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00320773.Pdf LA-2000 PHYSICS AND MATHEMATICS (TID-4500, 13th ed., Supp,.) LOS ALAMOS SCIENTIFIC LABORATORY OF THE UNIVERSITY OF CALIFORNIA LOS ALAMOS NEW MEXICO REPORT WRITTEN: August 1947 REPORT DISTRIBUTED: March 27, 1956 BLAST WAVE’ Hans A. Bethe Klaus Fuchs Joseph 0. Hirxhfelder John L. Magee Rudolph E. Peierls John van Neumann *This report supersedes LA-1020 and part of LA-1021 =- -l- g$g? ;-E Contract W-7405-ENG. 36 with the U. S. Atomic Energy Commission m 2-0 This report is a compilation of the dedassifid chapters of reports LA.-IO2O and LA-1021, which 11.a.sbeen published becWL’3eof the demnd for the hfcmmatimo with the exception d? CaM@mr 3, which was revised in MN& it reports early work in the field of blast phencmma. Ini$smw’$has the authors had h?ft the b$ Ala.mos kb(mktm’y Wkll this z%po~ was compiled, -they have not had ‘the Oppxrtl.mity to review their [email protected] and make mx.m%xtti.cms to reflect later tiitii~e ., CONTENTS Page Chapter I INTRODUCTION, by Hans A. Bethe 11 1.1 Areas of Discussion 11 1.2 Comparison of Nuclear and Ordinary Explosion 11 1.3 The Sequence of Events in a Blast Wave Produced by a Nuclear Explosion 13 1.4 Radiation 16 1.5 Reflection of Blast Wave, Altitude Effect, etc. 21 1.6 Damage 24 1.7 Measurements of Blast 26 Chapter 2 THE POINT SOURCE SOLUTION, by John von Neumann 27 2.1 Introduction 27 2.2 Analytical Solution of the Problem 30 2.3 Evaluation and Interpretation of the Results 46 Chapter 3 THERMAL RADIATION PHENOMENA, by John L. Magee and Joseph O. Hirschfelder 57 3.1 Radiation Hydrodynamics: the Radiation Flux’ 59 3.1.1 The Hydrodynamical Equations Imluding . Radiation 60 3.1.2 The Radiation Flux 61 3.1.3 Steady State Smearing Out of a Shock Front by Radiation 66 3.2 The Strong Blast Without Radiation 68 3.3 The Opacity of Air 69 -3- CONTENTS (Continued) 3.3.1 High Temperature Opacity of Air 70 3.3.2 Intermediate and Low Temperature Opacity of Air 74 3.3.3 Absorption of Air at Normal Conditions 84 3.4 Radiation Expansion Period and the Formation of the Blast Wave 87 3.5 Radiative Effects in Strong Blast Period 90 3.5,1 Qualitative Effects of Radiation in Strong Air Blast 90 3..5.2 Diffusive Motion of the Internal Radiation Front 92 3.5.3 Radiative Cooling of the Hot Core 95 3.6 The Ball of Fire 98 3.6.1 Radiation Expansion Period 99 3.6.2 Radiating Shock Front 103 3.6,3 Expanded Ball of Fire 103 3.6.4 Ball of Fire Radius 104 3.7 Scaling Laws 104 3.7.1 Radiative Expansion Period 104 3.7.2 Radiating Shock Front 105 3.7.3 Strong Shock Period and the Total Radiation Yield 106 Chapter 4 APPROXIMATION FOR SMALL y - 1, by Hans A. Bethe 107 4.1 General Procedure 107 4,2 General Equations 109 4.3 The Point Source 111 4.4 Comparison of the Point Source Results with the Exact Point Source Solution 116 4.5 The Case of the Isothermal Sphere 121 4.6 Variable Gamma 124 4.7 The Waste Energy 130 -4- CONTENTS (Continued) Chapter 5 ASYMPTOTIC THEORY FOR SMALL BLAST PRESSURE, by Hans A. Bethe and Klaus Fuchs 135 5.1 Introduction 135 5.2 Acoustic Theory 136 . 5.3 General Theory 137 5.4 Second Approximation 140 5.5 The Motion of the Shock Front 145 5.6 Results for Very Large Distances 146 5.7 The Energy 150 5.8 The Propagation of the Shock at Intermediate Distances 154 5*9 The Negative Phase. Development of the Back Shock 161 5.10 The Case of Two Pressure Pulses Catching Up with Each Other 166 5.11 The Continuation of the IBM Run 171 Chapter 6 THE IBM SOLUTION OF THE BLAST WAVE PROBLEM, by Klaus Fuchs 177 6.1 Introduction 177 6.2 The Initial Conditions of the IBM Run 179 6.2,1 The Isothermal Sphere 179 6.2.2 Initial Pressure and Density Distribution 180 6.3 The Total Energy 182 6.4 The IBM Run 182 6.5 Results 183 . - 6.6 Comparison with TNT Explosion. Efficiency of Nuclear Explosion 184 6,7 Scaling Laws 202 -5- CONTENTS (Continued) Chapter 7 THE EQUATION OF STATE OF AIR, by Klaus Fuchs and Rudolph E. Peierls 205 7.1 Equation of State of Air Between 2 x 104 and 2 x 106 Degrees 205 7.1.1 Outline of Method 205 7.1.2 The Partition Function of the Ions 208 7.1.3 The Partition Function of Free Electrons 211 7.1.4 Degree of Ionization 219 7.1.5 The Free Energy, Thermal