

state to the double layer. Although the present study is by

no means complete, field-aligned currents will be considered,

both in a plasma and in double layers.

To avoid unnecessary complications the following assump-

tions are made

(i) All ions are singly charged and of identical mass, m. .

(ii) The field-aligned current is vertical in a magnetic flux

tube with height-dependent cross-section A.

(iii) All velocity distributions are thermal in a frame of

6 .

reference following the average field-aligned velocity

of the particles considered, or their macroscopic

properties of importance here can at least be expressed

in terms of an equivalent temperature.

The following notations are used

nr.

E

Index

Index

T

Q

R

altitude above ground

earth's radius

vertical coordinate, positive upwards, with

z - 0 at h = h,

o0

lenotes value at z = 0

'X - e, i denotes electrons or ions.

Ten perature in energy units

ionizations per unit volume and time

recombinations per unit volume and time

force per particle of species ct , due to collisions

with other particle species

acceleration of gravity

proton charge

Other notations are self-evident.

e. = -e = ei e

Conservation of momentum and particles then give

ru*5 du

0 Va «a O =(2)

(& (A nauaa

FT (3)

A = A J -7-r0

r = rE + h = rE + h0 (4)

v2(5)

7.

Equations (2) and (3) give

• = n_i e E - F_ -\J - (6)

with

= Ta " Va' (7)

2 1 m u_

*a = W a (9)

Both double layer and plasma solutions of these equations

will be studied. The Poisson equation with n. * n musti e

be used to obtain a double layer solution. For the plasma

solution the Poisson equation is replaced by the quasi-neutral-

ity condition n. = n = n .

4. Stationary double layers.

Since quasi-neutrality is not valid in a double layer, it

can be thought of as a vacuum region that separates two plasmas

(sometimes with different properties) from one another.

Electrons from one of the plasmas are reflected by the layer,

and ions are accelerated to a beam into the other plasma. The

roles of particles from the other plasma are reversed.

If the total potential drop VQ across the layer is of

the same order as T/e of the plasma the layer is said to be

weak. If V » T/e the layer is strong.

In this section a strong time-independent double layer of

infinite extent transverse to the z-direction (magnetic field)

will be studied. Since the layer thickness is less than a

mean free path all collision terms of equation (8) can be

neglected. The current is assumed to be upward if the opposite

8.

is not specifically mentioned.

Choose the altitude h = h such that 2 = 0 at the

lower edge of the layer. At the upper edge 2 = 2 and

V = 0 . Index 0 refers to plasma properties at 2 = 0 or

to particles coming from that plasma. Index 1 is the same for

z = z . Index (3 is a general symbol for 0 or 1 .

Index ctp refers to particles a (e,i) originating in

plasma {3 (0,1). For example, u 1 (which is a function of

2) is the linear mass velocity of beam electrons originating

above the layer. Symbols with index 0 or 1 only are

always constants. Symbols with two indices (oc(3) depend on 2 .

The total current is

ni0UiO > 0 (10)

Particles of categories (eO) and (il) do not contribute

since they are reflected. Of course, particles in the high

energy tail of the distributions can overcome the layer

potential,but this may be taken care of by regarding a suit-

able number of the beam particles as really reflected (beyond

the layer). This point of view greatly simplifies the theory.

It makes it possible to regard particles retarded in the layer

as belonging to stationary populations. Hence, u _ and ueO

vanish at the layer»

Thus, there are four groups of particles present in the

layer, namely electrons and ions from below and above. The

time-independent version of (6) applied to these particles

gives for reflected particles

dn

eO dzeO -eE - FeO (Ha)

dn.- Fu) (lib)

and for beam particles

9.

weldnel -eE - Fel

dT

dz"el (12a)

d ni0wiO dz

= nio( dz(12b)

Equations (lla, b) do not contain any temperature gradient

terms since the temperature is not affected by a reflecting

potential. However, in a layer where collisions are unimport-

ant the "parallel" temperature of accelerated particles

approximately obeys the adiabatic law

dT dn dnui an / - \ un-~- = K = (.Y - 1)T n n

(13)

where n = 2 for one degree of freedom.

In the special case when F = m g (somewhat unrealisticex a

ally assuming other terms in (8) to be negligible) these equat-

ions may easily be integrated analytically, yielding exponent-

ial decrease of reflected particle densities with respect to

potential (including gravity potential) and approximately

V and (vo ~ V) ' density decrease for beam electrons

and ions, respectively. The results are illustrated in

principle in figure 2.

The Poisson equation is

dE f n - n - n )i l eO e l / (14)

Multiplication with E , substitution of n fleE obtained from

(ll) and (12), and integration yields

T

where

f«

+ " i 0m i u i 0

10.

In the limit of" infinitely strong double layers all

T _ may be neglected. The same is valid for F and F.

since the electric field provides the dominating force.

Equation (15) then becomes identical with (l).

The main deficiency of this theory is the assumption

of thermal distributions. These cannot be maintained under

electric field acceleration in the absence of collisions.

However, thermal distributions are often assumed, and the

results describe the layer interior quite well, but for a

detailed analysis of the plasma-double layer transitions

the Boltzmann equation must be used. No satisfactory theory

of this transition region has yet been formulated. For

further details spe Torvén (1969). Exact solutions of the

collision-les? Boltzmann equation (electrostatic waves) have

been obtained by Bernstein et.al. (1957).

For our purposes the deviations from thermal distribut-

ions cause no serious problems.

5. Self-consistency conditions.

Consider equations (l2a, b). Due to (13) these can be

transformed into

dnW elel dz

= nel(-eE - P ) (16a)

dn. ..w 12 - nlO dz ~ ni0 eE - F io)

where

W.

