• Source: 1946-LA-602-Konopinski-Marvin-Teller-Ignition-fo-the-AtmsophereAuthor: LANL Research Library LWW ProjectArchived: July 19, 2026
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§Source: 1946-LA-602-Konopinski-Marvin-Teller-Ignition-fo-the-Atmsophere
Author: LANL Research Library LWW Project
Archived: July 19, 2026

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It is shown that, whatever the temperature to which a sectior, of the a+mo .phere may be heate?, no seli’-propagatin~ chain of nuclear rFwLCti Q~i6 is Ijkely to be started. The energy losses to radiation alwuys overcompensate . *- tke gains due to the reactions. This is true even with rather extravagant nssumgtions.

concerning the reactivity of the nitrogen nuclei of tke air. The t}]y dsq~iet~~g

feature

is t~t

the “safety factorq, i.e. the ratio Of ~osSeS

whi.hgreatly exceed the bombs now under consideration. but even if bombs required voluze (i.e., greater thsn 1000 cubic meters; are employed, transfer from electroris to light i]uanta by Compt.un scattering will profurther safety fctor and will make u chair. reaction in air impossible.

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F. . 1., Introduction .- The Letonatian of a fission or thurmonuc]ear bomb produces a high . .

t.omper.aturewhich will stimulate the reaction of atomle nuclei of the air with each other. If an ignition point exists and is surpassed, tho thermonuole8r re~~tiorA my be prop~gated to all parts of the atmosphere…

Propagation of the raa:tim demands that the energy production iu each newly entered region exceed the losses from that region. The energy .

&Fpears in the farm of the kinetie energy of Particles which are prduats of e~~grgc nuclear

reactj.ofis. The product particles, through collisions, share their energy with the particles of the air an(? help maintain the temperature. 9n the o:her hand, the share of the energy given the electrons is rapidly ,,, ruliated away. Ahis constitutes the chief energy lass. ~he radiation c&.r.- not help to ]~inkin temperature becausti”of the great transparency of air, afid %ecause, even if the heated volume is great enough to lvoontai.anthe radiatlon, the heat capacity of space fo:-ra<iation is so.great that the energy produced in the reaction is many orders of’mapyit.ude too small to maintain the needed radiation temperature. . On R first evaluation of the danger or igniting the atmosphere, one .

cun assame that the reactio~. ?r~auct partio]es dcl not effectually disperse .

their energy but deposit it where they aro produced. Then Sne can compare this * rate of ?evositton with the radiation rate~ The temperature, if such exists, +. . at which the energy production rake equals the racliakive loss rate will be the temperature of ignition. gecause of the uncertainties in the “knowledge of – these proc~~ses, the policy should be ado?ted of exaggerating the dangers .’b

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l ::.. l . . so:l O. is ei’f’eoted with an Unh9Wli cross seot ion, and 6ince the transf’er 5e%ween . nuclei which %-;e comparable KWSS is us”lalYy more raDcl than the transfer to electrons, all th eri9rgy goes first to esta”91i6hing a naol ear temp2rnt’ure. .

.—

.+ trsnsl’ar ra\(e to electroas and radiation rate by the electrons. This temperazure rzy be considerably lcw;er ‘Aan the nuolesr temperature and thus increase . %. Tpe ~recg.tt.~gc~nsidsrations will yie?d an evaluation of’the mrgin 0 !7tiai’ety as a fuastion of the temperature o;’the atmosphere. ~ fir~l section will be devoted to the behavior of a hct air mass OF finite volume and “to the besting whi\)h a fisflion or themotiuclear born bmayactually be able to supply.

2. THE ENERGY FR(XXICTUMl

I

The nuolear reaztions most to be feareci in air are the rti2?~iMkS l ,

p i rti Ji’ nitrogen’ nucleic

cf Other notable constituents of the citm’osphere, o’xygcn ,- .

~ t>ar”ar:and rare gas nuclei are much more stable t’han nitroen, yielding 09inprStVf31y

little erwrgy.

There i~ perhaps one other nucleus that shmlc! be @fe9 care!’ul attention: tha proton. It.is ordinarily much less abundant in the atmosphere than is nitrogen, but clouds of steam raised over khe weans by intense heating, may raciically nltf3r that situation. This danger will be ::ivenattention after the tlsoussion of the reactions of nitro%en nuclei with etichother has been campleted. Tk,e,ltroqea-nikro~eflreuctions iriwhich stiffizient er&er4Y is -. procllx>edto enable the product particles to surmount each others Coulomb . .

barriers we the following: … .

