AD-A155 426 RECOMBINATION AND IONIZATION IN A NITROGEN PLASNA(U) i/iNAVAL RESEARCH LAB NASHINGTON DC R D TAYLOR ET AL.87 JUN 85 NRL-NR-5594

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NATIONAL BUREAU OF STANDARDSMKItOAOPY RESOLUTION TEST CHART

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NRL Memorandum Report 5594

Recombination and Ionization in a Nitrogen Plasma

R. D. TAYLOR

Berkeley Research AssociatesSpringfield, VA 22150

A. W. ALI

W Plasma Physics Division

NLfl

June 7, 1985

This report was supported by the Defense Advanced Research Projects Agency (Dot)), ARPA OrderNo. 4395, Amendment No. 54, monitored by the Naval Surface Weapons Center under Contract No.N60921-85-WR-W0131.

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Recombination and Ionization in a Nitrogen Plasma

3SRSCN,~ AUIORS)

Taylor, R.D.* and Ai. A.W.'3a 'YOE 09 SEPORT 3b rIME COVERED 4 DATE OF REPORT (Year, Manth. Day) S PAGE COUNTInterim FROM 184 o 1985I 1985 June 7 59

'6 SL, I-'E'ENrARV NOTAT;ON

*Berkeley Research Associates, Springfield, VA 22150 (Continues)

E,-:) I 5RouP tsL-GOuP Collisionalradiative model Emissions LTE and Non LTEI lNitrogen plasma Excited states

%8 RS-RAC- Continue on reverse If necessary and ,

*.. - :LASS-CP *C :F !' S PAGE

16. SUPPLEMENTARY NOTATION (Continued)

This report was supported by the Defense Advanced Research Projects Agency (DoD), ARPA Order No. 4395.Amendment No. 54, monitored by the Naval Surface Weapons Center under Contract No. N6O (85-WR-W0131.

}C .TAi

CONTENTS

I. INTRODUCTION ................................................. 1

II. COLLISIONAL AND RADLkTIVE PROCESSES ......................... 5

III. RATE EQUATIONS AND RATE COEFFICIENTS ....................... 7

" IV. NUMERICAL RESULTS ........................................... 14

V. CONCLUDING REMARKS ......................................... 22

REFERENCES ................................................... 46

,.",

SJUN 26 1985

.B -

1D1

.. . .,..-

S"Bt... .. . . ....

RECOMBLN XTION AN D IONIZATION LN A NITROGEN PLASMA

!. INTRCDUCTION

When air is heated and is highly ionized, nitrogen and its

ions become relatively abundant for electron temperatures of 1-3

e.v. Emissions from such air provide diagnostic information and

-'ay a role in cooling the heated channel. To describe such a

channel one must therefore perform a radiative transfer

calculation which requires a detailed knowledge of the air

species including excited states. To provide this information,

we develop as a first step, a collisional-radiative model for

nitrogen and its ion.

It is well known that a recombining plasma is a source of

radiation. The character of this radiation, line versus

continuum emission and absorption or uv versus visible and infra-

red radiation, depends on detailed aspects of the plasma. In

addition to species type important properties include electron

density, electron temperature, and optical character (thin,

thick, or optically thick in select spectral regions). To

quantitatively describe the spectral character of radiation

emitted from a plasma these properties must be incorporated in a

* model which accurately monitors the evolution of the plasma,

determines the extent to which the plasma is or is not in

equilibrium, and accounts for the radiative transfer accordingly.

E or example, in the simplest case of a plasma *n local

Manuscript approved April 16, 1985.

.nermodyna.mc equilibrium (LTE) the radiative transfer equation

may be solved assuming PlancK's function correctly represents the

source radiation _iD]. A more complete description, however,

requires 2oupling the radiative transfer equations to he rate

equations which provide the population densities of all bound and

continuum states involved in the radiative and collisionai

-.. processes of the specific plasma. The work presented in this

- paper is the initial step in constructing such a model.

A collisional-radiative model developed by Bates et. a!. F2]

has provided the framework for studies which give the excited

* state populations and their deviation from LTE for hydrogen and

hydrogenic ions. Their theory is statistical in nature and

treats the problem in a simple and tractable way. Effective

coillisional-radiative recombination and ionization coefficients

are defined and determined from a knowledge of the rate

coefficients for collisional excitation and ionization and the

spontaneous transition probabilities, for the case of an

optically thin plasma. The influence of self-absorption is then

demonstrated for the special cases of a hydrogen plasma

optically thick for various optical transitions. Their approach

• to solve a coupled set of rate equations for the steady state

alues of excited state densities at fixed electron densities and

. temperatures, thereby showing the extent to which the excited

"-" state populations deviate from Saha equilibrium

2

.. .".

'"Te work of Bates et. al. has motivated others to study thte

-. effeots of collisional and radiative processes in plasmas.

hrawin 3 nas used more recent cross section information and

recal'-;ated the collisional-radiative recombination and

or:zation coefficients for hydrogen and hydrogenic plasmas

analogcus to Bates et. al., but within the context of a more

general fsrmalism. Park [4] has used the method of Bates to

>Ompu:e spectral line intensities for specific non-equilibrium

2ond-tions in a collision-dominant nitrogen plasma. Kulander [5]

nas also studied the spectral properties of radiation emitted

from a non-equilibrium nitrogen plasma as well as the deviation

from Saha equilibrium of the excited and ionized states of an

optically thin plasma.

In the present work the focus is on an optically thin

nitrogen plasma, however, unlike Bates and others we solve the

time-dependent coupled rate equations explicitly, in a manner

similar to the approach taken by Ali & Jones [6) to study

recombination lasers in hydrogen and hydrogen like plasmas. The

calculations are for a given electron temperature, but allow the

electron density to evolve in time. As expected the population

lensities show an early transient behavior followed by a steady

state, from which we calculate effective collisional-radiative

recombination and ionization coefficients and compare the final

state populations to those expected if Saha equilibrium

conditions were satisfed. Our rate equations include the most

30

satisfied. Our rate equations include the most recent

-. :onization, excitation, and recombination rate coefficients

ava-ilable, some of which are similiar to those used by Drawin [3]

and Bates -21, and some are based on experimental data. Finally,

we consider the case of a nitrogen plasma optically thick in

specific uv bound-bound spectral lines.

