RATTAN MONA L LIS BG IG LA ELI EL SSE MN IL TA IS MN SL SOIL ISTE ITE TPO

Cf)

|: 0h ‘e

no ‘ " fay,
<p Ga grown
baled ue
hes lag ss a lode

bids hs hi , :
w my Lach or) ‘ food

HO .
te» ry f Wu CO ™, / /
a Ge Mi if
o. are vi (ey © y at
) ; (5 ae) bu f ony anne NINN DDS Praga, “2

" fe 3 @& Ne

aa ¥ aos oo when i: on f ing e.

pin ae a Tu Bea ’ * Rt monennelg ae a a

om ‘ \ ~
er ash P) ae @ <Uifercosvers #7 AC mn
le a to ae Hi t Woy, coma)
Y ar Sm Be Tork as, (pe ng angi
me | J “ mmm >. poe

Len or (A na ee)

f ae]

tH tence frsne honed
By wt ggm . : ao

oy | a ;
ee. Se ae

¥e i ; ij L be i
ef f Ov) fan (hea by te iis niet ah wer ha
whe a4 ee hdd ae

Perens . piel
a Gh ‘
i Peed be ot | “ Sant 7)
~

— «62
fad ae
= &§

bit a6

MOP SSM yh OI EA NEY GLY PO NU CE AR OL PORT PINK ARAL Te ORE PRES TTT IE, LPN OT AL FD

HANDBOOK OF
NUCLEAR WEAPON EFFECTS

Calculational Tools Abstracted From EM-1

Ist Edition
September 1996

A = T oF e " * ; SIKCL ()
VEU BF TAFE) ON Crassien ; pel SeeRET!)
WARNING: This documer
Act (Title 22, U.S1C A e ece
to severe crimipal penalties. Distributfen aithorized to U.S. Goveésnment agencies and their Contractors

(Critical TecHnology 06. ecient shall be referred! to Director,
Defense Special WeaponsAgency76801 Teléscaph Road, Alexafidria, V D-3398

export is registered by-tife Arms Export Control

sqgntains technical data

iii
PREFACE

At the time of publication of the Defense Special Weapons Agency’s (DSWA) eighth edition of
Effects Manual One* (EM-1), which was completed in 1993, it was recognized that its easy use would
be limited by both its length and its classification. This work, EM-1 Technical Handbook, addresses
those limitations. It is designed for the engineer who has a working knowledge of nuclear weapon
effects and, thus, does not need the extensive tutorial sections of the basic EM-/. Itincludes algorithms,
graphs, and tables required to make approximate quantitative estimates of nuclear weapon effects,
along with a brief description of their use.

Of the twenty-two volumes of EM-1, five were judged inappropriate for this handbook, either as
a result of their extensive classified database or because they were almost entirely qualitative and
tutorial. In addition, Volume 1, containing synopses of the other volumes, has been omitted. The
chapter numbering in this handbook maintains the nomenclature of the main EM-], with consequent
gaps for the omitted volumes. Most of the Sample Problems from EM-1, judged helpful in
understanding the application of the algorithms, have been included but in a more compressed form.
Other sacrifices, primarily in type font and figure size, have been made to allow the handbook to be
printed in a single volume. Additionally, to save space, all the primary source references in EM-1/, both
for specific data used as well as extensive bibliographies, have been deleted in this handbook. Readers
requiring more detailed information are referred to the original EM-1, for which all except Volumes
1, 3, and 13 are classified.

The actual publication date of each EM-J volume is indicated below. Because of the lengthy
writing, review, and publication process, the actual age of the technology provided is approximately
five years before this date. For the current status of the contents of any EM-1 chapter, write to the
Weapons Effects Division, Defense Special Weapons Agency, 6801 Telegraph Road, Alexandria, VA
22310-3398. Since the Editor of this handbook has simply abstracted the material from the basic multi-
volume series, with some liberties taken in compressing text, the following authors of the source
volumes of EM-1 deserve full credit:

Vol. 2: D.C. Sachs, E. Martin (Kaman Sciences); L. Kennedy, G. Schneyer, J. Barthel, T. Pierce,
C. Needham (Maxwell Laboratories); and J. Keefer, N. Ethridge; (1985).

Vol. 3: C.KB. Lee, L.P. Mosteller, and T.A. Mazzola (Logicon RDA); E.J. Rinehart, (DSWA),
A.V. Cooper, and S.H. Schuster (California Research and Technology Corp.); (1992).

Vol. 4: J.E. Cockayne and D.P. Bacon (SAIC); T.A. Mazzola (Logicon RDA); M. Rosenblatt
(The Titan Corporation), and J.A. Northrop, Editor (S-Cubed); (1992).

Vol. 5: R.M. Barash, J.A. Goertner, and G.A. Young (Naval Surface Warfare Center);
C.B.K. Lee (Logicon RDA); B.B. LeMehaute (University of Miami); and J.P. Moulton
(Kaman Sciences); (1991).

Wol. 6: JR. Keith and D.C. Sachs (Kaman Sciences); (1985).

Vol. 7: D. Steel, J.R. Keith, H.D. Bos, and EJ. Plute, Jr., (Kaman Sciences); H.C. Lindberg
(APTEK, Inc.); (1987, 1993).

Vol. 8: D.C. Kaul, F.Dolatshahi, W.A. Woolson, and W.Scott (SAIC); H.G. Norment (ASI);
(1990).

Vol. 9: W. Knapp and B. Gambill (Kaman Sciences); (1986).

Vol. 10: E. Quinn (Technical Integrator), J. Schlegel and W. Kehrer (Logicon RDA), C. Fore
(Editor) and T. Stringer (Kaman Sciences), R. Schaefer and W. Radasky (Metatech),
G. Morgan (TRW), and K. Casey and B. Stewart (JAYCOR); (1992).

"Requests for copies of the original 22 volume Effects Manual One (EM-1) should be addressed to the Defense Special Weapons
Agency, 6801 Telegraph Road, Alexandria, Virginia 22310-3398.

iv

Vol. 11: W.A. Alfonte and E.A. Wolicki (Kaman Tempo), J.R. Srour (Northrop Corp.), and
J.P. Raymond (Mission Research Corp.); (1988).

Vol. 14: M.K. Drake and W.A. Woolson (SAIC); (1993).

Vol. 15: D. Bergosian (Karagozian & Case), C.C. Deel (SAIC), and W.J. Hall
(H&H Consultants); (1993).

Vol. 16: R.D. Small (Pacific-Sierra Research Corp.); (1992).

Vol. 18: L.A. Twisdale, Jr., and R.A. Frank (Applied Research Associates), J.F. Polk
(U.S. Army Ballistic Research Laboratory); (1993).

Vol. 21: J. Eamon, J. Keith, R. Keefe, R. Ponzini, J. Betz, J.L. Forkois, J.L. Harper, J. Hess,
T. Stringer, P. Book, D. McLemore, R. Ruetenik, L. Mente, and G. Zarthaian
(Kaman Sciences), W. Lee (HTI), R. Halprin and B. Strauss (MDAC), and
H. Lindberg (APTEK); (1993).

Vol. 22: M. Bell, D. Breuner, P. Coakley, B. Stewart, M. Treadway, J. Sperling, E. Wenaas, and
A. Wood (JAYCOR); (1990).

The editor wishes to express his thanks to Dr. C. Stuart Kelley of the Defense Special
Weapons Agency for his consistent and enthusiastic support for this project, without which this
handbook could not have been completed. The editor is also indebted to the technical editing
(Chris Brahmstedt), graphics (Cindy Grooms, Donna LaFontain, and Will Larsen), and publication
(Dianne McCune) staff at DASIAC (the Information Analysis Center supporting DSWA) for their
long and patient labor in preparing this handbook for printing.

John A. Northrop

Editor

Maxwell Technologies, Inc.
September 1996

Preface. ......

Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 14
Chapter 15
Chapter 16
Chapter 18
Chapter 21
Chapter 22

TABLE OF CONTENTS
isis loca ccs base rca tecicdaesomedae peak Sac Nac tics b aah iodo aaa lil
FAI scatter bcinciodo ent svicnsncass pasion toga oncsn Sansa oa alba adadinoenbelngrcamamaes 1
I PU OD scien ck iaisessi pha nicnscciasina scorn nmewiceh wossniaeck enna basmati AE 73
eg eee a | oe ee a eee MEE CT I cen 163
POE ES in cssceno i eo reese ahiic sitcom 173
“TYRES TIS RRO: FENN a rs ciivige iv ne sad vnnr neste fT entmrnginsinnn tgnnersvnsnvinesessenads 223
be galery tien opie matint pennesing pets Sere ane ene 5 oc RADE at Sen oon TN RE 261
Pie TE FI iii igre sas ics cc gcse nv avnnbca tp maeaiendad eipeenrtaoos 325
CTIA OTE WOVE PCR sii cis eciesscsicesestcscre taliteentsasennrentenaconoeniian 401
PRC PUREE CI ovis ecscinnsncsvesccevensnsancatecteseasincentesneners nitiiameltide 437
‘Transient Radiation Effects G9 HRGCtrOmics oi... iciecesccgecscceecnonsecess sonnesossennssneosensnnss 483
Be GS I Ess dan sccdicennrsSastben caekiincoslea Gels ni pinay ote dew asbsaineeknicibaoaesseaoaea 495
I TiS PAREN isco cas occ wisn ionic basecncirioe senna onetonescinen attic coer Rg 509
EE eC SOO FOCI i Fie essa eo sienna or poe london taeabbansirearnenedaepeaeaettoensns 569
PSEC, EPA GS So FCC SGT ihe ccnrvionencincnss ister sanisntpansspianisisonntnnnt tei’ 611
EIN TIS TUES as cla sccinissuskiics dvs nthe aidan ations eta ickipinasasiadiptmansane eae 629

LPEEERIED GO SG Ta UCI ican wn din css Civncnniincs caventaniannnesivseinindtntie snes teneegtvinvcuavcarsriel 671

X-RAY RADIATION 7-13

10%

FRONT-SURFACE FRONT-SURFACE :

DEPOSITION DEPOSITION

Peon ene BLACKBODY
TEMPERATURE

re ee ee a
.

or ae 401
BLACKBODY

obo TEMPERATURE a 10

ENERGY DEPOSITED (caV/g per calicm?)

a

£

a4

@

rs)

$

= 0

§ (keV) 10

Q 5

= 1099 OR BI ee 1071

7)

4 2
-1 Ae ae OE eS a, ee, rr! oe ert aes 10°

Lu

wo

>

Oo -3

ioe 10
PE cls cn cot. nda rauneinale descesmegeibamacets

Ww 10

ud ill : : : = : ae :

bid 0 0.004 0.008 0.012 0.016 0.020

=_
°
Ww

0.04

0. 02 0. 06 0. 08
DISTANCE INTO TARGET (cm)
\ \ igure 7.8. ANISN Deposition Profile for Alu-

minum at Blackbody Temperatures of 1, 5, and
} 10 keV (Incident Fluence = 1 cal/cm7).

