ASA-CR-Z04685 Photoelectron effects on collisionless ... - NTRS - NASA

JOURNAL

OF GEOPHYSICAL

RESEARCH,

VO1,. 102, NO. A4, PAGES

7509-7521,

APRIL

1, 1997

_ASA-CR-Z04685 Photoelectron

effects

collisionless

polar

on

the

self-consistent

potential

in the f

wind

?

G.

V.

Khazanov,

M.

W.

Liemohn,

and

T. E. Moore

Space Sciences Laboratory, NASA Marshall Space Flight Center, Huntsville, Alabama

Abstract.

The

enhanced

presence

ambipolar

topside

ionosphere

above

the spacecraft

production.

of unthermalized

potential have

photoelectrons

and enhanced

polar

approach

magnetic is used

in the sunlit

upward

led to the conclusion

along

A kinetic

drop

that large-scale

field

lines

polar

ion acceleration. electrostatic

connected

cap

leads

to an

Observations

in the

potential

to regions

drops

exist

of photoelectron

for the O ÷, H ÷, and photoelectron

(p) distributions,

while

a

fluid approach is used to describe the thermal electrons (e) and self-consistent electric field (Ell). Thermal electrons are allowed to carry a flux that compensates for photoelectron escape, a critical assumption.

Collisional

processes

therefore

to the formation

compute

the steady

wind

state

electric

due to the presence

the thermal

plasma

polar

ionosphere,

wind

are excluded,

of the largest field

including

of our results

approach

1.

with

photoelectron thermal

the observed

polar

polar

boundary

content,

electron

wind,

ion upwelling

events,

wind

As the plasma

ionosphere,

the flow

and energy

flows

conditions

sionless

regime,

the ion velocity

non-Maxwellian, species occurs potential. The reason

for the

formation

plasma

trons tend to overtake of the plasma constrains

is violated

and

of the

drop

from

K. The

reasonable

the assumptions

of this

motion

become

of

forcing This

the ions

to be combined

with

As a result, them,

field

500

by accelerating to the electron

the gravitational

them.

by solar

radiation,

tial in the space

plasma.

tail in the of fast ions.

force

mg

function

The

presence

an initial

which

electric

and Axford

concept [1968].

This paper is not subject to U. S. copyright• American Geophysical Union.

wind

solution

that

is continuous

500

km

regime

at

developed to

the

provide

a

wind

measurements,

a numerical from

[1986,

of polar

satellite

polar

km that came

poten-

tial drop

high-

They

from

of only

also

the results

steady

state

the subsonic

col-

supersonic

collisionless

of the Tam et al. [1995a]

The

distri-

causes

escape

electron

the photoelectron

outflow.

photoelectrons

from

drop

that leads

to develop

Observations and

Heikkila,

1982]

have

Published in 1997 by the

large-scale

electrostatic

craft

polar

along

photoelectron occurrence

Paper number 96JA03343. 7509

polar

cap

to additional

ion

ionosphere

authors

drops

field

lines

Pollock

rate and magnitude

sunlit

by ISIS

1974] and DE 2 [Winningham

led these

potential

magnetic

production.

the

in the topside

1 [Winningham Gurgiolo,

500 km and 3 R e.

to help balance

of

a precipitating

and

that the

between

magnetosheath

rain,

a potential

model.

the photoelectron flux with a of an upward O ÷ flux, a poten-

5 to 6 eV results

introduced

flux, or polar

by Banks and Holzer

The latter also suggested

Akebono

have

acceleration.

was introduced

by

[1995a]

They found that by balancing downward electron flux, instead

may be changed.

The polar wind

motivated

[1996]

development

et al.

in the

Schunk

by Ganguli

was

sonic speeds at altitudes below 600 km and to reduce the high thermal electron temperatures in excess of 40,000 K at 1000

of the atmo-

electron

review

idea

by including origin

by

ions

the ions

regime at 2 R E. Wilson et al. [1996] reexamined this problem in order to reduce the large acceleration of O + ions to super-

affects

will increase the ion acceleration in

superthermal

magnetospheric

of the historical

the

This

[1984]

tutorials

Tam

lisional

to determine

of the enhanced

distribution of enhanced

picture

Recently,

of

on

flux is larger

electrons.