(16b)

(17)

The boundaries (z = 0 and z = z ) of a strong double

layer will now be considered. Only in this case are the

boundaries relatively well defined.

11.

At the boundaries charge neutrality is valid. Near

we have n = ne eO

and n. ~ n._i IO since nel

and

n. have decreased very much due to acceleration and

reflection in the layer. Hence, the contribution of neland n... to the space charge near 2 = 0 may be neglected

in the case of a strong double layer. Differentiating the

Poisson equation (14) with respect to z and using (lla)

and (l6b) then yields

d2E

dz iO

eE + Fe0 e0>

(18)

Since n = n. at 2 = 0 equation (18) shows that E cane i

only increase with increasing z (into the layer, that is)

if

2m.u .-i i0 e0

(19)

z = 0

It is easily seen from (lla) and (l6b) that

dn /dz = dn. /dze i

at z = 0 if (19) is just satisfied.

The same arguments applied to the region near

in the layer gives

z = z.

eE+Fm u 7 ̂e el el + Til \ eE-F,

el (20)il

z - z.

These are necessary but not sufficient conditions for

the stability of a double layer. Before beam particles (in

being) reach the layer they must be preaccelerated to

approximately sonic velocity in order to maintain the necess-

ary space charge within the layer. If their velocity is

lower, any tendency for a rising electric field will be

counteracted by the resulting space charges.

12.

Bohm (1949) developed a similar criterion for wall

sheaths

m .u .** > T

neglecting the influence of the ion temperature. Persson

(1968, 1969) has pointed out that the Bohm criterion for ions

and a similar criterion for electrons, namely

2m u > • .e e i

must be valid for free sheaths. If the influence of the beam

particle temperatures is accounted for, the Bohm criteria are

replaced by the self-consistency conditions (19) and (20).

See also Andrews :>nd Allen (1969), and Torvén (1969).

If the double layer is not very strong all the four

categories of particles must be included in the analysis.

Furthermore, the trick of assuming the reflected populations

to be at rest cannot be upheld, which means that retarded but

not reflected particles will be subject to the adiabatic law.

The result of these facts is that the limiting kinetic energies

may differ from those given by (19) and (20). However, that

is a much more complicated problem.

The self-consistency conditions are further analyzed in

section 8.

6. Pressure balance and the Langmuir condition.

Equation (15) describes the pressure balance through the

double layer. The integral /n F 6z is usually very small

and can be neglected. In a strong layer the terms in

P(z) - P(o) are of four different orders of magnitude. At

z = 0 the P(0) hierarchy is

il xl nel el neO eO.ÄT.rtiO xO

2 2.-m.u.- « n ,m u .xO x xO el e el

(21)

13.

provided all temperatures are of the same order of magnitude.

The third inequality is due to the self-consistency criter-

ion (19).

At 2 = 2 the corresponding hierarchy is obtained if

e and i , and O and 1 are interchanged.

If E = E equation (l5) gives

P(O) = P( 2 l

implying that

n . _ m . u. )lO i lO

= z.

~ In .m u )\ el e el/z = 0

(22)

(23)

Since these beam particles habe been accelerated through

the s«

equal

the same potential drop V their kinetic energies must be

( m.u.V i i

2iO 2 = 2.

Hence (»J2 = 2. (»J

2 = 0

and2 = 0

n . _ u . _ I. ,lO lO i /_ /_1 = —— = ( m /m.

n _u , I_ V e' i

1/2

(24)

where I. and I are the ion and electron current densities,i e '

respectively, through the sheath.

Equation (24) is the Langmuir condition which was derived

for an extreme case (zero temperatures) in section 2. However,

here it is seen that (24) is valid only for relatively strong

double layers, i.e. when eVQ » all T . If eV is of

the same order as some T/vO (21) and hence also (23) are notap

necessarily valid. In practical cases the validity of the

Langmuir condition can only be tested by analysis of the

pressure balance (15).

14.

7. Plasma rarefaction and compression instabilities»

In this section a plasma (acoustic) instability will be

considered, that should tend to develop into double layers.

Since a plasma is considered here, n. = n = n .

Equations (6), (13) and (17) applied to electrons and

ions give

w3n 3*

it

Wi 32 ~ s 1 / 3t

The sum of these may be written

W 3n3z

= -nF - a*3t

(25)

with

W = w + w.e i

= r(? + T.} -1 \ e 1/

2 2m u - m.u.

e e i i

F = F + F.e i

+ # . = n ( m u + m . u . )i s e e i i /

(25a)

(25b)

(25c)

F and F. are given by (8).

Consider a disturbance r\ in the equilibrium charged

particle density n so thats

n = n + TIs ' (26a)

Since F and W may depend on25a-c)

F = F + dFs

n (cf equations 8,

(26b)

W = W + dWS

(26c)

15.

The stationary solution is given by

Wdn

s 02- n F

s s(27)

Introducing (26a-c) into (25), regarding (27) and

omitting second order terms in the disturbance quantities,

yields

dnTT=-T)F - n dF - W ̂ - dW - :3t ' s s 3z 3z

(28)

A density instability will occur if 3$/3t enhances

a density deviation r\ •

Case 1 F = dF = 0 . According to (27) this gives

3n./3z = O . Equation (28) is then3̂

= - w3t

(29)

Figure 3a shows a density depression and a density enhancem-

ent. The arrows at the slopes of these indicate the direction

of mass flow acceleration 3$/3t when W < O . For example,

in the depression (where TJ < 0) 3$/3t is negative to the

left where 3T)/3Z < 0 , giving an outflux in the frame of

reference moving with the plasma, so that $ = O . Thus, in

this frame the center position of the disturbance region will

be at rest, but the disturbance amplitude will increase if

W < 0 (current associated with supersonic particle flow).