0.10

Oo

DISTANCE INTO TARGET (cm)

Figure 7.9. ANISN Deposition Profile for Iron
at Blackbody Temperatures of 1, 5, and 10 keV
(Incident Fluence = 1 cal/cm?).

Material response occurs on a time scale com- 103
parable to the wall thickness, while structural
response occurs on a time scale comparable to
structural dimensions such as body diameter.
Nosetips and antenna windows have lateral di-
mensions comparable to thickness, so must be
treated by three-dimensional shock codes that
do not distinguish between shock and structural
response.

102 | 3 +--+ BLACKBODY
: : TEMPERATURE

7.2.2.1 Stress Wave Generation and Propaga-

ENERGY DEPOSITED (cal/g per cal/cm2)
oe

tion. The dominant modes of material shock
104
response are often those of shock generation and
reverberation through the thickness of a struc- 105 ;
0 0.001 0.002 0.003 0.004 0.005 0.006

tural wall, with negligible lateral effect. The fol-
lowing discussion develops simple one-
dimensional equations of motion and wave the-
ory.

DISTANCE INTO TARGET (cm)

Figure 7.10. ANISN Deposition Profile for Tan-
talum at Blackbody Temperatures of 1, 5, and 10

x 2
Cold x rays (blackbody photon energies less than *°¥ (Incident Fluence = 1 cal/cm’).

about 2 keV) have small absorption depths, de-

positing most of their energy near the front surface of a material. Hot x rays (blackbody energies
greater than about 10 keV) have much greater absorption depths, and significant absorption
occurs throughout the thickness of a material. Representative deposition profiles in a two-layered
wall, consisting of an organic composite heatshield and a metal base structure, are shown in
Figure 7.11. These doses are normalized to an incident fluence of 1 cal/cm*. The materials and
thicknesses are typical of those used for a reentry vehicle aeroshell.

Immediately after energy deposition, the pressure P(t) in the material is given by
P(t) = [p,Ep(x), (7.45) |

where I is the Griineisen ratio and is a property of the material, p, is the initial material density,
and Ep(x) is the deposited energy at depth x into the material. [ may be estimated from thermal
expansion data using the following relation:

lr =Ca/(p,c,} (7.46)

279

7-14 X-RAY RADIATION

SUB:
STRUCTURE:

HEATSHIELD —————_»>

101 BLACKBODY PEAK
. : TEMPERATURE NORMALIZED DOSE
(keV) (calV/g per calcm2)

NORMALIZED DOSE (cal/g per cal/cm?)

10°3
0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

DEPTH (cm)
Figure 7.11. X-Ray Energy Deposition in a Typical Heatsheld and Substructure for

Blackbody Temperatures From Cold to Hot (1 to 10 keV) (Doses Normalized to an

Incident Fluence of 1 cal/cm7?).

where C is the bulk modulus at low pressures, @ is the volumetric coefficient of thermal expan-
sion, and Cp is the specific heat at constant pressure. The value for I from Equation 7.46 should
be relied upon only if all material property values are for the same density, pressure, and temper-
ature. For many materials, the value of I lies between 1.0 and 2.0, with metals tending to have
the higher values. La SS a fo Se eee
Es es yetieos

7.2.2.1.1 Deposition-Time Stress Relief. These discussions have all treated energy deposition
as near-instantaneous, although it actually occurs over a finite time, which can result in lower
peak stresses. The significance of the deposition timing depends on whether 2ct << 6 or 2ct >>
6, where c is the wave speed, T is the full width at half maximum (FWHM) of the deposition
time, and 6 is the effective depth of energy deposition from the free surface. For an exponential
deposition, 6 is the e-folding depth (i.e., the depth at which the energy deposition is 1/e = 0.37 of
the value at the material surface), whereas for a triangular deposition (linear drop from the
surface) 6 is two-thirds the ultimate depth of deposition. The resulting peak axial stresses 6, for
linear, elastic response are given by

o,(max)=Tp = [1 - exp{—2ct/ 5} for compressive response, and (7.47)
; D,6 ,
6, (min) =-Ip5o [1-exp{—ct/5}]x|1-exp{-2x/5}| (7.48)

for tensile response, where I" is the Griineisen ratio [Equation 7.46], p is the density, D, is the
peak surface energy deposition, and x is the depth into the material from the incident surface.

AON

X-RAY RADIATION 7-15

When 2ct << 6, the result is 6, (max) + I'pD,, which is the previously discussed condition of
“instantaneous” deposition. However, if 2ct >> 6,

-

o, (max) > 'pD,8/ (2ct) (7.49)

so the peak stress drops inversely with deposition time. The peak compressive stress occurs at
t = tT (end of deposition) and at the depth x = ct, whereas the peak tension occurs after deposition
and asymptotically reaches a maximum with increasing depth from the free surface.

The stress history at a small depth x from the surface, with x << 6, is given by

(7.50)

o, (max) =-o, (min) = Tp

C
7.2.2.1.2 Stress Wave Attenuation. The basic mechanism of stress wave attenuation is the
reduction of the compressive stress at the peak of a shock wave by rarefactions (tensile stress
waves) from a free or low-impedance surface. That is, as a stress wave propagates into a material,
rarefactions from this surface continually overtake the stress peak and decrease its magnitude.
This is accompanied by an increase in pulse duration and, hence, wavelength to conserve mo-
mentum within the wave. Wave energy is given up to heat in the process; kinetic energy varies as
the square of the particle velocity and pressure. As the pressure drops, the wave energy per unit
distance decreases faster than the increase in wavelength. This energy loss can also be viewed as
conventional hysteresis in a pressure-volume plot of the loading and unloading paths. A loading-
unloading path in a porous material results in a large hysteresis loop. The resulting energy loss
gives very rapid stress attenuation in porous materials.

Figure 7.12 is an example of shock attenuation versus distance in a representative heatshield
material, tape-wound silica phenolic. The attenuation shown is caused by its porosity as well as
the increase in wave velocity with pressure. Attenuation is very rapid at higher pressures and
fairly small at pressures of about 10 kbars and lower. At still higher pressures of about 200 kbars
produced by cold x rays, the rate of attenuation is even more rapid.

7.2.2.1.33 Shock Wave Reflection From a Free Surface. Damage is generally the result of
shock wave reflection from free or low-impedance surfaces. Damage can be caused by the high
compressive stresses as they propagate through the target wall, but this damage is generally
secondary compared with damage from later tensile stresses produced by reflection from a free

surface. By the time a stress wave from cold or 100
warm x rays reaches the rear free surface of a 90
target wall, it generally has a triangular-shaped 80
wave front because of the shock attenuation mech- 70
anisms just discussed. _. 60}
2
Transmission and reflection of an elastic trian- § 5
gular wave from a free surface is illustrated in w 7
Figure 7.13. This process is conveniently visual- 5
ized as the superposition of two waves: (1l)a ®@

t 30
transmitted wave that continues as a ghost wave a
(short dashes) beyond the free surface, and(2)a %
reflected wave with an incoming ghost compo- 4 =

nent beyond the free surface. The reflected wave
is tensile and has a phase complementary to the
transmitted wave relative to the free surface such
that its magnitude at the free surface is equal
and opposite to the incoming wave, in order to
meet the stress-free boundary condition. In Fig- be 0.1 0.2 0.3 0.4
ure 7.13(a), both waves are drawn as positive so

that this equality of stress and complementary
phase are apparent. Figure 7.12. Shock Attenuation in Tape-Wound

Silica Phenolic for a 10-ktap Pulse.

DISTANCE INTO SAMPLE (inches)

281

7-16 , | X-RAY RADIATION

The total stress in the material is the sum of the
incident and reflected waves, or the incident wave
minus the reflected wave in the construction.
Thus, proceeding from left to right in the total
stress plot, the stress is equal to the incident
stress until the reflected shock arrives. Then the

stress drops by the magnitude of the shock jump, T ie p |
resulting in tension. The magnitude of the ten- Ne |

sion is the excess of the reflected tension above Pepe Pies: >
the incident compression. Until the reflected jump y

reaches the tail of the incoming wave, the slope
of the stress-distance plot of total tension is twice
that of the incident shock wave. Thus, tensile
damage from the stress waves tends to be more
concentrated near the rear surface than might
first be imagined from the length of the incom-
ing compressive wave. If no damage occurs as
the reflected wave continues beyond the tail of (a) Incident and Reflected Waves (b) Total Stress
the incoming wave, the total stress assumes the
shallower slope of the incoming wave, as seen
in the last of the three sketches in Figure 7.13(b).

7.2.2.2 Stress Wave Calculational Methods.

Figure 7.13. Shock Transmission and Reflection
at a Free Interface.

7.2.2.2.1 Simple Analytical Methods. The application of simple analytical methods to stress
wave response is extremely limited. The nature of the problem, when considering shock attenua-
tion and the interaction between the trailing tensile rarefaction wave and the reflected rarefaction
wave from the rear surface, nearly always requires a hydrocode analysis. If a structure wall
consists of several layers of materials, such as a heatshield, bond, and substrate, the problem
becomes even more complex and dictates the use of a hydrocode to determine the stress wave
response. Nevertheless, the manual method presented in the following paragraphs may be used to
simply bound the problem for a thin wall composed of a single material.

From Equation 7.45, the maximum compressive stress 6, in the material is

Ox (max compressive) — PpEp(x,), (7.5 1)
where

[’ = the Griineisen ratio [Equation 7.46]

e) = the material density,

Ep = the deposited energy at depth x,

X; = Ct=material wave speed times deposition time.

If no shock wave attenuation occurs, the maximum tensile stress will occur where the trailing
tensile rarefaction wave from the front surface intersects the reflected rarefaction wave from the
rear surface. The maximum tensile stress is then

O(max tension) =2 TpEp(x;). | (7.52)

If this stress exceeds the material’s yield strength, yielding may occur. If it exceeds the material’s
ultimate tensile strength, spall may occur.

Equation 7.52 will give conservatively high results for the single-material wall. If the wall is very
thin (about 2ct), the results will be quite accurate. As the wall thickness increases, Equation 7.52
will overpredict the maximum tensile stress by an increasing amount.

Equation 7.52 is now extended, very conservatively, to include maximum tensile stress for a
structural wall consisting of several material layers as follows:

O max tension = 2{Ep(c,t) Py Ty + X (Evo ), Pi Tl} : (7.53)

IRI

X-RAY RADIATION
10°

OTWR SILICA PHENOLIC
~ — —- — ASBESTOS PHENOLIC

105
@
a
§
lJ
”
pe
=)
a
=
104
8
6f
4
2
103
10 e 4 6 8193 104
FLUENCE (cal/cm?) -

Figure 7.15. Impulse Intensity Versus Fluence
in Typical Heatshield Materials for Cold, Warm,
and Hot Blackbody X-Ray Spectra.

material (Figures 7.16 and 7.17). The energy dep-
osition is then in the form:

E(z) = Kz", (7.89)

where the negative sign reflects the negative slope
of this line; i.e., n is the absolute value of the
slope, and K is an open parameter obtained by
fitting Equation 7.89 to the log-log energy depo-
sition profile.