Energy$ Entropy, and Pressure 221 7.1.6 The Hugoniot Curve 234 7.2 The Equation of State of Air Below 25,000% 237 7.2.1 The Range from 12,000 to 25,000”K 237’ 7.2.2 The Range from 300 to 12,000”K 239 7.3 The Equation of State of Air at Low Pressures 240 7.3.1 Introduction 240 7.3.2 The Composition of Air 240 7.3.3 The Thermodynamkal Quantities 247 7.4 Collected Results 253 7.5 Approximate Form of Adiabatic for IBM Run of Nuclear Explosion 253 7.6 Approximate Form Used for IBM Run of HE Explosion 297 ILLUSTRATIONS Chapter I INTRODUCTION 1.1 Path of Acoustic Waves Starting from the Center ~’0~~ 23 Chapter 3 THERMAL RADIATION PHENOMENA 3.1 Itosseland Mean Free Path 72 3.2 Rosseland Mean Free Path 73 ILLUSTRATIONS (Continued) 3.3 Mean Free Path for Absorption of Radiation ~by 0- and 0~ 80 3.4 Absorption Coefficient of N02 for T ~ 300”K 81 . 3.5 Mean Free Path of Radiation in N02 82 3.6 Mean Free Path of Radiation in N02; Radiation the Same Temperature as the N02 83 3.7 Mean Free Path of Radiation in N02; the Radiation Temperature Above 10,OOO°K 85 3.8 Absorption of Ai5 T = 300°K; P = 1 atm 86 3.9 Radius of Internal Radiation Front vs Shock Radius 93 3.10 Over-all Time History of the Blast Wave 96 3.11 Shock Temperature vs Shock Radius 102 Chapter 5 ASYMPTOTIC THEORY FOR SMALL BLAST PRESSURE 5.1. Symmetrical Equal Shock Waves 151 , 5.2 Initial Pressure Pulse 158 5.3 Three Shocks Where the Reflected Shock Will Sometime Catch Up with the Rear of the First Pulse 166 5.4 Plot of g(s) Vs s 172 5.5 Overpressure vs Shock Radius 176 Chapter 6 THE IBM SOLUTION OF THE BLAST WAVE SOLUTION 6.1 Shock Pressure vs Distance for Nuclear Explosion 185 6.2 Pressure vs Time 186 6.3 Pressure vs Time 187 6,4 Pressure vs Time 188 6.5 Pressure vs Distance at a F~ed Time 189 6.6 Pressure vs Distance at a Fixed Time 190 6.7 Pressure vs Distance at a Fixed Time 191 6*8 Pressure vs Distance at a Fixed Time, 192 6.9 Pressure vs Distfice at a Fixed Time 193 6.10 Pressure vs Distance at a Fixed Time 194 6.11 Pressure vs Distance at a Fixed Time 195 6.12 Pressure vs Distance at a Fixed Time 196 -7- ILLUSTRATIONS (Continued) 6.13 Pressure vs Distance at a Fixed Time 197 6.14 Deviation of the Positive Phase of a Pulse at a Fixed Distance 198 . 6.15 The Positive Impulse and the Energy in the Blast 199 6.16 Efficiency of Nuclear Bomb as Cornpared to an Equivalent Charge of TNT 201 Chapter 7 THE EQUATION OF STATE OF AIR 7.1 Degree of Ionization 229 7.2 Hugoniot Curve; Density vs Pressure 236 7.3 Hugoniot Curve; Temperature as a Function of Shock Pressure 238 TABLES Chapter 2 THE POINT SOURCE SOLUTION 2.1 x/xshock 2*2 x/xshock 2.3 ~/~shock 53 2.4 U/Ushock 53 2.5 P/PShock 54 2.6 ei/6i shock = T/Tshock 54 2,7 E#c shock 55 2.8 Some Other Useful Quantities 55 Chapter 3 THERMAL RADIATION PHENOMENA 3.1 Data for Opacity Calculation ’75 3.2 Values of Number of Electrons per Cubic Centimeter in Air 79 3.3 Some Properties of the Blast Wave During Radiation Expansion Period 89 3.4 Some Properties of the Blast Wave During Radiation Expansion Period 90 -8- TABLES (Continued) 3.5 Effect of Shielding 101 L Chapter 4 APPROXIMATION FOR SMALL y - 1 4.1 Variation of Ratio of Internal Pressure to Shock Pressure with Gamma 112 Chapter 7 THE EQUATION OF STATE OF AIR 7*1 Ionization Energies 212 7.2 Energy Levels of Nigrogen and Oxygen Ions 213 7.3 The Integrals I(Q) and J(a) 217 7.4 The Integrals LV 218 7.5 The Degrees of Ionization and Number of Free Electrons 222 7.6 Pressure, Energy, and Entropy 232 7.’7 The Adiabatic 233 7.8 The Shock Wave Curve 235 7.9 Partition Functions of Molecules and Atoms 244 7.10 Low-Density Equation-of-State Data 251 7.11 Pressure vs Temperature for Various Compressions 254 7.12 Properties of Air Along the Hugoniot Curve 261 7.i3 Thermodynamic Properties of Air at a Pressure of 1 bar 262 7.14 Properties of Air Along the Adiabatic Terminating in the Hugoniot Curve 263 7.15 Thermodynamic Properties of Air 273 7.16 Properties of Air Along the Adiabatic 284 7.17 Rate of Change of Shock Pressure with Entropy 288 7.18 Smoothed E@ation of State of Air 291 7.19 Values of V., VA, a, and ~ as Functions of ps/pQ D “ 300 -9- ——.—— ‘., \ .
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