and Schunk

Several

and the recent

elec-

as the photoelectron

electrons

region.

acting

can accelerate

of the thermal

by Barakat

hot

cap

force

photoelectrons

1988a,b]

T e and has

can alter the self-consistent

electron Because

plasma,

The

temperature

electrostatic

complete studies.

to travel

significantly

the pressure distribution of the ions. Photoelectrons, which form due to ionization

an expanding

polar

away from the upper atmosphere flux. Lemaire [1972] pointed

as long

flux

further

precipitating

neutrality

on average,

also

additional

velocities

developed

highly

field appears

the

of the escaping

than the escape

potential

the electric

that

to higher

to collisionIn the colli-

High-mobility

and an electric

the ions.

force eE is proportional

[1968]

content

typical

a potential

because

from sub-

of a self-consistent

is quite clear.

ions.

the electrons, with

distributions

out for

and the coupling between various plasma through the development of a self-consistent

in the collisionless

bution

and We

in the polar

conditions

that

up and out of

change

sonic to supersonic, from collision-dominated less, and from O+ dominance to H + dominance.

velocity number

expected

of 8800

suggests

particles

approach.

photoelectron

we found

temperature

and plasmaspheric

of mass, momentum,

magnetosphere.

the topside

sphere

drop

wind

lighter ions must be dragged by the escaping photoelectron

are major sources

the entire

together

this general

of the fractional

Introduction The

of polar

with

and net potential

as a function

0.1%

escape

are valid.

refilling

the

to easier consistent

For a set of low-altitude

km to 5 RE of 6.5 V and a maximum agreement

drop

enhancement

of photoelectrons

characteristics.

leading

potential

exist

to conclude above

connected

to regions

et al. [1991 ] examined

of field-aligned

that

the space-

electrostatic

of the po-

7510

KHAZANOV ETAL.:PHOTOFJ_,F_,CIRON EP'FEL-q'S INCOLLISIONLESS POLAR WIND

tentialdropsovertheionospheric polarcaps.In thatstudy, signatures in upgoing anddowngoing photoelectrons were measured in thetopsideionosphere usingthelow-altitude plasma instrument (LAPI)onDynamics Explorer 2 (DE2) where function [Winninghara and Gurgiolo, 1982]. These data are compared with

ion data

mass

spectrometer

selected

obtained

from

mately

intervals

along

upflowing

O ÷ beams

were

1 and

observed

DE 2 were field

in which

n, u, and Q are

ion

the

moments

of

electron

distribution

n(s)=j'S(v,u,s)d3v v

approxi-

line and when data.

the

of

regarding

electrostatic

(4)

u(s)=n-_!Itvf:v,.,s)d3v

Pollock

comparison

is quite favorable

of a field-aligned

(3)

as_,B)

Data were

in the RIMS

one case

in terms

the retarding

1 spacecraft.

cap magnetic

the two DE spacecraft

interpretations tial

DE

polar

presented

using

on the DE

when

the same

et al. [1991] data from

at high altitudes

(RIMS)

B O_---(Q)-enEilu=O

its

poten-

v

drop. What

is the contribution

of a field-aligned cap?

What

of photoelectrons

electrostatic

is the

largest

potential

potential

drop

photoelectron

parameters

the self-consistent thermal

plasma

electron

density?

for the study

electric

field

parameters

2. General

leads

polar

is the volume in the velocity space.

The term with gravitationin (3) can be omitted forelectrons.

be ex-

The electron population in (4) can be separated into two

in the polar wind? the thermal plasma

parts:thermal electrons,with distributionfunction re; and

to certain

the result

questions

the

should

values

in the polar wind?

affect

These

presented

that

over

that

pected due to the presence of photoelectrons What is the quantitative relation between and

Here d3v=2Jrv2dvd/2

in the formation drop

of

How do the

for a given

are the primary

photoelectrons,with distributionfunction fp. Accordingly, the mass and energy conservationequations can be presented as

photo-

motivation

0_.(,,,u,0s t, +.pupB) = o

fs)

in this paper.