I=Co!", (7.90)

where C is an open parameter obtained by fitting
Equation 7.90 to measured or calculated impulse
values. The important assumptions in Equation
7.90 are that impulse is produced by processes
that do not depend on rates (for example, viscosi-
ty is unimportant) or on the microdimensions of
the material (such as fiber size in composite ma-
terials). These same assumptions are also made
in most of the standard hydrocodes and in the
semianalytical impulse formulas.

Impulse is:

Substituting Equation 7.89 into Equations 7.88
and 7.87 and integrating gives the following for-

mula for impulse:
2 1/2
1+I1n Fes eo
| ee |

(7.91)

=(2-n)
1=1.6971 aay

Z’E,,
2

289

="
°o
oh

5

BLACKBODY |
TEMPERATURE
(keV)

-_
i=)
(=)

anath
bs
=

.
Terrrrrrrerr rere re Seer eee ee ee

ENERGY DEPOSITION (cal/g)/(cal/cem?)

ened,
°
hOON

. *
Peewee ee ee rece r sense esersesareserersesesnseseseserescsssseressssees

2

1073

4073 2 4 684 0-2 10°!

DEPTH (cm)

109

Figure 7.16. Normalized Energy Deposition
Curves in TWCP for Several Blackbody Tem-
peratures. :

10°

sere cc ese eee eee ee eee eeees SESE SESE SHO HESEHH SMES SSH E HEHEHE ESO EE EEE

101 Ee: ee eee ore 3 i ae ae Bees
5 ese a :

EMPERATURE

eee e reer eee eee eee errs seseeseeresesseeereERssmssseseses

ak,
weal

eee em ee eee eee Pee H EES MELEE SETH THEE ETE ESOS EEE OE MOE EE Mes seeseserese

=~
be
nN

—_
Oo
4

Ww

Ree eee reece teresa ceererereseresssesersseercsssesersseMmesseeses

ENERGY DEPOSITION (cal/g)/(cal/cm?)

eee meee eee e cere eres e eee esse esses eeesssseseesyeserssesssessesessBes

—_
s
Bes

eee eee eee rete reer eases eee reese srs essesssStEEEmsseesseseesEEESEEHee®

-6
10 oo 2

4 6 849-2
DEPTH (cm)

107! 109

Figure 7.17. Normalized Energy Deposition
Curves in TWSP for Several Blackbody Tem-
peratures.

NUCLEAR PHENOMENA 8-1
8. NUCLEAR RADIATION PHENOMENA

8.1 Introduction. Although the radiation from nuclear explosions includes gamma rays, neutrons,
beta particles, and alpha particles, only the first two elements are transported over significant dis-
tances through matter, and thus are the only ones considered in detail in this chapter. The exceptions
to this are high-altitude explosions in which beta-particle phenomena occur over large distances, and
direct contact with fallout in which beta particles, and to a lesser extent and only at very late times,
alpha particles, may be significant.

Radiation from a nuclear explosion is Table 8.1. Approximate Emission Times and Energy Ranges
generally considered in two categories: of the Components of Radiation from Nuclear Weapons.
initial (< 1 min) and residual (> 1 min). RADIATION EMISSION ENERGY
Initial radiation is further subdivided into Cc TIME RANGE (Me
prompt radiation: neutrons and gamma MI
rays produced in the weapon fission and Se ee aaiot aas
fusion processes; secondary radiation: - Fission gamma rays < 0.01 1 sec
gamma rays produced by neutron inter- secondary Gamma Rays
‘ ; Inelastic-scattering gamma rays from: .

actions with material (air, ground, struc- - Weapon < 0.01 1 sec
tures) outside the weapon; and delayed : eae | ‘ ‘0 : see
radiation: fission-product neutron and - Elements in ground/structures < 10 1 sec
gamma rays, and neutron activation ee rays from: captaas
gamma rays. Residual radiation includes - Nitrogen Faw me= 005 06c
fallout from debris clouds (fission de- - Oxygen (negligible) a

‘ . : 6a d - Elements in ground/structures Few ms - 0.03 sec
bris, weapon activation products, and en- Gelaved Badiatian
trained environmental activation : - ms 1 —

: : sas - Fission-product gamma rays ms - 1 minute
products) and activation radiation from Ren opp say tan .s aie
neutron capture in environmental ma- Residual Radiation 3
terial not entrained in the debris cloud. en ee a
: ‘ - Fission-product gamma rays min. - many years

approximate emission times, and their - Environmental activation gammas Tens of years
: ‘ - Non-entrained environmental gammas Tens of years
energy range. Figure 8.1 shows an ide-
alized, normalized gamma-ray output,
both with and without those arising from g 9 Initial Nuclear Radiation.
neutron interaction in the atmosphere.
8.2.1 Definitions and Numerical Values.

Flux ( »): The particle track length per unit volume per
unit time, or equivalently, the product of the particle
density, i.e., number per cubic centimeter, and the
particle speed ( =nv). The flux is expressed as par-
ticles per square centimeter per second.

Fluence (@): The particle track length per unit volume,
or equivalently, the product (or integral) of particle
flux and time ( = nvt), expressed as particles per
square centimeter.

Dose (D): The amount of energy absorbed from the ra-
diation per gram of absorbing material. The traditional
unit of dose is the rad ( = 100 ergs/g). The Interna-
tional System of Units dose quantity is the gray (=
100 rads). A centigray equals 1 rad. Since the abil-

108 10% 104 102 100 402 ity of radiation to deposit energy in a given material

TIME (sec) is governed by the reaction cross sections of that ma-
terial for the particular radiation involved, the ma-
terial in which the dose is deposited must be stipulated:
thus, rads (tissue) or rad (Si).

ENERGY RATE (MeV/sec KT)

Figure 8.1. Idealized Time Dependence
of the Gamma-Ray Output from a Large
Yield Explosion, Normalized to 1 KT.

2292

8-2 NUCLEAR PHENOMENA

Dose rate (D): The rate (per unit time) at which absorbed dose is accumulated.

Kerma (kinetic energy released in material): The amount of energy imparted to charged
particles by neutral particles per unit mass of target material. Units of kerma are the same
as those of dose. It differs from rads in that the energy is only imparted to charged par-
ticles in reactions within the unit mass, but this charged particle energy is not necessarily
deposited within the unit mass, which is the criterion for rads. In practice, the energy de-
posited by charged particles at a given location is almost never determined because of the
difficulty of such calculations and because the range of charged particles is much less than
that of neutral particles in a given medium. Therefore, a condition of charged-particle equi-
librium is assumed to exist in which losses of charged particles produced at a given loca-
tion are balanced by the gain of particles from adjacent sites. This assumption allows dose
to be equated with kerma and they will be used rather interchan geably in this chapter. Kerma
for soft tissue and for silicon are provided in Tables 8.2 and 8.3 for neutrons and gamma
rays, respectively.

Kerma rate: The rate (per unit time) at which kerma is accumulated.

Free field: The intensity of initial radiation in the absence of shielding local to the detector
or target.

Fusion: The nuclear reaction (combination) of two light nuclei to form a heavier nucleus. The
fusion reaction having the highest probability of occurrence is that between deuterium and
tritium:

2D, +3T, =*He, + !ng + 17.6 MeV. Approximately 14 MeV of this reaction energy is car-
ried off as kinetic energy of the resulting neutron, and the remaining by the helium ion.
Table 8.2. Neutron Kerma by Energy Groups.

1-MeV NEUTRON

EQUIVALENT
UPPER GROUP IONIZING DAMAGE FLUENCE
BOUNDARY TISSUE DOSE SILICON DOSE IN SILICON
(MeV) (rad[tissue/n/cm?) (rad[{SiVn/cm?) (n/cm?)/(niem?)

6.6327 x 10-9 1.0103 x 10-9 9.9994
12.214 6.1563 x 10-9 9.1268 x 10-10 2 1203

10.000 5.6470 x 10-9 7.1390 x 10-10 1.9783
8.1873 5.2725 x 10-9 4.0598 x 10-10 2.0091
6.3763 4.7306 x 10-9 1.4966 x 10-10 2.0437

4.4767 x 10-9
4.2223 x 10-9

8.5471 x 10-11 1.7573
5.8964 x 10-11 1.4102

3.0119 3.5762 x 10-9 6.6914 x 10-11 1.8662
2.3852 3.2121 x 10-9 5.0890 x 10-11 1.5552
1.8268 2.7753 x 10-9 2.5495 x 10-11 8.8346 x 10-1

2.1072 x 10-9 2.0337 x 10-11 8.9212 x 10-1
11. 5.5023 x 10-1 1.3089 x 10-9 1.1842 x 10-11 6.5751 x 10-1
12 1.5764 x 10-1 8.0649 x 10-10 5.9340 x 10-13 4.1182 x 10-2
13. 1.1109 x 10-1 4.2273 x 10-10 5.1437 x 10-13 4.2761 x 10-2
14. 2.1875 x 10-2 7.1195 x 10-11 6.1825 x 10-14 7.4376 x 10-3
15 1.2341 x 10-3 4.9812 x 10-12 3.2015 x 10-15 6.0524 x 10-4
16 1.0130 x 10-4 1.0808 x 10-12 6.8608 x 10-16 8.9113 x 10-5
17 2.9023 x 10-5 1.0006 x 10-12 7.8884 x 10-16 1.0103 x 10-4
18 1.0677 x 10-5 1.4760 x 10-12 1.2572 x 10-15 1.4131 x 10-4
19 3.0590 x 10-6 2.5611 x 10-12 2.2895 x 10-15 2.4446 x 10-4
20 1.1254 x 10-6 3.7144 10-12 3.9798 x 10-15 4.2203 x 10-4
21 4.1399 x 10-7 1.4969 x 10-11 1.4942 x 10-14 1.5817 x 10-3
22 ~~ 1.0000 x 10-11

334

NUCLEAR PHENOMENA

Table 8.3. Gamma-Ray Kerma by Energy Group.

UPPER GROUP
ENERGY
BOUNDARY (MeV)

TISSUE DOSE
(rad[tissue]
1'¥ lem?)