0

4

-. .- * o

The coupled rate equations which describe the evolu-ion of

the nitrogen plasma incllde the following collisional and

radiative processes:

1. Collisional excitation - excitation of an uppereectronic state by collisions of electrons with atoms

(ions) in a lower state.

e N(i) -> N(j) + e j > i X(i,j)

e N (p) -> N(q) e q > p X4 (p,q)(

2. Collisional de-excitation - the inverse of 1.

e N(j) -> N(i) + e j > i Y(j,i)(2)

e N (q) +> N(p) + e q > p Y (q,p)

3. Collisional ionization - ionization of atoms and ions

e + N(i) -> e e + N (p) S(i,p)+ .~.(3)

e N+ S(p) -> e e N(u) S (pu)

4. Three body recombination - the inverse of 3.

e + e + N (p) -> N(1) e a3 (p,i)+ ( 4 )

e e 4+((u) -> N(p) e(u,p)

5. Radiative recombination.

e N4 (p) -> N(i) + hv Ct (p,i)4

e N (u) -> N p) + ,I' R(u,p)

5

.6.. . i .- . , -"i L... .. . . . .. . .. .

0. Spontaneous emission.

*]]] N(j) -> N(i) +hv j > iA(j,i)

+/ +

N(q) -> N hv ' + Ah(q

..nce we are Inially assuming a nitrogen plasma that is

optically thin for all spectral regions photo-ionization and

absorption have been excluded. These processes are accounted for

" mcst easily by describing photo-ionization as negative radiative

-- recombination and absorption as negative spontaneous emission as

was done by Drawin [3], and will be included in detail in a

subsequent report.

0

6

S ;

* . . . . . . . . . . . .* .

::'. RATE r'JAIrONS AND RATE COEF' EN7S

A. :cupled rate equations

Let N (m) denote the population density of the

(-1- 'h in (or neutral if z=1.) in the electronic state whose

index is m, where it is understood that the density depends on

trme. The rate equation describing the evolution of this state

subject to the collisional and radiative processes outlined in

the previous section is given by

__ = Ne [ [ NZ (.) Xz (Z,m) - Nzl(m) " Y' (m, ,) ]

r 7 zm-1

+ Ne [e NZ(n)a Z1 (n,m) 2. NZ(n)aZ-1n,m)3R n

- Ne NZ-1 (.n) sZ-1(m,n) (7)

,°" z-2( z-2(m t)- Ne [Me Nz - 1 ( m ) a 3 Q z - ( ) a

Se ,z-2(,,) z-2Le N JI 9.. .e.L- . - J (9..

+ e - Z 1 -1--1,

. ' I (n) Az - (n, m ) _ N (m) Nz (4) AZ _ ,,n>m* 7,,-1

7

wnere le eeectron Jensity. The time hlstcry of al

. species is obtained by solving the set of equations construczed

- from ecuaticn (, for al!_ ions and neutrals in all states, whose

in te are n, Z, and m.

3. Enerv Level Model

We nave chosen to study the nitrogen plasma for

electron temperatures in the range of 1.0 e.v. "o 3.0 e.v.. In

* this temperature range the important radiation is produced by

ccnszicuents which are atomic or ionic. 7n our calculation we

have ,ncluded the 1.we thirteen (13) levels for N i, the lowest

seventeen levels for N I, and two effective levels for N !!I.

:etails are presented in Tables I through Il; this information

:an be found in Weise :7]. We note that this model includes as a

s ~bse: the levels for N 1 and N II used in Kulander's studies

as well as most of the N III levels. While not as

comoreensive in describing N I as Park 4], we account for N Ii

an: f; :7 which he fails to do, since his interest is in a region

. -.wer electron densities and higher temperatures.

Within this model the important bound-bound radiative

transitions are listed in Table IV; each .transition is described

Sby s wavelength, the number given by Weise , spectral

cnaracter, transition index ( for exampie, + - + denotes

emission from the seventh to the first izvel in the ion N )

0and transition energy. This table shows, for instance, that the

80!

-L3:Ise radiation comes largely from transitions in tne ion N ..

'Therefore, one would expect this radiation to be important once

electron temoerat:res become sufficiently high that these upper

.s of N : are accessed.

The important free-bound radiative transitions are listed in

.able V. These include all transitions for the corresponding

ions considered by Kulander F5b]. While there is a large amount

of uv radiation the radiative recombination from N+ -> N(i) where

i> is a source of visible emission. This becomes the

predominant source of visible radiation at lower electron

lensities and temperatures; such that the abundance of N II that

is created resides in the ground state.

C. Rate Coefficients

The rate coefficients for the collision and radiation

processes outlined in section II. and used in the rate equations,

i.e. equations (7) were obtained from several sources.

1. Transitions amongst the levels of the ground state2 2

configurations of nitrogen ( S, D, 2) and

.itrogen ion (3p, D, S) are optically forbidden.

Electron impact excitation coefficients for the

transitions in N i were obtained from reference

r8] Transitions among the metastable states in N

T: were accounted for using the analytic

9°4

expressions for the :e-excitation rate coefficients:ven .n reference [._ The reverse rate

coe f c ents were obtained from detauled ba'ance.

2. Coll sional excitation rates of transitions which

are optically allowed, see Table .V, are obtained

using the following simple formula r9]:

% .-

X(m,n) 4.3 x 10 - . 'nn) exp (-E(n,m)/Tel (n,m) (8)1/2

E(n,m) Te

where E(n,m) = E(n) -E.n), m < n, f(nm) is the

* oscillator strength, and

S(n,m) - 0.2 for ions (9)

-..,n,m)=(1.04.(n,m))1 {(20.0+E(n,m)) ln[1.25(1.0-Te/E(n,m))]}' Te Te

for neutrals

The de-excitation rates are calculated from

detailed balance.

3. Collisional ionization from a specific level m to

* the appropriate level, n, of the next highest ion

was obtained using the formula of Drawin [3],

sZ- n = 2.38 x 0 H m) T AE , (10)E1(10

E (Te) I/2 'Te

100- I

-_. - . . . . v . .

where E3 is "3.5 e eo., (.'ne nu.ner o.

equivalent electrons, AE - '(- - - -I'

the oscillator strength, and Z- f- r .. utras a..-> I for ions. T is given by

f dx iE exp (-x) 4n, 725ix

Te Te Tj E/Tewhere 3 = 1 (z-1)/(z 2)]. The oscillator strength

was chosen so that rate coefficients given by

equation (11) matched closely the ionization data

in Table VI:: of reference .I0] which is based on

experimental cross sections for the ionization of

nitrogen; our choice was f(m) - 0.2. The rate

coefficient for three-body recombination, obtained

from detailed balance, is

z-1 (n,m) = 1.66 x 10-22 g () Z (m,n)x (12)z 3/2g (n) Te I TeJ

where g z(m) is the statistical weight of state m

and gZ(n) is the weight of the ionic state.