Relations (6)

In this

paper,

we will consider

limit

of the potential

wind

due to the presence

drop

that should

processes

leads

ticles

therefore

to the

field-aligned This

[1995b] source

to easier

electrostatic

argument and

should

where

formation.

only

transport

drop

be valid

above

a kinetic

field (Eu). steady state

sented

in the following

collisionless

distance netic The

component neutrality

is used

equation

and energy

equation

(a=p),

for this portion from (5) and (6). and energy

(1) for the photoelectron

we can find mass and energy and exclude the photoelectron This leads to the set of thermal

/.t

part

is coupled

-t

v

_

field

of the

the

)=0

(7)

os_. n )

is

=o

conservation

can

be pre-

As we pointed

out before,

these moment

with O +, H +, and photoelectrons and currentless

(8)

equations

should be

based on the quasi-

conditions

=0

(1)

of pitch of species

line,

B is the geomag-

polar

wind

problem

equations

in the electron

the electron

O ÷ and H + ions based conditions

angle, t_, s is

through collisionless for the total

plasma

on the quasi-

the

self-consisplasma,

electron

mass com-

where densities trons must be equation

(9)

and fluxes in (9) for O +, H +, and photoelecfound based on the solution of the kinetic

(1).

3. Solution The

Scherer

(2)

in great [1970,

into

the

wind detail

1971,

particles energy

particles

with

that

to escape two

particles

steady

mirror

state

applications in several

1972].

four categories

enough incoming

of

for polar

discussed ticles

of the Kinetic Equation

solution

equation

ballistic

in the form

&kB)

,,.(s)u,(s)+,.p(s),,p(s)=,.o+(S)Uo+ (s)+,,.+(s)u.. (s)

acceleration.

of collisions,

In a steady state

can be presented

component electron mass

for the O +,

is photoelectron-thermal

with

currentless

distribuconservation

equations

wind

neutrality

)( ,:

In the absence

field.

of

in polar

the kinetic

tion function

coupled

geomagnetic

delicate

and

tent electric

region

Using

,..(s) +,.p(s)="o_(s)+"w (s)

of photoelectrons

interactions.

ponent

kinetic

and g is the gravitational

most

presence

the

cap.

OBvo3fa

--sT

_a

along

polar

and a fluid approach (e) and self-consistent

is velocity, /.t is the cosine lt, s) is the distribution function

field,

par,

possible

form:

1-/./2

+_ El;-g km a

where v fa =fa(v,

wind

of Tam et al.

the

approach

of

as_, B )

electric The

(

the

process

H +, and photoelectron (p) distributions, used to describe the thermal electrons

.tv o3fa

over

the discussion

is the dominant

In this paper,

of polar

of the largest

potential with

in the polar

The exclusion

escape

formation

is consistent

of the upper

be expected

of photoelectrons.

collisional and

the calculation

collisionless

and

papers

and

They classify [Lemaire

cannot

and

escape; along

from the outermost

by Lemaire

the polar wind parScherer, (2)

to interplanetary points

kinetic

has been established

space;

the field regions.

1972]:

particles

(1) with

(3) trapped line;

and (4)

KHAZANOV

For the purposes ing particles static

particles,

of our study,

are absent.

potential

ET AL.: PHOTO--ON

This

it is assumed

assumption

distribution

with

and so this population

and Figure Since

leads

independent

(see section

distribution

to be collisionless,

function

in (1) depends

the timeonly

on

the

+eaU(s)-ma

!P(s)

(lO_

before

gration in (13), be written as

not =

potential

differences

electric

and

U(s)

The

particle

fields

from

the

therefore

_(s)=SSOg(S')ds

distribution

which

is constant

is characterized

the distribution

omagnetic

by

function

density

na(s').

s'.

MaB(s')

Using

density

(16)

these

as limits

of inte-

and flux for species

_ can

dM

7

.:ot(M.e)

dE

_t(s)+M=ll(s)

(E-

eaU +ma_-

MB) I/2

to the

"°u:

following

and

variables

integration

along

the

from

(12)

any particle

constants

provided

ionosphere above we will transform

motion (E, M). The particle then be written as

'

at any point

field can be calculated

boundary in the For convenience,

)

_rB(

2 _312

(17)

ifil(M,E)dEdM

(v,

along

the geat some

/a) to

the

on the electric

field,

constants

of

ot can

-

eotU

+ mot

ltu-

MB)

with

Tam

et al.

boundary)

with

distributions.

