Indian Journal of Radio & Space PhysicsVol. 20, December 1991, pp. 428-437

Transport modelca1culations of 5577 A and 6300A 01emissions in protonprecipitation --

V Srivastava" & Vir SinghDepartment of Physics, University of Roorkee, Roorkee 247 667

Received 23 November 1990; revised received 23 May 1991

The 01emissions (5577A and 6300A) are studied by using transport model for proton precipitation.All possible sources of these emissions are considered. Recent experimental cross-sections and the reac-tion rate coefficients are used in the calculations. The volume emission rates and the emission intensitiesof these emissions are calculated for Maxwellian distribution of precipitating protons and are comparedwith those obtained from the continuous slowingdown approximation (CSDA).The yield of O] ID) dueto the reaction of N(2D) with O2 is found almost negligible.The intensities of 5577 A and 6300A emis-sions during the 4 Aug. 1972 polar cap absorption (PCA) event are also computed and a comparison ismade with the measurements. The present calculated intensity ratio /(1577)/ /(6300) is found in reason-able agreement with the measurements. ) , .

1 IntroductionThe 01 emissions have been studied by many

workers for electron aurora!"; However, very fewtheoretical calculations of these emissions havebeen reported in literature so far for proton aurora"!'.Each of these models is an improvement over theearlier one. Edgar et al" have considered onlythe impact excitation of 01 level and calculated theintensities by using the continuous slowing downapproximation (CSDA). Singh'? has included thechemistry of the atmosphere in his study of 6300 Aemission for polar cap absorption (PCA) events. Re-cently, we have studied both these emissions'!' in-cluding the chemistry of the atmosphere for protonaurora as well as for PCA events using the continu-ous slowing down approximation. However, thereare certain limitations of the CSDA model. In theCSDA calculations, the transport has not been in-cluded and it is assumed that a constant energyWs - 32 eV is expended in creating an electron-ionpair which is not a good approximation, particular-ly, at low energies. In fact, Ws depends on the pri-mary proton energy". This dependence should alsobe taken into account. Another assumption made inthe CSDA model" is that the proton and neutral Hatoms follow the same path. However, the neutral Hatoms produced by charge changing processes cantravel across the geomagnetic field lines. This at-

"Present address: Center for Research in Earth and SpaceScience, York University, Toronto, Canada M3J IP3.

428

mospheric spreading results in the proton precipita-tion over a wider region and so diminishes the pro-ton flux.

In an analysis of co-ordinated rocket-satellitestudy of auroral processes, Rusch et al.4 have pro-posed that the reaction of N(2 D) with O2 (R20 ofTable 1) is a source of thermospheric O( 1D) in orderto provide an agreement between their predictedand observed 6300A emission rates. The results ofKennelly et al.13 also showed that the possibility ofoccurrence ofR20 would be 87% in the productionof 0(1 D). But Link':' has reported in an analysis ofrocket AMF-VB-41 measurements of spatial varia-tion of /(6300)/I(S200) in the day side cleft auroraand the polar cap ionosphere that R20 is not a signi-ficant source of 0(1 D). Langford et aI.'5,16, McDadeand Llewellyn 17 and McDade et al." have also dis-cussed that R20 cannot be a significant source ofO( ID). Thus the reaction of N(2 D) with O2 as asource of 6300 A has not been conclusively identifi-ed. In our earlier paper" we have, therefore, calcu-lated the production of O( ID) due to this reactionand found that R20 is a major source of O( ID) be-low 200 km. However, recent measurements'v-" ofthe reaction rate coefficients show that the reactionof N(2 D) with 0 would be so rapid that the channelfor the production of O( 1D) by the reaction of N (2 D)with O2 would be essentially closed.

Recently, Jasperse and Basu" and Basu et al/?have applied the transport theoretic methods to cal-

SRIVASTAVA & SINGH: TRANSPORT MODEL CALCULATIONS OF OI EMISSIONS

cuiate the proton and H atom fluxes, the energy de-position rates and the ionization-rates. They showedthat this method is very accurate.

In this paper, we therefore, have adopted thetransport model to study the 5577 A and 6300A 01emissions for proton precipitation. The spreading aswell as the transport are taken into account. Varioussources of these emissions are considered. The vo-lume emission rate profiles and the emission inten-sities are computed for the Maxwellian distributionof precipitating protons and are compared withthose obtained by using CSDA model. The intensit-ies of these emissions for the 4 Aug. 1972 PCAevent are also calculated and a comparison is madewith the measurements.

