Random Tracks Research Articles

Random Paths in Random Arrays of Cylinders

Distributions associated with random tracks in bodies are important to understanding the effects of radiation on objects and their response to it. Results of computer simulations are presented for the distribution densities, average lengths, and relative frequencies of the various types of random tracks resulting from the traversal of random arrays of cylinders by random lines. We consider arrays consisting of freely overlapping long circular cylinders distributed randomly with their axes parallel to a line or a plane, or oriented randomly in the three-dimensional space. The problem of random tracks lying outside the cylinders (external random tracks) is treated analytically, while the distributions of random tracks found within the cylinders (internal random tracks) are determined using a simulation procedure based on a discrete step-by-step random walk mechanism applied in finite samples of the arrays. The numerical results are used to validate various general analytical results for the distribution densities and average lengths of random tracks in structures of arbitrary shape. It is found that the distributions of internal random tracks exhibit strong dependence on the cylinder volume fraction, while the external random tracks are distributed independently of the cylinder volume fraction for all three cases of orientation distribution. At the limit of high cylinder volume fraction, the internal random track distributions approach the distributions of the external random tracks, while at the other extreme, they become, as expected, identical to those determined analytically for a single infinite cylinder.

Particle dosimetry in bone and the toxicity of bone-seeking radionuclides

Consideration is given to the tissues at risk in bone and a Monte Carlo method is described which determines the absorbed dose to endosteal tissues and marrow in trabecular bone. The method synthesises random tracks through the trabecular structures that deposit energy along a path through any given trabecular cavity. The path lengths through the trabeculae and marrow cavities are measured with a bone-scanning microscope and other bone data, such as trabecular surface areas, can also be derived. Results are given for human bones and for bones of the beagle, miniature pig and rhesus monkey. They show that, for the same radionuclide concentration, the doses to endosteal tissues and bone marrow are several times greater in animal than in human bone, and that higher doses in human bone from the Ca and Sr radionuclides are obtained if the initial deposition on bone surfaces is allowed for. Other studies show that the occurrence of osteosarcoma in the human long bones correlates well with trabecular surface area and also that, unlike the case of beta -particles from 90Sr+90Y, leukaemia is not a significant consequence of the alpha -particle doses from 226Ra in human bone or from 226Ra, 239Pu and other alpha emitters in beagle bone.

Penetration and energy loss of fast electrons through matter

A detailed scattering model, based on the continuous slowing down and the Born approximations, is shown to give results in good accordance with experiments when used in conjunction with the Monte Carlo method. Relativistic elastic and inelastic cross-sections adopted are derived from an analytical fit to the Dirac-Hartree-Fock-Slater atomic density with Wigner-Seitz boundary conditions. Random tracks are simulated in a completely analytical way; this fact largely reduces the complexity of the Monte Carlo procedure.

Energy loss of electrons in random motion

A subexcitation electron (energy range 1–6 eV or so) in a molecular medium losses energy in the excitation of molecular vibrations or phonons. One of the loss mechanisms involves the transient electric field generated by the motion of the electron and this paper presents an investigation of such energy loss. Ensembles of random tracks generated by a Monte Carlo procedure are considered. The Fourier transform of the electron displacement of each track is obtained by a fast Fourier transform (FFT) algorithm and the ensemble-averaged square of this transform provides a frequency spectrum which determines the average energy loss of the electron. Two mechanisms are considered as examples: the loss to dipolar relaxation in water, and the loss to infrared-active vibrations in benzene and polyethylene. The rate of energy loss to dipolar relaxation in water is in the range of 1013 eV/sec and the rate of loss to infrared-active vibrations in hydrocarbons is less by perhaps a factor of 3 or more. The relationship of this classical model to a more rigorous quantum mechanical treatment and the numerical methods are discussed in the Appendices.

Considerations on the Random Traversal of Convex Bodies and Solutions for General Cylinders

The basic concepts applicable to the random traversal of convex bodies are discussed, and a set of theorems relevant to the problem is presented. Formulae are derived for the chord length distribution in cylinders of arbitrary convex corss section in a uniform isotropic field of straight random tracks.