Steven S McCready

The deterministic transport sphere (DXTRAN sphere) is a technology that can be utilized in MCNP for improving sampling in the vicinity of a particular geometry, when the solid angle, between the source and particular geometry, is small. At a collision event, a DXTRAN particle is created and deterministically transported to the DXTRAN sphere, while the colliding particle (NONDXTRAN particle) continues transporting as if no DXTRAN event had occurred. Weight is balanced by killing the NONDXTRAN particle when traversing the DXTRAN sphere. If set up correctly, the DXTRAN particle placed on the DXTRAN sphere has a high probability of interacting with the geometry within the DXTRAN sphere. The Central Limit Theorem (CLT) states that the estimated mean approaches a normal distribution with known variance as the number of random samples grows sufficiently large. In reality the variance is seldom known and therefore must be estimated. In a Monte Carlo calculation, one must determine when the number of random samples is sufficiently large for the CLT to be satisfied. For the CLT to be satisfied, the first two moments (mean and variance) must exist. The second moment, the variance of a normal distribution is estimated. The slope test, which uses the largest 201 history scores of each tally fluctuation chart (TFC) bin fit to a Pareto function, is used to determine if the largest history scores decrease faster than 1/x{sup 3}. If the slope is less than 3, then enough histories have not yet been sampled such to meet the second moment existence requirement of the CLT. Usually, a slope of less than 3 indicates that the effects of high weight scores have not been satisfactorily sampled; such a consequence can also be manifested in examining trends in the 4. moment, the variance of the variance (VOV). For example, when examining the TFC, if the VOV is monotonically decreasing for a few sets of histories and then drastically increases for the next set of histories, chances are a rare high weight score, significantly greater than the average score, was encountered. As a result of the 1/R{sup 2} term, a point detector can achieve an extremely high weight, much greater than the average, as the distance from collision to point detector approaches zero. To remedy this difficulty, a 'radius of exclusion' is applied, where within the radius of exclusion 'the point detector estimate is assumed to be the average flux uniformly distributed'. A DXTRAN sphere can suffer from the same weight fluctuation as collisions in the vicinity of the DXTRAN sphere produce much larger weights than collisions happening far from the DXTRAN sphere. If the rare large weight put on the DXTRAN sphere then scores in a tally, there will be a significant increase in the VOV and the slope may drop below 3. To compliment that analysis, here we utilize an air composition and density that varies as a function of altitude, detailing the trials and tribulations of attempting to pass the 10 statistical checks for a variety of single and nested DXTRAN sphere approaches. The objective here is to illuminate important considerations for radiation transport problems with small solid angles in a scatter medium of few mean free paths (MFPs)

Computing neutron dosimetry involves transporting neutrons [n] from a source to a sink, determining the neutron heating within the sink and multiplying the neutron heating by a quality factor to compute the dose equivalent. The space and energy dependent neutron fluence is a measure of the amount of neutrons crossing a particular surface area, about a particular energy and is given in units of [n/cm{sup 2}]. Microscopic cross sections are given in units of area and vary by isotope and reaction type as a function of energy. The product of the atom density of a particular atom in a specie and the microscopic cross section of a particular reaction results in the macroscopic cross section of a particular reaction, given in units of per length [1/cm] as a function of energy. Summing the macroscopic cross sections of all isotopes, and all collisions resulting in heating, within a volume, results in a total collision heating macroscopic cross section for that volume. The product of the energy and spatial dependent collision heating macroscopic cross section and the energy and spatial dependent fluence, within an energy group, results in a collision heating reaction density for that particular reaction in that energy group. Weighting each energy group's collision heating reactions, with the corresponding energy dependent particle damage per collision heating event (usually biological damage), and then integrating over energy and volume results in the delivered dose. Therefore understanding dose delivery involves examining the spatial and energy (and time) dependent fluence behavior. Because of the coupled energy and space dependence of the heating weighting and macroscopic cross sections, the fluence is not so easily separable in energy and space; however, the energy integrated fluence can be used as a first order approximation of the relative magnitude of reactions as a function of space. Here we examine the first part in the dosimetry calculation process, transporting neutrons from source to sink, as applied to neutron transport in air, examining characteristics of the fluence. Presented here is analysis regarding the nature of the fluence peak between 10 g/cm{sup 2} and 100 g/cm{sup 2} for a typical air transport calculation. Due to the high concentration of nitrogen and oxygen isotopes of these elements, these isotopes tend to dominate the transport. From the analysis presented here, the fluence peak is the result of scatter back and forth across the peak regime, and (n,2n) has a minimal (<4%) contribution. Further evidence of minimal (n,2n) impact in the 10-100 g/cm{sup 2} span includes the 1 MeV fluence peak being so much larger than the 14 MeV peak; where 1 MeV is not above the (n,2n) threshold. Also presented here is the usefulness of using tally tagging with cell flagging to further dissect the nature of the fluence. These technologies allow us to understand the originating volume that makes a contribution to a scoring regime. (authors)