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TRANSCRIPT
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.t.% ~r”No.“35
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A5STRAC T.
.
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.e . 9** . ●.0 ● *...00
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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 d~sq~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]uantaby Compt.un scattering will pro-
further safety f~ctor and will make u chair.reaction in air impossible.
;
9.
UMMSSIFIEI)
..
● ● ● ● ☛☛● .*e● ● ●O. ●*: .=
● 06 . #● ● .4
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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 thermo-
nuole8r re~~tiorAmy 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 pr~duats of
e~~grg~c 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 radia-
tlon, 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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tiNtiASSIFIEn,Oe ..0 ..
● e ● .9* ● O..0. ..ao
● ~o:: .**8 O.*
. .ea .**●** 0 ● ● 8* .*
* ● ● @*
-4- ● e . . . ● .e ..: .:~ ●O..0. : .0 : •~● -*:ew● m .0
● *● :*:..
. . so:● O.
,
1:
.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 raD~cl than the transfer to
electrons, all th~ eri9rgygoes first to esta”91i6hing a naolear temp2rnt’ure..—
.
+ trsnsl’ar ra$e to electroas and radiation rate by the electrons.. This tempera-
zure rzy be considerably lcw;er ‘Aan the nuolesr temperature and thus increase
.%.
Tpe ~recg.tt.~gc~nsidsrations will yie?d an evaluation of’the mrgin
0 !7tiai’ety as a fuastion of the temperature o;’the atmosphere. ~ fir~l section
will be devoted to the behavior of a hct air mass OF finite volume and “tothe
besting whi$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 cf
p i rti Ji’ nitrogen’ nucleic Other notable constituents of the citm’osphere, o’xygcn ,- ~
●
✌
✎
t>ar”~ar:and rare gas nuclei~ are much more stable t’hannitro~en, yielding
09inprSt~Vf31y little erwrgy. There i~ perhaps one other nucleus that shm~lc!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:
.
.
.● ☛ ● 0.
:: :
::● O
● 0 ..:
● ☛✎ ✎
✚✚● ● 9●
● ** ..:
● *.● .O.
●:● 0:● .
99* .● O
:.
●°0 : :● ● -.
●
● ::9* .
8*. ;●0: ● .● m
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1 .“
#a In parenthesis foil owing the r~actians are given the heights of’the Ooulomb
barriers of the prod~.letoarticles. In a~cor~ 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 emissi~n. (The .x~ture 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$i>n for nitrogen encounters is not knowfifrom obi3erva.
tion. if the geometric cross section is adopted , and a reaction attributed ta
The geometric cross seccion amounts to just ak=2 barrls. The assumption that
this is a constant cross section for all energies will be referred to as tho
“canst.ant~assu-mptim and will be denatod.by the subscript “k”. Calculation will
also bo undertaken with the assumption that the geomtric oress section
.is reached only at energies surpassing the tarrier height, BZ8.5 WeV,
nitrogefi nuclei. For relutive energies lower than this barrier height,
*CYOSS section proportional to the G~mow penetratiori probability is assumed.
‘Me sub6cript G will denote tnis alternative set of ass~~mptions:
-.,
.
.
.
‘kbetween
a
= (Jk = 2 barns , E >9.6Mev.
..
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.-
.
nitrogen nuclei. E is the rel~tive energy, E =(1/2\w V2, as determinecl with
barns.
The rate at whi.zh the nuclear reactions will prod~ce energy is
i~~energy units pm seoond per rlit.rorennacleus. N is the atomic density of
zi+rogefi in air, N * 4(10j~9 nuc~eii’cm”$O flyUT is meant an average over
the &xwell distribution of the prcid~xt o!’cress sestioa antirelative velseity:
1? ffis simply 2of T is written for kx tem~eratl-u-e.
(x) ~ = 2 4m- tarns.cm!seco
FOY great-enough temperatures also
barns at all energies,
At low temperatures, with T in &v,.
(X) G%lo&(loj~Oe.~94/T1/3
barns.om/sec (T$O.Z Mev)
Iiesults for intermediate taparatur~s 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 =
.
.
.
wi,th tlx ‘ico~stantcross
a~ymptot~ in the case of
0.42 ~ (lfcYJ/t.L8fK)Tin M,v.
Sectim “ assumption. This is also the high-temperature
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, ~’he onYy 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
● *.ae :.
;“:~f;~:*UNCLASSIFIED:.:.:●:: ●0.9.
●8 . :0:9*.9 ● m. . .,,
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.UNCLASSIFIED
....
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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
prowi~e~t of thct primry Froducts are protons, The arguments of the preceding
par&graph, which iridicated that the proton
t,>the energy production attribuke~ to the
remtiofis csAnnotadd significantly
N~N reactions, are valid also he?e.
