DISTRIBUTION OF MOLECULAR AND ATOMIC OXYGEN
IN THE UPPER ATMOSPHERE
By H. RAKSHIT^
( R e c e i v e d f o r I ' u b l i c a i i o H , A/ >t i l
.rV, /<;;;)
ABSTRACT. The identification of the auroral .irrecn line a 5577 has established beyond
doubt the piesence of oxygen in the atonuc stale n the upper atmosphere. l^>r various
reasons a knowledge nf the dislribiition of nitleuilai and atomic (•xjgcn with heighti
pailicularly in the region of transitiun in which the atmosphi'r’c composition changes from
one of N2 and ()? to otic of
ami O, is important .Mtcmpls at didennining the distri­
bution have been made by Chapman (ig^p, by Wall and l)eming tic)3S) and by Mujumdar
(1938). Unfortunately the results obtained by these authors are based upon data which arc
not corroborated by recent observations.
In the present paper attempt has been inailc to delenniiic the distribution by adapting
I'annekoek’s method of studying the distribution of ioni.sation in the earth’s atmosphere
by tlie action of .solar ultraviolet radiation. The method is in its essentials the same as
that adopted by Majuindar in his analysis. In eanyiiig nit Ihe calculations recent data
based on radio and other observations have been used and the results riiav Ihu.s he expected
to represent more aeeuratciy the ac tual state of allairs.
It has been found that the density of 0 ^ nmleuiles decreases very rapidly with height
above loo km. The density of the 0 airnns, wliich is al mo t zero at 80 km., inereascs
rapidly with height, attains a maxinium at about ms km. and then gradually decreases.
Decrease in the density of 0 atoms at night duo to recoiubiiiiil ion has also been consi­
dered. It is .showm that tlie atoms wn'lt b e’ii suliicient density at night to emit iiie green
radiation with the observed intensity.
INTRODUCTION
The identification of the auroral green line A 5577 by McLenan (i 92s) as
due to the transition (0 ’ S - > 0 ®D) established beyond doubt the presence of
atomic oxygen as one of the constituents of the upper atmosphere.
Since
direct measurements with the help of sounding balloons show that up to 22
kin, the oxygen is in the molecular state, the atmospheric composition, a
mixture of N2 and O2. must begin to change to one of N;j and 0 at some
higher level. Accurate determination of iho distribution of the atmospheric
gases with height in the icgion of transition, as also above it, is important for
more than one reason.
It is now generally accepted that the different ionospheric regions, li,
F i, F2 etc., are produced by the ionisation of the clilkrent ujipcr atmospheric
constituents 0«, N2, t.) (it is not yet known with ceitaiiity if N2, like O2, is
also dissociated in the upper atmosphere). T.hc maximum of absorption of
f* Fellow of tlie Indian Phy.sif’al .Scx'k ty.
58
H, Ralishit
the ionising solar radiation by tlie different gases takes place at different levels
because the positions of these maxima are dependent not only on the absorp­
tion coefficient of the radiation but also on the distribution with height of the
absorbing gas.
In ])articular it has been show n by Milra (1938) and by Bhar (1938) and
also by Wulf and Deining (1938) that the problem of the formation of Region
li fioo-120 kill.) which presents difficulties, is solved if it is imagined that
this layer is formed by the ionisation of O2 in the region where its density
undergoes rapid diminution with hei;-:ht due to its dissociation by the absorp­
tion of solar radiation in the region KK 1751-1250 (Runge-Schuinann continuunj). An accurate knowledge of the distribution of C)2 with height in
the region of transition is llierefore very important in the theory of the
formation of the K layer. Again, it is believed that Region F2 is formed
by the ionisation of (); also the rale of decay of electron deiiS^ity in the
ionospheric regions has been found by Bates, Buckingham, Massey ana Unwin
(1939) to be controlled l^y the so-called effective rcco}}ibinaiion coemcAeni in
which tlie iiegalivc ion concentration (O") plays an essential part, por the
icmosidieric studies, as also for understanding certain features of distribution
of light intensity in auroral streamers, a knowledge of the distribution of
atomic oxygen with height is extremely important
The first attempt in this direction was made by Chapman (1Q51) ; the
next was by Wull and Deining (193S), and Majumdar in 1938 undertook a
rigorous solution of the problenn In what follows lirief accounts of these
investigations are first given.
