Theory of the Fireball

Technical Report · Sat Feb 01 00:00:00 EST 1964

DOI:https://doi.org/10.2172/4044355· OSTI ID:4044355

Bethe, Hans A. ^[1]

---

1. Los Alamos Scientific Laboratory (LASL), Los Alamos, NM (United States)

The successive stages of the fireball due to a nuclear explosion in air are defined (Sec. 2). 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 (C I), 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 (Sec. 5). The radiating temperature during this stage increases about as p^-1/4, where p is the pressure. To supply the energy for the radiation, a cooling wave proceeds from the outside into the hot interior (Sec. 5). 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 II). The temperature would decrease slowly (as p^1/6) if the problem were one-dimensional, but in fact it is probably nearly constant for the three-dimensional case (Sec. 6). 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 (Sec. 7), about 5000°. The cooling wave reaches the isothermal sphere at a definite pressure p_c ≈ 5(p₁/p₀)^1/3 bars, where p₁ is the ambient and p₀ the sea level density. The radiating temperature at this time is about 10,000°. The slight dependence of physical properties on yield is exhibited in approximate formulae.

• Research Organization: Los Alamos Scientific Laboratory (LASL), Los Alamos, NM (United States)
• Sponsoring Organization: US Atomic Energy Commission (AEC)
• DOE Contract Number: W-7405-ENG-36
• NSA Number: NSA-18-029822
• OSTI ID: 4044355
• Report Number(s): LA--3064
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
ADIABATIC PROCESSES
AIR
COMBUSTION
COOLING
DENSITY
DISTRIBUTION
EFFICIENCY
ENERGY
ENGINEERING
EQUATIONS
EXPANSION
HIGH TEMPERATURE
IMPACT SHOCK
LAYERS
LEVELS
MATHEMATICS
MEAN FREE PATH
MOTION
NUCLEAR EXPLOSIONS
PRESSURE
SPHERES
STABILITY
SURFACES
TEMPERATURE
THERMAL RADIATION
THERMODYNAMICS