4. The rate coefficients for radiative recombina-ion

were obtained using the approximate formul3 cf

Ba.es [2], e.g.[z-1p -14laR (p,i) - 5.2 10 exp rAE) If E13/2 E13)

,. Tej Te

Here El is the exponential integral

E E ' x exp ,AE x:Tej x T

!- 2

For exampe, eq. 3, gives tne rate coefficient for

-reecOa of level o of N :to eve' of 4

see ::. 5., 4f z - 1.

" . ?naily, the Einstein A coefficients for

spontaneous emission were taken from Weise [7].

. nization ?otential Reduction

:he ionization energy of an isolated atom or ion is

tifferent from one immersed in a plasma [11] and must be

0 orr'eced accordingly. The net ionization potential reduction is

due to energy released upon placing an electron-ion pair in a

plasma; one of the consequences is that electrons occupying

states which in an isolated atom would be bound now become

- unbound should the corrected Ionization potential be less than

the energy of the state. Our rate equations have been modified

to account for this high electron density (low electron

temperature) phenomenon.

At each step in the numerical integration of the rate

equations, eqs. (7), the e'ectron den5,ty and temperature are

Z-1noted and the ionization potential reduction, AE, calculated

according to

-A 0 ,e "/2*- ... - (15),TNe)

12

• S . " : : :: : .--:" : : : ": : : - : ::::: -; ) ;L ; i).

E- , :n :e are n e.v. and Me has units 1'cm3 . Reducing

: e zanizaton po tne a'. an amount determined by eq. (15) has

-rie effect of mcdifying the collisional ionization rate

.... 0 as folIlIOWs:coe..icient, eq.

, . .

NUMERICAZ RESULTS

A. Time-Dependent Population Densities

Figures (1)- (10) show representative results obtained

by integrating equations (7). Numerical integration was

accomplished by using CHEMEQ, a routine specifically designed to

solve stiff ordinary differential equations E12]. The initial

ccnditions for this set of figures are Te - 2.0 e.v., N(1) - 4.0

x I0 /cm 3 , Ne = N*(1) = 1.0 x 101 7 /cm3 (i.e. charge neutrality),

with all other population densities being set equal to zero

(actually ! x to 4 /cm 3 ). The general behavior of the time-

dependent solutions is as expected - an early transient behavior

followed by rapid relaxation to a steady state. The relaxation

time is on the order of 15 - 22 nsec. Such rapid relaxation led

* *. Bates et. al. '2] to solve for the excited state population

densities using a steady state approximation.

In Figure (1) the total population densities of the

electrons, neutrals, and ions are presented. At Te = 2.0 e.v.

'the number of N ions is negligible, i.e. approximately three

orders of magni-ude less than the neutrals. Consequently, the.+

total number of electrons nearly equals the total number of N

* ions which, in ;he steady state, exceeds the population of

neutrals by a factor of three.

0

14

0.-

Examination of Figures '2) - (4) shows that most of the

nitrogen popul.ation resides in the ground state and the

2o0metastable states, particularly the D state. The levels which

cont'ribute to the emission of bound-bound uv radiation,

- N(4-6,13), are approximately equal in population to those which

contribute to the emission of bound-bound ir radiation, N(8-12).

As in the case of N the ground and metastable states of4

N are the more heavily populated, see Figures (5) - (7). Unlike

N nly N (4) and N+(5), i.e. the first two excited states which

emit bound-bound uv, are highly populated because of the low

! electron temoerature. The rest of the uv and visible emitting

levels are two orders of magnitude less than the N radiating

levels. The population of the lower N levels is important for

the emmision of radiation resulting from radiative recombination,

*free-bound.

Figure (8) shows that the N + ions that are created

reside, as expected, predominately in the ground state.

*While a direct comparison cannot be made with the

* results of Kulander 75a] our steady state populations are in

' qualitative agreement. The relative population of the majorequilibrium species for Ne - 016/cm 3 to 1019/cm3 and Te 1.0

e.v. to 2.0 e.v. follows the trend obtained by Kulander. At Te -1.0 e.v. N(I) is the major species for Ne = 1016/cm3 to I1 m3

while at Te = 2.0 e.v. N4(1) predominates. At Te - 1.5 e.v.

15

N ( 3 is the major species at lower electron densities

/"- 0 ,om ' whi:e N) is at higher density ( C / )

K alancer also presents res.ilts on the distributicn of populatfon

alnongst species versus electron concentration. Again our results

are in general agreement. Detailed aspects of our population

distrioution are discussed in section IV. C..

3. Co!!isional-Radiative Recombination-lonization

Coefficients

Bates et. a!. [2] have defined effective recombination

and ionization coefficients which account for the net effect of

collisional ionization, three-body recombination, and radiative

recombination in a very simple way. These coefficients have been

tabulated exclusively for hydrogen and hydrogenic ion plasmas,

". :2] and E33. in this section we define the effective

ccefficients analogous to Bates et. al. and present results for

our optically thin nitrogen plasma as well as the case where all

bound-bound uv lines are assumed to be optically thick.

Denoting and the effective recombinationDe o i n CR , an Ca R as th

coefficients for N -> N and N ->N and and S+ as the

effective ionization coefficients for the reverse processes the

+ 44rate equations for N, N , N , and Ne may be written

dN Ne N 0R - Ne N SCR9 dt C

16

0°#

N -Ne e0 1.0 + 4. N4 Ne +NCR C RNeN CR CR CR

17)" 4- 4 - 4.4. 4. ( 7

, dN - Ne N S - Ne N aCR

C R CR

-dNe - Ne N 0 Ne N S - Ne N~a 0 Ne NCR CR

Tnerefore, in terms of the detailed rate coefficients outlined in

,... section :" and S are given byzecton -I.a CR OLR ICRI CR

a, - (Ne > 3 (p,i) N+(p) + R(p,i) N+(p)}/N +'R 3 R", 1 . , 9

,"4 - r~ .'-. N . 4. .4 -

a CR = A a3(u,p) (u) +. e a* (u,p) N (u)/N (18)p,u p,i

* S0 = [ N(i) S(i,O)}/NCR i,p

-CR = -0 N'(p) S+(p,u)}/N +"]-7 -CR'p,u

A quick check shows that these definitions satisfy the conditions

for particle and charge conservation.