Cha]>maii, on tlic basis of some tentative assumptions, concluded that
below So km the concentr.iLion of oxygen atoms should be very small com­
pared with that of oxygen molecules. According to this estimate there is only
one oxygen atom for every :,oo
molecules at 80 km., while at 120 km.
there is one for every three (). molecules. Chapman emphasised that although
his results are only approximate, there is nothing improbable in them.
Wulf and Dcniiiig 11936) derived an expression for the concentration of
O atoms as a function of the number of quanta absorbed by
molecules,
the concentralmn of 0_, nnlecules as they would have existed prior to irradia­
tion, the concenti ation of total molecules and the specific rale of the i^ostulated
thiee-ljody recombinat?on of oxygen atoms. As the density of total molecules
at any level depends upon height, this gave a method of estimating the
djgiee of dissociation at diflercnt heights. In a later paper (Wulf and Deming,
iu3vS) they gave resiilis of tnevr computation of dissociation at different heights
for an atmosphere as advocated by Chapman and Milne D930) in which diffusion
starts at 20 km. and the temperature is 219° K throughout. Assuming solar
ladiatioii to be that of a black-body at 6 0 0 0 K , Wulf and Deming estimated
that dissociation starts from about 70 km., increases very rapidly beyond
80 km, and is practically complete at about 100 km. lu regard to these results
it may l>e mentioned that the present accepted model of the atmosphere
Molecular and Atomic Oxygen in the upper Atmosphere
59
quite different from that assumed by Wulf and Deuiiug, Moreover the pressure
in the uppei legions of the atmosphere is so low that threc-liody collision may
be a rare phenomenon*
Majunidar adapted Paniiekoek’s method of studying* the distribution of
ionisation in the earth s atmosphere by the action of solar ultraviolet radiation.
Since the case of dissociation of molecules into atoms by absorption of radia­
tion is analogous to that of ionisation, the method of Paunekoek is applicable
to the divSSociatiou problem, (hi the basis of cerlaiii simplified assumptions
Majunidar estimated that dissociation of (_) > which is negligibly small at
147 km. is practically complete above 167 km. Majimular assumed that the
molecular absorption coefficient of
molecules remains constant f )r frequen­
cies within the absorption band, being equal to the maximum value.
For the sake of simplicity, a constant lemiKnaturc of 30o''K was also
assumed for the entire atmosiihere. Maiiimdar, liowever, realised the limitations
of his preliminary results in view of such approximations and promised to
give a more quantitative account of the problem. Unfortunately no further
investigation on the subject has yet been puldished. In the mean time certain
new problems of the upper atmosphere liave necessitated more precise know­
ledge of the distribution of O2 and O lu the upper atmosphere.
In the present paper a fresh attack on the problem is therefore being
made. The method, in its essentials, is the .srinie a.s that of Majunidar but
some of his approximations have been avoided, h'mtlier, Die calculations are
based on recent radio and other observations, As such, the results are
different from those obtained by Majunidar and are l)elievcd to represent mbre
accurately the actual state of affairs. Simplifying approximations have, of
course, been made, because a rigorous solution of the problem is beyond the
present state of our knowledge. The effect of these simplifications is, how­
ever, considered to be unimportant.
DISSOCIATION
BY
OF
GAS
RADIATION
AT
AT
A
CERTAIN
TEMPERATURE
PI I G H E R T E M P K R A T 17 R E
Consider a gas, at a temperature T say, being traversed by radiation from
an external source at a very much higher temperature T i, c.g , fiom the sun
considered as a black body at 6500°K . Some of the molecules, comj)Osed of
atoms A and B say, will be dissociated by absorption of radiation. These
atoms will in turn recombine and a steady equilibrium state will be reached
in which the rate of dissociation is equal to the rate al which the molecules are
formed by recombination.
If Ii/dv be the amount of energy in the dissociating radiation within the
frequency range v and v-f riv passing Ihrough unit area of the gas [>er second,
then the number of absorption processes per second per unit volume is
(i)
3—1639?—2
60
H. Rakshit
where
is llic number of molecules AB [)er unit volume of the dissociating
Kas and
is the molecular absorption coefficient.
