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The Vavilov–Cherenkov radiation arising at deceleration of heavy ions in a transparent medium
Nuclear Instruments and Methods in Physics Research A 431 (1999) 148}153
The Vavilov}Cherenkov radiation arising at deceleration of heavy ions in a transparent medium J. Ruz\ ic\ ka , S. S[ aH ro , L. Krupa *, V.P. Zrelov, P.V. Zrelov, E.D. Lapchik, H. Geissel, H. Irnich, C. Kozhuharov, A. Magel, G. Munzenberg, F. Nickel, C. Scheidenberger, H.-J. SchoK tt, W. Schwab, T. StoK hlker, B. Voss Comenius University, Bratislava, Slovak Republic JINR Dubna, Moscow Region, Russia GSI, Darmstadt, Germany University Giessen, Giessen, Germany TH, Darmstadt, Germany Received 2 November 1998; received in revised form 26 January 1999
Abstract Some results of the Vavilov}Cherenkov radiation arising at a nonuniform motion of a charged particle in a radiator are presented. Considerable broadening of the width of VChR ring in the case of the broader radiator compared to the thinner one is observed. The particle velocity variation in the radiator due to large energy losses of heavy ions is the only explanation of this e!ect. 1999 Published by Elsevier Science B.V. All rights reserved.
1. Introduction
2. Experimental results
Little is known about the characteristics of the Vavilov}Cherenkov radiation (VChR) arising at a nonuniform and non-rectilinear motion of a charged particle in a transparent medium and contradicting the classical Tamm}Frank theory [1,2]. Lately a few articles were dedicated to this problem [3}5]. Experiments made at the SIS accelerator (GSI, Darmstadt) with the relativistic Au beam [6] gave rise to these papers.
The experiment was carried out with a special Cherenkov detector made by one of us (V.P.Z). The scheme of the experiment is shown in Fig. 1. The collimated beam of Au ions passing through the radiator, in which the VChR was created, was focused by a lens to a photo "lm. The plane-parabolic lens was made of quartz with the thickness ¸ "12 mm and 12 mm cur vature radius. The cone diameter D of the incident VChR on the photo "lm was measured as a function of the emitted radiation angle h in 1 the lens (Fig. 1). The "tting function used has the form [7]:
* Corresponding author. Tel.: #7-096-21-64266; fax: #7096-21-65083. E-mail address: [email protected] (L. Krupa)
D(h )"C #C h #C h#C h#C h, 1 1 1 1 1
0168-9002/99/$ - see front matter 1999 Published by Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 9 ) 0 0 2 0 2 - 8
(1)
J. Ruz\ ic\ ka et al. / Nuclear Instruments and Methods in Physics Research A 431 (1999) 148}153
Fig. 1. Schematic view of the experiment.
where C "0.14784816, C "1.032364, C " 0.024576688, C "!0.000884875, C "1.37449 ;10\. Both LiF and H O radiators were used. The Au beam energy before entering the radi ator was E "(905$5) MeV/u. The photographs of the VChR cone with a LiF radiator is shown in Fig. 2a (¸ "1 mm) and in Fig. 2b (¸ "5 mm). Twenty-four photometric curves of both VChR images were scanned. An example of photometrization is shown in Fig. 3. Experimental results are given in Table 1. The Au beam energy losses in a medium were calculated by a program developed in Darmstadt. The energy losses in the LiF radiator are *E "14.7$0.4 MeV/u and *E "73.3$ * * 0.5 MeV/u for the thinner (¸ "1 mm) and the broader (¸ "5 mm) radiators, respectively, at
149
an input energy of the Au beam E " (905$5) MeV/u. The second experimental measurement was carried out with a H O radiator placed in a plexiglass (C H O ) box 0.5 mm in thickness. The refractive index of plexiglass was n "1.492. The resulting VChR images of both rings are shown in Fig. 4a (¸ "2.4 mm) and in Fig. 4b (¸ "10 mm). In Fig. 5 an example of photometric curves of the VChR rings shown in Fig. 4 is presented. Experimental results are given in Table 2. The Au beam energy losses in a plexiglass box were calculated by a program and were equal to 4.1$0.4 MeV/u. Thus the input energy of Au ions entering the H O radiator is E&-" (900.9$5) MeV/u. The calculated energy losses of the Au beam in H O are *E "16.7$ * 0.4 MeV/u and *E " 70.2$0.5MeV/u for the * thinner (¸ "2.4 mm) and the broader (¸ "10 mm) radiators, respectively, at an input energy E&- of the Au beam. 3. Theoretical calculations The width of the VChR ring, in the case of the constant motion of a charged particle in a radiator, is mainly determined by a medium dispersion. One
Fig. 2. The image of the VChR ring of the LiF radiator (a) ¸ "1 mm, (b) ¸ "5 mm. The inner ring is due to the ion beam, the middle one is due to the radiator and the outer one due to the lens.