Ore has available alsc these edeitionnl facts:
noutrvns and for alplti particlec (both typos cf
the primary reactions) have beefimeasured up tc
the cress section of nitrogen for
Particlt)s are also products of,
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 diff~r much from N+ n cro;s sactions, which havebeen measured UD to -1.- Mev. The cxasureaents indicate resonance in ;he crosssection which even at peek value aru only of’the crder of ari eighth of a barn.
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●☛✎✎☛✎:00 ●
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● *●:9● .e● **... ..●
● . :0 ●:..::●::: a● ● 9O●
: ::●-a:.0,*a,. TiihLNERGY LC.SEOz
The rain mcrgy loss is duo tc Brcmsstrahlung b:{the e]ectrnns, wt,ichI
has the rate:
correction factora E being the kinetic energ~ of the electrcn. f“9rIuw eneugl-,
- (dE/dt)E = 1.7 ~
In Fenera),
-LC
v(l+E! me’-) ~ —R
e = T/’mc 2 and, ~(1) ,
[i/e ) Ho;Ij
(i/e) 4H$1) (i/’0)
HI(I) are .Hankel f[mctions of the !’jrs%ldnd,
of zero ant first order, respectively ~ho 13remsstrahlur;grate is shown in f’ig.1,
tic a !’uncti.on of the electrcn tem.pera?.ure. A distinct.toriis ma?e here krtween
put +Zheccrr~spc,nding electrori an 2 nuclear tam[)erature at the same 0.13scis”sa.
● 9 9** ● 00 ● c● *W ●** ● ● ● ●**● 90 ●● 000 :0● ● ● ●,0 ●
● * ● ** * V< UNCMSSIFIEDV -”-’=:*. -
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,.
.
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~h!cLAS51FlED●*.:*.9 ●O.:8’*●
●980..● *. ●: ●O.● **.OOOO:90.●* a..:-I“G●..**m C!a6n-=
averagec over a A’axwelldistribution of temperatur’~ T@. For lcv~;temper~tt~res,
For higher temperatures, the relativistic .Maxwell distrikuticn must be used , giving :.
. (m) =(w)(a’wqC?+mw+!l e+’e
[\l)
(L;’6\i{,,(1)
( i;ej .2E, 1(i;$:.
-.The nuclear ant? electron temperatures which wil? co-exist
.
equti.kionDf the trer.sfer rate to the !lrcmsstrahlung rate.
will be given by the
This yields :
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%
..
k...
,......-...,
0s ‘. )2*otkler hULd the margin
,)btain a bettor experimental
temperatures approaching 10
of 8afcty teomnes only -2.5” It seems desi~~t~leto
knowledge ~f the reaction cress section even though
l!ev seem hardly imp~ssible..
Thcltemperate to w?,ich air can be heatie<by a bcml?tegenc?~ on tho
v$lure of air to be hetited. One can seek to estimate t.k,e size or this VOIZ.W ty
examining the mechanism of enwgy transfer frm bomb to air. It W;ll kijsufr5-
Cient, ant nl~h less diff~~uli, to discuss the oossibil ities Uf hea t,ing +,he mini. -
cum volume wt,ich must be braught up to a high temperat we in order
propagation of the reactior.*
The heating of too smll a volume will add enormously
tc instire
to the c?ralnti orI
● O ● *e 9 ● O* ● ●
● 00 ● *m ● ● ●’0● ** ● ● .* ●
● meo :0. . . . . . UNCLASSIFIED● 0
.* *..*:● 0 ● **
., —. .
9
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● *9
u~!LAJ~lFIEf’) :00 ● ●O. : ●O. ●●*
● m.. *e● 0. ● *.● 00 .OO :.O : 9*.● * ● *9:
●em.... .
SIAfe,however, we assume thut 1.? barns is tho efiergy..l~sscross section, i.e.,
● 9 ● ** ● e@ ● ●
● 00 ●** ● ● ● ●*9. . . . . ● OO ●
● ma*a 9*e●*: ●e, ● UI’ICLASSIF{[,● **●e●**● ●e
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● ☛☛:00 ● ●*9 : ●e. . ● 0● 0....● 0. :0: ●● 0.● 0
● ** : ,...: ;W●
900:●*89..
@=9!a-
,>f the ewr~y prodaced. At lenst such u vclume must be
free pth in air of
retain a substanti~l “~rt
heated ifiordar that the
theraonuc)ear reac$ian ho su.s+~i~d.
An air sphere ~i’ $7 meters rfi,iius C:3n&AirIt4 about L(lO)X1 nUel Pj9 anli
,y~3(lo)- 91eotrons. For it to ke heated to a nuclear temperature Tn = 10 Xev
(Te=\W
C).~?KISr)requires about. ‘).5(1G; h!evof energy.
