GB2286919A - Radiation sources - Google Patents

Abstract

The intensity of the radiation which impinges upon spacecraft has a directional dependence. In simulating this environment it is necessary to reproduce this directionality at all points in the modelling space. This cannot be achieved efficiently with the single disc source types which are currently available. A system of multiple disc sources has therefore been devised. In order to produce an even and symmetrical distribution of sources about the target, configurations based upon certain Archimedian polyhedra are utilised. Polyhedra with a relatively large number of faces of similar shape and area are the most suitable, particularly the truncated icosahedron (6) and triangularly sub-divided versions of the truncated icosahedron and the snub dodecahedron (9 Fig. 4 not shown). <IMAGE>

Description

RADIATION SOURCES ----- - - This invention relates to radiation sources, their simulation and the measurement of the doses produced by such sources. The invention is particularly applicable to the measurement of radiation doses to which electronic equipment in space-craft may be subjected.

Existing radiation sources for simulation purposes tend to be unidirectional beams from linear particle accelerators (LINACS), X-ray machines or radioactive material. With unidirectional sources, it is a good approximation to assume that all radiation particles passing through any small region have parallel trajectories. However, in the space environment radiation fluxes are encountered for which the intensity is a non-trivial function of directional variables. If it is required to establish the doses delivered to sensitive parts of a spacecraft system prior to launch, it is necessary to model or simulate the directional radiation fluxes in the laboratory.

The sources made available in some known facilities are typically based on discs which either produce a beam of radiation at right angles to the plane of the disc or emit particles into a cone of directions with its axis normal to the plane of the discs (e.g. the ITS modelling suite from Sandia National Laboratories, USA). In figure 1, a pair of such discs 1,2 are located either side of a spacecraft model to reproduce any axially symmetric radiation directionality in a volume 3 defined by the intersection of the two cones formed using the discs as bases and having half apex angles equal to the cut-off angle o for the radiation flux.

However, few of the radiation particles emitted by the discs 1,2 pass through the intersection volume 3, especially if the cut-off angle is large (as is necessary if the radiation flux has significant intensity over a wide range of directions), so this approach is usually very inefficient. In addition, it can not be used in cases where there is no axial symmetry and also, the correct directional biasing of the particles emitted by the discs requires a complicated calculation.

In an alternative, known arrangement, it is possible to produce a directional flux in a target region by arranging a large number of beam or disc sources around the region. The conventional approach to this exercise involves orienting the beams in directions defined by spherical polar angles o and for evenly spaced ranges of both. The main problem with this is that it results in concentrations of orientations near the poles. It is clearly desirable to space the selected orientations evenly over the solid angular sphere to eliminate the need for biasing according to solid angular coverage and to optimise the directional resolution of the source. However there is no exact means of achieving this in the general case.

An object of this invention is to provide a radiation source having arbitrary, yet operator-definable directionality within a pre-defined volume.

Thus the invention consists of a radiation source comprising a plurality of disc-shaped radiation sources which are orientated relatively to one another as the faces of a semi-regular polyhedron wherein the centre of each disc is in tangential contact with a spherical simulation space having the same radius as the discs.

The invention exploits the high degree of symmetry which is innate in semi-regular polyhedra i.e. certain Archimedean polyhedra and certain Archimedean polyhedra with some of their faces sub-divided. It is then possible to devise multiple disc sources at selectable levels of angular resolution, which have sufficiently evenly spaced sets of orientations that solid angular biasing is unnecessary and which give optimal angular resolution relative to the number of disc sources employed.

Some embodiments of the invention will now be described by way of example only with reference to the drawings of which: Figure 1 shows a known radiation source arrangement; Figure 2 illustrates the geometry of a component disc radiation source in accordance with the invention; Figures 3 and 4 are alternative forms of radiation source in accordance with the invention; Figure 5 is a table of vectors defining the directions for the radiation source of figure 3; and Figure 6 is a table of vectors defining the directions for a source defined by Figure 4.

A polyhedral source in accordance with the invention can produce a radiation flux in a spherical target region which has the same directionality at every point in the region. It comprises a number of unidirectional disc sources of the same radius as the target region (which could be the apertures of linear accelerator machines, for example, in the case of a simulation exercise).

In figure 2 each disc source 4 (only one shown for the sake of clarity) has its centre 0 in tangential contact with the surface of the spherical target region 5.

The spherical polar co-ordinates of the tangent point relative to the centre of the sphere define a direction which is diametrically opposite to the direction of radiation particles from the disc. By establishing a sufficiently large number of source discs with tangent points evenly distributed over the sphere surface, the angular difference between radiation particles from discs in adjacent orientations may be made sufficiently small that the actual continuous distribution of particle directions is satisfactorily approximated.

In order to define a suitable set of direction vectors for the orientations of the source discs it is possible to refer to the sets of vectors which define the face centres of certain semi-regular polyhedra. (The regular "Platonic" solids have insufficient faces to give good angular resolution.) If the faces are all of similar shape and size, then the requirement for even spacing of the direction vectors is automatically satisfied. The Archimedean polyhedra which best satisfy these requirements are the truncated icosahedron of figure 3 and a sub-divided version of the snub dodecahedron of figure 4.

The truncated icosahedron 6 of figure 3 has 32 faces, consisting of twelve regular pentagons 7 and twenty, regular hexagons 8. Two hexagons and a single pentagon meet at each vertex and all the vertices lie in the surface of a circumscribing sphere. The distribution of the face-centre vectors over the sphere for this polyhedron is sufficiently even for corrections to be negligible in most circumstances.

