Theory of the Fireball

More documents

Recommendations

Info

assuming the strong shock relation p - t -1 -2 . The ratio (5.40) is tnen I-Iere we use the relation (3.10) and find P - -yI y t - 1 e EE (5 945 where H has been labeled 3 because it refers to the radiating temperature. %re we may insert ( 3.30) and (3.31-), viz., We may then compare the result with (5 .IS), the velocity of the cooling vave (setting J = 0) 0 u= Ho - 5. The comparison gives 62
Inserting (3.33) for JIJ and changing the unit of p from dynes/cm 2 to 6 2 bars = LO dpes/cm we get Setting nar p1 = po and C ~ O O S ~ as ~ , in Sec. 5d, Tc 1 = 3.6 and T1 r = 1.08 yields p1 = 5.0 bars Thus the critical pressure is 5 bars, which was tne reason for the choice of this, number at t'ne end of Sec. 5d. Tnere it vas shown that 5 bars and T' = 3.6 leads to Ti = 1.08 so that our numbers are consistent. C We had to rely on Brode ' s solution to find Tc for a given p; this could only be avoided by obtaining an analytic solution for the isotneml sphere which will be discussed in a subsequent paper. Apart from this our treatment is analytical, making use of the equation of state and the absorption characteristics of air.
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 66 and 67: pressure is larger than pa, (5.50)
Page 68 and 69: inconsistency in our apyroximations
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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?