The dissociated atoms A and B will separate with a relative velocity V
given by
iv
where M is tlie reduced mass of the inolecule j^iveii l>y
M:
iuk
mu
)iu, uir, being the masses of tiic corresponding atoms,
and
/o'((—1), tJie energy of dissociation,
V(i being the threshold frequency for dissociation.
\
In case of (oxygen the aljsoiidinn of solar nltraviolct radiatiOT in the
Ruiige-Seliuniann coiitiniinni (AA 17 5 1-12 5 0 ) dissociates O2 inolecnl^s into
one normal and aiiotlicr excited atom as follows ;
\
(hj f/ir —> 0 («P) H-0 {^D).
In general, when one of the dissociated atoms, say A, is in an excited state A'
and E is the energy of excitation, then
/7Vf) = I)+ E.
(3)
TIk- aloiiis thus formed will, in turn, recombine to form back the original
molecule AI3. We assume that the mass of the gas absorbing radiation is
raised in temperature and that in spite of the fact that the dissociated atoms
arc ejected with velocities according to equation (2), tlie velocities of the
particles settle down to Maxwellian distribution eorres])Ouding to the equillibriuin temiierature of the gas.
Now the total number of collisions of the atoms with relative velocity
between V and V + dV is
(4)
where wA'and nn are respectively the numbers per unit volume of the free
atoms A^ (excited) and B. In equation (4) ot is a co'cificieiit having the dimen­
sion of an area which is a fimctiun solely of the alums and the relative velocity
with which they collide. But every one of these collisions does not result in
recombination. Tlie total number of sj^ontaiieous recombinations, due to
collisions, per unit v^olumc per second, may be written as
J c
V'MV
(5)
The q u a n t i t y i s proportional to ipf by the Einstein relation connecting the.
absorption and emission coefficients. This will be discus.sed later. Besides
Molecular and Atomic Oxygen in the upper Atmosphere
6/
spontaneous recombinations there imiy be rccombiualions stimulated by the
radiation field, given as usual by
stimulated recomlniiations _ c“ li
spontaneous rccombimitious
I'licrefore the grand total number of recombinations is
/« ^
\V
\ -M VV j A'T
(6)
IL should be noted that expressions <,t ) ami (6) will not he equal for every
frequency v > i'(, but tlie total energy involved in all tile absorption processes
taken together niust Ijc equal to that for all the reconibinalions. U'his is
fulfilled by multiplying both (j) and (h) by/n-, integrating and equating as
follows :
f
'lYn-
ll.^ni'A vdv= f
J
^
\2nkl / \
\ic
-nv^,'2kr
birhv'' /
\ ''^ h v d \
OQ
J
or
II ut
. V
4. / J
J
™
-ijjplvd
(7)
CX)
4
a v
V Y ih
\ 27rfcl /
\
^ '-'-3 ) e
V»vdV
(Stt/ j v ^ /
The expression for (ir is easily ol)tained from the ratio
for the
case of thermodynamic tquilibiium. In such a case, if neither of the disso­
ciated atoms be in an excited slate the equilibrium condition is given by the
so-called read ion inochcrc :
n^ii
h rn \
/
\
/
...
(8)
where
G = 0 aG b/G*n,
G a, G b— the statistical weights of the normal quanttim slates of the free
atoms,
G ab—the statistical weight of the ground stale of the electronic configu­
ration of the molecule, the nuclei being regarded as fixed,
5—the symmetry mnnbei of the molecule and is equal to a when the two
atoms produced by dissociation are identical (as in case of oxygen), but when
the atoms are not so, .<= i,
to —the mean separation between the atoms,
0,—the fundamental vibration frequency of the molecule.
If one of the dissociated atoms, .say A , be in an excited .state A ', then for
the relative nunibcr.s of the excited and unexcited atoms we have, from
Boltzmann's law,
Ha'
G a'
n,
G a
-E / fe T
‘C
62
H . Rakshit
where K is tlie energy of excitation of the atom A . This is justified in cases
where the life lime of tlie excited atoms is large compared with the time
between successive atomic collisions. Substituting in (S) we have
_ C . ' s ( MA;T
ni'tiu
H
ad
0
l
i
n
-fe«-/fcT
A
/
(9)
\
where the suffix (o) refers lo the case of th ermodynaniic equilibrium, and
It will be noted that equations (tS) and (9) giving the degree of dissocia­
tion of the molecules are derived from the condition that in the equilibrium
state the rate at which the molecules dissociate into atoms is equal to the rate
at which they are formed l>y iccombinalion. They do not make any reference
to the details of the mechanism by which the equilibrium is maintained.