The coefficients defined in equations (17) and (18) are

time-dependent, due to the time dependence of the contributing

population densities; see Figs. (9) - (10). The steady state

-"aues are presented in Tables VI - IX as a function of the .inal

-electron density and electron temperature (Te was fixed

* throughout the integration). Close examination of these results

reveals the following: At high electron densities the effective

reco ination coefficient is linearly proportional to Ne. This

-s due to the dominance of three-body recombination over

13rad-ati've (two-body) recombination in this regime, Ne > 10

17

"~~~~~~~~~~~~~~~~~~~~~~~~~~~.-.-,......-.,..- ....... . . -. .. ",.".,..-... ..... ... "". '.-.... .. -.. '.. ."-" ."-'

19

10 cm. For lower electron densities the opposite is true and

the effective coefficient approaches the two-body value. The

coisiona_-radiat-ve ionization coefficients show a rapid riseses""w el-to oeste Ie17 3

"-- for 018 /cm3 ). This is in

contrast to the behavior of the coefficients of Drawin and Bates

- which show a saturation at high Ne. The density dependence in

*. and SCR at h~igh Ne in our calculation comes from theR CR

correction discussed in section !II. D.. The level-specific

coi!isional ionization coefficients depend on Me and Te in the

manner of eq. (16); this carries through to the definition of SCRCR

and S in eq. (18). Neither Drawin nor Bates included this

correction.

The collisional-radiative coefficients in Tables V! and

VIIT can be loosely compared to the results of Bates et. al. [2]

and Drawin [3]. While there is no apriori expectation that the

results should be in strict agreement, to the extent that a

nitrogen plasma differs from a hydrogenic plasma, many of the

rate coefficients were obtained using similiar (hydrogenic)

-: exoresslons. However, it must be pointed out that the results of

Bates et. al. and Drawin are not, themselves, in agreement.

Specifically, the recombination coefficients of Bates et. al.

exceed those of Drawin by up to a factor of four while the

ionization coefficients are greater by an order of magnitude At

low electron densities, Ne- 10 /cm our recombinat

coefficients are generally a factor of one to four less than

18l

:i l: : : , . . * . - .. . •.:. : .: . -. . - - . ' -.-. .. - -. . . .. .. . ... . . . . . . ..

those of Drawin and Bates et. !., depending on temperature. AtLI 3higher Ne, - . , , or emnation coeficients, fall

between 3her resul's. ur tco3s oial-radiative icnization

coefficients are in good agreement (factor of 1.0 - 2.0) with

16 3 17/ 3those of Drawin at low Ne, 10 /cm to 10 /cm. At higher Ne

our coeffiients exceed those of Drawin by up to a factor of

ten. Thi4 difference is due primarily to the ionization

potential reduction correction discussed above. As a reminder,

the calculations of Bates and Drawin are for hydrogen where at

higher electron densities the character of the ion does not

change. In contrast, in nitrogen other stages of ionization

aarise.

In a subsequent report it will be shown that the

absorOtion coefficient for our model nitrogen plasma is on the

* order of 10 /cm in the uv spectral regime. This corresponds to a

-4mean free path of - 10 cm. In Tables X through XIII the

collisional-radiative coefficients are presented for the case

where all bound-bound uv lines are assumed to be completely

reabsorbed. As expected, there is very little difference between

the optically thin and optically thick recombination

coefficients. For high electron densities, > 19 cm , where the

plasma is collision-dominant (see the discussion in the next

section), the ionization coefficients are comparable. However,

for lower electron densities the optically thick ionization

oefficients are much larger than the ootically thin case, as

great as a factor of ten.

19

. aha qu: !b r im

When co1isinal :ransition rates exceed the

cc espcring radiative transitions the plasma is said to be

coll'sLon-dominated. It is then possible to specify the

ocoulations of the constit' ent species by using the Boltzmann-

Sana equation at the local electron temperat.re 7111. The onset

": Saha equilibri-um depends on Ne and Te; for example, an

optically thin nitrogen gas at Te - 1.0 e.v. becomes collision-

dominant at Ne - 10 1/cm 3 _5a].

One form of the Saha equation is, [11],

Ne 'z, ) 2Z (p) lmkTe) 3 /2 exp{ [EZ(p) - (i)2/kTe:i (19)-(i) gz(i) 2 M

We have used eq. (19), after correcting the exponential factor

for the ionization potential reduction (see section III. D., to

compare the steady state population densities with those expected

assuming a collision-dominant environment for a range of electron

1densities, Ne = [101 - i0 1/cm3, and temperatures, Te - [1.0 -

3. ev -. The ratio of the level population to the Saha

population may be defined as

0'" -1 , .Nz n' /N - n', (20;

20

* -- - * * .-. - . .

wneso 1. th souin t o tne -o r re-t edt e q. (9.

.3D)'_e X:7 we -resent tnreshold values 'for lie above wichn- I

n + 5 'fo r thne i n d i a t ed Ie Ve 13, i e . S ah a e qu Ibrium

3s ahe e j to0 wi**thi ',1 Colu-mn 1 reCuires this criteria to be

s-atisf:ed for a!-l N and N 1! 'Levels, column 2 restricts the

criteria to excited states of N 1 (specifically, i - 7 to 13),

*and column 3to excited sta-tes of N -1 (i.e. p - 7 to 17). 7he

esLts show the following: First , for any given Te, as the

number of electrons increases equilibrium is achieved for excited

*N states before excited N IT states and, as expected, before

the lower states. In addition to Ne the threshold values depend

on :e. As3 Te increases more electrons are neccessary to have a

completely collision-dominant environment, i.e. complete I-T.

For an optically thin nitrogen plasma a state of complete !.TE

e:x:sts if Ne - (2.2 - 5.0) x 10 /cm3 for Te ranging from 1.0 to

3.0 e.v.. '"he criteria given by Griem [11] and others on the

validity of LTE is3 that the electron deexcitation rate of the

resonance line must exceed ten times the radiative decay, i.e.

* for the nitrogen atom one must have

W~1) Ne > 10 A(4,1) (21)

/cm18 inou

:or ~ =1.0e.v., Eq. (21) gives Ne 2.3 x 10'cm iou

.a32e . zowever, hleradiative processes may be important to the

lwr evels tn-e excitedl states of N '_ are still controlled' by

17 3,o!1i4ional pccesses for Ne > (5.7 - 2.1) x 10' /2-1 over the

3ame temceratire range. This cuasi-stationary state exists for

21

eectron Iensi:ies "cur to tweny-f e times less than s

requ I red-r alI states to be in LYE.

- . L 17C:7J 'Z!A

,he recombination and ionization processes for an optically

-.in, homogeneous, charge neutral nitrogen plasma have been

studied for electron densities between 016 /cm3 and 10 /cm3 and

electron temceratur,'es from 1.0 .ev. to 3.0 e.v.. Effective

collisional-radiative recombination and ioniza:ion coefficients

are calculated which describe the net recombination and

ionization and may be used in sophisticated plasma chemistry

siflTJation codes. The bound-bound and free-bound radiation has

been Characterized. It has been shown that for electron

densities greater than - 10 1/cm 3 a state of local thermodynamic

* equilibrium exists whereas exited states may be in equilibrium,

collision-dominant, for electron densities as low as - 1017 /cm3 .

