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Experimental study of the multiple scattering lateral spread of MeV protons transmitted through polyester films
156
Nuclear Instruments and Methods in Physics Research B2 (1984) 156-158 North-Holland, Amsterdam
EXPERIMENTAL STUDY OF THE MULTIPLE SCA’ITERING LATERAL SPREAD OF MeV PROTONS TRANSMITIED THROUGH POLYESTER FILMS * D. SCHMAUS and A. L’HOIR Groupe de Physique des Slides 75251 Paris Cedex 05, France
de I’Ecole Normaie Supkrieure, Universii&Paris VII, Tour 23, 2 place Jussieu,
The lateral spread of MeV proton beams in Polyester (C,,H,O,) has been experimentally measured. The indirect method used consists of taking advantage of the broadening of the energy loss spectra of beams trans~tt~ through tilted targets. These experimental meausrements, which give the projected lateral spread of the beam at zero exit angle, are in fairly good agreement with the approximation proposed by Sigmund et al. for the combined angular and lateral spread.
1. Introduction and theory This very short paper gives the main results of experimental work ** on the multiple scattering of MeV protons in polyester films (the trade mark of the films studied is Terphane from Rhonc Poulenc Films, which is very similar to Mylar from DuPont). Only results on the lateral spread are developed in the present paper. Experimental measurements of the lateral spread of ion beams are generally performed in gaseous targets (see for example ref. [l]) and many experimental results are in this case available in the literature. On the contrary, lateral spread measurements in solid targets are very few; in ref. [2] lateral spread measurements on bulk targets (C, Al, Cu) were performed in backscattering geometry (RBS and nuclear reactions). Our experiments were performed in transmission geometry, i.e. in a somewhat more direct way. The distribution, at a given depth x in a given medium, of the lateral deviation p of an initially wellcollimated beam was calculated by Marwick and Sigmund 131. It may be calculated from the angular distributions F( x,cy) tabulated in ref. [4]. Similarly, but with poorer precision (especially for thin targets), the combined angular and lateral spread ditribution G(x,a$), where p = p/x may also be calculated [S] from the tabulated F. In our case, where OL= 0 (see below) and where rather thick targets were used, the approximate result of ref. [S] yields: G(x,cr
=O,@) = F2(x/2$/0.S8p),
which
is valid
for monoatomic
(1) targets
in the small
* Work supported by the Centre National de la Recherche Scientifique (R.C.P. no. 157). ** D. Schmaus and A. L’Hoir, submitted to Nucl. Instr. and Meth. 0168-583X/84,/%03.00 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
angles and small mean energy losses approximation (normaiization factors are omitted in eq. (1)). For our polyatomic targets, C,,HsO,, it is derived in ref. [6] that replacing these targets by a mean monoatomic target with a mean monoatomic number z2 = 5.13 yields very nearly the correct angular distribution, F, it was hence concluded that eq. (1) was also valid, provided that F was calculated with the above z2 mean -_ value. In our experiments, the mean energy loss AE m the targets was generally not small when compared to the initial beam energy E,; it can be shown that replacing E, (which acts as a scaling factor on the width of F) by E, - AEf2 is an excellent approximation even for dE/E, = 0.5. From the above considerations, a theoretical calculation of G(x,a = O$) in the case of our rather thick polyatomic targets was in ail circumstances easily performed.
2. Experimental procedure and data reduction The energy loss spectra and angular dist~butions of MeV protons, produced by a 2 MV Van de Graaff accelerator transmitted through polyester films were recorded using a 25 cm2 area movable silicon surface barrier detector located in front of the incident beam, according to the procedure described in ref. (71. The targets were mounted on a sample holder which can be rotated around its horizontal axis, perpendicular to the beam direction. The experimental lateral distributions were determined by the following simple method, illustrated in fig. 1. The energy spectrum of the protons transmitted through target A, of thickness x, pe~endicul~ to the beam direction (B = O”) is recorded. Another spectrum is recorded with the same beam for target B, which is a thinner foil of thickness d tilted at an angle @= arc cos
157
D. Schmaus, A. L’Hoir / Muliiple scattering lateral spread of protons
3. Results
target A
Fig. 1. Schematic experimental transmission geometry for lateral spread measurements. Apparent thicknesses of target A (perpendicular to the beam) and target B (thickness d), tilted by an angle B = arc cos d/x, are the same. For this figure x = 4d and 8 = 75S”. This figure is not drawn to scale, in order to emphasize the effect of the lateral spread.
