Ionization distribution in cylinders irradiated with monoenergetic electrons

InternationaIJournalof

Applied

Radiation and Isotopes, 1963,Vol. 14,pp. 189-196.Pergamon PressLtd. Printed inNorthernIreland

Ionization Distribution in Cylinders Irradiated with Monoenergetic Electrons E. H. CORNISH Standard Telecommunication

Laboratories

Ltd., Harlow,

Essex

(First received 19 July 1962 and injnal form 27 August 1962) The distribution of ionization within a solid cylinder, irradiated normally to its axis by a parallel beam of initially monoenergetic electrons, has been studied with the aid of a physical model. This comprised an assemblage of laminae, each shaped to the profile of the ionization distribution curve which applies to a slab of material irradiated on its face. The laminae were stacked to simulate cylinders of different radii with respect to electron range, and ionization levels at any point within a real cylinder could be obtained from the model. Curves are presented showing peripheral ionization levels as a function of cylinder diameter, and average dose factor values have been computed from the results. Other experiments using dyed “phantoms” of wire cores and cables have shown the extent to which the conductor will throw a shadow in a parallel electron beam impinging normally to the wire axis. In most cases, where the conductor diameter is less than 50 per cent of that of the whole core, electron scattering is adequate to process the material in the shadow. DISTRIBUTION A

DE L’AIDE

L’IONISATION

DANS

D’ELECTRONS

DES

CYLINDRES

IRRADIES

MONOENERGETIQUES

La presente etude, consacree a la distribution de l’ionisation a l’interieur d’un cylindre plein soumis normalement a son axe au rayonnement d’un faisceau paralltle d’electrons de meme Cnergie initiale, a Ctt effect&e a l’aide d’un modele physique. Celui-ci Ctait constitut d’un empilement de feuillets, dont chacun Ctait decoupt suivant la courbe de distribution d’ionisation qui caracterise une plaque irradite sur l’une de ses faces. Les feuillets furent empiles de man&e a simuler des cylindres de differents rayons selon la gamme d’energie interessee. Ce modtle permit de determiner les niveaux d’ionisation en tout point a I’inttrieur d’un cylindre real. Les courbes presentees indiquent les niveaux d’ionisation en divers points de la periphtrie de cylindres de differents diametres, et c’est a partir de ces valeurs qu’a ete calcule le facteur de dose moyen. D’autres experiences, utilisant des “fantomes” de cables ou d’ames de cables, conjointement avec une technique de coloration, ont permis d’ttudier dans quelle mesure le conducteur projette une ombre sur l’isolation lorsqu’un cable est irradie par un faisceau parallele d’electrons perpendiculaire a son axe. Dans la plupart des cas, oh le diametre du conducteur n’excede pas 50 pour cent du diamttre de l’ame, la dispersion des electrons se trouve Etre suffisante pour que la portion d’isolation sit&e dans I’ombre soit encore correctement irradiee. PACHPEAEJIEHBE

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VERTEILUNG

DER

IONISATION

IN MIT

ELEKTRONEN

ENERGIE BESTRAHLTEN

VON

GLEICHER

ZYLINDERN

Die Verteilung der Ionisation in einem zylindrischen Festkorper, der senkrecht zu seiner A&se mit Elektronen von anfanglich gleicher Energie bestrahlt wird, wurde an Hand eines Modells untersucht. Dieses besteht aus einer Anzahl von Lamellen, deren jede die Form der Verteilungskurve der Ionisation besitzt, die fur einen, auf einer seiner FlPchen bestrahlten Materialblock zutrifft. Die Lamellen werden so aneinander gereiht, dass sie Zylinder von verschiedenen Radien, in Bezug auf die Streckenllnge der Elektronen bilden, so dass die an jeden Punkt eines wirklichen Zylinders bestehenden Ionisationsniveaus von dem Model1 erhlltlich sind. Kurven, welche die Ionisationsniveaus an der Peripherie als Funktion des Zylinderdurchmessers geben, werden dargestellt und die Werte durchschnittlicher Dosisfaktoren aus den Ergebnissen berechnet. Weitere Experimente, bei denen gefarbte Nachbildungen oder Drahtseelen und Kabel verwendet werden, zeigen, zu welchem Ausmass der Leiter in einem parallelen Elektronenstrahl der serikrecht zur Drahtachse lauft, einen Schatten wirft. In den meisten Fallen, wo der Leiterdurchmesser weniger als 50 Prozent der ganzen Seele betriigt, gentigt die Elektronenstreuung, urn such das im Schatten liegende Material zu bestrahlen. INTRODUCTION FOR an

industrial

successful

yet economic,

must receive by

the article

and

geometrical to conserve

tion

monoenergetic

produces

a complex

processeswhich rest.