This has oiplications for simplifying the description of

18radiative transfer in a plasma. For example, above Ne - 10 /cm

a transfer theory based on the assumption of LTE should be

adeauat-e whle below Ne - 10 7cm individual species must be

considered in detail. :n the intermediate regime hybrid theories

should prove useful.

220I

- - -- - -

Energy Levels for N 1

index State Configuration(1s2 2s2 ) Energy(e.v.) Weight

1 4S° 2p3 0.0 4

2 2D° 2p3 2.38 103 2pO 2p3 3.58 6

4p 2p 2(3p)3s 10.33 125 2p 2p2( P)3s 10.69 6

4p 2s2p 4 10.93 122 S 2p2 (3 P)3p 11.60 2

8D 2p2 (3 P)3p 11.76 20

,. 9 P (3P)3p 11.85 12

10 S 2p2 )3p 12.00 42,- 2211 2D 2p( 3 P)3p 12.01 10

12 2 p 2p2 (3 P)3p 12.13 62 2 1C13 D 2p (1D)3s 12.36 10

23

.. •. . . . .

Ener gy Levels for N

index State Configuration (Es2 ) Energy (e.v.) Weight

3p2s-2p 2 0.01 9s222

2 D 2 p 1.90 5

3 S 2s-2p 2 4.05 1

4 3D° 2s2p 3 11.44 155 3po2s~p13.54

1 010s2p 17.88 5

7 s2 2 0\3pO 2( p )3s !.L8 91 0 2 .2 03 p 2s 2p( pO)3s 18.50 3

9 3S0 2s2p 3 19.24 3

CP 2p( )3P 20.41 3S 3 D 2s22p( 2p )3p 20.66 15

10 232p 3 20.68 3

13 3S 2s2p( 2p )3p 20.94 3

. 3p 2322p( 2p )3p 21.16 9

15 'D 2322p(2PO)3P 21.60 512 2 016 S 2s 2p( p )3p 22.10 117 3F02s2 20 21p3FO 22p(2p)3d 23.14 21

.TTI

TAL III

E nergy Levels for N !If

2.nex State Configuration (1S) Energy (e.v.) Weight

2O 2s2 2p 0.0

22 2s.p 2 7.1 12

24

6 . . - . . : : "-" . . . - .. : - . . ,

,., .4:.: ... ' • -- ' . . . ." ',. ' _L . " .' " . - ' " '

Radilative Transitions (Bound - Bound)0

Wavelength(A) #(We-se) Spectrum Index Energy (e.v.)

644.99 3 uv 9+ - 1+ 19.23

660.28 5 uv 12+ - 2- 18.79

671.43 uv - 1+ 18.48

745.,4 6 uv 12+ - 3+ 16.63

76.98 3 uv 8+ - 2+ 16.60

775.96 4 uv 6+ - 2+ 15.99

916.34 2 uv 5+ - 1+ 13.541085.1 1 uv 4+ - 1 11.43

1134.6 1 uv 4 - 1 10.931199.9 2 uv 6 - 1 10.34

1,243.3 5 uv 13 - 2 9.98

1411.9 6 uv 13 - 3 8.79

1493.3 3 uv 5 - 2 8.31

1743.6 4 uv 5 - 3 7.12

3437.2 20 near uv 16+ - 8+ 3.60

3995.0 19 vis 15+ - 8+ 3.10

4623.2 17 vis 14+ - 7+ 2.68

5028.8 16 vis 13+ - 7+ 2.46

5679.4 15 vis 11+ - 7+ 2.18

6482.1 18 vis 10+ - 8+ 1.91

7452.2 23 vis 10 - 4 1.66

3211.8 22 ir 9 - 4 1.51

3 6Y.5 25 12 - 5 1.44

8691.6 21 8 - 4 1.43

* 9395.3 24 ir 11 - 5 1.32

11602.0 ir 10 - 6 1.07

25

,. .. . . . -

Ra Z fave Tr'ans tions 'Free - Bound Thresholds)

Wave'ensth(A) Spectrum index Eneriy (e.v.)

13. 9 uv !++ - 1- 29.59

* 447.58 uv 1++ - 2+ 27.70

485.24 uv I - 3+ 25.55490.82 uv 2 - 4+ 25.26

535. 32 uv 2" - 5+ 23.16658.77 uv 2'- - 6' 13.82

710.08 uv 2'- - 9+ 17.46

773.91 uv 2'. - 12+ 15.02

324.34 uv 4 -6 15.04

325.53 uv 3. - 3 15.00

852.68 uv 1+ - 1 114.54

382.42 uv 2. - 2 14.05

964.32 uv 2. - 3 12.35

1,019.57 uv 1 - 2 12.16

11-14.93 uv 1"+ - 7. 11.151116.94 uv ++ - 8+ 11.10

1132.20 u v 1+ - 3 10.96

1349.08 uv 1'' - 10' 9.19

1386.80 uv 1++ - 11+ 8.94

1431.64 uv 1++ - 13. 8.66

1468.96 uv 1+ - 14. 8.44

1549.75 uv I - 15+ 8.00

. 1653.07 uv 1'+ - 16' 7.50

919.20 uv I - - 17+ 6.L6

29a4.89 uv - 4 4.21

3046.19 uv 2+ - 13 4.)7

. 3220.26 uv 1 - 5 3.854217.01 vis 1+ - 2.94

4459-71 vis 1+ - 8 2.73

4608.92 vis +' - 9 2690 4881.10 v s * - 10 2.54

*4900.40 vis I - 1' 2.53

5144.40 vis I' + 2 2.4126

0

-. - VI

Collisiona-Radiati ve Recombination Coefficients

Optically Thin (A'! Wavelengths)

Neutral

Te(e.v.) 1.0 1.5 2.0 2.5 3.0

le

1.0E+16 2.5E-12 I I - 2 8.4E-13 5.5E-13 4. -1

2.0 2.9 1.5 1.1E-12 8.2 5.43.0 3.3 .8 1.3 1.0E-12 6.54.0 3.8 2.2 1.6 1.2 7.65.0 4.3 2.6 1.9 1.4 8.86.0 4.7 2.9 2.1 1.5 1.OE-12

4 7.0 5.2 3.3 2.4 1.7 1.13 .0 5.6 3.7 2.6 1.9 1.29.0 6.1 4.0 2.9 2.0 1.3

1 . 6.6 4.3 3.1 2.2 1.52.0 1.1E-11 7.4 5.6 3.9 2.63.0 1.7 I.1E-11 8.1 5.8 3.84.0 2.2 1.4 1.OE-11 7.5 5.05.0 2.7 1.7 1.3 9.4 6.36.0 3.2 2.0 1.5 1.1E-11 7.67.0 3.8 2.4 1.7 1.3 8.98.0 4.3 2.6 2.0 1.5 1 OE-119.0 4.8 3.0 2.2 1.7 1.1

