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Response of alanine dosimeters at very high dose rate
Appl. Radiat. lsot. Vol. 48, No. 4, pp. 497~,99, 1997 C~ 1997 Published by Elsevier Science Ltd Printed in Great Britain P I I : S0969-8043(96)00281-3 0969-8043/97 $17.00 + 0.00
Pergamon
Response of Alanine Dosimeters at Very High Dose Rate H. K U D O H 2, M. C E L I N A I, R. J. K A Y E I, K. T. G I L L E N 1 a n d R. L. C L O U G H ' 'Sandia National Laboratories, Albuquerque, NM 87185-1407, U.S.A. and -'Japan Atomic Energy Research Institute, Takasaki Radiation Chemistry Research Establishment, Takasaki, Gunma 370-12. Japan (Received 15 July 1996; in revised form 20 August 1996)
Alanine dosimeters were irradiated at 3 × 10~°Gy/s using a pulsed electron beam. The response measured by ESR showed good agreement with dosimetry by radiochromic film dosimeters, which are reliable at that absorbed dose rate. The results indicate that alanine dosimeters may be used at very high dose rate. within their nominal-usable dose range up to 100 kGy. (9 1997 Published by Elsevier Science Ltd
Introduction Certain organic materials are used for radiation dosimetry by monitoring properties such as discoloration at a given wavelength, or radical formation. These properties may depend on such factors as the dose range, dose rate, linear energy transfer (LET), temperature, humidity and atmosphere, as well as time-dependent changes following radiation exposure (McLaughlin et al., 1989; Kudoh et al., 1996; Clough et al., 1995). Such dependencies can dictate limits on the usability of particular dosimeters, in terms of range and environmental parameters. The question of range limits applicable to various dosimeters has been intensively investigated, and usable ranges of absorbed dose and dose rate for gamma rays and electron beams are tabulated (McLaughlin et al., 1989). Alanine dosimetry with ESR is a well established and particularly convenient dosimetry system with a usable dose range up to 100 kGy. As a result, this dosimetry method is becoming very widely used. Regulla and Definer (1982) found no dose rate dependence for alanine dosimeters from 3 x 10 -2 Gy/s up to about 5 x 10' Gy/s. In a later paper, the same authors (Regulla and Definer, 1983) indicated that the upper limit on the usable dose rate range for alanine-based dosimetry is 108 Gy/s, similar to the 107Gy/s reported by Janovsky (1991), although in both studies it was not mentioned whether this value was due to instrumental limitation or whether deviations at higher dose rates had in fact been observed. Sharpe and Burns (1995) reported no dose rate dependence of the alanine dosimeter with 16 MeV electrons up to 6 x 105 Gy/s. The ASTM
Standard E 1607-94 (1994) for alanine dosimetry currently suggests an absorbed dose range of 1-105 Gy at an absorbed dose rate of up to 102 Gy/s for continous radiation fields and up to 104 Gy/s for pulsed radiation fields. The present authors have been studying the dose rate dependence of radiation effects on polymers (including one polymer-based dosimeter material) in terms of spur overlapping, using the pulsed power system available at Sandia National Laboratories (SNL), which can generate 2 MeV electron beams at a dose rate higher than 10'° Gy/s. In our previous work (Kudoh et al., 1996), we reported that a cellulose triacetate (CTA) film dosimeter has the identical discoloration sensitivity at 4 x 10'" Gy/s for pulsed EB as found with commercial EB irradiation systems (Tanaka et al., 1984). Recently, we irradiated alanine dosimeters at a dose rate of 3 x 10" Gy/s. In this report, we briefly discuss our findings on dose-rate dependency in this material.
Experimental SNL's irradiation service division adapts the radiochromic film, (FWT-60, manufactured by Far West Technology Inc., Nylon with dye) for dosimetry of e-beams in SNL's Repetitive High Energy Pulsed Power system (RHEPP-2; Neau, 1994), because this dosimeter is reliable up to 10'2 Gy/s (McLaughlin et al., 1989). The ASTM Standard E 1275-88 (1988) suggests a limit of 100 kGy and 10~ Gy/s for the radiochromic film dosimeters. After five pulses on FWT-60 films, the change in the optical density (OD) at 600 nm was measured and the dose was determined from the pre-calibrated data. A pulse was