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In parenthesis foil owing the ractians are given the heights of’the Ooulomb barriers of the prod.letoarticl es. In acor with the policy of’ atiopting the + m9st dtifi~sroazassump%iozs, it will be assumed that 1’7.7Mev per reaction is

‘ xwlet.see,

tis is characteristic of the alpha emissin. (The .xture oi’ nitrogen by nitrogen, the first reaction listed, is certaicly infreqaqnt compared to ;artic.le e,nissim, as r6Sctions of this t:{pealways are, ~~oreover, energy in the form of y-rays will be uziavaila’u}efor carr:ying on the chain.) The cross sec\(i>n for nitrogen encounters is not knowfi from obi3erva. tion. if the geometric cross section is adopted , and a reaction attributed ta . . . The geometric cross seccion amounts to just ak=2 barrls. The assumption that this is a constant cross section for all energies will be referred to as tho “canst.ant~assu-mptim and will be denatod.by the subscript “k”. Calculation will also bo undertaken with the assumption that the geomtric oress section ‘k .is reached only at energies surpassing the tarrier height, BZ8.5 WeV, between .- nitrogefi nuclei. For relutive energies lower than this barrier height, a * CYOSS section proportional to the G~mow penetratiori probability is assumed. ‘Me sub6cript G will denote tnis alternative set of ass~~mptions: -. , . = (Jk = 2 barns , E >9.6Mev. . . ..  ## APPROVED FOR PUBLIC RELEASE I .’ nitrogen nuclei. E is the rel~tive energy, E =(1/2\w V2, as determinecl with . . barns. The rate at whi.zh the nuclear reactions will prod~ce energy is .- i~~energy units pm seoond per rlit.rorennacleus. N is the atomic density of zi+rogefi in air, N * 4(10j~9 nuc~eii’cm”\)O fly UT is meant an average over the &xwell distribution of the prcid~xt o!’cress sestioa anti relative velseity:

of T is written for kx tem~eratl-u-e. 1? ffis simply 2 barns at all energies, . (x) ~ =

2 4m-FOY great-enough temperatures also

At low temperatures, with T in &v, . (X) G%lo&(loj~O .

Iiesults for intermediate taparatur~s .- .

tarns.cm!seco

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Mev) were obtained

by nmerical

integration. Th9 contribution of the collisions with er,ergy greater tkn the barrier height .

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Using the above results for (~) , one obta ins the energy mwi-dction . 4. rnte per nitrogen nucleus : .. (dE/’dtjk = 0.42 ~

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wi,th tlx ‘ico~stant cross Sectim “ assumption. This is also

the high-temperature aymptot in the case of the C-amow.factor assumption, For low temperatures, the latter assumption yields.:

.

Fig. 1 exhibits the variak.ion of the production rate with temperature for the . two assumptions. . The pGCsible contributions by reactions of proton~ with nitrogen mtll now be discussed, ~’heonYy ones of these yielding enou&h energy to all’}w the product particles to surmount the %ulumb barrier are :

• -.

Tho saL’Al]abundance cf’N]”5weig!.> hgavily .%inst the second of these reaotions. . The crass section of & protxm against nitrogen at high energies oannok exceed th > barns asstumd for 1~+ N, sinse tha gwxnetrical cross section zmur is ex- … .

peeted to be about 1 barn. Xhe eometrica] cross section shoul persist down to an energy at which the protui VA”.G-I.M,:’:]is of thf”r”2&”~~~ t@:,qtiJ410e&r l *.ae

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4s the asswned nitrogen-nitrlt~en rea.~tions. .. ..

There remoins the possibility that the products of tho N-+Y rw.ctiGzs will themselves react with fresh gains. This cossillility is enhanced during product oartieles Lave not yet lost all the

m-mrgy to contrit.ute to fresh reections* %e magnitude of the eserEy release in such secondary reactiozs will be of the sama order 6s for the proton reactions discussed in the pr~cedir,g par&gra@.

As a matter of fict, one of the most prowiet of thct primry Froducts are protons, The arguments of the preceding par&graph, which iridicated that the proton remtiofis csAnnotadd significantly t,>the energy production attribuke~

to the N~N

reactions, are valid also he?e. Ore has available alsc these edeitionnl facts: the cress section of nitrogen for noutrvns and for alplti particlec (both typos cf Particlt)s are also products of, the primary reactions) have beefi measured up tc ecer~i6s

of “le- Nev. The , rosultfi b.owwidely spaced resonances which even a+. peak value are only of tho .- crder oi’an eighth of a tarn. This is much less than the two barns attributed to . %k.e primary N + X nrocass. Jn. 8 i p cross sections should not diffr much from N+ n cro;s sactions, which have .- .

been measured UD to -1.- Mev. The cxasureaents indicate resonance in ;he cross , section which even at peek value aru only of’the crder of ari eighth of a barn. .

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z,. Tiih LNERGY lLC.SEO-a:.0,*a ..