1 .OE+18 5.4 3.4 2.5 1.9 1.32.0 1 .1E-10 6.8 4.8 3.8 2.73.0 1.6 1.OE-10 7.2 5.8 4.14.0 2.2 1.4 9.6 7.7 5.65.0 2.7 1.7 1.2E-10 9.6 7.06.0 3.3 2.1 1.5 1 .1 E-I0 8.67.0 3.8 2.4 1.7 1.3 1.OE-108.0 4.4 2.8 2.0 1.5 1.29.0 4.9 3.2 2.2 1.7 1.3

'1.0E+19 5.5 3.5 2.5 1.9 1.5

27

.°

* h. ~ . % .h .%Th. ..... ., -

Co..isicnal-Radiative Recombination Coefficients

Optically Thin (All Wavelengths)

!on

1.0 1.5 2.0 2.5 3.0Ne

I .0E 16 3.6E-12 2.1E-12 1.7E-12 1.3E-12 9.7E-132.0 4.6 2.6 2.0 1 1 .1E-12

53. 5.3 3.1 2.4 1.8 1.34.0 5.9 3.6 2.8 2.1 1.45.0 6.4 4.1 3.1 2.3 1.66.0 6.9 4.6 3.5 2.5 1.77.0 7.4 5.0 3.8 2.8 .9

380 5.5 4.2 3.0 209.0 8.5 6.0 4.5 3.2 2.2

! .0E 17 9.0 6.4 4.8 3.5 2.32.0 1.5E-11 1.0E-11 8.1 5.8 4.03.0 2.2 1.5 1 .1E-11 8.1 5.84.0 2.9 1.9 1.5 1.17-11 7.45.0 3.5 2.3 1.8 1.3 9.25 5.0 4.2 2.7 2.1 1.6 1.IE-l1

, 7.0 4.9 3.2 2.4 1.9 1.38.0 5.5 3.6 2.8 2.1 1.59.0 6.2 4.0 3.1 2.4 1.7

1.0E+18 6.8 4.5 3.4 2.6 1.92.0 1.4E-10 8.9 6.4 5.2 3.93.0 2.1 1.3E-10 9.8 7.9 5.94.0 2.8 1.8 1.3E-10 1.1E-10 7.95.0 3.5 2.2 1.7 1.3 9.9b.0 4.2 2.7 2.0 1.6 1.2E-I0*7.0 4.9 3.1 2.3 1.8 1.4

3.0 5.5 3.6 2.7 2.1 1.5. 6.2 4.0 3..O 2.3 1.8

1.OE*19 0.9 4.5 3.3 2.6 2.0

286i . " i " "-

:AE-LE VIII

Coil sonal-Radiative Recombination Coefficients

Optically Thin (All Wavelengths)

Neutr'al

1.0 1.5 2.0 2.5 3.0Ne

i .0E 10' 4.1E-14 4.0E-12 2.27E-11 2.2E-10 4.5E-110

2.0 5.4 5.8 7.0 2.8 6.03.0 6.4 7.6 8.8 3.5 7.44.0 7.2 9.2 1.OE-0 4.1 8.65-0 7.9 . 1 .2 94.6.8

4 6.0 8.6 1 .2 1.3 5.1 1.1E-09- 7.0 9.2 1.3 1.5 5.6 1.2

.. 0 9.7 1..4 1.6 6.o 1.39.0 i.OE-13 1.5 1.7 6.4 1..4

1 .0E+17 1.1 1.6 1.8 6.7 1.42.0 1.5 2.1 2.4 9.0 2.03.0 1.9 2.4 2.8 1.OE-09 2.34.0 2.1 2.7 3.0 1.1 2.55.0 2.3 2.9 3.2 1.2 2.76.0 2.5 3.1 3.3 1.3 2.97.0 2.6 3.2 3.4 1.3 3.03.0 2.7 3.3 3.5 1.4 3.1

S9.0 P 8 3.4 3.6 1.4 3.1

I.0E 13 2.9 3.5 3.7 1.4 3.22.0 3.5 4.0 4.1 1 .5 3.63.0 4.0 4.2 4.3 1.6 3.7S0 4.3 4.4 4.4 1.6 3.8

5.0 4.5 4.5 4.5 1.7 3.9D. 1.7 4.7 4.6 1 .7 4.0

,. 4.9 4.9 4.6 1.7 4.03.0 5.1 5.0 4.7 1.7 4.09.0 5.3 5.1 4.8 1.8 4.1

* .0E '9 5.5 5.2 4.8 1.8 4.1

29

Co 1 isional-Rad jative Ioni zat ion Coet'fic I.ents

Optically Thin (All Wavelengths)

Ion

Teev. .0152.0 2. 3.0Ne

1.OE+16 2.9E-21 4.OE-17 5.8E-15 1.!E-13 8.14E-132.0 3.9 5.5 6.8 1.5 1.0E-123.0 4.9 7.2 1.OE-114 1.8 1.2

'5.8 3.2 1.3 2.2 1.45.0 6.6 1.1E-16 1.5 2.05 1.60.0 7.14 131.8 3.0 1.8'7 8.1 1.5 2.0 3.14 2.13.0 8.8 1.6 2.2 3.7 2.39.0 9.5 1.8 2.4 4.1 2.5

-1.OE-20 1.9 2.6 4.4 2.72.0 1.7 3.0 54.3 714 .3.0 2.2 3.9 5.6 I.OE-12 6.24.0 2.6 4.6 6.6 1.2 7.55.0 2.9 5.2 7.4 1.4 8.66.0 3.2 5.7 81 1.5 9.67.0 3.4 6.1 8.6 1.6 1.OE-118.0 3.6 6.4 9.2 1.7 1.19.0 3.8 6.8 9.6 1.8 1.2

2.0 5.4 9.1 1.2 2.14 1.63 3.0 6.5 1.OE-1 1.4 2.6 1.84.0 7.5 1 .1 1 .5 2.8 1.9

*5.0 8.14 1.2 1.5 2.9 2.0- 6.0 9 .3 .3 1.6 .0.