Obviously, W < 0 can only occur if the current density

is sufficiently large. Zero current gives W = Y(T 6+T^) > 0

in the frame moving with the plasma. When W > 0 (subsonic

flow) the arrows in figure 3a are reversed as shown in figure

3b and all disturbances are counteracted.

Thus, the instability condition is

(30)

16.

where2 T = T + T.

e i(31)

It should be pointed out that

2 2m.u. << m u1 1 e e

by a factor m /m. in the frame moving with the plasma so

that the term m.u. is actually meaningless within the

accuracy of the present theory.

The condition (30) was originally derived by Carlqvist

(1972), using a different but equivalent formalism. The

equality sign in (30) implies W = 0 . The plasma is then

unstable for rarefactions since W becomes smaller as the

rarefaction developes. However, compressions can only be

unstable when W < 0 , initially. The growth of a compress-

ion instability cannot proceed beyond the density correspond-

ing to W = 0 . If W = 0 initially, a compression will make

W > 0 so that all instabilities are counteracted.

The case when W < 0 is discussed further in section

10 f.

Case 2 F is given by equations (8) and (25b) but

with all particle encounters excluded except Coulomb collisions,

The latter contribute nothing to F but they help maintain

thermal distributions. Thus,

/ 2 2 \ 1 dA= mg - ( m u + m . u . ) — —

* \ e e i i / A d z

(32)

where

m = m + m.e i

In this case the dependence of

evaluated. Introduce

2 2U = m u + m.u.e e ii

u = « ( m u + m.u . )m \ e e i i/

v = u. - ui e

I = e n v

(33)

F and W on n must be

(34)

(35)

(36)

(37)

17.

The purpose of the present calculation is twofold:

a) to obtain an instability condition, and b) to find

the direction of plasma motion in rarefaction and compression

regions. It can be expected that the right hand side of (28)

will contain (to first order) some terms proportional to r\ ,

and other terms proportional to 9r)/3z . The latter should

give the instability condition, since the r̂ -terms are anti-

symmetric with respect to the center of the disturbance region

and thus deduct as much influx on one side as they add on the

other, with no net stabilizing or destabilizing effect. On

the other hand, the r\-terms give a finite 8$/Bt in the middle

where dr\/dz = 0 , thus accelerating the disturbance one way

or another.

Equations (34) - (37) give

2 2U = mu + j/n

J =m m.Ie 3.

2me

(38)

(39)

It is convenient to work in the frame where u = 0 •

The result of the analysis will then show whether the dis-

turbance tends to move faster or slower than the stationary

plasma. Equation (38) may be differentiated to give

dU = - 2 Jn/n3 = - 2 U -n

(40)

where r\ = dn according to (26a). Now, (25a), (31), and

(34) give

dW = 2 Y dT - dU = 2(yxT + U) —n

Equations (32) and (30) yield

dF = An dz

Now, (32) with F(28) to give

(42)

= F , (4l) and (42) may be introduced in

18.

= Wat w 32

s

L = Fs[3U + 2(*2- 1)T] - 2Ws 2 S

(43)

(44)

Hence, the instability condition (30) is valid also in

this case.

To determine the direction of plasma motion within the

disturbances the sign of the quantity L must be found.

Assume that a certain instability region 2 < 2 < 2

can be defined such that W < 0 there. Equation (27) then

implies that F < 0 there, provided 3n /32 < 0 . This iss s

expected in the ionosphere, of course. Furthermore, W = 0 ,F = 0 and hence L = 0 at 2 = 2. and 2 = 2_ . Tos 1 2determine the sign of L in the instability region we express

L as a function of U , noting that T and W are also

functions of U . Equations (13) and (40) may be integrated

to give

UT = U T- = constant (45)

provided x = 2 . Equation (44) may then be written

L = - i m U2 + 3 rag U + 36 mg

1 8 dAd2 (46)

Noting that tL = 2 y T- •• = 6 T it is then found that

dL _ d^LdU ~

= 0 (47)

U3= - 6 mg/U < 0 (48)

at U = t L . Hence, L behaves in principle as shown in

figure 4. It has an inflexion with zero derivative at U = IL ,

being positive for U < U- and negative in the instability

region where U > U- .

19.

Two cases may now be distinguished, according to the

sign ox 3n/dz , that is above or below the F -maximum.

Equation (27) shows that if 8n/dz > 0 (below F -max) then

F and W have opposite signs. At the boundary between

stable and unstable plasma W = 0 and hence F = 0 . Ons s

the other hand, inspection of (25a) and (32) shows that W

and F must then have the same sign if T is unaffected by

channes in U , or if it obeys the adiabatic law (13). This

paradox is resolved b\ noting that all collisional terms have

been left out in (32). The recombination term is particularly

important here. Thus, the present theory does not cover this

case.

The other case is the topside ionosphere, where Bn/3z< 0.Equation (27} ;. lien shows that W and F have the sameM ' s ssign in agreement with (32). Since L < 0 in the instability

region it is seen from (43) that plasma in compressions is

accelerated upwards (in the direction of F since 3$/Öt> O)

and downwards in rarefactions. It is physically sensible that

dense regions should be accelerated in the direction of F

and dilute regions in the opposite direction.

8. The transition from instabilities to double layers.

Carlqvist (1972) shows that a plasma rarefaction instab-

ility of the kind studied in the previous section tends to

develop into a double layer. Here the relationship between

the double layer self-consistency conditions (19) and (20)

and the plasma instability condition will be considered.