The rain mcrgy loss is duo tc Brcmsstrahlung b:{the e]ectrnns, wt,ich I has the rate:

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correction factora E being the kinetic energ~ of the electrcn. f“9rIuw eneugl-,

• (dE/dt)E = 1.7 ~ t . In Fenera), . - LC v(l+E! me’-) ~ — R

[i/e ) Ho ;Ij

(i/e) 4H\(1) (i/’0) e = T/’mc 2 and, ~(1) , HI(I) are .Hankel f[mctions of the !’jrs% ldnd, . of zero ant first order, respectively ~ho 13remsstrahlur;grate is shown in f’ig. 1, tic a !’uncti.on of the electrcn tem.pera?.ure. A distinct.toriis ma?e here krtween . put +Zheccrr~spc,nding electrori an 2 nuclear tam[)erature at the same 0.13scis”sa. . . . . . . . l 9 9** l 00 l c l *W l** l l l l** ll 00090 :0 l ll * l ll ** l,0 l* V< UNCMSSIFIEDV -”-’=: *. -  ## APPROVED80..:*.9l *.FORlO.PUBLIC: 8’*l lRELEASE9 . , # ~h!cLAS51FlEDlll ****..OOOO:: l 90.l O. . . . . # -I“Gl..**ma..: # C!a6n-= averagec over a A’axwell distribution of temperatur’~ T@. For lcv~;temper~tt~res, For higher temperatures, the relativistic .Maxwell distrikuticn must be used , giving : . C?+mw+!l . # (m) =(w)(a’wq [(L;’6\i{,, -. # e+’e ## \l) (1) ( i;ej .2E, (i;\):.1 The nuclear ant? electron temperatures which wil? co-exist will be given by the . equti.kionDf the trer.sfer

rate to the !lrcmsstrahlung rate. This yields :

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the margin of 8afcty teomnes only -2.5”

It seems des i~~t~le to ,)btain a bettor experimental

knowledge f the reaction cress section even though temperatures approaching 10 l!ev seem hardly impssible..

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v\(lure of air to be hetited. One can seek to estimate t.k,e size or this VOIZ.W ty examining the mechanism of enwgy transfer frm bomb to air. It W;ll kij sufr5-Cient, ant nl~h less diff~~uli, to discuss the oossibil ities Uf hea t,ing +,he mini. - cum volume wt,ich must be braught up to a high temperat we in order tc instire # , propagation of the reactior.* # . The heating of too smll a volume will add enormously to t he c?ralnti orI # ... # ..- # .. # ,. l O l *e 9 l O* l l l 00 l *m l l l’0 l ** l l .* l l.* meo*..*: :0 . . .l 0 . . . UNCLASSIFIED ## APPROVED FOR PUBLIC RELEASEl 0 l ** ., —. .  ## APPROVED FOR PUBLIC RELEASE:00 ll *9 lO. : l * # u~!LAJ~lFIEf’) l m.. *e lO. l l 0. l *. ll * 00 .OO :.O : 9*.l*9: ,. . .lem... I.. . .“ ti- # h .l # , # ... # .... # -. SIAfe, however, we assume thut 1 .? barns is tho efiergy..l~sscross section, i.e. , l 9 l ** l e@ l l l 00 l** l l l l*9 . . . . . l OO l ## APPROVED FOR PUBLIC RELEASElll e**ma*al **ll *: # 9*ele, l l e UI’ICLASSIF{[,  ## APPROVEDl:000.... ll **FORl*9 PUBLIC: le. . l 0RELEASE lll 0 0.0. l ** : l ,...: l*89..;W :0:900: l # @=9!a- free pth in air of retain a substanti~l “~rt ,>f the ewr~y prodaced. At lenst such u vclume must be heated ifiordar that the . theraonuc)ear reac\)ian ho su.s+id. An air sphere i’ $7 meters rfi,iius C:3n&AirIt4 about L(lO)X1 nUel Pj9 anli . ,y ‘7

3(lo)-

91eo trons. For it to ke heated to a nuclear (Te= C).~?KISr)requires about. ‘).5(1G;

temperature Tn = 10 Xev \W h!ev of energy. A ‘*isaion bomb rodacae abou.. ,+ ‘{10)26 Mm per kg of active tmaterial, when working with 100Y. efficieficy. If also all the produced energy goes to 4 nrd’ueetile air temper%tlre, theu 1.5(IO)J Kg of material would have to be huri!ed up in order to obtaiz the dngero:ls 10 !!kvtemperature. nctllelly at most 1 %CI’ the bob energy my be vila~le tO prudwe the temperature; the rest

A s:ipcr-bornb, buynin~ deuteriwn, may be mnre dangerous than a fission . bomi, becauae its el!e~~!:is not put !3Cm3.

into

radiation as it is within the fission. The deu+.eri”.unnuclei b~ve tcc small cmrte to CSUSe efficient ra.iiation.

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Severs] further effects exist which may nnke less of the anery l“e?eksed by bombs available for carryin on a reaction

in the air. I%erw may be .

\(rit.h till-lpalicy 01’ making the most ,:angsro~s assumption wherever any uncert.ain\)y e,tiEts, then the effeots in question must bs left out P

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wsve is a simplo plane pertar~ btitiar,. Ihere renains the distant ;r~L&bility that some other less simple mode of’burning may maintain itself in the atmospk.ere, hen if the reuction is stopped within a sphere of a few hundred meters raaius, the resultant

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contamination of the atmosphere might “neoomecatastrrprlic on a world-wide scale. One f!!y ccncl’;de that the arguments of this paper mke it unreason- . able to expect that the N Y N reaction could propagate. An unlimited propaga- .

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