source

(13)

for

trapped The

the

particle

density

at arbitrary

can now be easily

tion

function

The

region

is known

which

= Vii

_ \ ma )

is a function and

potentials

condition

condition

=0

of

(14)

of the particle, magnetic

particle. accessibility

According

to (14),

Equation

mot _P(s')+

MaB(s')

field is in-

the

above

solutions. the plasma

uncertainties

solution

above

into the

the

lower

I. Gombosi,

private

communication,

we separated

particles

that started

1992). In our calculations, the lower

boundary

and reached

point s on along

(part of the escaping

population

Scherer

particles

[1972])

from

discussed

by Lemaire

that have been

from

the field line

reflected

and below

this point (a component of the ballistic particles). In accordance with this, we call them the transient and reflected populations.

Depending

tional should

on the electrostatic

eaU(s)

and gravita-

mot W(s) energies of polar wind particles, two cases be considered separately: case 1, eaU(s)>mccW(s),

following

expressions

population

for the density

(denoted

and particle

tr) and the fluxes

of an

and

particles

n_(s)=noae"{l-_(zla/2)-yexpI_IIl-'Izla-_l]

}

(14) but not iono-

with

energy E > eaU(s')-

boundary

additional

and 1991]

for an expanding

in the kinetic

introduces (T.

et al.,

geomagnetic

a discontinuity

predetermines

level

that analytical

the local field,

For particles to gain access to s', they at intermediate positions (0 < s < s')

field.

and

our results (low-altitude

[Khoyloo

of a Maxwellian

the lower

km

ion and photoelectron

wind

in the diverging

choosing

region

problem

at 500

however,

for the polar

plasma

moments (4), the disof the simulation do-

Maxwellian

and case 2, eotU(s)< mot W(s). Case 1 only has a transient

s' and is a necessary

to guarantee

spheric particle to s'. must not be reflected the magnetic

position

of inte-

by

I_

and

of the charged

only on the final

sufficient

the

and is given

mag-

boundary.

(limits

by considering

of the total energy

gravitational

the

to

the distribu-

ionospheric

(E-eotU+maUL-MB)

due

along

provided

lower,

for vii =0,

sign and the mass

depends

positions

for the integrals

is obtained occurs

potential

determined

at the

of determination

in (13)

reflection,

electric

electrostatic

in the magnetosphere.

field

gration)

self-consistent

plasma

upper-half

and causes

boundary

[1977] and used by a steady state solu-

we start

that the adoption

consistent

.B( 2 12j iot M,e)aeaM ..,.=-7-t by Whipple to calculate

mag-

Function

For the sake of comparing

[1995a],

analyses

Additionally,

is similar to that found and Khazanov [1993]

potentials,

function.

Distribution

It must be noticed,

collisionless

I/2

of the Velocity

main must be specified.

indicate

f°:='=) (e

distribution

In order to calculate the hydrodynamic tribution function at the lower boundary

numerical

:

and gravitational

and ionospheric

4. Moments

it is known

and flux for species

netic

tra-

of motion;

the region of the source. our distribution function

density

°oTt-_-J;

along

particle

E=eaU(s)-maUt(s)+U.B(s)

jectory

the

7511

M=O

i=e_U(s)_m

and depend

which

reaching

2 _.mot)

(11)

and _U(s) can be related

gravitational

U(s)=Jo_EII(s')ds';

netic

the

_P(s')+

the particle

.

moment M = mot v2-12B

tion

to

WIND

energy

and magnetic

which Miller

contribute

E < eaU(s')-ma

7 are reflected

total

parallel relations

and

POLAR

having

of trapping

is also omitted

is considered

E = may2 2

The

s'

Particles

to an electro-

possibility

IN COLLISIONI__S

reach

that the incom-

1).

the plasma

particle's

no

_

(15)

tr

tr

not(s) ot(s) = Here

subscript

error

function,

"0" refers

to the lower

(18)

B(s)

boundary

level;

@ is the

7512

KHAZANOV ETAL.:PHOTO--ON

and the z and y parameters

are defined

[eaU(s)--ma_(s)! Ta

Ta

is the

Maxwellian

as

5. Thermal

_VBo-B(s)]I/2 Y-L ?ff

characteristic

for species

particle

flux that should

rentless

conditions

temperature

ot at the base. be used

ion

J

The

total

of

density

in the quasi-neutrality

particle

and fluxes

the

following

can be found

and reflected

expressions

for the

(denoted

red

density

and

to be

nt_(s)=noae_Z,[1

-

as functions loop

and

analYtical

electron

the

(7) and (8)

and gravitational

potential.

the corresponding

electrons.

