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Elements of Fission Weapon Design. Back to top of Section 4. Elements of Fission Weapon Design. Dimensional and Temporal Scale Factors. In Section 2 the properties of fission chain reactions were described using two simplified mathematical models the discrete step chain reaction, and the more accurate continuous chain reaction model. A more detailed discussion of fission weapon design is aided by introducing more carefully defined means of quantifying the dimensions and time scales involved in fission explosions. These scale factors make it easier to analyze time dependent neutron multiplication in systems of varying composition and geometry. You have not yet voted on this site If you have already visited the site, please help us classify the good from the bad by voting on this site. 1 I celebrate myself, and sing myself, And what I assume you shall assume, For every atom belonging to me as good belongs to you. I loafe and invite my soul. Issuu is a digital publishing platform that makes it simple to publish magazines, catalogs, newspapers, books, and more online. Easily share your publications and get. The best place to get cheats, codes, cheat codes, walkthrough, guide, FAQ, unlockables, achievements, and secrets for Gears Of War 3 for Xbox 360. By the time the flying plate converges from a radius of 1020 cm to collide with the levitated core, it is no longer a thin shell. The velocity difference that is. View and Download Mazda RX8 2004 service highlights online. Mazda RX8 2004. RX8 2004 Automobile pdf manual download. Express Helpline Get answer of your question fast from real experts. These scale factors are based on an elaboration of the continuous chain reaction model. It uses the concept of the average neutron collision which combines the scattering, fission, and absorption cross sections, with the total number of neutrons emitted per fission, to create a single figure of merit which can be used for comparing different assemblies. The basic idea is this, when a neutron interacts with an atom we can think of it as consisting of two steps the neutron is absorbed by the collision and. If the interaction is ordinary neutron capture, then no neutron is emitted from the collision. If the interaction is a scattering event, then one neutron is emitted. If the interaction is a fission event, then the average number of neutrons produced per fission is emitted this average number is often designated by nu. By combining these we get the average number of neutrons produced per collision also called the number of secondaries, designated by c. The total neutron mean free path, the average distance a neutron will travel before undergoing a collision, is given by. MFP 1crosstotal N. N is the number of atoms per unit volume, determined by the density. In computing the effective reactivity of a system we must also take into account the rate at which neutrons are lost by escape from the system. This rate is measured by the number of neutrons lost per collision. For a given geometry, the rate is determined by the size of the system in MFPs. Put another way, for a given geometry and degree of reactivity, the size of the system as measured in MFPs, is determined only by the parameter c. The higher the value of c, the smaller the assembly can be. An indication of the effect of c on the size of a critical assembly can be gained by the following table of critical radii in MFPs for bare unreflected spheres. Table 4. 1. 1 1. Critical Radius rc vs Number of Secondaries c. MFP. 1. 0 infinite. If the composition, geometry, and reactivity of a system are specified then the size of a system in MFPs is fixed. From Eq. 4. 1. 1 3 we can see that the physical size or scale of the system measured in centimeters, say is inversely proportional to its density. Since the mass of the system is equal to volumeensity, and volume varies with the cube of the radius, we can immediately derive the following scaling law. C2. That is, the critical mass of a system is inversely proportional to the square of the density. C is the degree of compression density ratio. This scaling law applies to bare cores, it also applies cores with a surrounding reflector, if the reflector is density has an identical degree of compression. This is usually not the case in real weapon designs, a higher degree of compression generally being achieved in the core than in the reflector. An approximate relationship for this is. Cc1. 2 Cr0. Cc is the compression of the core, and Cr is the compression of the reflector. Note that when Cc Cr, then this is identical to Eq. For most implosion weapon designs since Cc Cr we can use the approximate relationship. Cc1. 7. These same considerations are also valid for any other specified degree of reactivity, not just critical cores. Fission explosives depend on a very rapid release of energy. We are thus very interested in measuring the rate of the fission reaction. This is done using a quantity called the effective multiplication rate or alpha. The neutron population at time t is given by. Nt N0alpha. Alpha thus has units of 1t, and the neutron population will increase by a factor of e 2. This interval is known as the time constant or e folding time of the system, tc. The more familiar concept of doubling time is related to alpha and the time constant simply by. Alpha is often more convenient than tc or doubling times since its value is bounded and continuous zero at criticality positive for supercritical systems and negative for subcritical systems. The time constant goes to infinity at criticality. The term time constant seems unsatisfactory for this discussion though since it is hardly constant, tc continually changes during reactivity insertion and disassembly. Therefore I will henceforth refer to the quantity 1alpha as the multiplication interval. Alpha is determined by the reactivity c and the probability of escape, and the length of time it takes an average neutron for a suitably defined average to traverse an MFP. If we assume no losses from the system then alpha can be calculated by. MFPc 1. where tau is the average neutron lifetime between collisions and vn is the average neutron velocity which is 2. Me. V neutron, the average fission spectrum energy. The no losses assumption is an idealization. It provides an upper bound for reaction rates, and provides a good indication of the relative reaction rates in different materials. For very large assemblies, consisting of many critical masses, neutron losses may actually become negligible and approach the alphas given below. The factor c 1 used above is the neutron number, it represents the average neutron excess per collision. In real systems there is always some leakage, when this leakage is taken in account we get the effective neutron number which is always less than c 1. When the effective neutron number is zero the system is exactly critical. Nuclear Properties of Fissile Materials. The actual value of alpha at a given density is the result of many interacting factors the relative neutron density and cross sections values as a function of neutron energy, weighted by neutron velocity which in turn is determined by the fission neutron energy spectrum modified by the effects of both moderation and inelastic scattering. Ideally the value of alpha should be determined by integral experiments, that is, measured directly in the fissile material where all of these effects will occur naturally. Calculating tau and alpha from differential cross section measurements, adjusted neutron spectrums, etc. In the table below I give some illustrative values of c, total cross section, total mean free path lengths for the principal fissionable materials at 1 Me. V, and the alphas at maximum uncompressed densities. Compression to above normal density achievable factors range up to 3 or so in weapons reduce the MFPs, alphas and the physical dimensions of the system proportionately. Table 4. 1. 2 1 Fissile Material Properties. Isotope c crosstotal totalMFP density alpha tdouble. U 2. 33 1. 4. 3 6. U 2. 35 1. 2. 7 6. Pu 2. 39 1. 4. 0 7. Values of c and total MFP can be easily calculated for mixtures of materials as well. In real fission weapons unboosted effective values for alpha are typically in the range 2.

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