2 ModelThe excitation of O( IS) and O( ID) levels may re-

sult from the processes of H atom, proton and elec-tron impacts on 0 and the dissociative recombina-tion of 0';-. Besides these processes, the energytransfer from N2(A3L ,;) and 02( CI L';) states to 0are also significant sources of O( I5). The productionof O( ID) emission is also considered by the reactionof N (2 D) with O2 and by cascading of 0(1 5). Recent-ly, Langford et all':" have measured the relativeyields of O( ID) and O( I5) from the reaction of N +

with 00 to be 70 ± 30% and ~ 0.1%, respectively,by using the flowing afterglow and visible chemilu-minescence. We have, therefore, also included thisreaction as a source of O( ID) in our model. These

Reaction No.

Table I-Chemical reactions

ReactionRl (W,H)+O(-,P)R2 e+O(-,P)

R3 e + Nl(X'l:g+)R4 e + 02(X'l:nR5 e + N2R6 N2(A'l::) + 0('1')

R7 N2(A'l:,:) + O2

R8 Nl(A'l:,;)R9 Ol(CIl:,~)+O(3P)RIO 01(C'l:,;)+N2

RIl 0l(C'l:,;)RI2 0(15)+0(,1')

RI3 0(15)+02

R14 0('5)

R15 0('5)R16 O('D)+Nl

R17 0(ID)+02RI8 O(ID)

RI9 N('D)+OR20 N(,D) + 01R21 NeD)R22 N; +0R23 N; +02R24 N; +0R25 N2' +eR26 0l'+NlR27 0; + eR28 0; +eR29 O' +NlR30 0' +01R31 NO' +eR32 NO' +eR33 N' +0,R34 N' + 01

R35 N' + 0,

(W,H)+O(IS,ID)O( l.s~ID) + e

N2(A'l::)+e02(CIl:~)+eNeD) + N(·S) + eN2(XIl:;) + 0(15)Nl(XIl:;)+02N2(XIl:;) + hv02(X'l:g~) + 0(15)

02+N202(X'l:n+ hv0(31') + 0(3p, ID)

01+0O(ID)+ hv(5577A)

0('1') + hv{2972A)O+Nl0+010('1') + hv(6300A)N(·S) + 0NO+O(ID,'P)

N(·S) + hv(5200A)N(2D)+NO'

0; +N2

N+NO'N+NNO+NO'0(15) + 0('1')

O(ID)+O('P)

N+NO'0; +0NrD)+O

N+ONO' + 0(' D.'!')0; +N(2D)

NO+O'

Rate coefficient, cm ~3 S- I

impact cross-sectionimpact cross-sectionimpact cross-sectionimpact cross-sectionbranching ratio = 0.6a; = 2.8 x 10 - II

a7=2.3x lO~llAt.=2S~1ay = 2.1 x 10-111exp( - 1l361T)alO=lxI0-"All = 1 x IO-'s-Iall=2x 10- I.a,,=4x 1O-12exp(-865IT)A"77 = 1.065 - IA1Y71= 0.045 s Ialo = 3 x 10 - II

a17=2.9x 10 "exp(67.51T)Ah.,oo=9.lxlO '5 Ialy=3.4x 10 "expt -1451T)alo=6xlO 11A~:!oo=1.07xlO 5S-1

a21 = 1.4 x 10 - IIIal1=5.1 x 10- II

a2-l = 1.4 x 10- IIIal, = 1.8 x 10 7

alh = 2.0 x 10 I.

a17 = 0.1 [2.2 x 10 7(3001 T.)tJ5]alH= 1.6 x 10-7

aly= 1.2x 10 12a,"= 1.9 x 10 II

all = 4.3 x 10- 7

aJ2 = 4.2 x 10 - 7

YI= 0.43, a" = 6.0 x 10 IIIY2=O.51.a,,=6.0x 10 IIIy, = 0.06, U" = 6.0 X 10 - III

429

INDIAN J RADIO & SPACE PHYS, DECEMBER 1991

reactions with their rate coefficients are given inTable 1 along with the other associated reactions.

The method to calculate the volume emissionrates of the 01 emissions due to impact excitation isbased on the transport theory+-". The forward scat-tering approximation and the average discrete ener-gy loss approximation are used. In the plane parallelgeometry, the volume ionization rate 1/(z) can becalculated from

... (1)

where, n(z) is the density of the assumed single con-stituent neutral atmosphere, up(E) the total cross-section for all inelastic processes involving protons,J.(E) the fraction of energy deposited that is avail-able for the creation of electron-ion pairs?", Ws(E)the average energy expended in creating an elec-tron-ion pair due to impact ionization and chargeexchange processes, p. the cosine of angle betweenthe particle velocity and the positive z-axis and~ p( r,E,p.) and ~ H( r,E,p.) are the proton and hy-drogen fluxes, respectively. The scattering depth l"

is defined as

T = T(Z, E) == up(E) t4n(Z')dZ' ." (2)

where, Zeq is the height at which equilibrium mixtureof proton and H atom fluxes is formed by charge ex-change processes. The procedure to calculate 1/(z) isdiscussed in detail by Jasperse and Basu".