Suppose that the electron velocitv is such that

m u = YT + XT.e e ' e i (49)

while the ions are at rest. If the arbitrary constant X is

put equal to y an instability occurs. Equations (lib) and

(16a) with (4 9) inserted now shows that

20.

eE +

eE -el

= \ (50)

Z = 2.

when n ., = n., and dn ^/dz = dn.,/dz . Hence, the selfel il el il

consistency condition (20) seems to be fulfilled for any

value of \ . However, (20) may be written

2m u Ae el

YTel1 +

eE-F.(51)

due to (25b). If \ < 1 (51) cannot be satisfied above a

certain maximum electric field. Hence, the growth of E will

be limited. On the other hand, if X £ 1 there is no limit-

ation on the growth of E as long as (l8) is valid. Hence

a sheath of unlimited strength can only exist if

m u ,e el 'el il

(52)

It is easily shown that (19) may similarly be reduced to

miui0 e0 (53)

These two conditions are necessary for the existence of strong

sheaths.

It should be observed that the manipulations made here

are not obviously allowed if F = F. + F = 0 since then the

density gradients vanish in the plasma and hence also at

2 = 0 and 2 = z1 • However, equation (18) and its correspond-

ence valid at z = z are so reduced that (52) and (53)

follow at once when F = 0 .

Thus, it has been shown that when a plasma rarefaction

instability occurs the double layer self-consistency cond-

itions are amply satisfied.

Laboratory experiments corroborate the view that rare-

faction instabilities develop into double layers. Torvén

and Babic (1972) have found potential peaks in a low-density

discharge just before the current has reached the critical

value for a double layer. This was predicted by Alfvén and

21.

Carlqvist (1967) and Carlqvist (1972). Torvén (private

communication) has found noise in the typical frequency

range of ion-acoustic waves when double layers are formed.

9. Stability of double layers.

Although conditions (52) and (53) are necessary for

the existence and stability of double layers they are not

sufficient . No sufficient conditions are known at present.

Only a few remarks will be made here.

In the laboratory it is observed that quite stable double

layers occur only at constrictions in the discharge tube.

In space a diverging magnetic field may perhaps serve the same

purpose. The gravitational force may also help to anchor a

sheath at some altitude.

However, it is also observed in the laboratory that

double layers often appear and disappear at a regular frequency

(10 - 100 kHz) at the same place so that it looks quite

stable to the bare eye. This may be explained as a wall effect.

When the layer appears the walls are bombarded with energetic

particles that release neutral molecules from the walls. When

these are ionized the current-carrying capacity of the plasma

increases and the layer breaks down. Then no energetic

particles reach the wall, no more neutral particles can be

ionized and the layer reappears (Torvén, 1968).

In space no such effect can occur, so the double layers

may be more stable.

Remembering that in the frame moving with the plasma

n.u. « n uii e e

(30) may be written

2 2and m_.u_. « m u the instability conditioni i

l o m DA = An T $ - ~ -

2e Y

if equation (10) is used.

(54)

22.

In the polar wind ionosphere A is varying with altitude,

qualitatively as shown in figure 5. (The situation when there

is no polar wind is discussed in section 10.) To the left is

shown a case when the field-aligned current is upward.. The

plasma above a topside ionospheric double layer would be un-

stable, because if (54) is just fulfilled at that layer, it

is amply fulfilled above it. However, below a layer in the

F-region the plasma can be stable since the current is carried

by the beam electrons there. The plasma electrons do not

have to carry any current to speak of.

The conclusion is that for upward electric fields stable

double layers would only exist in the F-layer. For downward

electric fields stable double layers may exist in the topside.

This agress both with laboratory experiments (Torvén

and Babic, private communication) and with observations in

space. Measurements of parallel electric fields have only

been made so far at F-region altitudes. Only downward electric

fields have been found with the double probe technique (see

e.g. Mozer and Fahleson, 1970). These would occur in the

unstable plasma where resistivity would be anomalously high.

Furthermore, the only observations that may more directly

be interpreted in terms of double layers (Albert and Lindström,

1970) clearly indicated upward electric field within the layer.

The stability of a double layer may be further enhanced

by plasma convection around the field-aligned currenc-carrying

plasma. As pointed out by Block (1969) and by Carlqvist and

Boström (1970) the electrostatic equipotentials in a double

layer must turn upwards to become field-aligned around the

field-aligned current (figure 6). This means that there is

convection around the field-aligned currents. The inertia of

this convection should tend to prevent break-down of a double

layer. The existence of such convection is strongly indicated

by the field-reversals observed by Cauffman and Gurnett (1971).

The Langmuir condition requires supply of electrons and

ions in the right proportion from both sides to the double

layer. If that is not possible the layer will be charged.

The resulting external electric field will accelerate it to

23.

an equilibrium velocity such that the Lanqmuir condition is

fulfilled in the frame of the layer. For example, if the

high potential plasma is unable to supply sufficiently many

ions the layer moves towards that plasma, increasing the ion

velocity and flux relative to the layer.

Note that this effect is also of importance for the

self-consistence conditions.

Moving sheaths may live as long as they can move un-

hindered by for example a too dense plasma, where they may

stop and perhaps become stationary.

Moving double layers (usually called striations) are

extremely common in laboratory discharges (see Olesen and

Cooper, 1968).

It is observed in the laboratory that when a double layer

has appeared somewhere, there is a strong tendency for another

layer to appear at about a thermal relaxation mean free path

of the beam electrons towards the anode. This distance may

be typically 10 - 50 cm. The presence of a b^am of supra-

-thermal particles creates good conditions for another11 layer-creating" instability when these particles are thermal-

i2ed and become part of the background plasma.