By taking into account the details of the absorption and recomt)||nation
processes as in (t) and (6) and remembering that in case of thennod;^uaraic
equilibrium these should be identically equal for any frequency v>V o> w e
have,
'
JVI/c
- sT
t
V ^
" ' U
34- E
-h w / u r
) / / v' T / ’
) ’
[ - ‘
^
_______
4nliv{
____
;-!-7p
i^Avdv/liv
\^/
I +
\ -MV2/2/;T
V^dV
l''or lliib case of isotropic radiation,
, _
__i_
ln'/kT
C
- I
On substituting this value of li- and remembering that from (2)
m j j
-^^V2/2frT
-H A kl' {B+m/kT
MV(/V = /idv and c
-e
c
,
wc get, after simplification,
o d 2
feT
Putting this value of fii> in (7) and converting V in terms of v by (2), we find
n^•rlu _
Vxu
S ttU
n\"u 11
n AH
/
CO
Ivdv
......>ii„_
(10)
of
. J ^ c H . \ -W feT
i ./ * 'V ^
j'
For the case of dissociation in the earth’s atmosphere it will be noted that the
atmosphere is receiving diffuse dilute radiation within a small solid angle fl
Molecular and Atomic Oxygen in the upper Atmosphere
from the black body (sun at T i —65oc)''K) at a large distance.
li/ at the top of the atmosphere is given by
l.- W
hv/kTi
C
63
The value of
“ 1
where W— the dilution fa c lo i= — = R ^ '47^
47T
R —radius of the
suii =
6 q5 x
r—sun s distance from earth = 1*494 x 10^
The intensity is further weakened as the radiation penetrates into the
atmosphere. If N he the total number of absorbing gas molecules above one
sq. cm. at the desired level having absorption coefficient i'r, the reduced
intensity at that level is
r _\17 S tt/jv ‘
^
—l/'i'N
Thus finally
uwnn _
Uau
U a ' II
u
/ yi,ehy/kTi - I
w
H ati
®
Wc
-^,-N ,
_
\ ~Id lin '
(ii)
pv'M I H
r/v
e
»'o
If X denotes the degree of dissociation, i.c., tlie fraction of molecules A B
dissociated into atoms h ! and B, then for N niolecules/c.c, before dissociation,
we get
N (i-.c ) molecules AB,
and
Nx
atoms A',
N.v
atoms B,
a total of N( i + a:) particles/c.c. after dissociation. Therefore if I’rf
represents the equilibrium pressure due jointly to AB, A' and B after disso*
I. C.,
ciatiou, then
^
where ^ —pressure dtie to A B hcfofc dissociation, expiesscd in dyncs/cm •
Therefore
Ha’ tin
iu» "
I. C.,
I —X
feT
p
feT
P
l>
i - . v ’ fe T ’
nn'iiu
Wad
«
a
’ » I)
H ad
I'D^
w
"
j
i/Q
..V
3 1+
------- c
'
hy/kTi
'
^
e
• I /
............ .. .
dv
(13)
64
H. Rahhit
The integral in lljc denominator on the right hand siide is practically
= I
dv
*^0
on account of the extreme smallness of W* To evaluate this we must know
the values of absorption cocfTicicnl 'py, for all frequencies within the absorption
band. C)ur only knowledge of this in case of oxygen is from the cxpeiimental
results of Ladenburg and Van Voorliis (1933) and the values of
m Table I
are obtained from their paper. Further, considering the rapid variation of
c~hyiUT ;vith v as seen from Table I, the quantity ^pyv'^ may, for the purjiose
of integration, be regarded as a constant liaving the value corresponding to 1^0
for which the value of
is a maximum.
T able I
'1‘ = 30o”K (average value for the region concerned)
Ilcncc
vSubstitutiug in Eq. (12) and introducing the numerical values of the
quantities involved, we finally get
-^ = 8 -5 8 8 X
_
—
dv.
In tins equation /> the partial pressme of Og at the level consicleied is
expressed in dyncs/cin®. lixpressiut^ p in nini. of niereury, the foinmla
reduces to
..