(d/x). The mean energy loss of particles is the same in both cases, but the spectrum recorded with target B is broader and more asymmetrical. This is essentially due to the spread in energy loss related to the spread in actual pathlength in the tilted target B. If, for each single collision, a total independence between energy loss and angular deflections is assumed, the only difference between the spectrum recorded with perpendicular target A and tilted target B (with an appropriate angle e) is the lateral spread contribution, which can be determined by means of the stopping power in our polyester films [8] from the two experimental spectra, according to the following procedure. Under several approximations, the energy spectra gA( E) and ga( E) of beams transmitted respectively through target A and tilted target B are related through: ga(E)=LX(E)*h(E)*
30
(2)
where * stands for the convolution product and where h(E) is the energy spread curve arising from the fluctuations in pathlength travelled, and hence related to the lateral spread of the beam. Our experimental spectra, g,(E), have been compared to theoretical predictions [9] of energy straggling for large energy losses 181. Calculations of h(E) have been made (see footnote **, preceding page) from the projected combined lateral and angular spread distribution (which can easily be calculated from eq. (1) and which is not very different from the distribution G for our rather thick targets) at zero exit angle, which corresponds to our experimental conditions (small solid angle of detection). This distribution was modified until a good fit of ga( E) in width was obtained from the convolution product (eq. (2)).
In our experiments, the thickness x of the targets of type A was - 24 pm, which corresponds, with the notation of ref. [4], to a dimensionless reduced thickness T = 4000; the thickness of targets B were either - 12 pm -or - 6 pm. Typical tilting angles were then about 57’ and 75”. Results for the lateral spread hwhm (&z),=O around the reduced thickness T = 4000 are presented in fig. 2; they are compared with the theoretical values calculated from eq. (1). Our experimental values /3 are, on average, 5.7% larger than the calculated ones. This systematic discrepancy is very near to the one obtained from our angular distribution measurements (measured independently through similar polyester targets of 12 to 27 pm thicknesses): the experimental angular distributions were 5% (+2%) wider than predicted by the tabulations of ref. [4] which were also used in the theoretical calculation of h(E). In fact, if h(E) is calculated from eq. (1) but with our experimental angular distributions F, the experimental lateral spread hwhm (&,2)a=0 are on average, only 0.6% larger than the calculated ones. From these experiments, we can confirm (within the estimated 5% precision on our &,z measurements) the validity of the approximate theoretical treatment of ref. [5] for the combined lateral and angular spread for a zero scattering angle, around 7 = 4000. However, in order to verify this statement, the lateral spread had to be calculated from the experimental angular distributions, which are 5% (+ 2%) wider than predicted by the theory.
.
.
tzzo 10
*
ov 0
I
1000
I
I
I
I
2000
3000
LOO0
so00
I
T
of the hwhm of the combined proFig. 2. Values (&,),_a jected lateral and angular spread for a zero exit angle, as a function of the reduced thickness T. Points represent our experimental values for protons of various energies (from 1.21 up to 2.03 MeV) in polyester foils of apparent reduced thicknesses T between T = 3600 and T = 4000. The lower curve is calculated from theoretical predictions by means of eq. (1). Also indicated (upper curve) is the hwhm of the overall lateral spread distribution, calculated from refs. [3] and [4]. III. ENERGY
LOSS
158
D. Schmaus, A. L’Hoir / Multiple scattering lateral spread of protons
References [l] G. Sidenius and N. Andersen, Nucl. Instr. and (1975) 387. [2] W. Moller and J.S. Williams, Nucl. Instr. and (1978) 205. [3] A.D. Matwick and P. Sigmund, Nucl. Instr. and (1975) 317. [4) P. Sigmund and K.B. Winterbon, Nucl. Instr. 119 (1974) 541.
Meth. 131 Meth.
157
Meth. 126 and Meth.
[5] P. Sigmund, J. Heinemeier, F. Besenbacher, P. Hvelplund and H. Knudsen, Nucl. Instr. and Meth. 150 (1978) 221. [6] D. Schmaus and A. L’Hoir, these Proceedings (ICACS-10) p. 187. [7] D. Schmaus and A. L’Hoir, Nucl. Instr. and Meth. 194 (1982) 75. [8] A. L’Hoir and D. Schmaus, Nucl. Instr. and Meth. B, in press. [9] C. Tschalttr and H.D. Maccabee, Phys. Rev. Bl (1970) 2863.