The long thermal relaxation distance, mentioned above,

is calculated assuming binary collisions. However, wave-

particle interactions may shorten this distance considerably.

A striking example of this has been reported by Morgulis

at.al. (1967, 1968) who also found that the dispersion of

the beam electrons was accompanied by noise in the GHz range.

In any case, when the beam particles, sooner or later,

are thermalized and dispersed through interaction with the

background plasma, this plasma must take up the beam pressure.

This is greater than the plasma pressure already when the

particles enter the double layer, due to the self-consistency

conditions. Hence, after acceleration in the layer it is

still greater. If the interaction distance is short, the

plasma must then be pushed back so that the layer is widened.

Then the layer potential rises, the beam pressure increases

still more, and so on. The situation is unstable and the

24.

double layer roust break down very soon, perhaps to reappear

again and go through the same instability. However, if the

interaction distance is very long (as for auroral particles

where the layer may be hundreds or thousands of kilometers

above the aurora) the plasma or neutral pressure may be

sufficiently high to balance the beam pressure so the double

layer may be stable.

10. Double layer altitudes.

Double layers should preferably occur where A given

by (54) exhibits a minimum. Such minima may exist when the

relatively dense and hot plasma sheet is in contact with the

ionosphere, and when there is no polar wind, as shown below.-4 2

Field-aligned current densities up to about 10 A/m

have been observed (Zmuda et.al. 1970) at altitudes above

1000 km. Assuming the maximum current density that ever-3 2

occurs is of the order of 10 A/m it may be concluded

from (54) that the maximum electron density where a- double

layer can exist is about 10'- 10 electrons/cm provided the

temperature is of the order of 1000 K. However, still higher

densities may be conceivable if there are particles trapped

between the layer and the magnetic mirror below, as observed

by Albert and Lindström (1970). This may be explained as

follows.

Assume that a double layer is created because of an in-

stability at minimum A . Assume also that the current is

upward. Energetic electrons with large pitch-angles may then

be trapped below the layer as described by Albert and Lindström,

If the "parallel" kinetic energy of these electrons is compar-

able to the potential drop across the layer they may contribute

significantly to the space charge within the layer, since they

penetrate deep into it before being reflected. Their number

may transiently increase at first, thus increasing the negative

space charge region within the layer. As a compensation the

25.

positive ion flux through the layer must increase. Hence, the

layer must move downwards (cf. section 9) towards more dense

plasma, until the number of trapped particles is saturated due

to equal scattering of electrons into and out of the trapping

pitch-angle cone. During the downward movement of the layer

the trapped electrons may be Fermi-accelerated but that is

probably a small effect.

Equation (54) may be regarded both as a plasma instabil-

ity condition and as an approximate condition for double layer

self-consistency. The latter concerns the space charges within

an existing (but possibly moving) layer. Then, the direction

of motion of the charged particles through the layer does not

matter but only the time they spend in the layer. The self-

consistency conditions (5 2) and (53) were derived assuming

that the energies of practically all reflected particles are

small relative to the layer potential. If not, the charges

of reflected particles from the opposite side must be consid-

ered. The trapped particles were assumed to have non-negligr-

ible energy. Their contribution may be accounted for in (54)

by a larger value for the current j , thus including a proper

fraction of the flux of trapped electrons, even though these

do not contribute to the actual current, of course. Hence,

for a given current the electron density n may be larger than

given by (54) if electrons are trapped below the layer. This

may explain the low double layer altitudes found by Albert and

Lindström (250 - 300 km).

If the "parallel" energy of all the trapped electrons is

exactly equal to the potential drop across the double layer

the current j in the formula (54) for A should be replaced,

by

= 3 2e (55)

where (p is the one-way total flux of trapped electrons

within the flux tube and j is the real net current.

Obviously the space charge balance in a double layer

depends on the velocity distributions of the particles involved.

26.

Addition of energetic trapped particles may be equivalent to

raising the corresponding temperature of ambient plasma part-

icles. According to laboratory experience weak layers are

most stable, whereas strong layers are usually explosive, i.e.

their voltage increases explosively. The high double layer

potentials ( - 100 volts) reported by Albert and Lindgtrom

(1970) correspond to very strong layers in terms of normal

ionospheric temperatures. However, the trapped energetic

particles may make them equivalent to weak layers, which may

explain their good stability.

Bearing in mind that double layers apparently may appear

at quite low altitudes, the most likely altitude may neverth-

eless be much higher up where A is minimum. The altitude

where that occurs depends strongly on the ionospheric-exospheric

model. The simplest model would be a stationary isothermal-2ionosphere with gravity decrease as r

3crease as r . This gives a A-minimum at

and flux tube in-

ho = ro1250 M - 1 (56)

6 T

where r = earth's radius, M = ion mass in atomic mass units,

and T, = average ion-electron temperature in degress K .

If there is an outflux of ionospheric particles, such

as in the polar wind, the situation is different. Using the

exospheric polar model of Lemaire and Scherer (1970) the

critical current j in a flux tube of one m cross-section

at 2000 km altitude is given as a function of altitude in

figure 7. The current j is calculated from equation (54)

for each altitude, using the temperature and density given by

Lemaire and Scherer. The corresponding current density I

at 2000 km is then calculated and given in the figure. It is

seen that quite low current densities give plasma instabilities

above a few thousand kilometers. However, there is no minimum

Ic (corresponding to minimum A ) in a polar wind flux tube.

This is natural since the pressure tends to zero at infinite

altitude.

In figure 8 the well-known solutions of Bank's and

Holzer's (1968) polar wind equations are shown, in principle.

27.