497
498
H. Kudoh et al.
found to deposit 2.34 + i 7% kGy in the film over the irradiated area. The uncertainty in the total dose is dominated by the local beam uniformity where the measurement was made and is estimated to be approx. + 15%. The error in the dose determination is approx. + 8%. Electric signals showed that the time profile of a pulse is well described as a trapezoidal shape with full width at half maximum of approx. 70 ns. The pulse width for the entire dose is not greater than 150 ns. Thus the average dose rate during a pulse is estimated as 3 + 1 x 10 '° Gy/s and cannot be lower than 1.6 x 10 '° Gy/s. It is estimated that in the electron energy spectrum, 80% of the electrons are greater than 1 MeV, resulting in full penetration of the 3 mm alanine dosimeters. Detailed energy spectrum measurements have not been performed to date. Alanine dosimeters, Amino-gray, manufactured by Hitachi Cable Co. Ltd (approx. 30 mm length and 3 mm in diameter) were irradiated at RHEPP-2 as provided by the manufacturer in a protective gel coating (approx. 0.5 mm wall thickness). Irradiation was performed under circulated nitrogen (maximum exposure time 4 h), and the temperature of the samples was kept at ambient by waiting for 15 s between each pulse. After irradiation, the dosimeters were sent to JAERI Takasaki and kept in the protective gel coating until the ESR measurements. The alanine-ESR dosimetry system of JAERI Takasaki provides the exposure in relative response units R (in air), which is an applicable unit to photon (X-ray or gamma) only, in this case from calibration data by 6°Co gamma ray irradiation. Details of the system have been published previously (Kojima et al., 1986; Kojima and Tanaka, 1989).
Results A comparison between radiochromic and alanine dosimeters is shown in Table 1. The doses in the radiochromic film are converted into the electron beam absorbed dose in air, D~r as follows (McLaughlin et al., 1989): Old,
= D~i,m X ( S c o , / P ) a i , / ( S c o , / p ) s y , o
n =
D~,~
x 1.68/1.80 = Oalm x 0.933
(1)
where Sco, is the electron mass collision stopping power, p is the density, and D,,m is the number of Table I. Dosimetry of pulsed electron beams by radiochromic film and alanine dosimeter No. of pulses 4 43 427
D]~, (kGy) from film'
D~, (kGy) from alanine
8.73 93.9 932.2
8.82 95.2 134.4
Ratio 1.01 1.01 0.144
~These values were simply obtained by multiplying the number of pulses with the accurately determined dose for a single pulse (2.34 kGy) and 0.933 [see equation (l)], and arc not a direct measurement of OD of the film.
pulses times 2.34 kGy per pulse. Data of (S¢o./p) for 2 MeV electrons were taken from ICRU (1984). The value of the absorbed dose of the alanine dosimeter was determined from the relative response units R (in air) measured by the alanine-ESR dosimetry system o f J A E R I Takasaki, and a conversion factor obtained by calibration (in this case R = 8.73 x 10 -3 Gy for Da~r 6°Co gamma). As shown in Table i, the agreement between the two dosimeters is excellent, except for the highest dose level which is outside the recommended dose range for the alanine dosimeter. This suggests that the usable dose rate range of alanine dosimeters may be extended up to approx. 3 x 10 '° Gy/s. The usable dose range evidently extends up to at least 94 kGy, but must be well below a total dose of 932 kGy, which appears consistent with the results at lower dose rates (Regulla and Definer, 1985; McLaughlin et al., 1989). The lifetime of radicals in alanine is very long. Regulla and Definer (1982) and Regulla and Definer (1985) reported that the decay rate is less than 1% over 3 years. Similarly, Hansen and Olsen (1985) demonstrated very low fading for doses below 10 kGy, but also reported a more pronounced fading for doses above 50 kGy (Hansen et al., 1987). If we assume that the lifetime is infinite, then the number of radicals would steadily increase with dose, irrespective of dose rate. Radicals may begin to interact with each other above a certain concentration, but this should depend only on the dose, and not on the dose rate. An approximate usable dose range of 100 kGy may correspond to a dose at which significant overlapping of spurs (formed with a random spacial distribution within the matrix) begins to occur. An assumed overlapping dose of 100 kGy and the infinite lifetime of radicals would allow calculation of the effective 'reactive volume' of a spur [the volume in which energy deposition of a single track occurs (Clegg and Collier, 1991)] in the alanine material as 6 × 10-2°-1.5 x 10-2°cm3, since D m~nOL = l0 s e/(Gvp) (Kudoh et al., 1996), where DS[" is the overlapping dose assuming radicals of infinite lifetime, e is the charge of an electron, G is the radiation chemical yield of radical formation, v is the effective volume of a spur, and p is the density of the material, respectively. The density p = 1.3 (Kojima et al., 1986), and we assumed that G is in the range 2-8 (100eV)-'. Henrikson et al. (1963) reported that G = 7.7 and Regulla and Definer (1982) reported a G value of 3. Nakagawa et al. (1993) presented G values in the range 2.5-5.0 +_ 10% for alanine at various doses, and small differences between oL-alanine and L-alanine. If we assume that the area of a spur is a sphere, then the radius of the effective volume is 2.4 x 10-7-1.5 x 10 -7 cm (2415 ,/k), which is a reasonable estimation as a spur radius (see, for example, Mozumder and Magee, 1966).