The

Now

tron momentum

expression

implicit

d(neTe)

l O(amene

Os

A

enEli = 0

Bs

(23)

where A is the cross-sectional area of the flux tube. Simple integration of this equation leads to the following expression for the thermal

( B za ]] y_xpt--_-Tj]

electron

density

re(s)+meU2(S)

and Now,

.__z_: :lt "LLoyd)Jl

, nreS(s)uref(s)=no=uo=B'_-O[y2exp(-Zal-e

"L

t

-z_ ] j

y2j

(21)

consistent rameter

in (24)

of quasi-neutrality

to find the distribution

in the

still

To find

thermal

above,

corresponds

to the

point

to the base.

s back

s, though, tube must and particle currentless

and the be taken

that

These

have

population

been

quantities

conditions

be used

below at point

in the quasi-neutrality

flux

(22)

of panicles

particles

reflected

between

that reached

_L_--t._

the total

ther-

a thermal

conductivity

flux

[1973],

(25)

electron

temperature

can be writ-

z oxe

o_l'e

B

ds

.+

(26)

U s"b is potential

s the

in (22)

domain,

and

the thermal

U)-_-_-}

difference

= 0

at the upper

X0 is the appropriate

conductivity.

tron particle flux in (26), (9) should be used.

To calculate neue,

the

Equation (26) can be integrated presented as

level of the sim-

constant

currentless

twice

with

associated

the thermal condition respect

elecin

to s and

7,1r

r7'2:-,0 +--T7:2 J'B n,., _5r, + 2ZOo [ Bt,2

[ exp x,-yS, boundary

with

point s and the upper

8---2e

at the upper

Here ulation

point

level of the simulation domain s _', The flux equation can be rewritten in a more simple form as

ys,b is taken

as

and Kockarts

the equation for the thermal ten in the form

and

)

we add to the transient

pa-

(8) in the conventional

by separating

area of the flux the total density

-¼[°::(:1,,:'(..,)-,,;,(.).::

where

one

tempera-

(9) are

n,_(s)._,(s)" =na(s)ua(s "

component

the electron

Qe into the thermal energy flux QeT and motion. Then, using (6) and consider-

ie(U:'-

Here

of the selfOnly

in (21)

reflected

are needed

changing cross-sectional into account. Therefore

flux that should

plasma.

unknown,

temperature

in (9), an itera-

QT .1-5/2 °_e e =-X0"e -_s

the reflected

particles

wind

it, let us present

energy

to Banks

F(x) = e-x2 j'o eY2dy out

remains

mal electron heat flux the convective particle the

polar

(24)

J J

can be used

for the electron

according

I

A

the condition

potential

Te(s ).

form

ing

integral,

using

tive procedure

ture

pointed

for the

u2 )

+A,

As was

for the

relation

equation

Lds

F is Dawson's

fields

we should

of the thermal electrons as a function of the self-conelectrostatic field can be found from the thermal elec-

ne(S)=

where

for the

self-consistent

fluid equations

electrostatic find

expressions

in

of the magnetic

of the thermal

density sistent (19)

particles,

the

density

the

moments

the thermal

and

nff (s)

both the transient

with

and the self-consistent

._ (,)u.(,)=._ (s)._(s) 2 includes

section,

are found close

Fluid Equations

photoelectron

the

and cur-

POLAR WIND

Electron

previous

and

coupling

(energy)

(9) in this case are na(s)=

Case

IN COLLISIONLESS

In the

zo:l where

EFFECTS

.jj level.

