**Theory of the Fireball**

**Local PDF:** ADA383922.pdf

AD Number: ADA383922

Subject Categories: NUCLEAR EXPLOSIONS AND DEVICES(NON-MILITARY)

Corporate Author: LOS ALAMOS NATIONAL LAB NM

Title: Theory of the Fireball

Personal Authors: Bethe, Hans **A**.

Report Date: 17 JUN 1964

Pages: 84 PAGES

Report Number: LA-3064

Contract Number: W-7405-ENG-36

Monitor Acronym: XJ

Monitor Series: XD

Descriptors: *NUCLEAR EXPLOSIONS, *NUCLEAR FIREBALL, EXPLOSION EFFECTS,
ABSORPTION COEFFICIENTS.

Identifiers: COOLING WAVES

Abstract: The successive stages of the fireball due to **a** nuclear explosion in
air are defined. This paper is chiefly concerned with Stage C, from the minimum
in the apparent fireball temperature to the point where the fireball becomes
transparent. In the first part of this stage, the shock (which previously was
opaque) becomes transparent due to decreasing pressure. The radiation comes from
**a** region in which the temperature distribution is given essentially by the
Taylor solution; the radiating layer is given by the condition that the mean
free path is about 1/50 of the radius. The radiating temperature during this
stage increases about as p(exp -0.25) , where p is the pressure. To supply the
energy for the radiation, **a** cooling wave proceeds from the outside into the hot
interior. When this wave reaches the isothermal sphere, the temperature is close
to its second maximum. Thereafter, the character of the solution changes; it is
now dominated by the cooling wave (Stage C). The temperature would decrease
slowly (as p(exp 1/6)) if the problem were one-dimensional, but in fact it is
probably nearly constant for the three-dimensional case. The radiating surface
shrinks slowly. The cooling wave eats into the isothermal sphere until this is
completely used up. The inner part of the isothermal sphere, i.e., the part
which has not yet been reached by the cooling wave, continues to expand
adiabatically; it therefore cools very slowly and remains Opaque. After the
entire isothermal sphere is used up, the fireball becomes transparent and the
radiation drops rapidly. The ball will therefore be left at **a** rather high
temperature, about 5000 deg C. The cooling wave reaches the isothermal sphere at
**a** definite pressure. The radiating temperature at this time is about 10,000 deg
C. The slight dependence of physical properties on yield is exhibited in
approximate formulae.

Limitation Code: APPROVED FOR PUBLIC RELEASE

Source Code: 211350

Citation Creation Date: 29 NOV 2000