These equations are equivalent to the time-independent

equation (25) of the present paper, with F given by (8) and

(25b), and with 2ero current. Curve A - A of figure 8 is

the polar wind solution, which qualitatively best resembles

Lemaire's and Scherer's model.

However, there are also breeze solutions given by curves

of type C - C . These may exist on closed field-lines if

there is magnetospheric convection that is continually remov-

ing plasma through field-line merging at the day-side magneto-

pause, or if there is plasma with finite pressure on open

field lines, for example the plasma sheet. In such a case A

is minimum near maximum Mach number on curve C • If a

sufficiently strong current is turned on a switch to a curve

of type A' - P - B occurs with minimum A at P . A layer

will then appear there, with stable plasma on both sides

regardless of the current direction. The current densixy I

will be limited to

= e n ( (57)

where index P denotes values at minimum A .

This is perhaps the most likely place for stable double

layers. The theoretical solutions then predict double layer

altitudes of about 1000 - 3000 km, depending on the ion

composition and the temperatures at these altitudes.

11. Anomalous resistivity through random unstable double layers.

It has often been argued that E caused by anomalous

resistivity could be responsible for so called "monoenergetic"

particle fluxes, double peaked velocity distributions of

auroral particles, and other similar phenomena. Anomalous

resistivity is often thought of as being due to turbulence.

However, it is difficult to see how such electric fields could

accelerate particles, since the turbulence must impede the

acceleration through an increased effective collision frequency.

28.

That is the mechanism through which the resistivity is

made anomalously high. In any case it could not cause extra

velocity distribution peaks or unusually sharp high or low

energy cat-off (Block, 1972).

Double layers, on the other hand, are limiting the

current through space charge effects. They are also laminar.

All particles getting through the layer are accelerated. Any

desired velocity distribution can be explained by a large

number of layers with suitable injection of particles into the

flux tube between them.

The layers must not necessarily be stable. Fluctuating

or flickering layers, appearing and disappearing at random,

will also accelerate particles. A region with a large number

of such unstable layers could have an essentially constant

or slowly varying total potential drop.

The theory of plasma instabilities presented in section

7 is one-dimensional, and as such it can only handle laminar

flow. Carlqvist's (1972) theory of the development of rare-

faction instabilities into double layers is also one-dimension-

al. It is not clear if a complete 3-dimensional theory would

predict turbulence or laminar flow. However, if nature is

kind enough to maintain laminar flow, it seems that double

layers would inevitably appear and disappear in a disordered

random way in an extended unstable plasma region. This would

then cause anomalous resistivity that is not turbulent and

that could explain observed auroral spectra.

Figure 9 illustrates how anomalous resistivity could

develop in a region around a A-minimum, (for example around

the altitude given by (56), which may be somewhere between

about 1000 and 5000 km) provided no turbulence destroys the

laminar flow. Suppose the current is rising gradually. A

rarefaction first develops at minimum A when W = 0 there.

The plasma from the rarefaction wells up on both sides

(figure 9a). This causes A to increase a little there,

allowing the current to rise a little more. The rarefaction,

of course, becomes a double layer but the minimum value of A

in the plasma has increased, and that determines the plasma

29.

instability condition. When the current has risen W = 0 in

a small region around the layer so that one or two new rare-

factions can develop, more plasma wells up and the minimum

A is increased still more, corresponding to a still higher

current in the flux tube. The region W = 0 gets still

larger and so on. The end result is a large number of layers

with W = O in all the plasmas between them (figure 9b).

This could be characterized as a region with average W < O

in terms of the plasma distribution before the instabilities

developed.

If the double layers are unstable, some are breaking

down while others are built up, all the time.

As was pointed out above a large: number of double layers

may produce any spectral distribution of precipitating particles,

However, it is also of interest to compare energy distributions

produced by laboratory double layers with observed auroral

distributions. Figure 10 shows an energy distribution obtained

from one weak double layer in a laboratory discharge (Andersson

et.al. 1969). It is remarkably similar to the spectra

observed by Westerlund (1969) at 400-800 km altitude. The

high energy peak in figure 10 is due to beam electrons from

the double layer, and the low energy peak is plasma electrons

trapped between the layer and a reverse electric field at the

anode.

This, of course, is just an example of what double layers

can do. Westerlund*s low energy electrons may for example

ha ,-s- been injected between a strong upper layer and a weaker

lower layer further down.

30.

12. Depletion of plasma in the upper ionosphere.

Block and Fälthammar (1968) have shown that a field-

aligned current can more or less deplete the topside ion-

osphere if the ratios between electron and ion current at

the top and bottom (F-region) of the flux tube differ from

one another. The stationary electron density altitude

distribution is such that the net outflux of plasma exactly

covers the height integrated difference between ionization

and recombination.

If a double layer exists high up in the topside

ionosphere the plasma current just below the layer is carried

by one kind of particles only. If the beam current is not

dispersed by wave-particle interaction the beam particles

will not be stopped until they reach the E-region, and they

do not contribute to the topside electron density. In the

E-region the rate of recombination is high, so the precipit-

ation will not very much influence the topside density.

Hence, for upward current the net outflux of plasma

from the topside ionosphere is given by the upward ion flux

at the double layer minus the negligible upward ion flux in

the F-layer. According to Block and Fälthammar (1968) the

most drastic reduction of topside density occurs if the

current carried by the upward moving ions at the double layer

is about 3 y 10 A/m , provided the ionization rate is as

high as that due to daylight solar UV radiation. In case

the ions are protons at the double layer the total current,—4 2

including the beam electrons, would be about 10 A/m for

the most drastic density reduction. Of course, some reduct-

ion effect occurs also for weaker currents. At night, the

reduction at stationary state is larger at a given current,

because of the lower rate of ionization.