The volume excitation rate Pik(Z) due to primaryprotons and H atoms at altitude Z for the state i ofconstituent k can be calculated by the following ex-pression

JOO Jil .u;

P;dz) = 2 nn(z) dE p._' £Up(£)e.: -I dE

ax - [<I> p( T, E ,p.) + <I>H (T, E,p. )]dp. ... (3)aTwhere, Jik is the population of excitation i for consti-tuent k with energy E and is given by

I (E).= JI: Uik(E') dE'Ik . L(E') ... (4)

f·'h

where, Uik(E') is the excitation cross-section of ith

430

excitation in constituent k, Ll; E') the loss-functionand Eth is the excitation threshold.

The secondary electrons are produced by ioniza-tion processes. The secondary electron productionrate ~k(Es, z) at altitude Z with secondary electronenergy Es is given by

ax - [<l>p( T,E,p.) + <l>H( T,E,p.)] dp. ... (5)ill"

where, f( E,Es) is the shape parameter defined as theratio of differential and total ionization cross-sec-tions. We have adopted an analytic expression forf(E,Es) as given by RUdd23.

The secondary electron flux ~(Es, z) can be cal-culated from

... (6)

where,y= [dEs/dx]e-N, + [dEs/dxle-o, + [dEs/dxle-o

+ [dEs/dx]e-e

The terms in Yare the stopping powers of elec-trons by N 2' O2, 0 and thermal electrons, respect-ively.

Assuming that the secondary electrons are de-graded locally, the volume excitation rate Ri/,(z) ofstate iof constituent k at altitude z is computed as fol-lows

... (7)

In the above expression nk(z) is the density of kthspecies, Uik(Es) is the cross-section for excitation ofith state of constituent k:

All the above calculations are carried out in theplane parallel geometry. However, an estimate of thetransverse proton-H atom beam spreading correc-tion factor E for the particle fluxes can be obtained asdescribed in Sec. 9 and Appendix B of the paper byJasperse and Basu". This factor E should be includedin Eqs (1), (3) and (5) to take into account the spread-ing of proton- H beam. These calculations are doneby using the pseudo particle method".

We, now, discuss the method to calculate the vo-lume emission rates of 5577 A and 6300A emissions

SRIVASTAVA & SINGH: TRANSPORT MODEL CALCULATIONS OF 01 EMISSIONS

due to various sources. The volume excitation ratesdue to proton and hydrogen atoms are calculated byusing Eq. (3). The cross-sections are taken from Ed-gar et al". The volume excitation rates due to secon-dary electrons are calculated by Eq. (7) using the im-pact cross-sections of Gattinger and Vallance Jones"for O( IS) and of Shyn and Sharp" for O( 1D). The vo-lume emission rates of 5577 A and 6300A emissionsdue to impact excitation is, therefore,V;E[5577] = Q.sRIE[OeS)] .. , (8)

andV;d6300] = QVRIE[O(ID)] ... (9)

where, RIE[O(iS)] and RldO(i D)] are the total excit-ation rates of 0(lS) and 0(1 D), respectively, by pri-mary protons, hydrogen atoms and secondary elec-trons, and Qs and QD are the quenching factors ofO( IS) and O( 1D), respectively, which are given by

... (10)

... (11)

where, AS577, AZ972 and A6300 are the Einstein coeffi-cients for the reactions R14, R15 and R18, respect-ively (Table 1), a, is the rate coefficient of ith reactionand n(x) the number density of constituent xof the at-mosphere. The rate coefficients for all the reactionsexcept R19, R33, R34 and R35 are taken from Sri-vastava and Singh II.

The dissociative recombination of O{ producesboth 0(15) and O( 1D) (R27 and R28). In the atmos-phere, O{ is produced by ionization and by the reac-tions of 0+ with 02(R30), N{ with 02(R23) and N+with 02(R34). Thus, the total production rate R'(O{)of O{ is calculated at equilibrium by using the fol-lowing expression

R'(O;) = R(On + R'(O+) a30n(02)- - az9n(N2) + a]On(Oz)

+ R'(N;) a23n(OZ)(a22 + a24)n(O) + a2Jn(02) + a2Sn(e)

... (12)

where, R( 0;) is the ionization rate of O2 andR' (0 + ), R' (N; ) and R(N + ) are the total productionrates of 0 +, N; and N +. The N + is formed in the at-

mosphere via dissociative ionization of N 2 which isabout 24% of the ionization reaction". The parame-ter Y2 is the branching ratio for the reaction R34. Thereaction with O2 is assumed to be the only importantsink for N+(R33, R34, R35). The total rate coeffi-cient a 33 of these reactions:" is 6 x 10- 10 em - 3 S - 1 at300K and the branching ratios YI' Y2 and Y3 for thechannels R33, R34 and R35, measured at 300K are43 ± 5%,51 ± 5% and 6 ± 2%, respectively/V".