2.7272 x10-9
2.3471 x10-9
2.0616 x 10-9
1.8496 x 10-9
1.6445 x 10-9
1.4352 x 10-9
1.2152 x10-9

SILICON DOSE
(rad(Si) Y ‘cm

3.5851 x 10-9
2.9440 x 10-9
2.4850 x 10-9
2.1750 x 10-9
1.8620 x 10-9
1.5450 x 10-9
1.2220 x 10-9

7.00 x 10-1
4.50 x 10-1
3.00 x 10-1
1.50 x 10-1
1.00 x 10-1
4.50 x 102

1.0412 x 10-9
9.0414 x 10-10
7.5648 x 10-10
5.8513 x 10-10
4.2645 x 10-10
2.9573 x 10-10
1.9196 x 10-10
1.0378 x 10-10
5.1977 x 10-11
3.2540 x 10-11
6.0114 x10-11

9.8030 x 10-10
8.2840 x 10-10
6.7180 x 10-10
5.0740 x 10-10
3.6810 x 10-10
2.6570 x 10-10
1.8410 x 10-10
1.1200 x 10 -10
7.4540 x 10-11
1.1137 x 10-10
9.9441 x 10-10

8-3

Relationship between neutron energy and velocity:

v = 1.38 x 10? (MeV)!” in units of cm/sec.

Fission: The splitting apart of aheavy nucleus into

(generally) two smaller nuclei accompanied by
the release of several neutrons (on average) and
gamma-rays. The fissioning of U2*°, U78, and
Pu??? following capture of a neutron are the
relevant fission reactions in nuclear weapons.
Each fission releases about 200 MeV of energy,
primarily carried off a kinetic energy of the fis-
sion fragments, with about 180 MeV contrib-

uting to the force of the explosion. 1 KT is
equivalent to approximately 1.45 x 10” fis-
sions.

Hydrodynamic enhancement: The increase in

dose arising from the reduced area density of
air through which delayed gamma rays are
transmitted as a result of the explosion energy
displacing a large volume of air into a shell at
a larger radius than its pre-explosion distribu-
tion.

Standard atmosphere: Refer to Table 2.1 in
Chapter 2, Airblast.

1.00 x 102

8.2.2 Weapon Radiation Sources.

8.2.2.1 Generic Weapon Types. EM-] con-
tains a complete description of 13 generic
weapon types and extensive data on the at-
mospheric transport of their several types
of radiation outputs. Table 8.4 is an abstract
of four of these types. In general, the data
in this handbook are the subset of the EM-
1 data for these types.

Table 8.4. Representative Types of Nuclear Weapons.

DESCRIPTION
Unboosted fission implosion weapon, contemporary design
Boosted fission implosion weapon, modern design

Thermonuclear secondary

Enhanced radiation thermonuclear secondary

8.2.2.2 Neutron Sources. Figure 8.2 shows notional fission, thermonuclear, and fusion weapon source
spectra (not those from Table 8.4) as well as their spectra after transport through 1 km of moist air:
p = 1.122 x 103 g/cm’, water 0.56 percent by weight. Both the initial and transported spectra are
normalized to unity. The detailed transport calculations presented by weapon type which follow have

used the neutron output (neutrons per KT) and spectrum, normalized to one neutron, as shown in Table
8.5

8.2.2.3 Gamma-Ray Sources. For most weapon designs (Table 8.6), the range of gamma-ray pro-
_ duction efficiency as a percent of total yield ranges from 0.1 to 0.5 percent, with the larger gamma
| yields attributed to those weapons that are physically the smallest. Average gamma-ray energy de-
' pends more on the origin of the weapon yield (fission or fusion) and the physical size of the weapon
than on the yield itself. Small weapons and those that obtain a large fraction of their yield from the
fusion process tend to have the highest average gamma ray energies. Source and transported spectra
for prompt and fission-product gamma radiation are shown in Figure 8.3 for the same notional weap-
ons as used in Figure 8.2. Transport is through 1 km of uniform moist air, unperturbed by blast ef-
fects, as specified in Section 8.2.2.2. Source and transported values are normalized to unit source and
unit fluence, respectively. Figure 8.4 shows normalized secondary gamma-ray spectra at a distance
of 1 km in the same uniform moist air for the fission, thermonuclear, and fusion neutron sources, as
shown in Figure 8.2.

335

NUCLEAR PHENOMENA

Table 8.5. Neutron Source Spectra and Output for Types 3, 5, 8, and 13.

ENERGY RANGE
(MeV)

UPPER LOWER
1.49 x101 — 1.22 x 101
1.22 x101 — 1.00 x 101
1.00 x101 — 8.19 x 100
8.19 x109 — 6.38 x 100
6.38 x109 — 4.97 x 100
4.97 x109 — 4.07 x 100
4.07 x109 — 3.01 x 100
3.01 x109 — 2.31 x 100
2.31 x100 — 1.83 x 100
1.83 x109 — 1.11 x 100
1.11 x100 — 5.50 x 10-1
5.50 x 10-1 — 1.58 x 10-1
1.58 x 10-1 — 1.11 x 10-1
1.11 x10-1 —- 2.19 x 10-2
2.19 x 10-2 — 1.23 x 10-3
1.23 x10-3 — 1.01 x 104
1.01 x10-4 — 2.90 x 10-5
2.90 x 10-5 — 1.07 x 105

NEUTRONS PER KT

SOURCE 3

8.85 x 10-5
5.63 x 10-4
2.06 x 10-3
5.26 x 10-3
1.34 x10-2
2.81 x 10-2
4.19 x10-2
8.11 x10-2
1.37 x 10-1
1.85 x10-1
2.88 x 10-1
4.37 x10-1
4.56 x10-1
1.27 x109

3.50 x 100

7.08 x101

2.29 x 102

3.15 x 102

2.70 x1023

NEUTRONS PER MeV

SOURCE 5

9.47 x 10°3
2.38 x 103
3.14 x 103
6.27 x 103
1.59 x 102
3.05 x 10-2
4.59 x 102
8.76 x 102
1.44 x 10-1
1.89 x 10-1
2.99 x 10-1
4.56 x 10-1
4.85 x 10-1
1.11 x 100

5.15 x 100

1.22 x 101

2.72 x 100

7.61 x 10-1
3.38 x 1023

SOURCE 8

1.65 x 10-2
5.49 x 10-3
3.86 x 10-3
6.00 x 10-3
1.25 x 10-2
2.22 x 10-2
3.39 x 10-2
5.85 x 10-2
9.75 x 10-2
1.42 x 10-1
2.73 x 10-1
4.77 x 10-1
6.82 x 10-1
2.25 x 100
4.10 x 100
4.42 x 100
4.61 x 100
6.41 x 10-1
1.95 x 1023

SOURCE 13
1.42 x 10-1
2.03 x 10-2
2.11 x 10-2
2.06 x 10-2
2.33 x 10-2
2.74 x10-2
3.05 x 10-2
4.87 x 10-2
8.65 x 10-2
9.83 x 10-2
1.23 x 10-1
2.12 x 10-1
2.27 x 10-1
5.93 x 10-1
1.93 x 10-1
5.01 x 100
0.00 x 100
0.00 x 100
1.77 x 1024

Table 8.6. Weapon Gamma-Ray Output.

TOTAL GAMMA-RAY
WEAPON ENERGY *
TYPE (MeV/KT)

9.80 x 1022

PEAK GAMMA-RAY
OUTPUT RATE 2: ©
(MeV/nsec-KT)

4.92 x 1021
5.22 x 1021
1.79 x 1022 W-0.29
3.37 x 1022

AVERAGE
GAMMA-RAY
ENERGY (MeV)

1.04 x 1023
3.55 x 1023x W-0.29
6.70 x 1023

Notes: a - W is yield in kilotons.
b - Illustrative values based on a hypothetical prompt gamma-ray pulse duration of 20 nsec.

8.2.3 Radiation Transport.

8.2.3.1 Uniform Air. In uniform air, the uncollided particle fluence o from a point source is:

(R) = N,e*P8/4nR? , (8.1)
where k is the mass attenuation coefficient (cm2/g), R is the radial distance from the source, and N,
is the total number of particles emitted by the point source.

The equivalent expression in terms of energy is:
D, =W pWAe SPR/4nR? (8.1a)

where D, is the dose, y, the total energy (MeV/KT), W the yield (KT), A is the unitless coefficient
0.523, and p is the air density (g/cm?). The uncollided fluence may be enhanced by secondary scat-
terings which redirect initially scattered particles back towards the target. This buildup effect is
approximated by a second exponential term used forR = 100 meters: _

D, =[y pW/40R7][(Ae™1P8)(1+BeX2PR)) [kerma] , (8.2)

where B is the unitless coefficient 1.356 (for gamma rays), K, is the effective mass attenuation co-
efficient (cm*/g), having a value of 0.0371 for the collided and uncollided components, K, is the
coefficient in the buildup factor exponent (cm?/g) having a value of -0.0061, and (kerma) is the
effective kerma factor for prompt gamma rays [obtainable from Table 8.3, as a function of photon

337

8 — 22 NUCLEAR PHENOMENA

Table 8.9. Summary of Figures in Section 8.3.

Variable Parameter Fixed Parameter(s) Figure Numbers

Weapon Types European soil 8.26, 8.27, 8.28, 8.29
Soil Types Boosted fission weapon 8.30, 8.31, 8.32, 8.33
Soil Types Enhanced radiation (ER) 8.34, 8.35, 8.36, 8.37, 8.38
Ground Moisture Boosted fission weapon 8.24
Soil Constituents Boosted fission weapon 8.23
(European soil)
Detector Altitude Boosted fission weapon 8.25

(European soil)

8.3.2 Important Parameters of Ground Activation.

8.3.2.1 Weapon Types. The activation dose model used provides data for five generic weapon types:
pure fission, boosted fission, thermonuclear, low-yield enhanced radiation (ER), and high-yield, with
the first three generally quite similar and the ER weapons producing significantly higher levels of
activation because of their large yield of high-
energy neutrons. These five types encompass
the range of neutron spectra expected to be im-
portant for ground activation. Table 8.10 gives
the HOBs used to produce the data in Section

Table 8.10. Height of Burst and Yield Range for
Generic Device Types.

DataHOB HOBRange Yield Range

8.3, the HOB range over which the results should Device Type (meters) (meters) (KT)
be reliable, and the general yield range to which Enhanced Radiation (ER) (13)

the data apply. In general, the data presented have Low Yield % 50 - 100 1-5
been normalized to 1 KT, and may be scaled di- High Yield oem <n caan <a
rectly with yield within this range. The dose for

other HOBs than the dataHOB, but withinthe — | /e"monuciear(8) 200150 - 500

HOB range, may be found by maintaining acon- iaeeesacnt tein A nin

stant slant range for use in the HOB figures. rission 9) iss pease

8.3.2.2 Soil Types. The activation model used
35 target nuclides, 90 different reaction cross

; a ee 2 eee
sections, and 33 radioactive product nuclides. The dose rate is usually dominated by one or two radioactive
nuclides whose half-lives are of the order of the time since the detonation’ Table 8.11 lists these nuclides,

eir half-lives, and the target nuclidés and neutron reactions which lead to them.