" 7.0 9.5 1.3 1.7 3.1 2.O'8.0 3.OE-19 1 .4 1.7 3.2 2.29.0 1.1 1.4 1.8 3.3 2.2

1.0+19 1.2 1. .8 3.3 2.3

-30

jX

.o1._i3ional-Radiative Recombination Coefficients

Optically Thick (All UV Bound-Bound Wavelengths)

Neutral

Te(e.v. 1.0 1.5 2.0 2.5 3.0Ne

1.OE-16 2.6E-12 1.1E-12 8.2E-13 5.4E-13 4.8E-132.0 2.9 1.4 1.1E-12 6.7 5.83.0 3.3 1.8 1.3 8.0 7.04.0 3.3 2.2 10.6 9.4 8.25.0 4.3 2.6 1.8 1.1E-12 9.46.0 4.7 2.9 2.0 1.3 1.1E-127.0 5.1 3.3 2.3 1.4 1.28.0 5.6 3.7 2.5 1.6 1.39.0 6.1 4.0 2.8 1.8 1 .4

* 1 .0E+I7 6.6 .3 3.0 1.9 1 .52.0 1.1E-ii 7.4 5.6 3.6 2.73.0 1.7 1 .1E-11 8.1 5.4 4.0

4.0 2.2 1.4 1.OE-11 7.3 5.25.0 2.7 1.7 1.3 9.1 6.56.0 3.2 2.0 1.5 1.1E-11 7.87.0 3.8 2.4 1.7 1.3 9.08.0 4.3 2.6 2.0 1.5 1.0E-119.0 4.8 3.0 2.2 1.7 1.1

1.0E+18 5.4 3.4 2.5 1.9 1.32.0 1.1E-10 6.8 4.8 3.8 2.73.0 1.6 1.OE-10 7.2 5.8 4.14.0 2.2 1.4 9.6 7.7 5.65.0 2.7 1.7 1 .2E-10 9.6 7.06.0 3.3 2.1 1 .5 1 .1E-10 8.67.0 3.3 2.4 1.7 1.3 ! .OE-108.0 4.4 2.8 2.0 1.5 1.29.0 4.9 3.2 2.2 1.7 1.3

I .0E 19 5.5 3.5 2.5 1.9 1 .5

31

T A-E XI

0o12 islonai-Radiative Recombination Coefficients

Optically Thick (All Bound-Bound UV Wavelengths)

IonTe~e.v,) 1,0 1,5 2.0 2.5 3.0

Ne

1,0E.16 4.4E-12 2.1E-12 1 .7E-12 .11E-12 1.0E-122.0 4.6 2.4 1.9 1.3 1.23.0 5.1 3.0 2.4 1.5 1. 44., 5.6 3.6 2.8 1.7 1.6

. 5.0 6.2 4.1 3.1 1.9 11.7* 6.0 6.8 4.6 3.5 2.1 1.9

7,0 7.4 5.0 3.8 2.4 2.18 30 8.0 5.5 4.2 2.6 2.39.0 8.5 6.0 4.5 2.8 2.4

1i.0 17 9.0 6.4 4.8 3.0 2.62.0 1.5E-11 I.OE-11 8.1 6.3 5.73.0 2.2 1.5 1.1E-11 7.7 6.24.0 2.9 1.9 1.5 1.OE-11 8.05.0 3.5 2.3 1.8 1.3 9.66.,0 4.2 2.7 2.1 1.6 1.1E-117.0 4.9 3.2 2.4 1.8 1.33.0 5.5 3.6 2.8 2.1 1.59.0 6.2 4.0 3.1 2.4 1.7

S.OE+18 6.3 4.5 3.4 2.6 1.92.0 1.4E-10 8.9 6.4 5.2 3.93.0 2.1 1.3E-10 9.8 7.9 5.94.0 2.8 1.8 I.3E-10 1.1E-10 7.95.0 3.5 2.2 1.7 1.3 9.96.0 4.2 2.7 2.0 1.6 1.2E-10

3.1 2.3 1, 1.43.0 5.5 3.6 2.7 2.1 1.69.0 6.2 4.0 3.0 2.3 1.8

* .CE+19 6.9 4.5 3.3 2.6 2.0

32

0

- i - -. * - - -2

Collisiona!-Radiative :onization CoefficientsOptically Thick (All Bound-Bound UV Wavelengths)

Neutral

Te1e.v.) 1.0 1i.5 2.0 2.5 3.0N e

1.0E.16 3.6E-13 2.OE- 1 1 1.6E-I0 4.1E-10 1.OE-092.0 3.3 2.2 1.8 5.0 1.23.0 3.2 2.4 2.0 5.6 1.4a.0 3.1 2.7 2.2 6.2 1.55.0 3.1 2.8 2.3 6.6 1.66.0 3.1 3.0 2.5 7.0 1.7

.0 3.1 3.0 2.6 7.5 1.88.3 3.1 3.1 2.7 8.0 1.99.0 3.1 3.2 2.8 8.3 2.0

1.0E*17 3.1 3.2 2.9 8.7 2.02.0 3.1 3.4 3.4 1.1E-09 2.53.0 3.2 3.5 3.6 1 .2 2.84.o 3.3 3.6 3.7 1.3 3.05.0 3.4 3.7 3.8 1 .4 3.16.0 3.4 3.8 3.9 1.4 3.27.0 3.5 3.8 3.9 1 .5 3.28.0 3.5 3.9 4.0 1.5 3.39.0 3.6 3.9 4.0 1.5 3.3I.0E018 3.6 4.0 4.0 1.5 3.1

2.0 4.0 4.3 4.2 1.6 3.63.0 4.3 4.5 4.4 1.7 3.84.0 4.5 4.6 4.5 1 .7 3.95.0 4.7 4.7 4.6 1.7 4.06.0 4.9 4.9 4.7 1.7 4.1

5.1 5.0 4.3 1.3 4.13.0 5.3 5.1 4.89.0

3.E+ 9 5.6 5.3 4.9 1 .3.2

33

Coll i s i o n a l - R a d _i t i n z a on_ -oeff4c,*ents,

Zptcally T.o!< (All Bound-Bound UV Wavelengths)

Ion

5.0 2.0 2.5 3.0• -Ne

* . zE 5 4.0E-20 4.9E-16 6.8E-14 .OE-12 67E- 22.3 4.1 5.3 7.5 1. 7.63.3 4.4 5.8 8.1 1.2 8.24.3 4.8 6.2 8.6 1.3 3.95.5.1 6.5 9.0 1.4 9.5.05.4 0.8 9.4 1.4 9.9

5.6 7.0 9.7 1.5 .0E-113.3 5.9 7.1 9.9 1.6 1.19.0 6.1 7.2 1.OE-13 1.6 1.1

. 6.4 7.3 1 .0 1.7 1 .12.0 8.4 7.8 1.1 2.0 1 .43.3 1.OE-19 8.2 1 .2 2.1 .64.0 1.2 8.4 1.2 2.3 1.75.0 1.3 8.6 1.3 2.4 1.7

1.4 8.8 1.3 2.4 1.87.0 1.5 8.9 1.3 2.5 1.93.0 1.5 9.1 1.3 2.5 1.99.0 1.5 9.2 1.3 2.6 1.9

1.OE-' 1.7 9.4 1.3 2.6 2.02.10 2.1 1.OE-15 1.5 2.8 2.23.D 2.4 1.1 1.5 3.0 2.3a . 2.7 1.2 1.6 3.1 2.3

3.1 1.3 1.6 3.1 2.46.0 3.4 1.3 1.6 3.2 2.0 3.6 .4 1.7 3.2 2.5

3.? '.4 1.3 3.3 2.5-2 1.5 ",.3 4 2. 5

. 4.5 1.5 1.3 3.4 2.5

0

34

0 . . ,, - . ..