. , ..s
£ i - 6'527 X io~'^^ v'T f “ - ,■3 C
■ dv.
... (14)
p~
J >'0
In order to find the value of x at different levels a knowledge of tem­
I - . X
'
‘
perature and partial pressure of O2 at each level is necessary. These data
are not known with certainty but those that are best available and are consi­
dered as most plausible will be used.
Regarding temperature we assume, after Martyn and Pulley (1936),
a value of idD'K at 80 km, and a linear temperature gradient, increasing with
Molecular and Atomic Oxygen in the upper Atmosphere
65
height at the rate of
per km. I'his is in accordance with the latest view
that the tcmpcralure in the vicinity of ^ layer is abmil ^so'K.
Regarding partial picssure we assume that il O^, were not dissociated,
the condition of thoiough mixing of No and t) j would liave l>een nuiintainod
up to at least 130 km. as exists at lower levels. Tliis is justiiied because even
up to this height the tendency for dilTusive separation is. as shown by Milra
and Rakshit (1938), negligibly sinali. ()ur only kncvvledge of pressure in
tliis region is that obtained from radio oUservatioiis. being ju"'^ mm. at
100 km. vSiuce tliis conespuiuls to aboiil o.e cm. of Oo at S. T. l\ above
tliis level, most of the dissociating radiation will be alisorbed higher ui», We
can therefore assume that the atiuospiiei ic i^oiupositioii at lou km. is practicaby No and Oo and also that they exist almost in the sanie jirupoititm as
near the ground, 20 per cent O2 and -'O [ler cent No, m round figures.
vStartiiig witli this pressure and assuming the tLMn]ieiature distribution as
indicated above, the iiarliai pressure of O.j at different heights (if there were
no dissociation) can be calculated.
The initial total pressure
due to N;> and 0,> at any level z cm. above
So km. (ill the 80-130 km. region) is thus given by
- AflL ,
F .- - P „ f i + ar)
where Po is the pressure and T(, tlic tcuiiperature at the So km. level; « is
the rocfficicnt of increase of lemi)erature with lieighl above this level
( = 2.5 X
per cm. j'cr decree); £ is the accelerilioti due to Knivily ;
m is the mean molecular mass of the aii in llie region and k the univirsal gas
constant. On suhslitution,
P ,- P o ( i
Assuming Pi oo*m= io"'hmn., w’e find P „ - 3' i 4 ^
P . = 3 ‘ J4
hence
io"^(i + oii)"*-''’min.
Table II gives the values of P , a n d t h e partial pressure due to Oa,
at different heights above 8o km.
'I'Asr.K II
f
Z X 10
T
j
P a in III)
/>t(unn)
X 10
j
T
l_....
P>Onm)
p i (vim)
10
200 4 ‘7i X ro“ ''
c/42 X
AS
;’iSo i 2*70 X 10 “ ^ 5'4o X 70 ” ^
(
i
; l"so X 10“ ' ! 3 ' o o x i o ~ ' ^ ’
IS
220 2'09 X 10"^
4’ i 8 X io“ ^
40
320 i ST)K X 7 0” -'’
20
240 I ’oo X 1 0" ®
2’00 X 10 “ ’
45
3 4 <)
25
260 5'05 X io~^
I'O T X
5
180
j I ' i 5 X lo " '''
1
2 ' jO X '
1
i ’ 7/\ X io~*
5 'iy X 70“ '’ ; i'0 4 X lo"'^
’
360 3 ' UJ X 10 “ '^ 6-38XIO -®
[
66
H. Ra^shit
DISSOCIATION
AT D I F I' E R B N 'I' I. E V E L S
The quantity N in liq. (14) is ^ivcn by N = />HN, where p is the partial
pressure of
before dissociation expressed in atmospheres, H the height
of the liomogeneous atmosphere foi O2 and N the number of molecules of gas
per c.c. at S. T. P. Hence N = ^’S6i x 10'^•y’ , where p is expressed in mm.
of niercuiy. liq. (14) thus finally reduces to
i- .T
^ 6 5 2 7 x 10 < V I
p
/•
...
(,5)
I ’he values of p and 'J' for any level are obtained from Table II ^iid the
iiitei’ ral is evaluated by graphical method* Tabic III gives the values ipf the
fraction \ of O2 molecules dissociated at various heights, the equilibrium
concentratioiib
of Oj and
of O and also the total amounts of Uo auid ()
above e.u'li level in the region studied.