The volume emission rates of 5577A and 6300Aemissions due to dissociative recombination are,therefore, given by

,+ a27n(e)J!;)R [5577] = Q.\R (02 ) () ( ) ( )a21>n N 2 + a27 + a28 n e

... (13)and

... (14)

The reactions involving energy transfer from theexcited molecular states N 2(A3~:) and 02( Cl ~.:-)have been found to be the major sources of O( 1S)production in aurora'<". The volume emission ratesof 5577 A due to these processes under photo-chemi-cal equilibrium are evaluated by the following ex-pressions

, .. (15)

and

where, As and All are the Einstein coefficients for R8and RIL The production rates R[N2(A3~:)] andR[02( CI ~.:-)] are calculated by using Eq, (7), Directexcitation of N2(A) state by electron impact popu-lates mainly the higher vibrational levels and the v= 0state is populated by cascading, We have used thecross-sections of Cartwright et apo to evaluate thepopulation of N2(A), In Eq. (15), q is the 0(15) yield.Piper" has presented the results of experimentalmeasurements of the rate constant for the excitationof 0(15) in the reaction of N2(A) with 0 and showedthat 75% of all quenching events lead to 0(15) excit-ation. This value may have an uncertainty of overall27% including all experimental uncertainties and the

431

,.1l\DIAN JRADI0 & SPACE PHYS. DECEMBER 1991

uncertainty in Vagard Kaplan transition probabil-ity". Since no other recent measurements are avail-able for the O( IS) yield, we have used the value of qto be equal to 0.75. The cross-sections for O2 ( C1 ~ /~ )

state are taken from Solheim and Llewellyn".The total volume emission rate of 5577A emission

is, therefore, given by

V[5577] = V;E [5577] + VDR [5577] + VN,A[5577]+ Vo,cl5577] ... (17)

As discussed in the introduction, the reaction ofN (2D) with O2 is controversial. In our earlier paper II ,we have calculated the production of O( ID) due tothis reaction using CSDA method and found thatR20 is a major source of O( ID) below 200 km. How-ever, the new measurements of the rate constant ofthe reaction of NeD) with 0 (Refs 19 and 20) showthat the reaction [NeD) with 0] would be so rapidthat the production of O( ID) via the reaction ofNe D) with O2 would be almost negligible. We have,therefore, again calculated the contribution due tothis reaction to the O( 1D) emission using the new ratecoefficient and the transport model to find thechange in the results. The production of O( 1D) due tothe reaction of N (2 D) with O2 can be calculated at eq-uilibrium by

where, AS200 is the Einstein coefficient for R21. Therate constant al9 of R19 is taken from Jusinski etal. 20 In the above expression, R[N eD)] is the produc-tion rate of NeD) and is calculated by using the rela-tion

+ Y2R(N+) ... (19)

where, d(N 2) is the dissociation rate of N2 which isset equal to its ionization rate.

The production rate of NO+, R(NO+) can be cal-culated under photochemical equilibrium by usingthe following expression

432

+yIR(N-) ... (20)

Thus, the volume emission rate profile of 6300Aemission due to this process can be given as

V".n[6300] = Q nRN,J)[O(1 D)] ... (21)

The volume emission rate of 6300A emission dueto cascading is given by

VCAS [6300] = Q n V[5577] ... (22)

where, V[5577) is the total volume emission rate of5577 A emission and is given by Eq. (17).

The reaction of N + with O2 is also found as asource of 6300A emission'<". The production ofO( 1D) due to this reaction is calculated as follows. Ifthe reaction with O2 is the only important sink forN+ , the concentration of N+ is given by

n(N+) = R(N+ )la33n(02) ... (23)

The O( 1D) yield by reaction R33 is 70% (Refs 15and 16). Thus the volume emission rate of 6300Adue to this reaction is

VN• [6300] = 0.70 YIQDa33n(N+)n(02) ... (24)

Thus the total volume emission rate of 6300A emis-sion is given by

"

/

~It1

V[6300] = V;E [6300] + VDR [6300] + VN,v[6300]+ VCAS [6300] + VN• [6300] ... (25)

The volume ionization rate and the volume emis-sion rate profiles calculated for an isotropic Maxwel-lian distribution of flux of precipitating protons aregiven by

~()(E) = Qo 3 E exp( - E/ a), - 1 ".u < 0 ... (26)2 na

where, Q0 is the total energy flux in the downward di-rection and a the characteristic energy of protons.The model atmosphere of Jacchia" at lOOOK is usedin the calculations. The values of Ws (E) are takenfrom Fig. 5 of Ref. 12. The total cross-sections forvarious inelastic processes involving N2' O2 and 0are adopted from Basu et al ", The total cross-sec-tions for various processes in the assumed single con-stituent atmosphere are obtained by averaging the to-tal cross-section for each process weighed by therelative concentrations of N 2, O2 and O.