Nuclear Instruments and Methods in Physics Research B2 (1984) 156-158 North-Holland, Amsterdam
EXPERIMENTAL STUDY OF THE MULTIPLE SCA’ITERING LATERAL SPREAD OF MeV PROTONS TRANSMITIED THROUGH POLYESTER FILMS * D. SCHMAUS and A. L’HOIR Groupe de Physique des Slides 75251 Paris Cedex 05, France
de I’Ecole Normaie Supkrieure, Universii&Paris VII, Tour 23, 2 place Jussieu,
The lateral spread of MeV proton beams in Polyester (C,,H,O,) has been experimentally measured. The indirect method used consists of taking advantage of the broadening of the energy loss spectra of beams trans~tt~ through tilted targets. These experimental meausrements, which give the projected lateral spread of the beam at zero exit angle, are in fairly good agreement with the approximation proposed by Sigmund et al. for the combined angular and lateral spread.
1. Introduction and theory This very short paper gives the main results of experimental work ** on the multiple scattering of MeV protons in polyester films (the trade mark of the films studied is Terphane from Rhonc Poulenc Films, which is very similar to Mylar from DuPont). Only results on the lateral spread are developed in the present paper. Experimental measurements of the lateral spread of ion beams are generally performed in gaseous targets (see for example ref. [l]) and many experimental results are in this case available in the literature. On the contrary, lateral spread measurements in solid targets are very few; in ref. [2] lateral spread measurements on bulk targets (C, Al, Cu) were performed in backscattering geometry (RBS and nuclear reactions). Our experiments were performed in transmission geometry, i.e. in a somewhat more direct way. The distribution, at a given depth x in a given medium, of the lateral deviation p of an initially wellcollimated beam was calculated by Marwick and Sigmund 131. It may be calculated from the angular distributions F( x,cy) tabulated in ref. [4]. Similarly, but with poorer precision (especially for thin targets), the combined angular and lateral spread ditribution G(x,a$), where p = p/x may also be calculated [S] from the tabulated F. In our case, where OL= 0 (see below) and where rather thick targets were used, the approximate result of ref. [S] yields: G(x,cr
=O,@) = F2(x/2$/0.S8p),
which
is valid
for monoatomic
(1) targets
in the small
* Work supported by the Centre National de la Recherche Scientifique (R.C.P. no. 157). ** D. Schmaus and A. L’Hoir, submitted to Nucl. Instr. and Meth. 0168-583X/84,/%03.00 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
angles and small mean energy losses approximation (normaiization factors are omitted in eq. (1)). For our polyatomic targets, C,,HsO,, it is derived in ref. [6] that replacing these targets by a mean monoatomic target with a mean monoatomic number z2 = 5.13 yields very nearly the correct angular distribution, F, it was hence concluded that eq. (1) was also valid, provided that F was calculated with the above z2 mean -_ value. In our experiments, the mean energy loss AE m the targets was generally not small when compared to the initial beam energy E,; it can be shown that replacing E, (which acts as a scaling factor on the width of F) by E, - AEf2 is an excellent approximation even for dE/E, = 0.5. From the above considerations, a theoretical calculation of G(x,a = O$) in the case of our rather thick polyatomic targets was in ail circumstances easily performed.
2. Experimental procedure and data reduction The energy loss spectra and angular dist~butions of MeV protons, produced by a 2 MV Van de Graaff accelerator transmitted through polyester films were recorded using a 25 cm2 area movable silicon surface barrier detector located in front of the incident beam, according to the procedure described in ref. (71. The targets were mounted on a sample holder which can be rotated around its horizontal axis, perpendicular to the beam direction. The experimental lateral distributions were determined by the following simple method, illustrated in fig. 1. The energy spectrum of the protons transmitted through target A, of thickness x, pe~endicul~ to the beam direction (B = O”) is recorded. Another spectrum is recorded with the same beam for target B, which is a thinner foil of thickness d tilted at an angle @= arc cos
157
D. Schmaus, A. L’Hoir / Muliiple scattering lateral spread of protons
3. Results
target A
Fig. 1. Schematic experimental transmission geometry for lateral spread measurements. Apparent thicknesses of target A (perpendicular to the beam) and target B (thickness d), tilted by an angle B = arc cos d/x, are the same. For this figure x = 4d and 8 = 75S”. This figure is not drawn to scale, in order to emphasize the effect of the lateral spread.