150
J. Ruz\ ic\ ka et al. / Nuclear Instruments and Methods in Physics Research A 431 (1999) 148}153
Fig. 3. Typical photometric curves of the image of the VChR ring shown in Fig. 2.
Table 1 LiF Radiator thickness L (mm)
Outer radius of the ring D /2 (lm)
Full width at the mid-height D"(D !D)/2 (lm)
1 5
21075$40 21023$78
697$43 1411$88
can see, from Table 1 and from Fig. 2, that the width of the VChR ring (LiF radiator) in the case of the broader radiator (¸ "5 mm) is almost twice as wide as that in the case of the thinner one (¸ "1 mm). Both VChR images (Fig. 2) were ob tained under the same conditions but for di!erent thickness of LiF radiators. Accordingly, the di!erent width of both the VChR rings is due to di!erent energy losses of the Au beam in a medium. In the broader radiator the energy losses of Au are much greater than in the thinner one. A non-rectilinear motion of charge in a medium can a!ect the width of the VChR ring too, but in the case of heavy ions the beam motion in a radiator can be considered as rectilinear due to the small angle of multiple scattering.
The velocity variation *b for the broader radiator is greater than that for the thinner one, which corresponds to broadening of the VChR ring. This characteristic is consistent with the theory of the VChR arising at a nonuniform motion of a charge in a transparent medium [5]. To calculate theoretical values of the VChR ring width we will use the following generalized Tamm}Frank condition [5]: 1 cos0" n(j)b(z)
(2)
where n(j) is the refractive index of a medium as a function of the wavelength j of the emitted radiation and b(z) is the charge velocity as a function of the traveled path. The relation between the angle 0 at which the VChR originates in a radiator and the angle h in a lens acquires the form 1 n sin0"n sinh , (3) 1 1 where n and n are the refractive indexes in the 1 radiator and in the lens, respectively. The outer radius of the VChR ring presented in Fig. 2 is determined by the input particle velocity b "b(z"0) at the wavelength j of the emitted
J. Ruz\ ic\ ka et al. / Nuclear Instruments and Methods in Physics Research A 431 (1999) 148}153
151
Fig. 4. The image of the VChR ring of the H O radiator (a) ¸ "2.4 mm, (b) ¸ "10 mm. The inner ring is due to the ion beam, the middle one is due to the radiator and the outer ones are due to the lens and the plexiglass box.
Fig. 5. Typical photometric curves of the image of the VChR ring shown in Fig. 4.
radiation, and an inner one is determined by the output velocity b "b(z"¸) at j . The wave length j is determined by a permeability of the lens and the radiator for the emitted radiation and j is determined by a spectral response of the "lm to this radiation.