Response of alanine dosimeters Acknowledgements--The authors thank Drs T. Kojima and N. Yokoo of JAERI Takasaki for ESR measurements. They are also grateful to Dr W. L. McLaughlin of the National Institute of Standards and Technology (NIST) for fruitful discussions, and to Drs M. Desrosiers and J. C. Humphery of NIST and Dr D. Vehar (SNL) for valuable comments. This work was performed at Sandia National Laboratories and supported by the U.S. Department of Energy under Contract No. DE-AC04-94AL85000.
References ASTM Standard E 1275-88 (1988) Standard practice for use of radiochromic film dosimetry system. American Society for Testing and Materials, Philadelphia, PA. ASTM Standard E 1607-94 (1994) Standard practice for use of the alanine-EPR dosimetry system. American Society for Testing and Materials, Philadelphia, PA. Clegg D. W. and Collier A. A. (1991) Radiation Effects on Polymers. Elsevier Applied Science, London, pp. 161 Clough R. L., Malone G. M., Gillen K. T., Wallace J. S. and Sinclair M. V. (1995) Discoloration and subsequent recovery of optical polymers exposed to ionizing radiation. Polym. Deg. Stab. 49, 305. Hansen J. W. and Olsen K. J. (1985) Theoretical and experimental radiation effectiveness of the free radical dosimeter alanine to irradiation with heavy charged particles. Radiat. Res. 104, 15. Hansen J. W., Olsen K. J. and Wille M. (1987) The alanine radiation detector for high and low LET dosimetry. Radiat. Protect. Dos. 19, 43. Henrikson T., Sanner T. and Pihl A. (1963) Secondary processes in proteins irradiated in the dry state. Radiat. Res. 18, 147. ICRU (1984) Report 37, Stopping power for electrons and positrons. International Commission on Radiation United Measurements, Bethesda, MD, U.S.A. Janovsky I. (1991) Progress in alanine film/ESR dosimetry, High Dose Dosimetrv for Radiation Processing. IAEA-SM-314/47 Vienna, pp. 173.
499
Kojima T. and Tanaka R. (1989) Polymer-alanine dosimeter and compact reader. Appl. Radiat. lsot. 40, 851. Kojima T., Tanaka R., Morita Y. and Seguchi T. (1986) Alanine dosimeters using polymers as binders. Appl. Radiat. Isot. 37, 517. Kudoh H., Celina M., Malone G. M., Kaye R. J., Gillen K. T. and Clough R. L. (1996) Pulsed e-beam irradiation of polymers--a comparison of dose rate effects and LET effects. Radiat. Phys. Chem. 48, 555. McLaughlin W., Boyd A. W., Chadwick K., McDonald J. C. and Miller A. (1989) Dosimetry .[or Radiation Processing. Taylor & Francis, London, Chap. 8. Mozumder A. and Magee J. L. (1966) Model of tracks of ionizing radiations for radical reaction mechanisms. Radiat. Res. 28, 203. Nakagawa K., Eaton S. S. and Eaton G. R. (1993) Electron spin relaxation times of irradiated alanine. Appl. Radiat. Isot. 44, 73. Neau E. L. (1994) Environmental and industrial applications of pulsed power systems. IEEE Trans. Plasma Sci. 22, 2. Regulla D. F. and Definer U. (1982) Dosimetry by ESR spectroscopy of alanine. Appl. Radiat. lsot. 33, 1101. Regulla D. F. and Definer U. (1983) A system of transfer dosimetry in radiation processing. Radiat. Phys. Chem. 22, 305. Regulla D. F. and Definer U. (1985) Progress in alanine/ESR transfer dosimetry. IAEA publication, STI/PUB/671, International Atomic Energy Agency Vienna, pp. 221. Sharpe P. H. G. and Burns D. T. (1995) The relative response of Fricke, dichromate and alanine dosimeters to 6°Co and high energy electron beam radiation. Radiat. Phys. Chem. 46, 1273. Tanaka R., Mitomo S. and Tamura N. (1984) Effects of temperature, relative humidity, and dose rate on the sensitivity of cellulose triacetate dosimeters to electrons and ~,-rays. Appl. Radiat. Isot. 35, 875.