SPENCER(~) general infinite these

and

others

distribution medium have

time.

electrons and

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basic

applied

are

range. the

HERRING et ~1.t~) determined distribution

monoenergetic

of particle

energies beam

in which

to select

uniform

material

is then

lack

an

ionization Fig.

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the

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optimum

the

factor

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otherwise

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with

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as 30

ionization

ionization

accurate

which

the use of a beam an

material

for the target

to calculate

of symmetry

2 shows

these

of ionization

the target

absorption

as much

Briefly,

the use of this relationship

and so permits by

range.

in calculating

of the electrons

for the target.

dose,

as

material

maximum

intensity

within

within The

dose factor

target

madets).

range

to establish dosimetry

of

the

the

a beam

symmetry.

illustrates

initially

than

and

distribution

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slabs

distances

bombardment,

high

maximum

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up to the extreme

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A summary

from many other workers.(3-7) These experiments were made on aluminium, copper, lead, water, glass and polyethylene, using monoenergetic electron beams with initial energies of O-3 to 3 MeV, the target thickness results

in relation only

principles

to

which

transfer

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thin

considered

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Figure

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1

191

Ionization distribution in cylinders irradiated with monoenergetic electrons

Percentage

of

electronrange

FIG. 1 described by GROSS et al.@), being the integral of that shown in Fig. 1. Average dose factors, for various increments of electron range in a target, are computed by dividing the percentage of the maximum range represented by the target, into the percentage of the available dose which has been absorbed by it. Such an average dose factor relationship, for polyethylene, is given in Fig. 3, and is similar in shape to the “range distribution” curves, for aluminium and polyethylene, described by GROSS. A problem in irradiating the plastic insulation of wires and cables (usually done to cross-link it and so improve the mechanical strength at elevated temperatures) is to estimate a mean

dose factor which can be applied in the dosimetry calculations, since it is economically desirable to avoid overdosing by the lo-30 per cent margin which would occur if this factor was ignored. It is not sufficient to assume without proof that average dose factor values for a slab of material can be applied to a wire core of circular cross section and similar thickness. A further problem is to predict the extent to which the relatively dense conductor of a core will cast a “shadow” on the insulation on the side away from the electron source. Many irradiation processes make provision for successive irradiations, first on one side of the core and then on the other, or permit it to turn so that any point on its surface describes a spiral path under the electron beam. Such mechanical devices add complication and expense, and may often not be necessary. An attempt has been made to find values of 1’3,

1.2-

50 Percentage

Of

electron

100 range

FIG. 3 mean dose factor for insulated wires and to estimate the shadowing effect in them by using models on which measurements could be taken. EXPERIMENTAL

Mean dose factor of cylinders

100

Percentage

of electron range

FIG. 2

Insulated wires and cables, which usually approximate a circular cross section, may be considered as cylinders for most purposes; since their irradiation by electrons is usually effected by drawing them under a fixed source, the effects of length may be neglected. In the present context, a cylinder is considered as a number of thin laminae, all with their planes

192

E. H. Cow&h

FIG. 4 parallel with the axis but having their leading edges normal to the direction of the electron beam, which irradiates the cylinder as shown in Fig. 4. The average dose factor of each lamina can be found, being a function both of cylinder diameter and the position of the lamina with respect to the axis. A mean value of the average dose factors is taken to apply to the cylinder as a whole. Such a “mean dose factor” is a function only of cylinder diameter, provided a single incident electron energy is assumed. Figure 5 illustrates the physical model which was made, the plan of which is shown in Fig. 4; this represented the cross section of a cylinder irradiated on one side, and the problem resolved itself into determining ionization values along the back surface of the unirradiated hemicylinder (shown dotted). This was done by making each lamina in the shape of the ionization range curve for polyethylene, as in Fig. 1, the vertical leading edge being that assumed exposed to electron irradiation. An assemblage of such laminae, all with the leading edges in line, would then represent the ionization profile within a flat slab during irradiation. However, the appropriate curvature for each desired cylinder was impressed on the leading edge of the stack of laminae, as at A in Fig. 5, so that the rear part of the imagined cylinder’s cross section lay in the doubly curved hollow made by the backs of the laminae. The curve of Fig. 1 illustrates ionization conditions within the target up to the maximum

electron range. Should the target be thinner than this range, for example 20 per cent of it, the electrons will dissipate energy as shown in the first 20 per cent of the curve. After escaping from the rear face of the target they are of no further interest from a dosimetry viewpoint. It is therefore presumed justifiable to consider the cylinder as an assembly of identical ionization curves, and to use only the part of these appropriate to their position in the model. The virtual position of the rear curved cylinder surface was found by painting the upper edge of each lamina with a fluorescent dye, and projecting a circular section, parallel beam of ultra-violet light on to the model from above. This light beam had the same radius ofcurvature as that of the cylinder being simulated, and was so positioned that there was coincidence between