The di!erence between the VChR ring widths of the broader radiator and the thinner one, which is equal to *0"arccos
1 1 !arccos , (4) n(j )b (¸ ) n(j )b (¸ )
152
J. Ruz\ ic\ ka et al. / Nuclear Instruments and Methods in Physics Research A 431 (1999) 148}153
Table 2 H O Radiator thickness L (mm)
Outer radius of the ring D /2 (lm)
Full width at the mid-height D"(D !D)/2 (lm)
2.4 10
17252$43 17295$89
964$49 1880$109
does not depend on a medium dispersion. The di!erence between the widths of the VChR rings *D "D !D as a function of j is shown in * $ * * Fig. 6. The following LiF refractive index n as * $ a function of j was used in the calculations [8]: 0.20618;10\ 0.86473;10\ ! , n (j)"1.3863# * $ j j (5) where j is given in lm. The mean refractive index of the used lens was n "1.512. As one can see from " Fig. 6, the theoretical value *D is almost con* $ stant over the wavelength range j "600}700 nm. The edge of the spectral response of the "lm to the emitted radiation is within this range. The mean value is equal to *D"775 lm and the ex* $ perimental value is *D "(714$88) lm (see * $ Table 3). Like in the LiF radiator the theoretical value *D "D !D (Fig. 6) for the H O radiator is &* * almost constant over the wavelength range j "600}700 nm. The mean value is equal to *D "743 lm. The following H O refractive & index n as a function of j was used in the &calculations [7]: n (j)"1.425207!3.60576;10\j#4.77343 &;10\j!2.228416;10\j,
(6)
where j is given in nm. The experimental value is *D "(916$109) lm (see Table 3). &The main error in the experimental value *D, for both the H O and LiF radiators, gives the uncer tainty in the determination of the inner and outer radii of the VChR ring presented in Tables 1 and 2. The error of the input Au beam energy E is
Fig. 6. Di!erence *D in the widths of the VChR rings as a function of j . Table 3 Radiator
*D (lm)
*D (lm)
LiF H O
714$88 916$109
775 743
equal to $5 MeV/u, which corresponds to the VChR ring width error of $10 lm. The uncertainty in the radiator thickness of 51}2% causes an error in the determination of the width of the VChR ring equal to $20 lm. 4. Conclusion The value *D"D !D does not depend on * * the medium dispersion and in the case of the classical Tamm}Frank theory this value is equal to zero. Accordingly, one can see from the obtained experimental results that the broadening of the VChR ring width in the case of the broader radiator in comparison with that of the thinner one is mainly due to di!erent energy losses in both radiators, because *D and *D are much greater than * $ &any errors discussed above. This agrees quite well, mainly for the LiF radiator, with the theoretical calculations. Acknowledgements The authors express their gratitude to Prof. P. Kienle (GSI, Darmstadt) and Prof. Ts. Vylov
J. Ruz\ ic\ ka et al. / Nuclear Instruments and Methods in Physics Research A 431 (1999) 148}153
(JINR, Dubna) for supporting the experiment. We also thank V.I. Sidorova, V.G. Sazonov, N.N. Lebedev, G.V. Gorbunova, A. Brunle, G. Otto and R. Janik for their technical assistance.
References [1] I.E. Tamm, I.M. Frank, Dokl. Akad. Nauk. SSSR 14 (3) (1937) 109. [2] I.E. Tamm, J. Phys. SSSR 1 (5}6) (1939) 439. [3] E.S. Kuzmin, A.V. Tarasov, Short Communication JINR 4[61]-93, Dubna, 1993, p. 64.
153
[4] L. Krupa, J. Ruz\ ic\ ka, V.P. Zrelov, Is the criterion of constant particle velocity necessary for the Vavilov}Cherenkov e!ect?, Preprint JINR P2-95-281, Dubna, 1995. [5] L'. Krupa, Vavilov}Cherenkov radiation arising at an arbitrary rectilinear motion of a charged particle in a transparent medium, submitted for publication. [6] J. Ruz\ ic\ ka, S. S[ aH ro, V.P. Zrelov, P.V. Zrelov, E.D. Lapchik, H. Geissel, H. Irnich, C. Kozhuharov, G. Munzenberg, A. Magel, F. Nickel, C. Scheidenberger, H.-J. SchoK tt, W. Schwab, Th. StoK hlker, B. Voss, Nucl. Instr. and Meth. A 369 (1996) 23. [7] J. Ruz\ ic\ ka, Theoretical and experimental investigation of Vavilov}Cherenkov radiation, Thesis, Dubna, 1993 (in Russian). [8] S.Yu. Budyakova, V.P. Zrelov, E.S. Kuzmin, Nucl. Instr. and Meth. A 277 (1989) 304.