-A-K- XiV

Saha Thireshold Values ( /cm3

Te e.v. All states N(i) (i>7) N (p) (p>7)

2.27--13 4.5E-- 7 E6 . E 7

.5 2.5E 8 3.6E+17 6.8E+ 17

2.9E 83.OE I7 7.5E+17

35 •E 1 2.1E 11 77.8E+17

* 3.9E+'3 * 2.OE 17 8.2E+17

SEx 'din g N(13?

35

A4-'

U- --" 7

/.

LN

-,- /

-- /.

O-] '

. . . . -- - -- --

Figure 1.

Population densities for N (solid line, toD at

t=O), N (solid line, bottom at Z=,), N

dashed line), and Ne (same as N ). All figures

are for Te=2.0 e.v.

36

S

U- I(S)~

Fiur 2

Pouato deste o (),N2,adN3

(sld dotd an-aheriesepetvl

'37

-- -

.. . . .. . . . .. . . . .. . . . . .. . . . .. . . . .. . . . .. . . .

.:,71 ,I'S

Figure 3.

Population densities for uv emitting N states;

ie ()(solid line, top), N(5) (dotted line),

> (d(ashed 14ne), and >1(13) (solid line, bottom).

38

0%

r *ilO

i4 •I7

I. .r E. .. . .

---- - - - - - -

.2. -S ET! ME (5E

Figure 4.

Population densities for ir emitting N states;

qi.e. N(8) (solid line, top), N(9) (dotted line,

top), N(10) (dashed line), N(11) (solid line,

bottom), and N(12) (dotted line, bottom).

39

I' : _} . . _ . , . - , .: _ , , : . " : -

- -/

- .7

Fiue5

Pouato desiie for. N rudcnfgrtos

0-0 /N()(i d ieN ()(otdln) n 3

(dahe lie)

0h

* 40

0 E- I7=

1 0

+- +

N (4) (sli lie top),____N__(5)___ (dotted____line, __

op),~ N26.(ahe ie-o)%1 7 (o~

N 4 ldline, topdl), N(5) (dotted line, to)

N +(9) (dashed line, bottom), and N +(12) (solid[ line, bottom).41

R. , o 17 _ ,

2II.

L/ -- -o- '

0. , .

V -. i / /,-/

/T

P"' /

/.

s ; / o1 E '0 /

: .I

:. LE 09 /,,_ _ __ _ _ _ _ __ _ _ _ _ __ _ _ _ _S.EE08 2.=.E-08 S.GE-QF

" TI ME (5P

Figure 7.

+Population densities for visible emitting N

"-" states; final order from top to bottom is N+(11),

+ + +10) , N 17), N4 (1), N 15), N' (13), and

N (16).

42

0: . " " " " " "- ' - " '

..............................

.0 E~ I

OE+ i Ij0 OE-OC 2. SE-0R S. 0E-0TI ME (S)

Figure 8.

Population densities for N +levels; N + (1)44

(solid line) and N (2) (dotted line).

43

"h-.- I 2L77U

7/7

tj

t.°: E - : =..... ............ ................................ ........................

// 00

] i.OE-Ka __________________C. OE._-J] 2. SE_-03 S. OE-08

TI ME (S)Figure 9.

Collisional-radiative recombination coefficients

for optically thin neutral (solid line) and ion

(dotted line) cases.

K- , .44S ,

* 7

' g -' ........... ............... .. ............ .. .....................

71 M ~

Figure 10.

Collisional-radiative ionization coefficients for

the optically thin neutral (solid line) and ion

(lotted line) cases.

44

°. ' ' °' ' °

°45

..

- .' --'--

REFERENCES

* . See fzr example, Y.B. Zeldovich and Y.P. Raiser, "Physics ofShock Waves and High. Temperature Hydrodynamic Phenomenon" -Vol 1, Academic Press, New York (1966)

2. a. D.R. Bates, A.E. Kingston, and R.W.P. McWhirter, Proc.Roy. Soc. A267, 297 (1962).

t"b. i d. A270, 155 (1962).

c. D.R. Bates and A.E. Kingston, Planet Space Sci. 11, 1(1 953).

t. D.R. Bates and A. Dalgarno, in Atomic and MolecularProcesses, D.R. Bates, ed. Academic Press, New York"(I 962>)

e. D.R. Bates and A.E. Kingston, Proc. Roy. Soc. A279, 10

''964).

f. i~id. 32 (1964).

3. a. H.W. Drawin, Z. Physik 225, 470 (1969).1. ibi., 83 (1 9691)

* 4. C. Park, J. Quant. Spectrosc. Radiat. Transfer 3, 1633 (1968).

5. a. J.L. Kulander, J. Quant. Spectrosc. Radiat. Transfer 5,

253 (1965).

b. ibid. 6, 31 (1966).

0 . A.W. Ali and W.W. Jones, Physics Letters 55A, 462(1976) andW.W. Jones and A.W. Ali, Appl. Phys. Letters 26 450(1975).

4. W:. Weise, M.W. -i-th, and B.M. Glennon, Atomi-c Transition? roca !i~ies, NBS Publication 'ANSRDS-IBS4, (1966).

8. A.W. Ali, R.H. Kummler, F.R. Gilmore, and J. William McGowan,*• "Upper Atmospheric Excitation Processes", NRL Memorandum

Report 3920 1979). ADA067330

9. H.W. Drawin, "Collision and Transport Cross Sections", ReportR-CEA-- - , ontenay-aux-Roses, 166 Re,,ised (,967).

4

46

*

A.W.Ali "Eecrn Exci*ta'tion and .on~zat*cnRat:e C.efficien~s For N2, 02, NO, N, and 'C", NRL Memorand~un.eCot "756 p982;. AD A110988

*H. Gr'ier, Plasma Spectroscopy, McGr'aw-Hill Book Co., New York

~.TR. Young, ??CHEMEQ - A Subrout-ine 'or Solving Sti' Cr--.ariDiff'erential Equatfons", MRL1 Memorand'um Report 4091 810).AD A0835 45

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