HFIG. 5

Ionization distribution in Gylinders irradiated with monoenergetic electrons

the edge of the beam and the curved leading edge of the model. The rear boundary of the beam, lying in the hollow made by the curved rear edges of the laminae, cut them at points representing the individual values of ionization on the periphery of the cylinder remote from the electron beam; it was shown up by the interface between the light and dark areas on each lamina. A probe, tipped with fluorescent dye, was used to locate the interface more precisely. Lines were scribed on the laminae to represent percentages of their height, so that at any point on the model, within the circle of Fig. 4, representing a position within the irradiated cylinder, a corresponding value of ionization could be found. Ionization values, which could be read to &I per cent, were expressed as a percentage of the maximum value attained by the desired irradiation conditions, so the results quoted later can be applied to any desired electron dose. The scale of the model was such that a 1/16 in. thick lamina represented a polyethylene target thickness of 20 mg/cm2; 56 such laminae, totalling 3#-in. thickness, made a cylinder model with diameter equivalent to approximately the maximum range of 2 MeV electrons, for which the model was made. Dimensions were such that a range of cylinder diameters from 1401120 mg/cm2 could be simulated. Cable phantoms The metal conductor of a wire or cable can be assumed to throw a shadow on the insulation remote from the incident electron beam, because of its greater electron-stopping power. Very thin conductors, such as may be used in miniature coaxial cable, should transmit sufficient electrons to overcome the shadow effect, but in cases where the conductor diameter is an appreciable proportion of the total, shadowing may be presumed appreciable. Although it is recognized that electron scattering may to some extent process the insulation beneath the conductor, it is more usual to ignore this effect and to turn the cable over, mechanically, and reprocess what was at first the underside. Such a process is mechanically complicated and wasteful of radiation, since some of the insulation inevitably will be overdosed. This procedure must of necessity be used when the overall insulation 2

193

diameter is almost twice the range of the fast electrons available, but the present experiments were made to determine the shadowing which occurs with small diameter insulated wires. Gels, coloured with radiation-labile dyes, are useful for constructing models of irregular articles being irradiated, since the extent of fading is roughly proportional to the absorbed dose. Methylene blue is a suitable dye for this purpose, and its use for dosimetry has been well documented.(10-12) Agar gels (I.5 per cent) were found to be more suitable than those of gelatine or egg albumen for the present purpose, both on the score of strength and transparency. Furthermore, egg albumen contains a substance which recolours the dye within a few seconds of fading by radiation. It was necessary to filter the agar solutions carefully to remove small lumps of undispersed matter which bleached more slowly than the rest of the gel. Models of short lengths of core were made by casting dyed gels in glass tubes fitted with copper rod inserts; dimensions were chosen so that the ratio of conductor to “core” diameters was varied from 5 per cent to 50 per cent, with a maximum core thickness I.8 times the maximum range of the 2 MeV electrons used. It was assumed that the gel density and electron stopping power approximated those of polyethylene. The phantoms, removed from their tubes, were irradiated normally to the copper rods for times up to 30 set with a scanned but virtually parallel electron beam of 50 ,uA, delivered from a Van de Graaff electrostatic particle accelerator. About 2 Mrad of ionization were delivered to fade the dyed upper surface of the gel, but no attempt was made to assess doses accurately as their absolute values were unimportant. Observations that electron scattering did occur beneath the copper rods could be extrapolated on a pro rata basis to the usual dose of 15-20 Mrad for polyethylene. RESULTS Data obtained from the laminar cable model are presented graphically in Figs. 6, 7 and 8. Figure 6 shows the ionization values which were measured at a number of points on the rearward semi-circumference of cylinders with various

194

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Ionization distribution in cylinders irradiated with monoenergetic electrons 1.3-

near: the extreme range can be considered. 2 MeV electrons have a maximum range of about 1070 mg/cm2, so that in several tests the underside of the wire could not have been irradiated except through electron scattering or X-ray production.

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Phantom dimensions are given in Table 1 with observations which apply only to the shadowed part of the gel. The radial thickness is calculated from the dimensions of gel and copper on a line along the direction of the electron beam and is quoted so that the cases where the conductor centre lies

The scatter of individual results on the curve of Fig. 9 is probably due to cumulative errors occasioned by taking data in succession from several unsmoothed curves. As the shape and absolute values of this curve are very similar indeed to the average dose factor curve obtained for polyethylene slabs(s), it is reasonable to assume that a cylinder may in general be considered as an infinite plane whose thickness is equal to the diameter; calculations of mean dose factor for cylinders irradiated by incident electron energies other than 2 MeV could then be made on this basis. The model described may be used for evaluating ionization levels within objects of regular or irregular, cross sections, other, provided that a correspondingly shaped light spot is provided and the leading edge of the lamina stack is shaped to the profile facing the electron beam. Observations on the wire core phantoms

TABLE 1 Ratio of conductor/ total dia.