I

SRIVASTAVA & SINGH: TRANSPORT MODEL CALCULATIONS OF or EMISSIONS

3 Volume emission rate profiles of 5577 A and6300A emissions

·Observations have shown that the characteristicenergy of precipitating protons varies from event toevent, causing the variation in the emission intensitiesof the emissions. We have, therefore, calculated the

volume emission rates as well as intensities of 5577 Aand 6300A emissions for various values of a. Wehave adopted the values 4, 10,20 and 40 keY for a.

Figures 1 and 2 show the volume emission rateprofiles of 01 5577 A and 6300A emissions fora = 10 keY, respectively. The contributions from dif-

220

EoX lBO -~wo=>~~ 160-<t

5577 A

200o<.=lOkeV

00= 1·0 erg Crii25-1

--- Impact excitation--x- N2(A3~) +0

----02+e_.- 02(C'~)+0

-- Tota~

VOLUME EMISSION RATE, cm-3 5-1

Fig. I-Volume emission rate profiles of 5577A emission for a = 10 keV in Maxwellian distributiondue to different sources

140 -

120

300

260E.x:w§ 220~::.<t

lBO

140

"" ,,\, ,,\'" ,,\.. , \"+ -, "\6300 A "'+ '\ \"

co( = 10k eV ". ' \ \Q.,=l.Oerg cm2s~ \ \

+ + \ I I---N +02 "" \ J

-·-lmpaclexcilaliJni- \. '\ J ,/-"-N(2.01+02 '.

_ ..- 0.(15I-Ol!rJ)+hll\ /' I //----02+e \ I / /

-- Total \ / ../ .. //1-: ./ ,,"

~ -- ..~'-.....-'"-..;:::::::ri- --., --""":~~~~~,~.=-.-.-.-.-~-

\\

\.

\\\II

I/

//

//

""

Fig. 2- Volume emission rate profiles of 6300A emission for a = 10keV in Maxwellian distributiondue to different sources

VOLUME EMISSION RATE,cm-35-1

433

INDIAN J RADIO & SPACE PHYS, DECEMBER 1991

fcrent sources are shown separately. The total energyinput is 1 erg em - 2 S - I. Figure 1 shows that the pro-duction of 0(15) from N2(A3~:) and OZ(CI~:)states is significant at the peak. The contribution ofthese states, however, decreases rapidly as altitudeincreases. Above 140 km, the impact excitation be-comes the major source of 0(15). The N2(A) and02( C) states contribute about 25% each to the totalintensity. From Fig. 2 it is clear that the impact excit-ation is the major source of 0(1 D) followed by thedissociative recombination of O{. From Fig. 2 wealso conclude that the production of O( ID) due to thereaction of N(2 D) with O, is almost negligible and thereaction of N+ with O2 contributes very little to theO( ID) emission. However, its contribution is morethan that of the reaction of N(2 D) with Oz.

Figures 3 and 4 show the comparison of total vo-

5577 A200

180E'"

Qo• l.rg cm2 .-1

Tran spo rt

----- C SOAwc::::> 160!::~«

140

120

----IOOLO~~~~~~~~~~~==~2~~~~wW~310 10 10 10VOLUME EMISSION RATE, cm-3 5-1

Fig. 3 - Total volume emission rate profiles of 5577 A emissionfor a = 10 keV and a = 20 keVin Maxwellian distribution: A

comparison between the transport and the CSDA model

E.:<

6300;..300-- Transport

260 --- C SOA

Qo= lerg cm-2 5-1

20koV

\\\

\ \I \\ II II I

I // /

////

////

.... ~::~/-::;....

10ot;~~~;;;;~~~~f·~~:~-:~~~~~~--L-~~~J10-1 100 101 10

2

VOLUME EMISSION RAT E. cm-3 5-1

Fig. 4-Same as Fig. 3 hut for 6.10oA emission

wo 220:::>I-

~« 180

140

434

lume emission rates of 5577 A and 6300A emissionsobtained by using the transport and the CSDA mod-els, respectively. Figures 3 and 4 show that the CSDAmodel predicts higher results than the transportmodel does at lower altitudes. The difference in theresults from both models decreases as a increases.Also the maximum of the volume emission rate for6300A emission occurs at a higher altitude in trans-port model calculations [Fig. 4]. These may be ex-plained on the basis of the secondary electron flux.Figure 5 shows the secondary electron fluxes at alti-tude 120 km for transport and CSDA models. Theupper pair of curves (A) is for a = 20 keV and thelower pair (B) is for a = 10 keV.The B pair curves areplotted after dividing the results by 10. It is evidentfrom Fig. 5 that at a = 10 keY, the secondary electronfluxes from the two models differ significantly, whilefor a = 20 keY both models are in good agreementbelow 20 eY. The secondary electrons below 20 eYmainly contribute to O( I5) and O( ID) excitations astheir excitation cross-sections peak at about 9 and 6eY, respectively. A close agreement between thetransport and the CSDA models at higher values of acan be explained on the basis of the fact that the par-ticles with lower a deposit their energies at higher al-titudes where the density is less and the transport ef-fects are significant due to large mean free path.