+ ‘{10)26 Mm per kg of active tmaterial,A ‘*isaionbomb ~rodacae abou.. ,
when working with 100Y. efficieficy. If also all the produced energy goes to
4nr~d’ueetile air temper%t~lre, theu 1.5(IO)J Kg of material would have to be
huri!ed up in order to obtaiz the d~ngero:ls 10 !!kvtemperature. nctllelly at most
1 %CI’ the bo~b energy m~y be ~v~ila~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 into radiation as it is within the fission.
!3Cm3. The deu+.eri”.unnuclei b~ve tcc small cmrte to CSUSe efficient ra.iiation.
,
.,.
. .
.
.
● b ● 9*● . . ●*9● me● bem :. ● ● 9**● * ● **
.9* ● 00 ● 0
y %.7+;+,● 9
● 00 :00 ● * e
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Tk.ea~pareut]y dangerous sltuaticn discu~sed in the precs~ing para-.
Severs] further effects exist which may nnke less of the aner~y
l“e?eksedby 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 outP
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APPROVED FOR PUBLIC RELEASE
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am ● ** ● “● m.● ...:*: ●*. ●
● 9
● **::: .**:e: ● 0.● m
● ● ● s.:● ** . .
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e: :*.::gl+ ●
●:* . ● ::● OO :00 ● *
● ✍✍
● ✚●
inverse Comptofi
as soon as this
6iiiia-
effect acts to quench nuclear disintegration of
reaction has ex$ondsl over a racliusof a few
If a relatively still air mass Ls heated, t!;eradiation emitted will
simply ecwzpe. nut if a grtiter sphe~e or air is hsted, the quajl~a of’
e!ectrorr~~gneticradiation are likely to nuLkeGa.mptonCO1 Ilsloris with tha elec-
trons Defore leaving ttiesphere of hot air. In such collisions the quantu will,
on the avera~:e, gain energy from the hct electror,s. The end effect is that
more energy is going into radiation and more omsrgy will become unavailable to
t!lethermor~ticloarre.a~tiona It cafibe shown% tnat the ratio of the Coinptonlosses
to the bremsstrahlung losses for an electron at temperature Te
in air is
108s
since
.● ● e* ● ● ** ● *9 9*
.——-—.-----P- ---- 1● eae:e
● .0 ::
* Uee IA4J11 ● :0 :060● 0 ● om ● 9* 99* 8*O ● 9
● ☛ ● ☛☛ ● ☛☛ ● ●
● O9 :Yl ● ● ● ●*9● OO ● ● 9* ●
● mmee* ● *9● * ● ●m. ● ● *9● e ● om ● O ● *
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APPROVED FOR PUBLIC RELEASE
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● 9 ● . .● .O ●°0 :● **9.● me● a. :y{.e●. ...
● 0●m* .● m.
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th!? Cornptcm effect.
● ☛ ● ☛☛ ● 00 b..
‘rilw,i;”sj:”:”+i● 9*O : ●:.
0 **000 . .
by Lhe reacti:l:.
I
%0 metersu After sono time this shol~ oan be traiteri as a ~lane detonationi
I
-1
become K“ +.iK5&the sqc~re of the meen free path ?,. For t,k.eJifi%sicri velocity
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APPROVED FOR PUBLIC RELEASE
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● m ● *. 9** 99* ● om ● 9● .* 8..
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With A s L& meters one see$e~.h.~:.~he %u~fic~.~g by Conpton effect mist be.● ●99 ● ●:; ●** ●*
eo~.e important as soon SS the ietorxiticn ‘wave has-tr~velleci rvIOb me%ers.
Shcb this len@h is quite mall com~ared tc the depth of the atmosphere .
there ia
&nd thus.
Wile the above wmccrs may be somewhat in error, th~ quenchir~ must
eventfully take place as Icng as the aetorition 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 e~rth-shock gnd the radioactive contamination of
the atmosphere might “neoomecatastrrprlic on a world-wide scale.
One f!!yccncl’;dethat the arguments of this paper mke it unreason-
able to expect that the N Y N reaction could propagate. An unlimited propaga-
tion is even ?*s6 likely. However, the complexity of the argument and the
absence of-satisfactory experimental foundations makes further work on the
sub$eot hig,hljrcesj.rabt?.
● ● *m b ●:e ● 00 ● e● -00 ● ● O
● O**,● ● ● * :1 :0 ::
● bo ● 0● * ● O* ● a- ● ** ● 9* ● *
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APPROVED FOR PUBLIC RELEASE
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b., .,’- .,..,- .,.
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