Theory of the Fireball

More documents

Recommendations

Info

inconsistency in our apyroximations . In our one-diniensional tneoqy, tne end of Stage C I narks -the max- Snrrm. of radiation, both in temperature and total emission. In Stage C I because the material becomes more transparent. In Stage C I1 the reverse is the case, (5.39), because the material which has gone through the cooling wave becomes thicker with time, (5,.32). Tnis material provides opacity for the visible light from the fireball; since it becomes more opaque, the radiation must now come from a layer of smaller absorption coefficient, (5.35), and therefore of lower temperature. As (5.36) sha~s, the increase of thickness (t 2n the denominator) is more important than the continued decrease of density (factor p 1/3 ). Tnese results will be modified in the three-dimensional theory, Sec. 6. 1 The maximum temperature has been calculated as T = 0.92 or 1.08, from om two calculations; it is clearly close to 1, i.e., ~O,OOO~. This number is not too mucn out of line with observation considering tnat we have calculated a maximum. In fact, tne transition from Stage C I to C I1 cannot be sudden as we have assumed; the cooling wave must begin gradually, and tnerefore the temperature peak which we have calculated will actually be cut off (Fig. 3). The observable maximum may easily be 1000° lower than our calculation. 66 k
f LOG t CALCULATED Fig. 3. The calculated increase in temperature in Stage C I, and decrease in Stage C I1 (straight lines), and the estimated actual behavior. The radius of the radiating surface increases with time in Stage C I. Inserting (5 .?4) into (5.51) gives 0.34 -0.225 t0.27 R-Y P (5 057) In Stage C 11, Yne surface moves rather rapidly inward relative to.the material, due to the cooling wave. In addition, for sea level explosions at least, the pressure is no longer much above ambient, so that the out- ward motion of the material slows dm. Thus the geometric radius of the radiating surface no longer increases much, and soon begins to decrease. Tnerefore, the total radiation will reach its maximum at the same time as, or very soon after, the maximum of the temperature.
Page 1 and 2:
, - Ip.L ,. : CIC-14 REPORT COLLECT
Page 3:
LA-3064 UC-34, PHYSICS TID-4500 (30
Page 6 and 7:
i.e., the part which has not yet be
Page 9:
1. INTRODUCTION 2. PHASES IN DETELO
Page 12 and 13:
6 radiation .(Stage A of Sec. 2) is
Page 14 and 15:
frequency, the opacity, which is su
Page 16 and 17:
elations as (3.2) between shock rad
Page 18 and 19: in this case there is no Stage D 11
Page 20 and 21: highest possible density of about l
Page 22 and 23: \ and the average of y' is taken ov
Page 24 and 25: The radius R is given R3 = I"- P P
Page 26 and 27: T-R -10 (3.16) 8 The numerical calc
Page 28 and 29: Since the interesting values of R a
Page 30 and 31: Most of the radiation comes from a
Page 32 and 33: higher frequency (above, and Sec. L
Page 34 and 35: 4. ABSORPTION coEFF1c1ms a. Infrare
Page 36 and 37: (3.21), it is small compared to the
Page 38 and 39: hv (ev) P/Po = 1 ff N2 0- Table N.
Page 40 and 41: w Q P/Po 1 0.1 0.01 T 4,000 6,000 8
Page 42 and 43: Table VI. Average Mean Free Paths (
Page 44 and 45: The fraction of the Planck spectm b
Page 46 and 47: The W beyond 3.5 ev will be strongl
Page 48 and 49: The equation of continuity is aH aJ
Page 50 and 51: U" J, A Ho - H(T1) To determine u w
Page 52 and 53: temperature is aromd Tb, and in whi
Page 54 and 55: internal energy in that sFhere; in
Page 56 and 57: y integrating (5.8); it depends on
Page 58 and 59: a log I1 - y' - 1 a log p at - y' a
Page 60 and 61: 2 vitn A = 0.1G q/cm and n = 6.3. T
Page 62 and 63: or a radiating temperature of 10,80
Page 64 and 65: assuming the strong shock relation
Page 66 and 67: pressure is larger than pa, (5.50)
Page 70 and 71: G. We& Cool-ing Wave In Stage C I1
Page 72 and 73: 6. EFFECT OF THREE DDENSIOUS a. Ini
Page 74 and 75: 6. Sinrinkage of Isotnemal Sphere W
Page 76 and 77: Pa f(x) = - P and obtain the simple
Page 78 and 79: From y = 1.18, y=l-A Y= -1 2.2 - 0*
Page 80 and 81: where Re is the outer edge of the l
Page 82 and 83: esult of the three-dimensional cons
Page 84 and 85: 4 dF: = - 4KaT at where a is the St
Page 86 and 87: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10 . REF
show all

Theory of the Fireball

Create successful ePaper yourself

Delete template?

Save as template?