Table 8.11. Important Radioactive Nuclides for Ground Activation Dose.

Dominant Target Nuclides
Time Radioactive Half-Life Capture Fast Neutron
(hours) Nuclide (hours) Reaction Reactions

Si28
Fe56, Fes7, Fes8

3.0 - 200
200 - 5,000
5,000 - 40,000 7,500 Fes4, Fesé
> 40,000 22,800

Four soil types, with varying concentrations of sodium, silicon, aluminum, manganese, and iron, are
used to cover the range of activation levels that might be expected. Table 8.12 gives the composition
of the critical target elements for each of these soil types. The Mojave and Dade Country types were
selected to produce, respectively, reasonable upper and lower limits of activation. The other two types

Q&A

NUCLEAR PHENOMENA 8 — 23

will give nominal levels of activation. Table 8.12. Critical Target Composition of Soil Types.
Figure 8.23 shows the fractional con-

tribution to the dose rate for each of the Percent by Weight

nuclides versus time after burst for Eu- Soil Type Sodium Silicon Aluminum Maganese Iron
ropean type soil. Mojave 3.30

Moisture in the soil can reduce the ac- European 1.39

tivation by as much as 50 percent. This Nevada Area7 —0.80

is illustrated in Figure 8.24 showing the Dade County 0.12

1-hour dose rate for a boosted fission
device over European soil of varying
moisture content up to 28 percent. Sim- 10°
ilar results are obtained for other weap- ATE Hy} will a
on types, including ERs. All other data AMT TPMT TT

: -NA- h mail
peccemmmet sh 3! 4 Ae CEE TT TT
8.3.2.3 Detector Altitude. The activa- —~-: N58 an

ditin dotactor cient giead ee tt euee

This variation is caused by the change

in the slant penetration from the soil
Sat REE aH al

source of radiation through ground to
PL Ey B11 AR

the air and by additional air attenuation.
This effect is illustrated in Figure 8.25

San rar ie TH H SARI
CEI TUTE TOT TUTTI ETT TTT TTT

for the boosted-fission device and Eu-
ropean soil. All other data in this sec-

sn a cc aN iit LE au Mi
LM UIE TTI ARTLINE! TT

tion are for a detector height of 1.5
meters.

HA A
a a

8.3.3 Graphical Calculational Data-

1071

FRACTIONAL TISSUE DOSE RATE

base.

8.3.3.1. Variation with Weapon Type
for Nominal (European) Soil. Figures
8.26 through 8.29 provide ground-ac-
tivation dose and dose-rate data for the
five weapon types for nominal Euro-

pean type soils. The HOB and yield SS - 101 a 40°
ranges appropriate for these curves have TIME AFTER BURST (hours)

been given in Table 8.10. Figures 8.26

and 8.27 are the dose rate and dose, re- Figure 8.23. Fraction of Total Gamma-Ray Dose Rate at
spectively, versus slant range at 1-hour Ground Zero Versus Time From the Activity of Various
time. Figure 8.28 gives the dose rate at Radioactive Nuclides Produced in European Soil by Neutrons
ground zero versus time for the five From a Boosted-Fission Device.

weapon types. Figure 8.29 gives the
cumulative fractional dose at ground zero versus entry time after the burst for the five weapon types.

Table 8.13 gives the total (integral) dose in European soil at ground zero, that is, the time-integrals
of the dose-rate curves from Figure 8.28.

To find the dose rate for some slant range (not ground zero) at a particular time, the dose rate at ground
zero at the appropriate time (Figure 8.28) is multiplied by the ratio of the total dose at the appropri-
ate slant range (Figure 8.27) to the total dose at ground zero (Table 8.13). Gamma-ray dose at a given
slant range for a particular stay period can be found by correcting the data of Figure 8.27 (dose for
an infinite stay time starting at time zero) by a factor which is the fractional dose at time of entry
minus that at time of departure (from Figure 8.29).

355

NUCLEAR PHENOMENA _ 8-25

DEVICE
403 LOW YIELDER _] 49-2

2

pi

J 10°4

2,
‘il

pete

10° 105

1071

a
5
Oo
&
i
<
om
Li
”
©
oO
uJ
a}
”
”
=
>
<=
&
<
=
=
<
]

ee a oan Hee
ERE, A SE eee
BSS FS SR = Se a SS
sot Ns

10°8
0 0.5 1.0 1.5 2.0 2.5 3.0

SLANT RANGE (km)

Figure 8.26. Gamma-Ray Dose Rate per Kiloton Yield at 1 hour Versus Slant Range From Neutron
Activation of European Soil for Various Nuclear Weapon Types.

10° 40°
DEVICE
LOW YIELD ER
— — - HIGH YIELD ER
— — THERMONUCLEAR
gd ae So —-— BOOSTED FISSION
ERE AS —-= FISSION 10°!

7 10°
~
9 10°
=
o
OQ 104
WwW
2 10°
”
=
>
= 10
o
=
= 104
6 10°

1071 ——— i

10°2
0 0.5 1.0 1.5 2.0 2.5 3.0

SLANT RANGE (km)

Figure 8.27. Total Gamma-Ray Dose per Kiloton Yield Versus Slant Range From Neutron Activation of
European Soil for Various Nuclear Weapon Types.

2&7

8 — 26 : NUCLEAR PHENOMEN,
10 peers silinieaaeeiinapiiasitiiguainiasiniinaectpiaemtimaitinstian 40"

aoe om = Poot TE SAMS! BE eke SE Ce wee =a. |) == —SGSSs Gaauasaaese:
He a +h aD as Ht

Hat t—
He
all om I mal

J 100

=
oO
uo

ttt tt ttt Sects eee SS estes amecet
Bll) t es a ae
SSsimawee ese

Sar ae GS ttle ee oe

Series ta 00 Ho

Po = \ ee Mt nl
HiiN VEU 3 cei assis eesti

a a Si totitiee meat eet

aii CUTE UT

See eee te eee amet ry ai TNC

=H ee INOUE UU

1071

=k
Qo
Bas)

Hy toe aioe
THT FA NN Si CO ms SS NE
® Vie N ‘ A mail ipo Sai Ste

SH STI ll
HN Vesti eseiiesestz 40°3

Con 4
Ht a et tt —

10°2

Saiiiimaiilim NUR italien a! See ie th
WU TST ETN, TT | maul >

10? CSS SU Ne 10%

es SL ae ee
S26) a a Ss SS) a ee et Rt At a ‘meee
26: eel eee 1 iS ane —. a eee aH a+ masa

tt et tt NS NT eatin Gn

Cr PC Sa nim ail

got LUM LLL LT LM SNL Sti seme

EE -a weess

Pt
Hit aan ia ee =, Suan

ee @ear i
0 a eS 0 ee A

10°75

GAMMA-RAY TISSUE DOSE RATE (cGy/hr-KT)

HH
HHH Met aH VHiMGt i eee eteae

UMN Teh 11 06 Ih Bay, MEE MONTH Ge eh 10

1

103 102 107 100 101 102 103 105
TIME AFTER BURST (hours)

Figure 8.28. Gamma-Ray Dose Rate per Kiloton Yield at Ground Zero Versus Time After Burst From

Neutron Activation of European Soil for Various Nuclear Weapon Types.

10° pq

ae SL TY |
Sat Se St ae

DEVICE

TT NIN RN (il .. = towvietper {||
Bi ag --—-HIGHYIELDER [|||

THT TAR —— = THERMONUCLEAR
i

—-==* FISSION

\ - BOOSTED FISSION
FISSION

ea a
TCC ita int a
Hi Hi SE TTT

a
ai a a av a MEL UT
NCTC TT sae

B00 0 a en
ck meee a

10-2 (the HE

10-3 02 107 100 #10! 102, 103)—=Ss- 10*~—S 108
ENTRY TIME AFTER BURST (hours)

“=

CUMULATIVE EXPOSURE DOSE FRACTION

Y WEEK nie YEAR |

Figure 8.29. Cumulative Gamma-Ray Dose Fraction at Ground Zero Versus Entry Time After Burst Fron
Neutron Activation of European Soil for Various Nuclear Weapon Types.

282

JFoT

"JUDDIOg [ < JO JUDjUOZ JINISIOPY B SLY YOY 19M
"sIng Jo yJdaq paeds snsJ9A JsINg dORJINsqns & WO pjalx AsJou_q Jo uonoely

‘93in¢ ase g UI UOTIORI “Op’g IINSI

(y-¢/;-L¥ S40}0Ul) Z ‘pho[D ule] Ul UONDeIY ‘cp’g aan
‘LSHNE 4O HLd3ad G3a1V9S
OL 09 OS Ov O€ O2@ Ot 0 ot (yey 1} $49}9W) 7

‘LSYNG AO HLdad GA1Vv9S

MWOS GNV
MIOY LAM

4) ‘3DYNS ASV NI ADYANA G73IA 4O NOLLOVHS

™}‘GNO1D NIVW NI ADYANA G731A 4O NOLLOVHS

PARTICULATE CLOUDS 4-1
4. NUCLEAR PARTICULATE CLOUDS

4.1 Introduction. The particulates in nuclear clouds are combinations of (1) surface dust raised
by the blast wave passage over the ground, (2) crater ejecta lofted by the rising fireball, and (3)
condensed water in several forms arising from the condensation of moisture in the air which is
cooled as it rises and expands. The research database consists of atmospheric test observations,
HE testing, and hydrocode modeling. The atmospheric test data are generally limited to photo-
graphic measurements of cloud dimensions, while quantitative data on internal cloud dynamics
and particulate sizes as a function of time and location in the cloud are essentially nonexistent.
Thus the quantitative data in this handbook are limited primarily to algebraic expressions for
some of the macroscopic features of clouds such as dimensions and total particulate entrainment.

Detailed characterization of the spatial and temporal effects in the particulate environments
requires the use of hydrocodes which model the physical processes involved and are adjusted to
be consistent with the macroscopic features of experimental data. The DICE and TASS linked
hydrocodes are the primary models used to calculate the detailed characteristics of the lofted
dust/ice concentrations and distributions of solid material by particle size as functions of altitude,
radius, and time. EM-/ contains the results of a relatively small number of such calculations,
which are tutorial and illustrative of trends but do not provide the basis for further numerical
analysis.

4.1.1 Dust Size Distributions. Particle size distributions (PSDs) are a function of geology,
terrain, and meteorology, as well as differing between ejecta and sweep-up sources. Figure 4.1
shows the currently accepted range of PSDs. The DICE/TASS calculations use power-law ap-
proximations to "incohesive soil" for the swept-up mass and "coarse alluvium" for ejecta.

4.1.2 Particulate Slip Velocities and Settling Times. The slip speed of a particle is its equilibri-
um settling speed (or terminal velocity) in quiet air under the influence of gravity alone. It
depends on the diameter, roughness, and density of the particle, and the density p, and viscosity
of the ambient gas which change with altitude and temperature.