For downward currents the density reduction is less

than for upward currents by about a factor three or four

according to the theory by Block and Fälthammar (1968).

The time constant for reaching stationary state after

a depleting current is switched on is of the order of a few

31.

hours. However, most of this time is used up for reduction

of the lowest parts near the F-region maximum. Reducing the

topside above, say 500 km, takes only a few minutes.

If there is an extended instability region and not

just a double layer the same reduction will, of course, also

occur below the region of plasma instability or afiomalous

resistivity. However, in this case a net upward flux will

also occur within the instability region, due to the upward

acceleration of compression regions according to the theory

in section 7.

During the removal of plasma from the flux tube (before

stationary state has been reached) the total potential dröp'

must increase or the current must decrease due to the diminish*

ing apparent conductivity. However, complete depletion of

plasma can never occur since a current is always closed. New

particles must be carried dqto the flux tube due to perpendic-

ular currents even if there is no convection whatsoever.

Thus, there is no particle depletion problem, contrary to

what has been claimed by e.g. O'Brien (1970). Such a problem

exists only in models where auroral particles arc assumed to

be squeezed out of the flux tube, or in "leaky bucket models".

If the field-aligned current (which may be in the form

of a current sheet above an auroral arc, see figure 11) is

moving sideways, for example north-south, the topside

ionosphere may be depleted over a large region. This may

be important for the explanation of the nightside ionospheric

ttough..

13. Concluding remarks.

Many authors have considered plasma instabilities

associated with field-aligned currents in the upper ionosphere

(Swift, 1965, 1970; Kindel and Kennel, 1971). A rarefaction

instability has been considered here and Carlqvist (1972) has

shown that this instability leads to formation of double

32.

layers. When this double layer is formed certain self-

consistency conditions for double layers are already amply

fulfilled.

The most likely altitude for stable double layers is

1000 - 3000 km on closed field lines and perhaps a few

thousand kilometers higher up on open field lines, if they

reach the hot and dense, expanded plasma sheet before

substorms. The stability of the double layers should be

enhanced by the plasma convection around the field-aligned

current. This kind of convection has been observed as

electric field reversals by Cauffman and Gurnett (1971).

According to the observations by Albert and Lindström

(1970) stable douole layers can also exist at F-region

altitudes if the current is upward. Measurements of E

in the F-region (Mozer and Fahleson, 1970) show only down-

ward electric fields» This agrees with theory and laboratory

experiments since the F-region plasma should be unstable if

double layers occur in the F-region at downward electric

field. This unstable plasma should then develop anomalous

resistivity. If this anomaly is caused by turbulence it

should not produce double peaked or sharply cut-off precipit-

ation spectra, It is even questionable if it can at all

accelerate auroral particles.

However, if laminar flow is maintained in the unstable

plasma, double layers should arise and disappear at random.

Any kind of precipitation spectrum may be produced, depending

on the details of the current system»

When double layers (stable or unstable) are formed, a

reduction of the topside ionospheric electron density should

occur, as described by Block and Fälthammar (1968). If there

is a region of anomalous resistivity in the topside, due to

randomly appearing and disappearing double layers, an

additional mechanism of topside density reduction sets in,

due to upward acceleration of the compressed plasma regions.

Thus, large amounts of plasma may suddenly move up from

the ionosphere into the magnerosphere when strong field-

aligned currents are switched on, for example near midnight

33.

during auroral breakup. Large fluxes of particles should

at the same time be accelerated through the double layers,

both upward and downward.

Finally, it is not difficult to understand how both

ions and electrons can be accelerated in the same direction

by a parallel electric field (see O'Brien, 1970). Figure 12

shows a simple potential distribution taylored for this

purpose. Block (1969) proposed that a potential asymmetry

between conjugate points can do that for one hemisphere.

This should occur in nearly all cases since perfect symmetry

should be rare. However, figure 12 shows how it is possible

to get simultaneous ion and electron precipitation at both

conjugate points, provided that the particles are not too

much dispersed by wave-particle interactions on their way

down towards the ionosphere.

Réme and Bosqued (1971) have suggested a model of this

kind where the parallel field is downward at low altitude,

due to the negative space charge deposited by high energy

electrons in the E-layer.

Acknowledgements.

The author is indebted to C.-G. Fälthammar and, in

particular, to P. Carlqvist for stimulating discussions and

positive criticism.

References

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Alfvén, H., 1958, Tellus, 10, 104.

Alfvén, H. , and Carlqvist, P., 1967, Solar Phys. , _1, 220

Andersson, D., Babic, M., Sandahl, S., and Torvén, S.,

1969, Ninth International Conference on

Ionized Gases, Contributed paper 3,1.2.2,

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Banks, P.M., and Holzer, T.E. , 1968, J. Geo phys. Res. , 73,

6846.

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Phys. Rev., 108, 546.

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Phenomena in Ionized Gases. Bucharest,

Rumania, (invited review paper), Preprint*

Electron and Plasma Phys.. Royal Inst of

Tech., 10044 Stockholm, Sweden, Rep.69-30.

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73, 4807.

Block, L.P., 1972. in Earth's Maanetospheric Processes.

Ed. B.M. McCormac, in press.

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Bohm, D,, 1949, The Characteristics of Electrical

Discharges Magnetic Fields, Ed. A.Guthrie

and R.K.Wakerling, McGraw-Hill, 77.

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Carlqvist, P., 1972, Cosmic Electrodynamics. 3_.

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7140.

Cauffman, D. P., and Gurnet t , D.A., 1971, J.Geophys.Res..

76, 6014.