The relative intensities of the disc sources in each of the 32 directions are found by integrating the directionality function for the required environment over the solid angle defined by a cone, the axis of which is the relevant face-centre vector and the base of which subtends a solid angle of 1/32 of the sphere (i.e. s/8 steradians). The value obtained is expressed as a fraction of the overall environment by dividing by a sum of all 32 such integrations for all the faces.

The snub dodecahedron 9 of figure 4 consists of eighty equilateral triangular faces 10 and twelve regular pentagonal faces 11. Four triangles and a single pentagon meet at each vertex, all of which lie in the surface of a circumscribing sphere. Because the pentagonal faces subtend a much larger solid angle at the centre of the circumscribing sphere than do the triangular faces, it is necessary to sub-divide them to generate an even spread of face-centre vectors. The pentagons are sub-divided by splitting then into five triangles 12, two points being pentagon vertices and the third being the intersection point of a straight line passing through the centres of the circumscribing sphere and the pentagonal face with the surface of the circumscribing sphere. The division of a pentagon in this fashion is shown with dashed lines in figure 4.The direction vectors associated with each of the new triangles are those at right angles to their planes. It may be calculated that the areas of the new triangles are only slightly smaller than the areas of the equilateral triangles, so the even distribution requirements are satisfied to a good approximation.

The sub-divided snub dodecahedral configuration 9 defines a set of 140 direction vectors, so it is useful where better angular resolution is required than is available from the truncated icosahedral configuration. For finer angular resolution still, it is feasible to sub-divide each of the 140 triangles in the snub dodecahedron into four smaller triangles 13 of similar area. This is also illustrated with dashed lines in Figure 4. The additional vertex points required are generated by finding the intersections of straight lines through the centre of the circumscribing sphere and through the midpoints of the edges of the triangles with the circumscribing sphere.

For polyhedra entirely comprising equilateral or near-equilateral triangles the vertex vectors also constitute an evenly distributed direction set over the circumscribing sphere.

For the finer resolution polyhedral sources it may be satisfactory to fix the relative intensities of each disc source in proportion to the value of the required directionality function in the direction of the disc source.

Otherwise the same integration procedure over a cone of space as for the truncated icosahedral source may be adopted.

A radiation dose deposited in a structure, e.g. a spacecraft, can be determined using a polyhedral source in the following manner. The polyhedral radiation source is implemented by using the disc type sources which are commonly available in Monte Carlo modelling facilities such as the aforementioned ITS system.

In Monte Carlo modelling a large number of radiation particles is tracked through a target with the outcome of the various interaction processes being decided by the value of a random number within a biased range of possibilities. In this way radiation dose deposition in defined regions of a complicated (i.e. spacecraft) structure is determined. This is a critical issue, because many of the electronic components in spacecraft are acutely radiation sensitive and the dose deposition by space radiation in spacecraft structures varies over orders of magnitude from one place to another.

Firstly a look-up table of unit vectors for the disc sources, which are the face-centred vectors for the chosen polyhedral configuration, is provided. A table of 32 unit vectors defining the face orientations for a truncated icosahedron is listed in Figure 5.

A similar table of 140 such vectors for the subdivided snub dodecahedron is cited in Figure 6.

A facility to re-orientate the polyhedral source by rotating the ensemble of direction vectors about the origin is provided in order to align a symmetry axis of the polyhedral source with a convenient modelling axis.

A rotation through an angle a about the x-axis is achieved by multiplying each direction vector by the matrix:

#1 0 0 # #0 cos &alpha; sin &alpha; # #0 -sin &alpha; cos &alpha; # Similar matrix multiplications may be used to effect rotations about the y and z axes if required.

Next a target sphere is fitted to the unit model; it needs to be of minimal volume in order to optimise the efficiency of the modelling. A simple (but not necessarily optimal) procedure is to find the maximum and minimum values of x, y and z for the model; the sphere centre is then located at: ((xmax - xmin)/2, (ymax - ymin)/2, (Zmax - zmin/2)) and its radius is given by:

For each particle history one of the set of disc sources needs to be selected (and an injection point in the disc is then chosen randomly in the usual way). It is necessary to bias the selection of the particular disc in proportion to the relative intensity of the radiation in that disc's direction.

If the fraction of the radiation that the ith disc is required to produce is fi, then for a random number r in the range zero to one the jth disc should be selected such that:

Regions of interest within the unit model for which the radiation dose is to be calculated are defined and a shielding factor can be assigned to each region if desired.

As an option, it is possible to implement a unidirectional source by setting the fraction equal to one for one disc and zero for all the others. Similarly an isotropic source is modelled by making all the fractions equal to 1/n for a polyhedral source having n directions. For a general directionality function the fractions fi can be calculated on the basis of the values of the directionality function in the disc source directions or a better approximation may be derived using the integration over a cone of solid angle as outlined above. In the case of a complicated directionality function the integration must be effected numerically.

Claims (3)

1. A radiation source comprising a plurality of disc shaped radiation sources which are orientated relatively to one another as the faces of a semi-regular polyhedron wherein the centre of each disc is in tangential contact with a spherical simulation space having the same radius as the discs

2. A radiation source according to claim 1 in which said polyhedron is a truncated icosahedron.

3. A radiation source according to claim 1 in which the polyhedron is a snub dodecahedron with its pentagonal faces sub-divided into triangles.