The Vavilov}Cherenkov radiation arising at deceleration of heavy ions in a transparent medium J. Ruz\ ic\ ka , S. S[ aH ro , L. Krupa *, V.P. Zrelov, P.V. Zrelov, E.D. Lapchik, H. Geissel, H. Irnich, C. Kozhuharov, A. Magel, G. Munzenberg, F. Nickel, C. Scheidenberger, H.-J. SchoK tt, W. Schwab, T. StoK hlker, B. Voss Comenius University, Bratislava, Slovak Republic JINR Dubna, Moscow Region, Russia GSI, Darmstadt, Germany University Giessen, Giessen, Germany TH, Darmstadt, Germany Received 2 November 1998; received in revised form 26 January 1999
Abstract Some results of the Vavilov}Cherenkov radiation arising at a nonuniform motion of a charged particle in a radiator are presented. Considerable broadening of the width of VChR ring in the case of the broader radiator compared to the thinner one is observed. The particle velocity variation in the radiator due to large energy losses of heavy ions is the only explanation of this e!ect. 1999 Published by Elsevier Science B.V. All rights reserved.
1. Introduction
2. Experimental results
Little is known about the characteristics of the Vavilov}Cherenkov radiation (VChR) arising at a nonuniform and non-rectilinear motion of a charged particle in a transparent medium and contradicting the classical Tamm}Frank theory [1,2]. Lately a few articles were dedicated to this problem [3}5]. Experiments made at the SIS accelerator (GSI, Darmstadt) with the relativistic Au beam [6] gave rise to these papers.
The experiment was carried out with a special Cherenkov detector made by one of us (V.P.Z). The scheme of the experiment is shown in Fig. 1. The collimated beam of Au ions passing through the radiator, in which the VChR was created, was focused by a lens to a photo "lm. The plane-parabolic lens was made of quartz with the thickness ¸ "12 mm and 12 mm cur vature radius. The cone diameter D of the incident VChR on the photo "lm was measured as a function of the emitted radiation angle h in 1 the lens (Fig. 1). The "tting function used has the form [7]:
* Corresponding author. Tel.: #7-096-21-64266; fax: #7096-21-65083. E-mail address: [email protected] (L. Krupa)
D(h )"C #C h #C h#C h#C h, 1 1 1 1 1
0168-9002/99/$ - see front matter 1999 Published by Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 9 ) 0 0 2 0 2 - 8
(1)
J. Ruz\ ic\ ka et al. / Nuclear Instruments and Methods in Physics Research A 431 (1999) 148}153
Fig. 1. Schematic view of the experiment.
where C "0.14784816, C "1.032364, C " 0.024576688, C "!0.000884875, C "1.37449 ;10\. Both LiF and H O radiators were used. The Au beam energy before entering the radi ator was E "(905$5) MeV/u. The photographs of the VChR cone with a LiF radiator is shown in Fig. 2a (¸ "1 mm) and in Fig. 2b (¸ "5 mm). Twenty-four photometric curves of both VChR images were scanned. An example of photometrization is shown in Fig. 3. Experimental results are given in Table 1. The Au beam energy losses in a medium were calculated by a program developed in Darmstadt. The energy losses in the LiF radiator are *E "14.7$0.4 MeV/u and *E "73.3$ * * 0.5 MeV/u for the thinner (¸ "1 mm) and the broader (¸ "5 mm) radiators, respectively, at
149
an input energy of the Au beam E " (905$5) MeV/u. The second experimental measurement was carried out with a H O radiator placed in a plexiglass (C H O ) box 0.5 mm in thickness. The refractive index of plexiglass was n "1.492. The resulting VChR images of both rings are shown in Fig. 4a (¸ "2.4 mm) and in Fig. 4b (¸ "10 mm). In Fig. 5 an example of photometric curves of the VChR rings shown in Fig. 4 is presented. Experimental results are given in Table 2. The Au beam energy losses in a plexiglass box were calculated by a program and were equal to 4.1$0.4 MeV/u. Thus the input energy of Au ions entering the H O radiator is E&-" (900.9$5) MeV/u. The calculated energy losses of the Au beam in H O are *E "16.7$ * 0.4 MeV/u and *E " 70.2$0.5MeV/u for the * thinner (¸ "2.4 mm) and the broader (¸ "10 mm) radiators, respectively, at an input energy E&- of the Au beam. 3. Theoretical calculations The width of the VChR ring, in the case of the constant motion of a charged particle in a radiator, is mainly determined by a medium dispersion. One
Fig. 2. The image of the VChR ring of the LiF radiator (a) ¸ "1 mm, (b) ¸ "5 mm. The inner ring is due to the ion beam, the middle one is due to the radiator and the outer one due to the lens.