HoIgIII - I 20 "'"410- 1 ••• __ Ze-l,.., .!\=Trz-t

'T>••

'T", 10'

N

IEu-:

:::> 107-'LL

Z0a:•....u

10'W-'W

>a:«0

10'Z0uWIII

A+c-20Wt•~c. 10...,

10 3 '-- __ ~ __ __'

100 10 I 102

ELECTRON ENERGY,eV

Fig. 5-Secondary electron fluxes at altitude 120 km for a = 10keV and a =20 keV: A comparison between the transport and

the CSDA model

SRIVASTAVA & SINGH: TRANSPORT MODEL CALCULATIONS OF 01 EMISSIONS

However, in case of higher a, the particles penetratedeeper into the atmosphere and deposit their ener-gies mainly at lower altitudes. The transport effect is,therefore, less due to the higher collision frequency.

The emission intensities are computed by integrat-ing the volume emission rates over the vertical co-lumn of altitude. Table 2 gives the absolute intensitiesof 5577 A and 6300A emissions for different valuesof a along with those obtained from the CSDA mod-el. The total energy input is 1 erg ern - 2 S - I. The in-tensity of 5577 A emission increases as a increaseswhereas the intensity of 6300A emission decreases.This is due to the fact that as the value of a increases 0

the protons penetrate deep into the atmosphere t-

where the quenching of O( ID) state is very large and ~less emission is produced. On the other hand, the >-quenching of O( IS) state is much less than that of t-

V)0(' D). Thus, more 5577 A emission is observed at zlower altitudes for higher a. It is also evident from ~Table 2 that for higher a, the agreement between the Z

transport and the CSDA model is good. In Fig. 6 theintensity ratio 1(6300)//(5577) is plotted as a func-tion of a. The present results of 1(6300)//(5577) arealso compared with those obtained from CSDAmodel. Figure 6 shows that both models agree well athigher energies.

4 5577 A and 6300A emissions during 4 Aug.1972 peA eventIn this section, we present results of the emission

intensities of 5577 A and 6300A emissions for the 4Aug. 1972 PCA event which was the largest in thelast two.solar cycles. Weber et al.33 have measured theintensities 2000R of 4278 N;, 1200R of 6300 OIand 300R of.HtJemissions during the period of maxi-mum auroral brightness of the peA event, i.e. at2230 hrs UT on 4 Aug. 1972. The measured ratio,1(5577)/1(4278), at this tirne" was 2.7. This impliesthat the corresponding intensity of 5577 A emissionwould be 5400R and the measured 1(5577)11(6300)is, thus, 4.5.

The observed fluxes of low energy protons flowingpast the magnetosphere during the maximum auroral

Table 2-Intensities of 5577 A and 6300A emissions fordifferent values of a in Maxwellian distribution

a,keV 1(5577), R 1(6300), R

Transport CSDA Transport CSDAmodel model model model

4 850 1850 750 155010 1590 2630 740 105020 2960 3600 725 82040 4700 5100 580 600

1.l.

1.2ror-,r-.L[)L[)

L-..J 1.0

----rc;0M 0·8c:'..

0.L.

III\\ -- Transport\\ - --- C SO A\\\\\\\\\\\\\,,,,.•... ....•

-c

0.6

0·2

OL-__~L- ~ __ ~~ __ ~~ __ ~_a 10 40 50

0::: ,keY

Fig. 6-lntensity ratio 1(6300)/1(5577) as a function of a

brightness can be represented by Maxwellian distrib-ution " with a = 3.9 keV below 100 keY. The elec-tron density profile is taken from the measurementsof Doupnik et al." The intensities of 5577 and6300A emissions are calculated using a = 3.9 keY.The present calculated intensities 1(5577) and1(6300) due to protons with energy less than 100 keYare 850R and 750R, respectively.

The high energy proton spectrum for this eventwas measured by EXPLORER 41 (Solar GeophysicalData, Part II, Yol. 342, 1973, pp. 86-91) which maybe fitted by a power law distribution given by<l>u(E)=AE-m protons cm-2 S-1 key-I ... (27)with A= 1.43 x 105 and m= 1.2. The contribution tointensities due to these high energy protons was cal-culated" by using the CSDA model. The intensitiescomputed were 1400R for 5577 A and 80R for6300A due to the protons with energy greater than100 keY.