Jcxobsen, C., and Carlqvist, P., 1964, Icarus. 3_, 270.

Kindel, J.M», and Kennel, C.F., 1971, J.Geophys«Res.. 76,

3055.

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Lemaire, J., and Scherer, M., 1970, Planet.Space Sci.,

, 103.

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Eight Intern.Conf. on Phenomena in

Ionized Gases. Vienna, Austria.

Morgulis, M.D., Korchevoi, Yu. P., and Dudko, D.Ya., 1968,

Zhurnal Tekhnicheskoi Fisiki. 38. 1065.

Mo2er, F.S., and Fahleson, U.V., 1970, Planetary Space

Sci.. 1£, 1563.

O'Brien, B.J., 1970, Planetary Space Sci.. 18, 1821.

36.

Olesen, N.L., and Cooper, A.W. , 1968, Advances in

Electronics and Electron Phys. , Ed. I..

Marton, Academic Press, New York, 24, 155.

Persson, H., 1968, Electron and Plasma Phvs., Royal Inst.

of Tech., 10044 Stockholm, Sweden. Rep.

68 - 18.

Persson, H., 1969, Electron and Plasma Phys., Royal Inst .

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69 - 05.

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Miinchen 2.

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37.

Figure 1.

Figure captions.

Distributions of potential, electric field,

and space charge in a typical plane double

layer.

Figure 2.

Figure 3.

Approximate distributions of reflected and

beam particles in a double layer if the potent-

ial drop is about 100 kT/e and the particle

density at z = z is 80 % of that at z = 0 .

Development of rarefaction and compression

disturbances.

a) The instability condition is satisfied, and

plasma is accelerated from rarefactions and

towards compressions, as indicated by the arrows,

b) The instability condition is not satisfied

so the disturbances are suppressed by the plasma

flow.

Figure 4.

Figure 5,

The behaviour, in principle, of the quantity L

given by equation (46). L < O in the plasma

instability region U > U , showing that plasma

in compression instabilities is accelerated

upwards in the topside ionosphere.

Stable and unstable plasma regions. To the left

is shown that the topside polar wind ionosphere

is unstable above a certain altitude for upward

currents, but stable double layers and plasma

can be expected in the F-region. To the right is

shown how the stability conditions are reversed

for downward currents. If there is no polar wind

the topside is stable regardless of current

direction, (not shown in the figure).

38.

Figure 6. Equipotentials from a double layer turning

upwards around a field-aligned current sheet.

Figure 7. Critical current densities at 2000 km altitude,

for which double layers and plasma instabilities

can be expected, as a function of the altitude

where marginal instability occurs.

Figure 8.

Figure 9.

Solutions, in principle, of the polar wind and

field-aligned current equations (Banks and

Holzer, 1968). The wind solution is given by

A' - P - A , and the breeze solutions A' - P - B

and C - C . Stable double layers may be

expected at P when A' - P - B applies.

Unstable layers with anomalous resistivity is

expected on P - A in the polar wind.

Development of anomalous resistivity through

unstable double layers in a region around minimum

A , i.e. the weakest point of the plasma in the

flux tube.

Figure 10. Electron energy distributions observed in a

laboratory discharge with a double layer (sheath)

according to Andersson et.al. (1969). The big

peak around about 12 eV in the second lowest

curve is produced by the layer, but further down

the tube (+ 1 cm and + 6 cm) this peak is

gradually dispersed and the beam particles are

thermalized.

Figure 11. Depletion of topside electron density by a

north-south moving sheet current associated

with an auroral arc.

Figure 12. Potential distribution for a parallel electric

field that may simultaneously precipitate posit

ive and negative particles.

id. 1.

"•n

10

'to ne1

n i1

z = 0 = Z 1

t f >y i\+1 i)

mt ut2<Y(T,*Ti)

M

Fia. 4

tUNSTABLE STABLE

STABLE STABLEIit

layers

STABLE UNSTABLE

•m

n t or A » A2 nt2 T

Fig. 5

5 10Altitude (1000 km)

Fig. 7

15

AltitudeFig. 8

norA

norA

b.Fig. 9

Electronenergy

distribution

2.1010+

1 10

eV

Discharge current 0.9 Amps

Pressure incathode vessel 0.87 m torr

(•6 cm)

(•1cm)

anode side ofsheath (tubeorifice 0cm)

cathode sideof sheath(1-2cm)

> | i i i I5 10 15

i i i i I i iI20 eV

Fig. 10.

Not yetdepletedtopside

Depletedtopside

Sheet current

Double layer

Auroral arc

Motion of sheet current andauroral arc.

Fig, 11.

Equatorial plane

Ionosphere

Electrostatic potentialFig 12.

TRITA-EPP-72-07

Royal Institute of Technology, Department of Plasma Physics,

Stockholm, Sweden

POTENTIAL DOUBLE LAYERS IN THE IONOSPHERE

Lars P. Block

April 1972, 51 p. incl. 12 illus., in English.

In this paper the acceleration of auroral particles in double

layers is considered. The theory of double layers, including

the instability leading to double layers, is presented. It

is shown that both stable and unstable double layers should

occur in the topside ionosphere above 1000 km altitude and

also in the F-region for observed field-aligned current

densities. The stability of double layers depends on the

current direction in some specified cases. Double layers

accelerate particles both towards and away from the earth.

Unstable layers may cause anomalous resistivity. When double

layers are formtd, plasma is accelerated upwards from the

topside ionosphere. This effect may be very important for the

explanation of the ionospheric trough.

Key words; Auroral particles, field-aligned current,

ionosphere, topside, F-region, parallel electric field,

anomalous resistivity, double layer, sheath, instability.