Theory of the Fireball

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The radius R is given R3 = I"- P P J ;+ = m - Y - 1 - const. 7 (3.9) We shall set the constant equal to zero which amounts to the (incorrect) assmption that ( 3.8) holds dam to m = 0. Actually, the isot'nermal sphere gives the constant a finite, positive value. To find the temperature distribution, we note that the enthalpy H = 7' E Y 1 - l P We are using the enthalpy rather than the internal energy because the interior of the shock is at constant pressure, not constant density. The thermodynamic eqmtion for H is TdS=dH-~dp At given pressure, i.e., given time, (3.8) to (3.10) give 22
Now the approximate relation between internal energy and temperature is given by Gilmore,” Fig. 5, viz.,* * using p = from (3.3) and setting y’ = 1.18, which is a reasonable 4 where T ’ is the temperature in units of 10 degrees. average (see Table 11) we may rewrite (3.13) : where p is the pressure in bars. Since H is proportional to E, (3.12) and (3.14) give %e thermodynamic relation @) = T (g) - P T V leads to a relation between y - 1 and the exponents in the relation -x y E=& T Since we have chosen y = 1.18 and y = 1.5 this relation gives x = 0.09. This is in sufficient agreement with x = 0.1 as used in (3.13) .
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 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 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
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Theory of the Fireball

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