As mentioned earlier, the transport and the CSDAmodel agree well with each other at higher energy.We have, therefore, adopted the values of the inten-sities from Ref. 11 due to protons having energiesmore than 100 keY. Thus, the total intensities calcu-lated are 2250R and 830R, respectively, for 5577

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INDIAN J RADIO & SPACE PHYS, DECEMBER 1991

and 6300A emissions. The difference in the mea-sured and the calculated intensities may be due to theuncertainties in the measurements as well as due tothe substantial electron fluxes associated with thePCA events. For an exact comparison between themeasurements and the calculation, one should studythe effect of these electrons also. However, we cancompare the contributions only due to protons, as-suming the intensity ratios 1(4278)/ /HiJ and1(6300)/ lHtl to be - 2.5 for auroral proton excit-ation". This implies that 1(4278) and 1(6300) arenearly equal for auroral proton precipitation. Now,utilizing the measured 1(5577)/1(4278) to be 2.7, themeasured ratio 1(5577)/1(6300) can also be as-sumed as - 2.7 for proton precipitation correspond-ing to the total energy flux of - 7.6 ergs ern - ~ s - I

(Ref. 33). The present calculated intensity ratio,1(5577)/1(6300), is also 2.7, but corresponding to anenergy flux of - 8.5 ergs ern - 2 S - I. Therefore, we cansay that the present results are in reasonable agree-ment with the measurements.

We can also predict the information about the elec-trons associated with this PCA event using the intens-ity ratios:". The measured absolute intensities are5400R and 1200R for 5577 and 6300A emissionsrespectively. The present calculated residual electro~contributions are, therefore, 3150R and 325R for5577 and 6300A emissions, respectively, where anadditional 45R due to airglow" has been subtractedfrom 1(6300). So 1(6300)/1(5577) due to residualelectron excitation is - 0.1. Using the intensity of427SA as estimated by Weber et al.33 and the presentcalculated intensity ratio 1(6300)/1(5577) due to re-sidual electron excitation, we get the average electronenergy" to be - 6 keV and the corresponding energyflux - 1.9 ergs em - 2 S - I. The measured intensity ra-tio 1(5577)/1(427S), which is 2.7, also confirms thepresence of significant fluxes of low energy particles,as we know that the ratio 1(5577)/1(4278) is a usefulparameter to assess the energy of the precipitatingparticles. If the ratio is greater (Jess) than 1.5 the low(high) energy particles dorninate-". Consequently, weconclude that the present model is a better approachto calculate the emission intensities as well as the vo- .lume emission rates of various emissions than theearlier models.

5 DiscussionIn the derivation of transport theoretic results we

assume ap(E) = aH(E), where, aH is the total cross-section for all inelastic processes involving H atoms.This assumption is quite accurate for E= 40-80 keY;above SO keY the discrepancy is less than 15% andbelow 40 keY it is much higher. However, Basu etalP have shown that these discrepancies have small

436

effects on the calculated electron density profile.Hence, the present calculated volume ionizationrates and emission rates ean be considered quite ac-curate, the discrepancy being not more than 15%.Another assumption made in these calculations isthat the secondary electrons are degraded locally. Infact the transport of secondary electrons could havealso been considercd v", but we believe that its ef-fect would not be substantial.

In the present calculation. it is simply consideredthat the O( IS) is produced by the energy transfer from02( C1 ~,~). However, the more recent works38-40

have shown that the 02( C1 ~,~) molecules arecontinuously formed by a three-body atomic recom-bination process into some vibrational levels abovev= 10, from which they are subsequently de-activat-ed into the lower vibrational levels. The populations~f these lower lev~ls are assumed to be controUed bysingle quantum VIbrational de-activation, electronicquenching and spontaneous emissions. It is, thus, nota simple matter to calculate the green line emissionintensity. One would have to take into account the al-titude dependence of the fractional populations ofthese levels to get more accurate results for the O( 1 S)yield by 02( CI1; .: However, from the present cal-culation, we can say that for lower a, our results arequit~ ~ccurate, as the contribution from 02( C'1;;;) isnegligible to the total 5577 A intensity. As the valueof a increases, its contribution also increases up to30% at 40 keV. Thus, we expect a change of 10% inthe results of total intensity at higher a if the vibra-tional excitation of 02( C'1;;;) is also considered.

6 ConclusionsThe intensities of 5577 and 6300A emissions have

been calculated by using the transport model. Thetransport model predicts better results than theCSDA model, particularly, at low energies. At higherenergies both the models are in good agreement witheach other. The present calculated intensity ratio1(5577)/1(6300) is found to be in reasonable agree-ment with the measurements for 4 Aug. 1972 PeAevent. These calculations also show that the produc-tion of O( 1D) from the reaction of N(2 D) with O2 isalmost negligible.

