Programs for the Landau and the Vavilov distributions and the corresponding random numbers

We detect regular particle showers in several compact pixel detectors, distributed over the International Space Station. These showers are caused by high energy galactic cosmic rays, with energies often in the 10 s of TeV or higher. We survey the frequency of these events, their dependence on location on ISS, and their independence of the location of ISS, on its orbit. The Timepix detectors used allow individual particle tracks to be resolved, providing a possibility to perform physical analysis of shower events, which we demonstrate. In terms of radiation dosimetry, these showers indicate certain possible limitations of traditional dosimetric measures, in that (a) the dose measured in small sensor may be less than that received in a larger distribution of matter, such as a human and (b) the spatial and temporal extent of these events represents a regime of poorly documented biological response.

Unlike for external beam treatment, Model Based Dose Calculation Algorithms for Brachytherapy are still under development, and have been recently encouraged by the American Association of Physicists in Medicine. This delay is at least partially caused by the extreme complications associated with the multidimensional considerations underlying Brachytherapy dose calculations. These algorithms require detailed mathematical description, based on extensive radiation physics considerations, of the spatial and angular distribution of the points where the decay photon first interacts in matter, called TERMA points, along with the functions describing the radial and angular dose spread around each TERMA point, called Kernel. This work contributes to this global effort by providing these functions for the individual photon lines in the decay of the exactly modeled Nucletron microSelectron $v_3$ ¹⁹²Ir source. The underlying physics of all photon and electron interaction mechanisms has been extensively considered. Furthermore, the effect of the absorbing media has been also investigated. Ultimately, three-dimensional integration of dose Kernel contribution at a specified position, running all over TERMA points in the irradiated volume, has been conducted to generate the dose at that specific location. This methodology is much less time, data storage, and CPU consuming compared to repeating the extensive Monte Carlo simulations. The work is merely intended to provide a launching point and basic key physics elements for anticipated future quantitative clinical use.

We present a saddlepoint approximation for ionization energy loss distributions, valid for arbitrary relativistic velocities of the incident particle $0<v/c<1$, provided that ionizing collisions are still the dominant energy loss mechanism. We derive a closed form solution closely related to Moyal’s distribution. This distribution is intended for use in simulations with relatively low computational overhead. The approximation generally reproduces the Vavilov most probable energy loss and full width at half maximum to better than 1% and 10%, respectively, with significantly better agreement as Vavilov’s $\kappa$ approaches 1.

Straggling functions for protons in thick silicon radiation detectors are computed by Monte Carlo simulation. Mean energy loss is constrained by the silicon stopping power, providing higher straggling at low energy and probabilities for stopping within the detector volume. By matching the first four moments of simulated energy-loss distributions, straggling functions are approximated by a log-normal distribution that is accurate for Vavilov $\kappa \gtrsim 0.3$. They are verified by comparison to experimental proton data from a charged particle telescope.

A Bayesian probabilistic data analysis method for energetic proton and ion data from charged particle telescopes in space is described. The telescope is assumed to consist of only a series of planar silicon detectors with graduated thicknesses. The method is based on a range-straggling function and makes optimal use of energy loss measurements in each detector. It provides accurate incidence angle estimates for particles stopping in the telescope, allowing accurate element identification and possible isotope identification. It also provides energy estimates for high-energy particles going through the telescope without stopping. Examples are shown for simulated telescope design performance tests and application to real space-particle data.

We performed a time-of-flight (TOF) single-crystal neutron diffraction experiment with a diffractometer (the IBARAKI Biological Crystal Diffractometer (iBIX)) using single-crystal silicon, and we determined several candidates for fundamental fitting functions to faithfully reproduce the Bragg reflection profile with asymmetries in the TOF direction. The Vavilov and Landau distributions used to describe the energy loss of charged particles traversing a thin absorber were found to be in excellent agreement with the observed TOF profile. We have evaluated the obtained functions and the convolution of back-to-back exponentials with a Gaussian to determine which function provides the best fit to the data. Further, we have applied the obtained functions to the practical Bragg reflection profiles of proteins after subtraction of the background using the Statistics-sensitive Nonlinear Iterative Peak-clipping (SNIP) algorithm.