Pergamon
Response of Alanine Dosimeters at Very High Dose Rate H. K U D O H 2, M. C E L I N A I, R. J. K A Y E I, K. T. G I L L E N 1 a n d R. L. C L O U G H ' 'Sandia National Laboratories, Albuquerque, NM 87185-1407, U.S.A. and -'Japan Atomic Energy Research Institute, Takasaki Radiation Chemistry Research Establishment, Takasaki, Gunma 370-12. Japan (Received 15 July 1996; in revised form 20 August 1996)
Alanine dosimeters were irradiated at 3 × 10~°Gy/s using a pulsed electron beam. The response measured by ESR showed good agreement with dosimetry by radiochromic film dosimeters, which are reliable at that absorbed dose rate. The results indicate that alanine dosimeters may be used at very high dose rate. within their nominal-usable dose range up to 100 kGy. (9 1997 Published by Elsevier Science Ltd
Introduction Certain organic materials are used for radiation dosimetry by monitoring properties such as discoloration at a given wavelength, or radical formation. These properties may depend on such factors as the dose range, dose rate, linear energy transfer (LET), temperature, humidity and atmosphere, as well as time-dependent changes following radiation exposure (McLaughlin et al., 1989; Kudoh et al., 1996; Clough et al., 1995). Such dependencies can dictate limits on the usability of particular dosimeters, in terms of range and environmental parameters. The question of range limits applicable to various dosimeters has been intensively investigated, and usable ranges of absorbed dose and dose rate for gamma rays and electron beams are tabulated (McLaughlin et al., 1989). Alanine dosimetry with ESR is a well established and particularly convenient dosimetry system with a usable dose range up to 100 kGy. As a result, this dosimetry method is becoming very widely used. Regulla and Definer (1982) found no dose rate dependence for alanine dosimeters from 3 x 10 -2 Gy/s up to about 5 x 10' Gy/s. In a later paper, the same authors (Regulla and Definer, 1983) indicated that the upper limit on the usable dose rate range for alanine-based dosimetry is 108 Gy/s, similar to the 107Gy/s reported by Janovsky (1991), although in both studies it was not mentioned whether this value was due to instrumental limitation or whether deviations at higher dose rates had in fact been observed. Sharpe and Burns (1995) reported no dose rate dependence of the alanine dosimeter with 16 MeV electrons up to 6 x 105 Gy/s. The ASTM
Standard E 1607-94 (1994) for alanine dosimetry currently suggests an absorbed dose range of 1-105 Gy at an absorbed dose rate of up to 102 Gy/s for continous radiation fields and up to 104 Gy/s for pulsed radiation fields. The present authors have been studying the dose rate dependence of radiation effects on polymers (including one polymer-based dosimeter material) in terms of spur overlapping, using the pulsed power system available at Sandia National Laboratories (SNL), which can generate 2 MeV electron beams at a dose rate higher than 10'° Gy/s. In our previous work (Kudoh et al., 1996), we reported that a cellulose triacetate (CTA) film dosimeter has the identical discoloration sensitivity at 4 x 10'" Gy/s for pulsed EB as found with commercial EB irradiation systems (Tanaka et al., 1984). Recently, we irradiated alanine dosimeters at a dose rate of 3 x 10" Gy/s. In this report, we briefly discuss our findings on dose-rate dependency in this material.