(d/x). The mean energy loss of particles is the same in both cases, but the spectrum recorded with target B is broader and more asymmetrical. This is essentially due to the spread in energy loss related to the spread in actual pathlength in the tilted target B. If, for each single collision, a total independence between energy loss and angular deflections is assumed, the only difference between the spectrum recorded with perpendicular target A and tilted target B (with an appropriate angle e) is the lateral spread contribution, which can be determined by means of the stopping power in our polyester films [8] from the two experimental spectra, according to the following procedure. Under several approximations, the energy spectra gA( E) and ga( E) of beams transmitted respectively through target A and tilted target B are related through: ga(E)=LX(E)*h(E)*
30
(2)
where * stands for the convolution product and where h(E) is the energy spread curve arising from the fluctuations in pathlength travelled, and hence related to the lateral spread of the beam. Our experimental spectra, g,(E), have been compared to theoretical predictions [9] of energy straggling for large energy losses 181. Calculations of h(E) have been made (see footnote **, preceding page) from the projected combined lateral and angular spread distribution (which can easily be calculated from eq. (1) and which is not very different from the distribution G for our rather thick targets) at zero exit angle, which corresponds to our experimental conditions (small solid angle of detection). This distribution was modified until a good fit of ga( E) in width was obtained from the convolution product (eq. (2)).
In our experiments, the thickness x of the targets of type A was - 24 pm, which corresponds, with the notation of ref. [4], to a dimensionless reduced thickness T = 4000; the thickness of targets B were either - 12 pm -or - 6 pm. Typical tilting angles were then about 57’ and 75”. Results for the lateral spread hwhm (&z),=O around the reduced thickness T = 4000 are presented in fig. 2; they are compared with the theoretical values calculated from eq. (1). Our experimental values /3 are, on average, 5.7% larger than the calculated ones. This systematic discrepancy is very near to the one obtained from our angular distribution measurements (measured independently through similar polyester targets of 12 to 27 pm thicknesses): the experimental angular distributions were 5% (+2%) wider than predicted by the tabulations of ref. [4] which were also used in the theoretical calculation of h(E). In fact, if h(E) is calculated from eq. (1) but with our experimental angular distributions F, the experimental lateral spread hwhm (&,2)a=0 are on average, only 0.6% larger than the calculated ones. From these experiments, we can confirm (within the estimated 5% precision on our &,z measurements) the validity of the approximate theoretical treatment of ref. [5] for the combined lateral and angular spread for a zero scattering angle, around 7 = 4000. However, in order to verify this statement, the lateral spread had to be calculated from the experimental angular distributions, which are 5% (+ 2%) wider than predicted by the theory.
.
.
tzzo 10
*
ov 0
I
1000
I
I
I
I
2000
3000
LOO0
so00
I
T
of the hwhm of the combined proFig. 2. Values (&,),_a jected lateral and angular spread for a zero exit angle, as a function of the reduced thickness T. Points represent our experimental values for protons of various energies (from 1.21 up to 2.03 MeV) in polyester foils of apparent reduced thicknesses T between T = 3600 and T = 4000. The lower curve is calculated from theoretical predictions by means of eq. (1). Also indicated (upper curve) is the hwhm of the overall lateral spread distribution, calculated from refs. [3] and [4]. III. ENERGY
LOSS
158
D. Schmaus, A. L’Hoir / Multiple scattering lateral spread of protons
References [l] G. Sidenius and N. Andersen, Nucl. Instr. and (1975) 387. [2] W. Moller and J.S. Williams, Nucl. Instr. and (1978) 205. [3] A.D. Matwick and P. Sigmund, Nucl. Instr. and (1975) 317. [4) P. Sigmund and K.B. Winterbon, Nucl. Instr. 119 (1974) 541.
Meth. 131 Meth.
157
Meth. 126 and Meth.
[5] P. Sigmund, J. Heinemeier, F. Besenbacher, P. Hvelplund and H. Knudsen, Nucl. Instr. and Meth. 150 (1978) 221. [6] D. Schmaus and A. L’Hoir, these Proceedings (ICACS-10) p. 187. [7] D. Schmaus and A. L’Hoir, Nucl. Instr. and Meth. 194 (1982) 75. [8] A. L’Hoir and D. Schmaus, Nucl. Instr. and Meth. B, in press. [9] C. Tschalttr and H.D. Maccabee, Phys. Rev. Bl (1970) 2863.