The density of a dust particle, p,, is set at 2 g/cm’ in the DICE/TASS calculations, and a
multiplier of 1.5 times the drag coefficient approximates the enhanced drag on rough spheres.
Other terms are the sphere diameter, d and the acceleration of gravity, g = 980 cm/sec’. The slip
velocity is calculated through the following equation:

30u 3 &PgPa
=| —— |] -1+ h+d — |. 4.1

Figure 4.2 shows slip velocity as a function of particle diameter at sea level and an altitude of 10
km, as calculated from Equation 4.1. Settling times as a function of particle diameter are shown
in Figure 4.3. Particles in the 10- to 100-ltm range require from several hours to many days to fall
from nuclear cloud stabilization altitudes above 10 km. Particles larger than 1 mm, which fall out
in about 10 minutes or less, will generally be retarded by the modest but sustained updrafts
possible below the cloud in that period.

4.2 Simple Formulae. This section provides simple formulae for some parameters. These equa-
tions represent an effort to systematize the limited data from atmospheric nuclear tests and
available calculations, but it should be recognized that the test sites are special cases of terrain
and atmospheric conditions.

4.2.1 Cloud Dimensions. The most obvious parameters are the geometrical dimensions of the
photographic cloud. The top of the main cloud rises to and possibly overshoots an equilibrium
altitude. The yield-dependent relation of the main cloud stabilization height above the burst point
is the empirical formula:

AH,,.,= 4.5 W°”? (km) , (4.2)

top

167

4-2 PARTICULATE CLOUDS

100

p

oS ae Soa SEE © eES <a a ee ee SET Se
"“INCOHESIVE SOIL" : :
: GEOLOGY: "COARSE ALLUVIUM"
: : GEOLOGY :

Ss Berner Ss a ne ; Eats a5oh Soe coe Soeeesy ener sneradat
PS ne Bereessag sesiest SII ert | Sa ceva lapviwnckt ox ie Coes iad, =

20 fog (See hee 00S SES Se eaee te ee Sees Spenei ceases gees sors: boc POS Rave eO reas

“COMPETENT ROCK"
GEOLOGY

PERCENT MASS WITH DIAMETERS SMALLER THAN d

‘ :
10-4 10°3 1072 1071 109 101 102 10°
PARTICLE DIAMETER, d., (cm)

Figure 4.1. Particle Size Distributions for a Range of Site Conditions.

where W is the yield in kilotons and AH op is in kilometers. The stabilized bottom of the main
cloud for most yields is not perfectly correlated with the top. Nevertheless, an approximate
relation exists for the thickness of the main cloud at stabilization:

AHin, = 2 W"* (km), for yields greater than 2 KT. (4.3)

The cloud diameter is the important horizontal extent. A combined yield- and time-dependent
relationship is:

D = 0.65 7 W@ + 108 9/7 (kin) , (4.4)
with W in KT and for time t < 10 minutes.

This formula is not appropriate at late time due to the dominance of the wind shear effect on the
cloud width after stabilization. Also, note that low yield (< 50 KT) clouds can easily be much
larger than this formula by 10 minutes after burst. |

4.2.2 Dust Pedestal. The pedestal refers to the slowly varying sweep-up layer that develops by
about 1 s/KT'. The Scaled Maximum Height (SMH) of the dust pedestal (at the scaled time of
approximately 1 s/KT™) is:

SMH = 525 SHOB~865 (m/KT") , (4.5)

1A&

PARTICULATE CLOUDS 4-3

104 where the scaled height of burst (SHOB) is
: 3 3 restricted to >10 m/KT!”. The time-depen-
10° dent algorithm is shown in Figure 4.4.
g 102 The SMH occurs at the Scaled Ground Range
Ss : Fé for Maximum Height (SGRMH) (m/KT"?)
E 10! : 2 : of:
I 10° : ; SGRMH = 120 + 2 (SHOB) (m/KT") ,
= (4.6)
= 10"! : : ; 1/3 13
a 7 ; with SHOB in m/KT”” at t ~ 1 sec/KT"”.
10°72 : The time-dependent fit is shown in Figure
* : 7
10°10 10! 107 10° 104

The Maximum Scaled Ground Range
PARTICLE DIAMETER, d (mm) (MSGR) of the dust pedestal is variable due
to the thermal layer variations. The time-
dependent fit is shown in Figure 4.6. The
empirical results are that the MSGR is:

Figure 4.2. Slip Velocity Versus Diameter for Rough
Dust Particles at Sea Level and 10 km Altitude.

104 - MSGR = 150 + 2.5 (SHOB) (m/KT"”) ,
for SHOB < 68 m/KT", (4.7a)
and MSGR = 320 m/KT"”?
for SHOB > 68 m/KT™”’. (4.7b)

Note that there is also a low-lying dust layer
~ extending on out to about 1,000 m/KT™”.

4.2.3 Dust Mass Loading.

Surface Bursts (SHOB <5 ft/KT"*). The
collected and analyzed soil and saltwater par-

PARTICLE SETTLING TIME (seconds)

io1 : ae Ss ticles provide estimates of the lofted mass
“490 «= 4 6 8401 402. in nuclear clouds. The empirical relation from
PARTICLE DIAMETER, d (mm) combining the soil and saltwater data for

| scaled mass in stabilized surface burst clouds
Figure 4.3a. Particle Settling Time(s) in Still Air Ver- — jg-

sus Large Particle Diameter (mm).

Mosp/W = 0.62 wo ; (4.8a)
where W is the yield in KT and Meg is in
KT = 10’ grams, or

- Mgp/W = 0.29 WO! (4.8b)
where W is in MT and Mg is in Mt = 10! g.

Airbursts (SHOB 2 5 ft/KT"%). The
experimental mass loading data have large
scatter. DICE/TASS calculations have been
used with these experimental data to gener-
ate the following approximated main cloud
mass loading relationship with SHOB.

M/W(KT/KT) = 0.25 exp(-SHOB/75)+

PARTICLE SETTLING TIME (hours)

0.04(1-SHOB/800) (4.9a)
PARTICLE DIAMETER, d (um) for 5 < SHOB < 800 ft/KT", and
Figure 4.3b. Particle Settling Time(s) in Still Air Ver- | M/W =0 for SHOB > 800 fv/KT'” .
sus Small Particle Diameter (micron). (4.9b)

1A9

4-4 PARTICULATE CLOUDS

PEDESTAL HEIGHT (feet)

PEDESTAL HEIGHT (feet)

2 fir : 4} E SHOB = 400 tT 8
100 |------: , a pe nels bicieuaiie rakes

: ,°'SHOB = 600 fvKT 3
: FRENCHMAN'S FLATS

0 2 4 6 8 10
TIME (seconds) TIME (seconds)

Figure 4.4. Maximum Pedestal Height Versus Time for Various SHOBs.

This relationship tends to be on the high side of the data and calculations. The uncertainties are
estimated to be a factor of 3 higher or a factor of 20 lower.

17

PARTICULATE CLOUDS 4-5

16

“* SHOB = 200 f/KT 1S

ee ere Bete s ths ete eee sew enh oe cs ee eb cee cee 5 oo sete Opiate oe emiens } Ur
* ° # . —— * . .

Cee eh eee, eee. eee ee ee ee ee es Se err areas ara

§ EME SS AE NS MRS Re Ce BCE Se
0 1 2 3 4 5 0 1 2 3 4 5

PEDESTAL RADIUS AT MAX HEIGHT (kft)

vaeeeee Eee eee ec Re een ey: Se eee Creer ee cerry eee eee eee er ere ee

oe oe oe oe oe oe ob oe

PEDESTAL RADIUS AT MAX HEIGHT (kft) .

TIME (seconds) TIME (seconds)

Figure 4.5. Radius at Maximum Height of Pedestal Versus Time for Various SHOBs.

PEDESTAL MAXIMUM RADIUS (kft)

Sseeeaevan

PEDESTAL MAXIMUM RADIUS (kft)

sens cuueect amencas ceoess eminem: aeons

TIME (seconds) TIME (seconds)
Figure 4.6. Maximum Radius of Pedestal Versus Time for Various SHOBs.

171

EMP EFFECTS

Em (V/m)

10° 10° 10°! 10° 10!
Y Akt)

Figure 10.4. Maximum Estimated Peak

Electric Field Versus Gamma Yield for

Various Heights of Burst.
10°

=- 107

0 100 200 300 400
HEIGHT OF BURST (km)

Figure 10.5. n Versus Height of Burst
for Various Gamma Yields.

E(t) (V/m)
°,

E(t) (V/m)

10!

EMP EFFECTS.

10° 10° 107 10° 10°5
TIME (s)

Figure 10.6. Electric Field Versus Time for
Y,= 1 KT for Various Heights of Burst.

10°

10" 9 : 8 3 : -6
10° 10° 10 10 10>
TIME (s) :

Figure 10.7. Electric Field Versus Time for
Various Gamma Yields at 100 km

EMP EFFECTS
10!
a
— «
0 ¥ =
19 - ¥e
T=
— S
10°! Og =10°2 Sim =
observer
height = 0 km
= 107 3
£
oa
a4
roe
eae :

104

10°3
6
‘4
2 . ° °
1 06 : : : :
0.0 1.0 2.0 3.0 4.0 5.0
GROUND RANGE (km)

Figure 10.13. Variation of Peak Air Conductivities
with Range from a Surface Burst for Various Total

Yields.

18 Y=0.4 KT
2; Y=1KT
3; Y=10KT
4: Y = 100 KT
5: Y=1MT
6; Y=10MT
Og =10°2 Sim
a observer:
E height = 0 km
>
x
a.

Eg

6.0

5.0
GROUND RANGE (km)

2.0 3.0 4.0

Figure 10.15. Variation of Peak Theta Electric
Fields with a Surface Burst for Various Total
Yields.

10-/

<<<<<<

observer
height = 0 km
E
S
=x
>
TW)

5.0
GROUND RANGE (km)

2.0 3.0 4.0 6.0

Figure 10.14. Variation of Peak Radial Electric
Fields with Range from a Surface Burst for
Various Total Yields.

10°2 :
: Y=O040
> ¥Y=1KT
: ¥= 10KT
: Y=100KT
: Y=1MF
>: Y=10MT
Gg =10°2 S/m
1073 ee So Tee Fab See ee ee : | ee
observer:
a height = 0 km
%
2
~~»
rot
a
ree)
104 fe a Fe ee ee Re ee ee eres
8
6
4
2
1075 : * c > H
0.0 1.0 2.0 3.0 40 5.0 6.0
GROUND RANGE (km)

Figure 10.16. Variation of Peak Phi Magnetic
Flux Densities with Range from a Surface Burst
for Various Total Yields.