Experimental SNL's irradiation service division adapts the radiochromic film, (FWT-60, manufactured by Far West Technology Inc., Nylon with dye) for dosimetry of e-beams in SNL's Repetitive High Energy Pulsed Power system (RHEPP-2; Neau, 1994), because this dosimeter is reliable up to 10'2 Gy/s (McLaughlin et al., 1989). The ASTM Standard E 1275-88 (1988) suggests a limit of 100 kGy and 10~ Gy/s for the radiochromic film dosimeters. After five pulses on FWT-60 films, the change in the optical density (OD) at 600 nm was measured and the dose was determined from the pre-calibrated data. A pulse was
497
498
H. Kudoh et al.
found to deposit 2.34 + i 7% kGy in the film over the irradiated area. The uncertainty in the total dose is dominated by the local beam uniformity where the measurement was made and is estimated to be approx. + 15%. The error in the dose determination is approx. + 8%. Electric signals showed that the time profile of a pulse is well described as a trapezoidal shape with full width at half maximum of approx. 70 ns. The pulse width for the entire dose is not greater than 150 ns. Thus the average dose rate during a pulse is estimated as 3 + 1 x 10 '° Gy/s and cannot be lower than 1.6 x 10 '° Gy/s. It is estimated that in the electron energy spectrum, 80% of the electrons are greater than 1 MeV, resulting in full penetration of the 3 mm alanine dosimeters. Detailed energy spectrum measurements have not been performed to date. Alanine dosimeters, Amino-gray, manufactured by Hitachi Cable Co. Ltd (approx. 30 mm length and 3 mm in diameter) were irradiated at RHEPP-2 as provided by the manufacturer in a protective gel coating (approx. 0.5 mm wall thickness). Irradiation was performed under circulated nitrogen (maximum exposure time 4 h), and the temperature of the samples was kept at ambient by waiting for 15 s between each pulse. After irradiation, the dosimeters were sent to JAERI Takasaki and kept in the protective gel coating until the ESR measurements. The alanine-ESR dosimetry system of JAERI Takasaki provides the exposure in relative response units R (in air), which is an applicable unit to photon (X-ray or gamma) only, in this case from calibration data by 6°Co gamma ray irradiation. Details of the system have been published previously (Kojima et al., 1986; Kojima and Tanaka, 1989).
Results A comparison between radiochromic and alanine dosimeters is shown in Table 1. The doses in the radiochromic film are converted into the electron beam absorbed dose in air, D~r as follows (McLaughlin et al., 1989): Old,
= D~i,m X ( S c o , / P ) a i , / ( S c o , / p ) s y , o
n =
D~,~
x 1.68/1.80 = Oalm x 0.933
(1)
where Sco, is the electron mass collision stopping power, p is the density, and D,,m is the number of Table I. Dosimetry of pulsed electron beams by radiochromic film and alanine dosimeter No. of pulses 4 43 427
D]~, (kGy) from film'
D~, (kGy) from alanine
8.73 93.9 932.2
8.82 95.2 134.4
Ratio 1.01 1.01 0.144
~These values were simply obtained by multiplying the number of pulses with the accurately determined dose for a single pulse (2.34 kGy) and 0.933 [see equation (l)], and arc not a direct measurement of OD of the film.
pulses times 2.34 kGy per pulse. Data of (S¢o./p) for 2 MeV electrons were taken from ICRU (1984). The value of the absorbed dose of the alanine dosimeter was determined from the relative response units R (in air) measured by the alanine-ESR dosimetry system o f J A E R I Takasaki, and a conversion factor obtained by calibration (in this case R = 8.73 x 10 -3 Gy for Da~r 6°Co gamma). As shown in Table i, the agreement between the two dosimeters is excellent, except for the highest dose level which is outside the recommended dose range for the alanine dosimeter. This suggests that the usable dose rate range of alanine dosimeters may be extended up to approx. 3 x 10 '° Gy/s. The usable dose range evidently extends up to at least 94 kGy, but must be well below a total dose of 932 kGy, which appears consistent with the results at lower dose rates (Regulla and Definer, 1985; McLaughlin et al., 1989). The lifetime of radicals in alanine is very long. Regulla and Definer (1982) and Regulla and Definer (1985) reported that the decay rate is less than 1% over 3 years. Similarly, Hansen and Olsen (1985) demonstrated very low fading for doses below 10 kGy, but also reported a more pronounced fading for doses above 50 kGy (Hansen et al., 1987). If we assume that the lifetime is infinite, then the number of radicals would steadily increase with dose, irrespective of dose rate. Radicals may begin to interact with each other above a certain concentration, but this should depend only on the dose, and not on the dose rate. An approximate usable dose range of 100 kGy may correspond to a dose at which significant overlapping of spurs (formed with a random spacial distribution within the matrix) begins to occur. An assumed overlapping dose of 100 kGy and the infinite lifetime of radicals would allow calculation of the effective 'reactive volume' of a spur [the volume in which energy deposition of a single track occurs (Clegg and Collier, 1991)] in the alanine material as 6 × 10-2°-1.5 x 10-2°cm3, since D m~nOL = l0 s e/(Gvp) (Kudoh et al., 1996), where DS[" is the overlapping dose assuming radicals of infinite lifetime, e is the charge of an electron, G is the radiation chemical yield of radical formation, v is the effective volume of a spur, and p is the density of the material, respectively. The density p = 1.3 (Kojima et al., 1986), and we assumed that G is in the range 2-8 (100eV)-'. Henrikson et al. (1963) reported that G = 7.7 and Regulla and Definer (1982) reported a G value of 3. Nakagawa et al. (1993) presented G values in the range 2.5-5.0 +_ 10% for alanine at various doses, and small differences between oL-alanine and L-alanine. If we assume that the area of a spur is a sphere, then the radius of the effective volume is 2.4 x 10-7-1.5 x 10 -7 cm (2415 ,/k), which is a reasonable estimation as a spur radius (see, for example, Mozumder and Magee, 1966).