Overall core dia.

Radial thickness

(mm)

(mg/cm2)

(mm)

(%)

14 9 14 22 9

980 730 1170 1890 920

0.7 0.7 1.2 2.0 1.2

5.0 7.8 8.6 9.1 13.3

No No No No No

fading fading fading fading fading

No fading No fading No fading No fading Mostly faded

All All All No All

14 4

1490 480

2.0 0.7

14.3 17.5

No fading No fading

No fading All faded

No fading -

9

1240

2.0

22.2

No fading

4 4

670 990

1.2 2.0

30.0 50.0

No fading Blue streak

Mostly faded All faded All faded

All faded -

Conductor dia.

Irradiation 10

left

time (set) 20

30

faded faded faded fading faded

196

E. H. Cornish

showed that after irradiation, material in the shadow of a conductor representing 50 per cent of the cable diameter, was processed to a dose of approximately half that of the upper surface, provided that the available electron range was not exceeded. Large phantoms, with a radial thickness already greater than the electron range, showed shadow formation even when the conductor occupied only 9 per cent of the cable diameter ; as the relative conductor diameter increased, so the cable thickness necessary for shadow formation decreased. In irradiating cores, therefore, it would be safe to assume that the shadowed area received adequate dosing only if the conductor was relatively thin and the overall thickness approximated no more than the electron range; in thicker cores, or those where the conductor was relatively large, the shadowed area would receive some radiation dose which might be inadequate unless the upper surface was overdosed by a factor of perhaps 2. X-radiation might be considered a major factor in the processing of the shadowed area, such radiation being of relatively high penetrating power and produced by the impact of electrons on the conductor. In the present experiments it seemed that X-radiation was more probably a minor factor, because little fading of the shadow occurred after 10 set of electron irradiation, while in some cases an additional 10-set treatment completely faded the dye. Where a shadow was produced by 20-set treatment, a further 10 set of electron bombardment sufficed to fade it in cases where the phantom was not too thick. Had fading been due solely to X-rays, then the dose from this cause must have approximated at least one third of that from the electrons themselves, and this is unlikely to have happened in view of the relatively poor conversion efficiency of electrons to X-rays on a copper target.

Another factor, possibly leading to misinterpretation of the results on core phantoms, could conceivably be the diffusion of radiolysis products of the gel into the shadowed area, leading to chemical reduction of the dye. Diffusion experiments in which dyed gels were immersed in 1 per cent sodium dithionite solution, leading to progressive decolourization of the dye as diffusion proceeded, showed that the dithionite ion travelled in the gel at the rate of 0.12 mm in 20 set, equivalent to a thickness of 12 mg/cm2. The increased diffusion rate of, for example, hydrogen produced by radiolysis would be more rapid than this, but the rate would be small because of the small concentration gradient. A calculation showed that 20-set irradiation would have produced the equivalent of about 0.01 per cent of reactive hydrogen by radiolysis of the gel, and the diffusion rate due to this concentration differential across the boundary of the shadow would not of itself be sufficient to produce the fading effects which were observed.

REFERENCES 1. LANDAU L. J. Phys., Moscow 8, 201 (1944). 2. SPENCERL. Phys. Rev. 98, 1597 (1955). 3. TRUMPJ. C., VAN DE GRAAFF R. J. and CLOUD R. W. Amer. J. Roentgenol. 43, 728 (1946). 4. TRUMPJ. C., WRIGHT K. A. and CLARK A. M. J. u&11. Phys. 21, 345 (1950).

5. DAVISONS., GOLDBLITHS. A. and PROCTORB. E. Nucleonics 14, 38 (1956). 6. GROSSB. and WRIGHT K. A. Phys. Rev. 114, 725 (1959). 7. CORNISHE. H. Unpublished data. 8. HERRING J. R. and MERZBACHER E. J. Elisha Mitchell

Scient. Sot. 73, 267 (1957).

9. CORNISHE. H. J. xi. Znstrum. 38, 82 (1961). 10. GOLDBLITHS. A., PROCTORB. E. and HAMMENCE A. 0. Zndustr. Engng. Chem. 44, 3 10 (1952).

11. PROCTORB. E. and GOLDBLITH S. A. N.Y.O.3339 (1952).

12. LAFUENTE B., GOLDBLITH S. A. and PROCTOR B. E. Znt. J. a/@.

Rad. Zsotopes 3, 119 (1958).