\
T abpk III
Height
above
ground
(km )
Amount of gas
(cm. al S T. P.)
Degree of
dissficiation
.T
1
O2
0
1
1
S
5
90
n ' o o
T'243 X 10^
000
2'302
o '260
c'()0 X
z i ’ ^ S i
X
1 0
a'712 X I0*‘
o’866
0*260
T ' S
X
1 0
^
2'624 X 10 '
o’3i 3
o’25(S
i q
I -
I
8'57 o X 10” ^
0'251
1 1 7 7 X 10"'^
0T90
X 10 ' 2
5'88 s X i o " ‘
0 T 13
X io ’ 2
5'254 X 10"^
6 ' 3 3
i ’057 X :o '2
6'336 X 10 "'’
3'68 X 10
5*95
T
7 '
t o
X
4 7
’
100
6'70 X 10"-
7 ’561
X
los
0*6302
I
'398
X
no
c ’g56T
S'250 X 10'
115
09941
3*8^5X10''
120
o’0(j8S
5 ‘ : : 8 R
i* - \S
o ' g c ) Q 7
i
1
09999
1
x
St . . Q2S ^
1*724 X
'086 X 10 ’
-
4’76i X 10 ’ ^
k
j
I ( V
“
3 * 5 8 5
1 i '752
"
7
‘
10^ '
3'45 X 1 0 ' '
i o " 2
X 10 " '’
2 20 X 10"^
4'ooo Xio~^
l ‘ 34X 10"'^
3
S
3
The variations of
and n(, arc shown plotted in Fig. i. It will be seen
that the density of
molecules decreases very rapidly with height above
ICO km. At the same time the density of the oxygen atoms, which is almost
zero at So km., increases rapidly with height, attains a maximum at about
Molecular and Atomic Oxygen in the upper Atmosphere
67
105 km. and then gradually decreases. The transition layer in which the
density of
rapidly decreases plays an extremely important part in the
production of the E i layer of the ionosphere as meiilioiK^cl in the Jutrodiiclion.
R R C
0
M B TN A T I O N
P R O C Ji S S E S
Finally the decrease in density of atomic oxyp,eii in the upper atmosphere
at night due to recombination of oxygen atoms to form oxygen molecules may
be considered- The tw^ different ways by which iicutial () atoms may dis­
appear are as follow :—
(i) Radiative recombination : O + O—>-0''^' + hv
(ii) Three-body collision : O O + M = 02 M,* where M is the third body.
Regarding the first process the coefficient of recombination has been shown
by Herzberg (1939) to be of the order of 10^^® cm.^/sec. At 105 km. level,
where the density of atomic oxygen is the maximum bp76 x
^
the fall in to hours will be 2.63 x 10^ ^ per c.c.
The contribution by the second jirocess may be* neglected on account of
the low pressure. According to Herzberg, even at a [)iessure of <>.t mm.,
recombination by the two-body process predoniinate.s.
There is also a third process by which the () atoms may recombine and
which ought to be considered. The atmospheric region wJicrc atomic oxygen
predominates is also rich in ionisation. Since atojnic oxygen lias consideral)le
electron affinity, we may expect copious formation of negative ions of atomic
oxygen and the following reaction is possible :
0 + 0 ’“—> 0 | +e.
4—1639P—a
H. Rak^hil
68
Here the attached electron acts as the third body carrying away the extra
energy and momentum, 'riie probability of this reaction has been examined
by Massey ^1938) and is found to be of the same order as that of radiative
recombination of 0 atoms. Hence the loss of 0 atoms due to this action is
also of the same order as that by radiative recombination of O atoms.
It is to be noted that this deerease in density~of about one order—is in
the region of maximum density of the () atoms at 105 km. In higher regions
(250 km ), the fall in the density of () will be much less. In any case, there
will always be sufficient atomic oxygen left tlirougliout the dark hours of the
night to account for tlie emission of the atomic oxygen lines.
A C K N n W Iv K 1) O M 1$ N T
I
It is a pleasure to record my sincere thanks to Piofessor S. K . Mitya for
suggesting the [>rol)lein to me and for liis kind interest and lielpfnl discussions
Ihroughoul the ])io,cress of the work.
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