# Fast Ion Speed Diffusion Effect on Distributions of Fusion Neutrons
## 1 Introduction  
Research and development activities on fusion neutron sources for fundamental science and technological applications are being pursued by universities, laboratories, and other organizations in various countries of the world, as indicated in [1; 2; 3; 4; 5; 6] and the references therein. An analysis of possibilities of constructing fusion neutron sources based on tokamaks, stellarators, and laser systems was recently published in [1]. In [2; 3], the long-standing concept of using controlled nuclear fusion systems as neutron sources was considered in light of the developments of the past decade. In [4; 5; 6; 7; 8; 9; 10; 11], the main attention was paid to tokamaks. In particular, in [4] and [5], neutron sources based on spherical and classical tokamaks, respectively, were investigated. Article [6] is dedicated to the analysis of the economic feasibility of tokamaks with conventional and superconducting windings as neutron sources applied to the transmutation of transuranium elements. Fusion neutron sources using deuterium-deuterium and deuterium-tritium reactions in a tokamak were considered in [7] and [8], respectively. In [9], an integral approach was applied to the modelling of a plasma neutron source based on a classical tokamak. Article [10] is devoted to a similar range of issues for a spherical tokamak. A three-dimensional model developed as part of the demonstration fusion neutron source DEMO-FNS project for neutronics calculations by Monte Carlo methods was presented in [11]. The yield and energy spectrum of neutrons belong to the main characteristics of the source. Along with conceptual and engineering design studies of fusion neutron sources employing magnetically confined plasma, calculations of energetic and angular distributions of fusion neutrons are essential for neutron spectroscopy [12], and for fast particle physics in plasma [13; 14], as well as for estimating loads on the first walls of reactors due to fluxes of neutrons and other fast particles [15]. Modelling of tritium breeding, subcritical fission, transmutation, and other purpose blankets also requires the knowledge of spectra of incident fusion neutrons [15; 16; 17; 18]. Reviews [19; 20] consider the stages of development and prospects of fusion-fission hybrid systems and emphasize the important role of the coefficient that takes into account the increased production of neutrons in subcritical systems in the initial generations of fission chain reactions. The value of this coefficient in the formula for the number of fission neutrons per one fusion neutron can exceed two. Energies of neutrons produced in the deuterium-tritium fusion reaction are much higher than the average fission neutron energy. In this regard, the energy spectrum of a fusion neutron source strongly manifests itself in the initial generations of subcritical fission. As a rule, in research and development works on controlled nuclear fusion in toroidal magnetic configurations, calculations of distributions of a plasma neutron source are combined with numerical modelling of the penetration of fast neutral beams into the plasma, with calculations of distributions of plasma ion velocities, simulations of neutron transport processes, and need to be included in more extensive integrated modelling. Studies [21] and [22] are devoted to the analysis of possible ranges of parameters of tokamak neutron sources with neutral beam-heated plasmas, and the examination of neutral beam-driven plasma operation scenarios of fusion neutron sources. In magnetic plasma confinement devices, the anisotropy of fuel nuclei velocity distributions due to beam and wave heating leads to anisotropy of neutron energy spectra. An approach to calculating energy spectra of fusion neutrons, based on the use of Monte Carlo methods, exists, for example in [23; 24], and an approach based on the explicit analytical formulae obtained in [25; 26; 27].