[n,",(5 L

-e(U

/ m,"2_l

",

s_' -U)_--}ds

./JsJb

+[Z0

]_,

(27, $1b

KHAZANOV

The square brackets in (27) the simulation domain. It should lytical

be pointed

description

simplified

Thus culate tion

of the

self-consistent

trons

and currentless

IN COLLISIONLESS

somewhere

solution which

conditions

to cal-

analytical

contains

all polar

wind

plasma

parame-

and can be determined

ceeds

but

this

altitude

points

since

checks

point

With

an initial

guess

inconsistent

all of the equations. ity

condition

each

line

so the integrals

rent

iteration.

iteration

at the base

and handles

step,

the quasi-neutral-

a root-finding

Te(s ) converge

altitude

method

and work

at a

up the field

upper

boundary

and the at every

quasi-neutrality

terms

process

the cur-

are taken

continues

step in the spatial

condition

with until

from

the

U(s)

and

domain.

in (9) can be rewritten

and then solved study, lation

for F(U)=0.

(28)

was

which combines the speed of inverse with the reliability of the bisection

used for this

quadratic method,

rameters These

interpoand is

(9),

all of the densities, with U. Since

the moments

the current any altitude the

no matter

how rapidly

of the kinetic

integrations

only

in n e and T e dictate

able step size must be used. 7.2. One

equation

spatial step and the upper and lower grid could be used for these equations.

numerical

possible

problem

balances

the densities

This is discussed

change

depend

arise

from

the

relation

This

plasma

species

is not a problem

always

satisfies

either

in section between

to 12 eV [Tam

et al.,

where

2. the

so eU always dominates. and gravitational potential

differences can be similar. For instance, while eU(3RE) has been shown to range 1996]

e U that

1 or case

for H + and the photoelectrons,

particle mass is sufficiently small For O +, however, the electrostatic

al.,

case

1995a].

mo+ tY(3Re) is 7 eV, from 6 eV [Wilson et Thus

it is unknown

be surpassed

in the O + cal-

by

What

of this

is the con-

of a field-aligned cap?

be expected

What

is the

due to the pres-

for a given

photoelectron

by iteratively

density?

solving

equations

along a polar cap field line from 500 km to

e U

obtain

for a given guess

that affect polar ion and plasma waves,

moour

content

=3 V and Te(s ub) =2000 Te(s ub) =25000 must

be reasonable

resulting to have

Equations

ever,

the

result

the initial

is independent as long

so)]t/2

to [sl(sUb-so)]

and Te(s)

distributions tial

that

spatial

I/2, and

that a linear

distribution

initial

to converge

the

to a will

initial

produce

guess

a positive

two

U(s)

proportional

to qt(s)

to the same solution. proportional to [sl(s ub-

to sin[.57tsl(sUb-so)] to the same

all produce

solution.

Thus

of U and T e is irrelevant,

boundary

boundary

temperature

of the simulation

electron

the ini-

as long

Te:

gradient

[oVFe/tgS]s,b. As we mentioned

study

on the form

to calculate

Teo and a temperature

domain

of this

escape

conditions

is to investigate

thermal

plasma

in the ionosphere

at

inte-

produce a positive integrand in (27) for the first iteration. As follows from the equation for electron temperature we need

be

of these two parameters U(s) as a linear fit, U(s)

converge fit, Te(s)

proportional converge

and (27) are

so these

velocities that can It was found, how-

of

as they

U(s ub)

n e distribution

unrealistic integrand.

grand in (27) for the first iteration. Several initial spatial distributions were also tested. Such choices for

distributions for Te(s),

(24) and

for the solution

in large, a negative

on npo,

from

up to U(s "b) =7 V and

U and T e distributions,

very low, cause (27)

produce Likewise

to the photoelec-

and ranged

K for npo=O.0%

If U/T e is too large,

that

limit

at the base,

K for npo=l.0%.

to the

guesses

an upper

set of input parameters.

for U(s ub) and Te(s ub) used depends

the photoelectron

photoelectrons

then

affect

in the polar wind? What is the quantithe thermal plasma and photoelectron

we should

tron influence

to dominate

and

itera-

not

the purpose

questions:

Although there are other factors tion, such as currents, precipitation,

the purpose

altitudes

each

our algorithm

potentials

over the polar

be addressed

(27), and (28)

what case O + will follow, and the potentials could even cross somewhere inside the spatial domain. In general, if m _u were at low

In summary,

in the formation

drop

the result

now

proportional

can

solutions,

with and will

in the Introduction,

U(s ub) and Te(sub),

that a reason-

the electrostatic and gravitational potential differences, and rn q/. The kinetic formulae above are derived assuming each

on

boundaries, However,

further

altitude

5 R E.

solution.