AcknowledgementThe work has been financially supported by the

Council of Scientific and Industrial Research (CSIR),New Delhi, India.

References1 Mayer J A, Setser D W & Stedman D H, Astrophys J( USA).

157(1969) \023.

SRIVASTAVA & SINGH: TRANSPORT MODEL CALCULATIONS OF OJ EMISSIONS

2 Parkinson T D & Zipf E C, Planet & Space Sci (GB), 18(1970)895.

3 Slanger T G & Black G, Planet &Space Sci( GB), 25 (1977)79.

4 Rusch D W, Gerard J C & Sharp W E, Geophys Res Leu(USA), 5 (1978) 1043.

5 Witt G, Stegman J, Solheim B H & Llewellyn E J, Planet &Space Sci( GB), 27 (1979) 341.

6 Solheim B H & Llewellyn E J, Planet &Space Sci (GB), 27(1979)473.

7 Gault W A, Koehler R A, Link R & Shepherd G G, Planet &Space Sci (GB); 29 (1981) 321.

8 Gerdijikova M G & Shepherd G G, ] Geophys Res (USA),92(1987)3367.

9 Edgar B C, Porter H S & Green A E S, Planet & Space Sci(GB), 23 (1975)787.

10 Singh V,] Hung Meteorol Serv(Hungary), 89 (1985) 202.11 Srivastava V & Singh V,] Geophys Res (USA), 93 (1988)

5855.12 Edgar B C, Miles W T & Green' A E S, ) Geophys Res

(USA),78(1973)6595.13 Kennelly J P, Delgreco F P. Caledonia G E & Green B D, )

Chern Phys( USA), 69 (1978) 1574.14 LinkR, GeophysResLell(USA), 10(1983)225.15 Langford A 0, Bierbaum V M & Leone S R, Planet &Space

Sci(GB),33 (1985) 1225.16 Langford A 0, Bierbaum V M & Leone S R,) Chern Phys

(USA), 84 (1986) 2158.17 McDade I C & Llewellyn E J, Can) Phys (Canada), 64

(1986) 1626.18 McDade I C, Llewellyn E 1 & Harris F R, Can) Phys( Cana-

da),63(1985) 1322.19 Jusinski L E & Slanger T G, EOS Trans AGU (USA). 68

(1987) 1389.20 Jusinski L E. Black G & Slanger T G. ) Phys Chern (USA).

92(1988)5977.

21 Jasperse 1R & Basu B, ] Geophys Res ( USA). 87 (J 982) 811.22 Basu B, Jasperse J R, Robinson R M. Vondrak R R & Evans

D S,) Geophys Res ( USA). 92 (19117)5920.23 Rudd M E, Phys Rev A (USA). 20 (11)71))787.24 Gattinger R L & Jones A V, Planet & Space Sci (GB), 27

(1979) 169.25 Shyn T W & Sharp W E, J Geophys Res ( USA), I) I (1986)

1961.26 Rees M H, Emery B A, Roble R G & Stamnes K, ) Geophys

Res ( USA), 88 (1983) 6289.27 Albritton D L, Atomic Data and Nuclear Data Tables

(USA), 22 (1978) 1.211 Smith D. Adams N G & Miller T M, ] Chern Phys ( USA), 69

(1978) 308.29 Howorka F, DOlan i, Fehsenfeld F C & Albritton D L, )

Chem Physi USA), 73 (1980)758.30 Cartwright D C, Trajmar S, Chutjan A & Williams W, Phys

Rev A (USA), Al6 (1977) 1041.31 PiperL G.] Chern Phys(USA), 77 (1982) 2373.32 lacchia L G, Special Rep 375, Smithsonian Astrophysical

Observatory, Cambridge, Massachusetts, 1977.33 Weber E J, Mende S B & EatherR H,] GeophysRes( USA).

III (1976)5479.34 Doupnik J R, Brekke A & Banks P M, ) Geophys Res (USA),

82 (1977) 499.35 Rees M H & Luckey D, J Geophys Res (USA), 79 (1974)

5181.36 Stamnes K, Planet &SpaceSci( GBl. 28 (11)80) 427.37 Stamnes K,) Geophys Res ( USA), 86 (1981) 2405.38 Greer R G H. Murtagh D P, McDade I C, Llewellyn E J &

Witt G, Phil Trans R Soc London A (GB), 323 (1987) 579.39 McDade I C, Llewellyn E 1, Greer R G H & Witt G, Can)

Phys( Canada), 62 (1984) 780.40 McDade I C. Murtagh D P, Greer R G H. Dickson P H G.

Witt G, Stegman J, Llewellyn E J, Thomas L L & Jenkins DB, Planet &Spl.lce Sci (GB). 34 ( 1986) 7119.

437