AAQ

10-8

10°

. 6-STANDARD: GROUND (P.=10%

: DRY GROUND (P\,=1.0%)
12-SEA WATER (og=4.3

S/m)
Y= 10 MT

observer
height = 0 km

10°

104 Pen ose MEFs nic Mei Nat ome aaa hore ee we wee 5 ae
£
a
x
=>
Ww
103 SES ee et COI. CR, SRS ors ae ES, a ee eee
ee Ne, ee et ae
10 3
6
4
2
10! :
0.0 1.0 2.0 3.0 40 5.0 6.0
GROUND RANGE (km)
Figure 10.17. Variation of Peak Radial
Electric Fields with Range from a Surface
Burst for Different Ground Characteristics.
107"
= Y=10MT
6 - STANDARD GROUND (P,, = 10%)
9 - DRY GROUND (P,, = 1.0%)
12 - SEA WATER (5g = 4.3 S/m)
oS : observer
10°72 height = 0 km:
re)
2
>
- .
”
&
3 10°
ae
a.
Ss
he]
-4
6
4
2
02 : :
0.0 1.0 2.0 3.0 4.0 5.0 6.0
GROUND RANGE (km)

Figure 10.19. Variation of Peak Phi Magnetic
Flux Densities with Range from a Surface
Burst for Different Ground Characteristics.

EMP EFFECTS

10°

: : Y= 10MT
6 - STANDARD GROUND (Py = 10%)
9 - DRY GROUND (Pw = 1.0%)
12 - SEA WATER (6g = 4.3 Sim)
: observer
height

=0km

E

= 10°

= 6

ur «Cs?

6

5

4

3

2
404

0.0 1.0 2.0 3.0 4.0 5.0 6.0

GROUND RANGE (km)

Figure 10.18. Variation of Peak Theta Electric
Fields with Range from a Surface Burst for
Different Ground Characteristics.

TIME (usec)

Figure 10.20. Generic Radiated Ground-Burst EMP
Waveform.

AEN

THERMAL RADIATION 6-1
6. THERMAL RADIATION PHENOMENA

6.1 Introduction. The term “thermal radiation” is conventionally restricted to that radiation emitted
by the fireball, specifically excluding the early x-ray emission that is, technically, also “thermal”. The
fireball thermal emission typically takes place over a period of seconds, with most of the energy in
the wavelength region between 0.3 um and 4.0 um. The energy delivered in the thermal pulse is usu-
ally specified in terms of thermal fluence, which is the energy per unit area incident on a target sur-
face (calories per square centimeter). The thermal fluence is:

Q = 100 WfTg/ 4nR,’” cal/cm’, (6.1)
where:
R, = slant range (km) from the source 4nR,” = spherical area of distribution
f = thermal fraction W = yield (KT)
T = transmittance = geometry factor (including extended
(including attenuation and albedo) source and target orientation).

Equivalent expressions are:
Q = 7.96 WfTg/R,*(km) cal/em* or Q = 85.7 WiTg/R,(kft) cal/cm?.

The rate at which thermal energy is emitted is the thermal flux (cal/sec). Bursts at low and intermedi-
ate altitudes typically emit thermal energy in two peaks, the first in the millisecond and the second in
the second time-scale. Figure 6.1 illustrates these two peaks for a 1-KT, low-altitude burst, empha-
sizing the variability in the first peak resulting from uncertainties in non-equilibrium absorption. Since
less than 1 percent of the thermal energy is contained in this first pulse, it has generally been exclud-
ed from the material presented in this chapter.

6.2 Thermal Radiation Source Characteristics. Data in this
section are taken from the RECIPE fireball radiation model,
an engineering model developed to reproduce the results of the
RHGEN first-principles code. RECIPE provides a complete
Ko fe] dimensional history and the time-dependent spectral power at
fe Ne} «56 wavelengths from 0.2 to 12.5 um with approximately 0.02
Lm resolution in the 0.2 to 1.0 um range. It has been extended
to include surface bursts. Although based on theoretical mod-
eling, the second peak flux of the airburst source module has
ul pl pl Ci) iG GN) = been validated dimensionally against extensive test data. The
tos 104108102 108-10 surface-burst source module also agrees well with the limited
on ees amount of available test data. The air transmission module takes
Figure 6.1. Illustrative Fireball Thermal into account the attenuation processes due to molecules and
Power Versus Time fora 1-KT, Low aerosol scattering, and absorption due to water vapor, carbon
Altitude Nuclear Explosion, Showing dioxide, and ozone. However, as noted above in discussing the
Variability of the First Pulse. first thermal peak, RECIPE does not account for nonequilib-
rium chemical species associated with the fireball.

Geer oe Tere eee ee ae Cae Pee ere Cree. ee eee oe

SOURCE POWER (cal/sec)

6.2.1 Fireball Expansion. The relationship between radius of the fireball and yield for both low-al-
titude and surface bursts is: |
R (at thermal minimum) = 27 W 4, (6.2)

where R is the fireball radius in meters and W is the yield in kilotons. The radius at breakaway of the
weakly luminous shock front from the fireball is different for air and surface bursts:

Airbursts: R (at breakaway) = 34 W°*4, Surface: R (at breakaway) =44W°*. (6.3 & 6.4)
The RADFLO physics code provides the following altitude-dependent fireball and shock radii data
for air bursts at the time of the second thermal maximum. It is accurate up to about 50 km altitude:

Rep (to max)(m) = 51.8 Wt gtk Royock (tomax) mm) = 83-5 Wess pws {6.5 & 66)

where p = p,/1.225, and p, is the ambient density in grams per liter at the burst altitude.

RECIPE data on fireball radius versus time for various altitudes are shown in Figures 6.2 to 6.6 for
yields from 1 KT to 10 MT. The 0 km altitude curves correspond to a contact surface burst. These
curves are estimated to be reliable to about +15 percent in both time and distance.

an9

o-Z LHERIVIAL KRAVIA LIVIN

104

FIREBALL RADIUS (cm)

10-4 10-3 10-2 1071 10° 101
TIME (sec)

Figure 6.2. Fireball Radius Versus Time Curves for a 1-KT Burst at Various Altitudes.

Ree a eee Cee eT eee ak EES RS Ce Oe EE es EK ee Ae Cs Re et Ce eee eee ere, Pee Te ee el le ee Cr ee Me

oe.’ 1 eee eee
oan Se |. 12, Sebmpaiien mee Wines sco

FIREBALL RADIUS (cm)

10-4 10-3 10-2 1071 10° 101
TIME (sec)

Figure 6.3. Fireball Radius Versus Time Curves for a 10-KT Burst at Various Altitudes.

AIQN

5 Ceca a LMHCNIVIAL RAVIA LIVIN

BURST Sse ES Le
ALTITUDES Dowels Seapine ots

FIREBALL RADIUS (cm)

10-3 10-2 1071 100 101 102
TIME (sec)

Figure 6.6. Fireball Radius Versus Time Curves for a 10-MT Burst at Various Altitudes.

6.2.2 Thermal Yield Fraction. The thermal yield fraction, or thermal partition, is the fraction of the
total energy which appears as thermal output, E,,./W. Figure 6.7 shows it as a function of yield for
several altitudes from 1 to 30 km. In practice the thermal energy emitted over extended times is of
little military significance, and it is frequent practice to terminate the integration at some multiple of
the thermal maximum time, e.g., 10 t,_.. At very low heights of burst (< 4 W'” meters) the inclu-
sion of surface material into the fireball radically changes the thermal fraction. Surface burst values
are shown in Table 6.1.

The RADFLO data are based on the following expressions for total radiant energy, E_(KT).
Surface Burst: 0.149W!074 ; Free Air (< 4.3 km): 0.350 W. (6.7)

ST ALTITUDE (km)

see

THERMAL FRACTION (E;,;/W)

i ee
YIELD (KT)

Figure 6.7. Thermal Yield Fraction as a Function of Burst Altitude and Yield (Altitude Contours).

232

THERMAL RADIATION 6-5

Table 6.1. Thermal Fraction Values for Near-Surface Bursts.

Surface Nonsurface Surface Nonsurface
Burst Burst Transition Burst Burst
Yield Thermal Thermal Height Thermal Thermal
(KT) Fraction Fraction (meters) Fraction Fraction

6.2.3 Thermal Power Versus Time.
Table 6.2 is a summary of the empirical thermal radiation scaling laws.

Table 6.2. Summary of the Empirical Thermal Radiation Scaling Laws.

Surface Free Air Free Air

41.7 Wwo.44 40.0 Wwo.45 p=?

Ejomac (KT) —0.118_ W024 0.277 W 0.276 W p-0.034

tain = ume to the first minimum Ey omax = thermal energy radiated prior
for the fireball as a blackbody to 10 times t, _..
tonax = time to the second maximum W = yield (KT) (Note: 1 KT = 10! calories’
Pomax = power at the time of the second
maximum.

An analytical approximation to the time-dependent thermal power, P(t), for the second peak of |
low airburst is: |

P(t)/ Ps ax = 2t7/(1 +t’), (6.8
where t is the normalized time (t/t,_,.). Figure 6.8 shows this curve of normalized power and percen
of total energy emitted versus normalized time. Figures 6.9 to 6.13 give the results of RECIPE calcu
lations of the source power versus time for a set of altitudes, for each decile of yield.

1.0

80

Ned
ror)

60

©
ro)

40

°
>

—— GLASSTONE AND DOLAN, 1977

20

NORMALIZED POWER (P/P,__.. )
hed
NO

ALGORITHM, EQ. (6.8)

THERMAL ENERGY EMITTED (percent)

a 5 6
NORMALIZED TIME (tt.,,,, )

Figure 6.8. Normalized Power and Percent of Total Thermal Energy as a Function of Normalized Time.

V2

6-6 ‘THEKMAL KADIA Irur

| 10'4

10'°
oO ~~
® ®
a i)
Cys] |
2 8 10%
oc
“ Tr
5 =
oO. e)
Ww ae add
ro) wi 10
4 oO
3 oc
5 S
D 2
io"L
3 er ae aie i 5 et ae S = ie 2 Rs tee E Eig ' 10° : ae 5 Pate 2 oe eee ‘ A ees ; eee
10° 107 10"! 10° 10! 10° 107 10°"! 10° 10'
TIME (sec) TIME (sec) |

Figure 6.9. Effects of Altitude on Thermal Figure 6.10. Effects of Altitude on Thermal

Power for a 1-KT Burst. Power for a 10-KT Burst.