U that

result. of crossing

drop that should

affect

will

tains

the exact

higher

pro-

make the lower

parameters that leads to certain values of the self-consistent electric field in the polar wind? How do the thermal plasma pa-

guaranteed to find the root given an interval that contains one [Press et al., 1992]. After finding an interval of U that confinds

the calculation

temporary

the following

potential

potential

sensitive

a root of F, this method

as

This could the

are

of photoelectrons

The initial method

in

lower

objective is to show the impact of just one factor, photoelectrons. Since we are solving the collisionless kinetic equation,

as

)

Brent's

similarly, be the

Results

we believe F(U)=Zeana(U a

and

would

it accordingly.

ence of photoelectrons tative relation between

that satisfies

for n e and T e are consistent

The

iteration,

The

iteration

using

Te(s ) distributions, solution

point, and then the electron temperature is calon this new potential and electron density. We

start

previous

At each

is satisfied

given altitude culated based

and

would the upper

based

Method U(s)

with

of the final

electrostatic

to a convergent

point

of U is converging

inconsistencies

As we mentioned

for the

to iterate

equations

altitude,

spatial

is corrected

for the condition

largest it is possible

crossover

this

the distribution

these

tribution

Solution

the governing

line, if necessary.

study is to answer

6. lterative

7513

this type of crossover occur in our calculaboundary is determined from the previous

up the field

7.

line,

be this

boundary. Should tions, the crossover

culation

the self-con-

of the quasi-neutrality

(9),

I equations,

case

the coherence

elec-

Because

ters and components are coupled on an iterative scheme.

would

the

tion,

equations

of the thermal

field

boundary

but

func-

(see section

of the fluid

also

up the

POLAR WIND

from case 2 to case 1. In the case 2 equations,

iteration,

potential

the distribution

potential.

by

and the O + and H +

electrostatic

temperature,

electrostatic

flux (25)

approach

as an explicit

analytical

an ana-

coefficient.

uses the kinetic

plasma

to calculate

and their

sistent

wind

of

we greatly

thermal

of photoelectrons

polar

an implicit

to provide

for the conductivity later in section 7.

model

the distributions

boundary

temperature,

of the electron

wind

in the

and (27)

electron

expression this issue

ions

(24)

at the upper

EFFECTS

switch

the

the calculation

our polar

4) and

are taken

out here that in order

of

using Spitzer's We will address

ET AL.: PHOTO--ON

the role parameters.

and flow

they (27),

a lower at the top before, of photoBecause

out along

the

7514

KHAZANOV El" AL.:

geomagnetic

field

lines,

in the collisionless self-consistent

omit

[a_TJOs]s,b=O. in the

Coulomb

of

section

7.3).

(see

illustrate

typical

the

ionospheric

tic temperature

particle

2500

K for the thermal

a characteristic 6x104

species

cm "3, and H + has

lxl03

were

and unrealistic

is 2000

upper

K for the ions, have

at 500 km is

by quasi-neutrality.

to the

limit

photoelectron

cap photoelectron densities and Liemohn, 1995].

The

Although convenient

the format to show

toelectron

to illustrate

influence.

rarely

of

from dendensity

of the Plates

the dependence

concentration

0.10%

throughout

The

potential

difference,

U(s)=_Oo-_(s), reference

where

altitude

boundary

is unconventional, the polar

U, is related

_P0is the potential

where

conditions

the

potential

listed

it is

altitude

range.

of the photoelecis shown in Plate by

points

potential,

tial energy

of the three

a photoelectron can

see,

these

will

not

domain. species

zero.

¢P0 is

there

of 0.10%

is no possibility along

a trap

line.

toelectron region.