150
J. Ruz\ ic\ ka et al. / Nuclear Instruments and Methods in Physics Research A 431 (1999) 148}153
Fig. 3. Typical photometric curves of the image of the VChR ring shown in Fig. 2.
Table 1 LiF Radiator thickness L (mm)
Outer radius of the ring D /2 (lm)
Full width at the mid-height D"(D !D)/2 (lm)
1 5
21075$40 21023$78
697$43 1411$88
can see, from Table 1 and from Fig. 2, that the width of the VChR ring (LiF radiator) in the case of the broader radiator (¸ "5 mm) is almost twice as wide as that in the case of the thinner one (¸ "1 mm). Both VChR images (Fig. 2) were ob tained under the same conditions but for di!erent thickness of LiF radiators. Accordingly, the di!erent width of both the VChR rings is due to di!erent energy losses of the Au beam in a medium. In the broader radiator the energy losses of Au are much greater than in the thinner one. A non-rectilinear motion of charge in a medium can a!ect the width of the VChR ring too, but in the case of heavy ions the beam motion in a radiator can be considered as rectilinear due to the small angle of multiple scattering.
The velocity variation *b for the broader radiator is greater than that for the thinner one, which corresponds to broadening of the VChR ring. This characteristic is consistent with the theory of the VChR arising at a nonuniform motion of a charge in a transparent medium [5]. To calculate theoretical values of the VChR ring width we will use the following generalized Tamm}Frank condition [5]: 1 cos0" n(j)b(z)
(2)
where n(j) is the refractive index of a medium as a function of the wavelength j of the emitted radiation and b(z) is the charge velocity as a function of the traveled path. The relation between the angle 0 at which the VChR originates in a radiator and the angle h in a lens acquires the form 1 n sin0"n sinh , (3) 1 1 where n and n are the refractive indexes in the 1 radiator and in the lens, respectively. The outer radius of the VChR ring presented in Fig. 2 is determined by the input particle velocity b "b(z"0) at the wavelength j of the emitted
J. Ruz\ ic\ ka et al. / Nuclear Instruments and Methods in Physics Research A 431 (1999) 148}153
151
Fig. 4. The image of the VChR ring of the H O radiator (a) ¸ "2.4 mm, (b) ¸ "10 mm. The inner ring is due to the ion beam, the middle one is due to the radiator and the outer ones are due to the lens and the plexiglass box.
Fig. 5. Typical photometric curves of the image of the VChR ring shown in Fig. 4.
radiation, and an inner one is determined by the output velocity b "b(z"¸) at j . The wave length j is determined by a permeability of the lens and the radiator for the emitted radiation and j is determined by a spectral response of the "lm to this radiation.