‘ef aE 40'*

—_—
©
—_
>

SOURCE POWER (cal/sec)
2 2
RC) w

SOURCE POWER (cal/sec)
site
nN &

2 Li —_ bal 5 40" eg Ne ETS i Re a ee Pe eee
10 10 10 10 10° 10°72 10°! 10° 10!
TIME (sec) TIME (sec)
Figure 6.11. Effects of Altitude on Thermal Figure 6.12. Effects of Altitude on Thermal
Power for a 100-KT Burst. Power for a 1-MT Burst.
3 ALTITUDE (ic a ee nia oe ae
a Soh Be bey sent Pee Sir = ‘\ :
8 pe Le
Oo cst Ss.
Lu
=
Oo
o
oo Siysdiis CAN
oO a SF fenee
oc pip’ AOD oe pb Sid
5 ee te Se ae i eet
fo)
10
107 10" 10° 10' 10”

TIME (sec)

Figure 6.13. Effects of Altitude on Thermal Power for a 10-MT Burst.

ADA

THERMAL RADIATION o-y

I KT(ALTITUDE =0km) _ _ 4 MT (ALTITUDE =0 km) _
” FRACTION = 0.25 x 1.2 = 0.3 FRACTION = 0.25 x 0.8 = 0.2

SPECTRUM (fraction per micro meter)
°

3.0 °5
WAVELENGTH (micro meter) WAVELENGTH (micro meter)

=
N

6.46 x10 "cals

_
i=)

1 MT (ALTITUDE = 0 km)

FROM TABLE 6.2:

Pymax(KT/sec)= 1.35 W
= 1.35 (47.9)
= 64.6 KT/s
= 1.35 (47.9)

1 KT (ALTITUDE = 0 km)
FROM FIGURE 6.9: x
(cal/s) =3.5x10 cal/
(ms) =34ms

0.56

Se
ro)

max

t omax

=
o

(ms) =41.93w°**
= 41.93 (24.66)

tomax (ms) = 1034 ms
1.29 x1 om cal/s

NORMALIZED SOURCE POWER P (t)/P(tomax)

2.0 4.0 6.0 2.0 4.0 = =
NORMALIZED TIME (t/t NORMALIZED TIME (t/t,

NORMALIZED SOURCE POWER P (tV/P(t,___)

0.4 11 (5,000 °K)

2.5

ALTITUDE (km).

Serre (ee 2, Chere ee eee eee Cee ee eee eee eee eee eee eee ee eee ee ee es

[1 82,0002H) es

SOURCE SPECTRUM (fraction per micro meter)

SOURCE SPECTRUM (fraction per micro meter)

“3.0
WAVELENGTH (micro meter)

‘Figure 6.20. Effect of Altitude on Spectral
Distribution for a 100-KT Burst.

4.0

1.0 2.0 3.0
WAVELENGTH (micro meter)

Figure 6.19. Effects of Altitude on Spectral
Distribution for a 1-KT Burst.

|
|
4.0 |

937

6 THERMAL RADIATION

| 6.2.6 Thermal Exposure. This section includes sev-

eral families of curves of radiant exposure (cal/cm7)

versus range for various parameters. Factors which
PUL ee influence the data are the thermal fraction, HOB, vi-
noe oa EY eas eee eee sual range, yield, and target altitude. All assume a
eet Sd a peas target with its normal oriented towards the source,
and no albedo from the earth’s surface or clouds.
Limited data sets are provided based on RECIPE.
More complete sets of figures are provided in EM-
; ree de oF 1, Chapter 6. Figures 6.22 through 6.27 show expo-
ceeheesctecebesssssesbeantesvedeneses beeen sure as a function of target altitude versus ground
See SS a range for surface and 1-km burst altitudes for several
combinations of yield and visibility. Figures 6.28
through 6.37 provide thermal exposure curves for a
target on the ground, as contours of HOB versus

ee eee ee ee eee eee eee eee. eee eee eee eee ee eee eee

conaeire

Pe SE epcmaee lahat = ape

|
SOURCE SPECTRUM (fraction per micro meter) -

"0 1.0 2.0 3.0 4.0 ground range, for various yields and visibilities. Also

ic acnatenhiner ip race tale shown on these figures for comparison are airblast

Figure 6.21. Effect of Altitude on Spectral peak overpressure on the ground under the same burst
Distribution for a 1-MT Burst ‘ conditions

D3R

THERMAL RADIATION 6-19

6.3 Atmospheric Transmission Effects. As introduced in Equation 6.1, transmission effects are given
by the product Tg, where T is the transmittance factor for a generalized geometry with idealized al-
bedo surfaces and model atmospheres depending on the visibility. The geometry factor g includes
fireball asymmetry and target orientation effects. Values of T and g have been computed for a wide
variety of situations and are presented in graphical form for predictive purposes. Such predictions
are intended only to bracket a particular case for which actual transmission factors will vary with time
and space, and may be very difficult to specify quantitatively. In addition, the normal variables of hu-
midity, dust, haze, fog, smog, and albedo factors will be even less predictable in rapidly changing wartime
environments.

The codes used to produce these data compute both the direct and scattered components as a func-
tion of wavelength over the range between 0.3 and 4.0 um. Scattering includes both Rayleigh (mo-
lecular) and Mie (aerosol), and absorption is calculated for water vapor, carbon dioxide, and ozone.
The cross sections for all of these processes are wavelength dependent.

Thus, it is customary to define discrete wavelength bands and perform the transport calculations with the
scattering and absorption parameters defined over the separate bands. The “buildup factor” is the ratio of
the total exposure to directly transmitted exposure, and thus is a measure of the importance of the scattered
or diffuse component of the radiation. Figure 6.38 illustrates this factor as a function of optical depth (in-
tegral of the product of the scattering cross section and number density of the scattering medium along the
path from source to detector) for Pacific Test Site conditions and the albedo of seawater, and shows that the
diffuse component may be much larger than the direct component at long ranges. The resulting angular
distribution for one wavelength (0.55 um) is shown in Figure 6.39.

6.3.1 Effects of Meteorological
Conditions. This section consid-
ers the effects of aerosols and mo-
lecular absorption. Albedo effects
will be discussed in Section 6.3.2.

6.3.1.1 Visibility. Daylight vis-
ibility is the distance at which a
large dark object is just recogniz-
able against the sky background.
Nighttime visibility is defined as
the longest distance at which an
unfocused light of moderate inten-
sity can be seen. Table 6.3 gives
the international visibility code,
relating a qualitative description of
the atmosphere to observed vis-
ibilities. It is usually assumed that
the transmittance is 5.5 percent
along the distance corresponding
to the visibility.

TOTAL RADIATION/DIRECT RADIATION

The “meteorological range” (MR)
is the horizontal distance for
which the transmittance of the at-
mosphere for a direct beam of
light is 2 percent. The meteoro-

logical range is related to the at- 0 0.4 0.8 1.2 1.6 2.0 24 2.8

mospheric extinction cross section | SCATTERING OPTICAL DEPTH
by:

Figure 6.38. Comparison of Buildup Factors for Various Radia-
0, = 3.91/MR (6.8) tion Wavelengths Simulating Pacific Atmosphere with Both Source
_ and Sampling at 1-km Altitude.

YAT

Oo-— ZU

LHERKMAL KAVIA

The relationship between the visibility and the meteorological range is:

V = 0.74MR.
In this section, all transmission predictions will be related to the visibility, and not to the meteorolog,

ical range.

FRACTION OF PHOTONS RECEIVED

Code
Number

0 20

Description

Dense Fog

Sos

Light Haze

40 60

80 100 120 140

FIELD OF VIEW (degrees)

Figure 6.39. Effects of Field of View on the Thermal Radiation for a Target on the Ground
from a 0.55 um Source at an Altitude of 1 km.

Table 6.3. International Visibility Code.

AAO

Visibility
50 meters (55 yards)

(550 yards)

so

11UP

(6.9)

THERMAL RADIATION 6-25

14

12

=
i=)

RECEIVER ALTITUDE (km)

6. & Ae 20 25 30 35 40 45 50
HORIZONTAL RANGE (km)

Figure 6.46. Transmission Contours for a 10-MT Surface Burst with a Visibility of 10 km.

14

12

—_
So

RECEIVER ALTITUDE (km)

= 2 2
HORIZONTAL RANGE (km)

Figure 6.47. Transmission Contours for a 1-MT Burst at an Altitude of 1 km with a Visibility of 50 km.

2453

ELEVATION ANGLE (DEGREES)
10 7 5 4

:50 km OR GREATER = EXCEPTIONALLY

45
90/ 30 20 15

1.0

:20 km - 50 km = VERY CLEAR

:10 km - 20 km = CLEAR

> 4km-10km = LIGHT HAZE
S| 2km- 4km = HAZE

‘1k — 2m = THIN FOG

exh,

ct See! Cee >) eee eee eee Ceri rere ea ee ee ei, aa rere

DIRECT
TRANSMISSION 2

-
S
sod

VISIBILITY (km)

5 7 9 11 13 15
SLANT RANGE/SOURCE ALTITUDE

Figure 6.48(a). Transmission from a
High-Altitude Burst to a Target on

THERMAL RADIATION

on ELEVATION ANGLE (DEGREES)
90/ 30 20 15 10 7 5 4

1.0

VISIBILITY (km)
“~~. BS .

“ey | :
=~

0.1
=
2)
Ww)
a2
—
Ow
Ez
<
om
=
0.01 TRE ER: Ae > TE Oe, NEE eRe. See Ie. | een ompR eee
50 km OR GREATER = EXCEPTIONALLY CLEAR |
20 km — 50 km = VERY CLEAR
10 km — 20 km = CLEAR
4 km — 10 km = LIGHT HAZE
2km-: 4 km = HAZE
1km—2km=THIN FOG :
0.001 l l

1 3 5 7 9 11 13 15
SLANT RANGE/SOURCE ALTITUDE

Figure 6.48(b). Transmission from
a High-Altitude Burst to a Target
on the Ground Surface (Total).

the Ground Surface (Direct).

Monte Carlo calculations are required when atmospheric transmission effects are included with the
albedo calculations. EM-/ contains figures showing the results of a series of such calculations for a
1-MT burst at 1-km altitude in a 50-km visibility, for various combinations of albedo surfaces. It is.
not feasible to interpolate to other parameter sets.

However, a generalized data set is available for the case in which atmospheric effects are neglected
and a diffuse reflecting plane has an albedo of unity. In Figure 6.52, A, and S, are the target altitude
and the horizontal range of the detector normalized by the source altitude. The quantity plotted is the
sum of the direct component and that due to the albedo surface. The target orientation was chosen to
maximize the exposure but is essentially aimed at the source. The transmission for an albedo (p) less
than unity can be approximated by:

T, = 1+ p(T,- 1), (6.12)
where T is the transmission for an albedo of unity.
For a surface burst with a hemispherical fireball on the albedo surface, the transmission is,

i = 1+py/n,- (6.13)

where the functions y, and 1), are given in Figures 6.53(a) and 6.53(b), respectively. In these figures,
R is the slant range to the target, R, is the radius of the hemispherical fireball, and 0 is the angle be-
tween a vertical line through the burst point and the line of sight to the target.

ALA