2 shows

calculation.

the thermal

While

ties, the temperature

electron

Teo is 2500

for this rise in T e is from toelectrons mum

with

temperature

the

the electrostatic

thermal for

a

plasma. realistic

that no+ decreases in z above

rapidly than nil.. the ratios shown Another

more

the entire

in Plate

spatial

to

the

no+ decreases

less in

is the ion speeds,

plots,

at a given

base.

are reflected

Mo+ is given

5. For these

at the

than nil+, while

be discussed number.

as the bulk velocity velocity

that

in the densities

that should

here with the Mach

thermal

rapidly

2 R e indicates

These trends in Plate 3.

feature

illustrated

altitude

Therefore

in Plate

the Mach

4

number

divided

by the

all of these

Mach

numbers are relative to an ion thermal speed for a 2000 K Maxwellian distribution, that is, 0.81 km s-I for O ÷ and 3.2 km s -l for H +. In Plate 4, Mo+ changes line at 0.01% to supersonic This

subsonic

.,

region

.

.

,

i

from subsonic for the entire field for most of the field line at 1.00%.

corresponds

....

i

....

to the classical

i

....

i

....

polar

i

....

0

÷

wind

i

..

potenfor

to trap

6

population for the same

redistributing

1/

densiK at

coupling that

photoelectron

."

/."

I

_e

/.' /,'

/."

Y ,

.

•

i

....

i

5000

maxi-

....

i

,

a function

1.

Total

potential

of altitude

,

j

I

energy

,

I

,

,

I

,

,

,

,

I

25000

Altitude Figure

,

15000

of the phodensity

..""

_a

the en-

the

/

4

from the low-alThe energy source

Notice

over

to 4.1 at 2 R E, and then decreases

decrease

0.01% up to 17,300 K at 1.00%. At any given npo, ?',rises quickly through the first one to two RE, then flattens into a nearly constant temperature for the remainder of the field line. smoothing the temperature distribution source region into the upper altitudes.

grav-

the relationship between the gravita, potential differences. At 1.00%, z is

R E means

#

ergy, titude

as the electrostatic

the O ÷ ions against

O ÷ dominates

zero at the base, increases

is defined

from less than 3600

conductivity

changes

to drag

our assump-

temperature

is due to the thermal

alti-

As you

well"

a trapped

This

has O ÷

at high

altitudes. By rip0=0.10%, the two ions have simalong most of the field line, and, above this pho-

for O ÷, which describes tional and electrostatic

for

K for all photoelectron

at the top varies

description

H ÷ dominating

situation

enough

O

Plate

and

of O ÷ to H ÷ densities,

wind

photoelectrons, drops to 28 near 2 R E and then increases up to 72 at 5 R e. This behavior can be explained by examining z(s)

the

kinetically

This justifies

tion earlier that we do not need to include in our model.

polar

The O÷/H ÷ density ratio increases near 5 R E at large npo concentrations. The ratio at the base is 60 and, for 1.00%

two mirror

at the base.

the

large

percentage,

V

the total

of a "potential

the field

ity to higher ilar densities

For

2.87

with

I shows

that were treated

concentration

particles

create

altitudes

though, grows

equals

for 1.00% is 7.25 V. It _p is almost constant for

Figure

centration,

and MH+ is given

with _P0 changing less than a volt. The poto reach an asymptote at low concentrations

in the spatial

is the ratio

classical

an R E above the surface and then H + completely dominating the total ion density. As we move up in photoelectron con-

at 500 km and s ub is a

also. For any npo, however, most of the potential drop occurs within the first 2 to 3 R E, smoothing out to zero at the top. Such electrostatic potential behavior, combined with the gravitational

result

The

3.65 at the top. Since exp(-z) is a multiplier in the O ÷ density calculation (see equations (20) and (21)), this increase below 2

on the pho-

to the potential

above,

npo=O.Ol%, while the total potential can be seen that the distribution of up0 above 0.10%, tential also starts

polar

[Khazanov

of the results

The electrostatic potential _p as a function tron relative density at the base and altitude 1.

an extreme

Ionospheric

exceed

3.

at low

potential

for a total ion density

but is shown

interesting

in Plate

tudes. This would appear as a ratio greater than one decreasing to a ratio less than one, reaching unity a few thousand kilome-

scale is npo=O.Ol% to 1.00% on the Plates because of the logarithmic axis. A photoelectron concentration of 1.00% at 500 km is huge

shown

the

cho-

ntot=6.1xl04 cm "3. The photoelectron density is varied 0.00% to 1.00% of this number, and the thermal electron sity at the base is determined

(np0 v

.m

t-

E 20000.

O £1_

=

4

o

15000.

o_

o