The di!erence between the VChR ring widths of the broader radiator and the thinner one, which is equal to *0"arccos
1 1 !arccos , (4) n(j )b (¸ ) n(j )b (¸ )
152
J. Ruz\ ic\ ka et al. / Nuclear Instruments and Methods in Physics Research A 431 (1999) 148}153
Table 2 H O Radiator thickness L (mm)
Outer radius of the ring D /2 (lm)
Full width at the mid-height D"(D !D)/2 (lm)
2.4 10
17252$43 17295$89
964$49 1880$109
does not depend on a medium dispersion. The di!erence between the widths of the VChR rings *D "D !D as a function of j is shown in * $ * * Fig. 6. The following LiF refractive index n as * $ a function of j was used in the calculations [8]: 0.20618;10\ 0.86473;10\ ! , n (j)"1.3863# * $ j j (5) where j is given in lm. The mean refractive index of the used lens was n "1.512. As one can see from " Fig. 6, the theoretical value *D is almost con* $ stant over the wavelength range j "600}700 nm. The edge of the spectral response of the "lm to the emitted radiation is within this range. The mean value is equal to *D"775 lm and the ex* $ perimental value is *D "(714$88) lm (see * $ Table 3). Like in the LiF radiator the theoretical value *D "D !D (Fig. 6) for the H O radiator is &* * almost constant over the wavelength range j "600}700 nm. The mean value is equal to *D "743 lm. The following H O refractive & index n as a function of j was used in the &calculations [7]: n (j)"1.425207!3.60576;10\j#4.77343 &;10\j!2.228416;10\j,
(6)
where j is given in nm. The experimental value is *D "(916$109) lm (see Table 3). &The main error in the experimental value *D, for both the H O and LiF radiators, gives the uncer tainty in the determination of the inner and outer radii of the VChR ring presented in Tables 1 and 2. The error of the input Au beam energy E is
Fig. 6. Di!erence *D in the widths of the VChR rings as a function of j . Table 3 Radiator
*D (lm)
*D (lm)
LiF H O
714$88 916$109
775 743
equal to $5 MeV/u, which corresponds to the VChR ring width error of $10 lm. The uncertainty in the radiator thickness of 51}2% causes an error in the determination of the width of the VChR ring equal to $20 lm. 4. Conclusion The value *D"D !D does not depend on * * the medium dispersion and in the case of the classical Tamm}Frank theory this value is equal to zero. Accordingly, one can see from the obtained experimental results that the broadening of the VChR ring width in the case of the broader radiator in comparison with that of the thinner one is mainly due to di!erent energy losses in both radiators, because *D and *D are much greater than * $ &any errors discussed above. This agrees quite well, mainly for the LiF radiator, with the theoretical calculations. Acknowledgements The authors express their gratitude to Prof. P. Kienle (GSI, Darmstadt) and Prof. Ts. Vylov
J. Ruz\ ic\ ka et al. / Nuclear Instruments and Methods in Physics Research A 431 (1999) 148}153
(JINR, Dubna) for supporting the experiment. We also thank V.I. Sidorova, V.G. Sazonov, N.N. Lebedev, G.V. Gorbunova, A. Brunle, G. Otto and R. Janik for their technical assistance.
References [1] I.E. Tamm, I.M. Frank, Dokl. Akad. Nauk. SSSR 14 (3) (1937) 109. [2] I.E. Tamm, J. Phys. SSSR 1 (5}6) (1939) 439. [3] E.S. Kuzmin, A.V. Tarasov, Short Communication JINR 4[61]-93, Dubna, 1993, p. 64.
153
[4] L. Krupa, J. Ruz\ ic\ ka, V.P. Zrelov, Is the criterion of constant particle velocity necessary for the Vavilov}Cherenkov e!ect?, Preprint JINR P2-95-281, Dubna, 1995. [5] L'. Krupa, Vavilov}Cherenkov radiation arising at an arbitrary rectilinear motion of a charged particle in a transparent medium, submitted for publication. [6] J. Ruz\ ic\ ka, S. S[ aH ro, V.P. Zrelov, P.V. Zrelov, E.D. Lapchik, H. Geissel, H. Irnich, C. Kozhuharov, G. Munzenberg, A. Magel, F. Nickel, C. Scheidenberger, H.-J. SchoK tt, W. Schwab, Th. StoK hlker, B. Voss, Nucl. Instr. and Meth. A 369 (1996) 23. [7] J. Ruz\ ic\ ka, Theoretical and experimental investigation of Vavilov}Cherenkov radiation, Thesis, Dubna, 1993 (in Russian). [8] S.Yu. Budyakova, V.P. Zrelov, E.S. Kuzmin, Nucl. Instr. and Meth. A 277 (1989) 304.