Response of alanine dosimeters Acknowledgements--The authors thank Drs T. Kojima and N. Yokoo of JAERI Takasaki for ESR measurements. They are also grateful to Dr W. L. McLaughlin of the National Institute of Standards and Technology (NIST) for fruitful discussions, and to Drs M. Desrosiers and J. C. Humphery of NIST and Dr D. Vehar (SNL) for valuable comments. This work was performed at Sandia National Laboratories and supported by the U.S. Department of Energy under Contract No. DE-AC04-94AL85000.
References ASTM Standard E 1275-88 (1988) Standard practice for use of radiochromic film dosimetry system. American Society for Testing and Materials, Philadelphia, PA. ASTM Standard E 1607-94 (1994) Standard practice for use of the alanine-EPR dosimetry system. American Society for Testing and Materials, Philadelphia, PA. Clegg D. W. and Collier A. A. (1991) Radiation Effects on Polymers. Elsevier Applied Science, London, pp. 161 Clough R. L., Malone G. M., Gillen K. T., Wallace J. S. and Sinclair M. V. (1995) Discoloration and subsequent recovery of optical polymers exposed to ionizing radiation. Polym. Deg. Stab. 49, 305. Hansen J. W. and Olsen K. J. (1985) Theoretical and experimental radiation effectiveness of the free radical dosimeter alanine to irradiation with heavy charged particles. Radiat. Res. 104, 15. Hansen J. W., Olsen K. J. and Wille M. (1987) The alanine radiation detector for high and low LET dosimetry. Radiat. Protect. Dos. 19, 43. Henrikson T., Sanner T. and Pihl A. (1963) Secondary processes in proteins irradiated in the dry state. Radiat. Res. 18, 147. ICRU (1984) Report 37, Stopping power for electrons and positrons. International Commission on Radiation United Measurements, Bethesda, MD, U.S.A. Janovsky I. (1991) Progress in alanine film/ESR dosimetry, High Dose Dosimetrv for Radiation Processing. IAEA-SM-314/47 Vienna, pp. 173.
499
Kojima T. and Tanaka R. (1989) Polymer-alanine dosimeter and compact reader. Appl. Radiat. lsot. 40, 851. Kojima T., Tanaka R., Morita Y. and Seguchi T. (1986) Alanine dosimeters using polymers as binders. Appl. Radiat. Isot. 37, 517. Kudoh H., Celina M., Malone G. M., Kaye R. J., Gillen K. T. and Clough R. L. (1996) Pulsed e-beam irradiation of polymers--a comparison of dose rate effects and LET effects. Radiat. Phys. Chem. 48, 555. McLaughlin W., Boyd A. W., Chadwick K., McDonald J. C. and Miller A. (1989) Dosimetry .[or Radiation Processing. Taylor & Francis, London, Chap. 8. Mozumder A. and Magee J. L. (1966) Model of tracks of ionizing radiations for radical reaction mechanisms. Radiat. Res. 28, 203. Nakagawa K., Eaton S. S. and Eaton G. R. (1993) Electron spin relaxation times of irradiated alanine. Appl. Radiat. Isot. 44, 73. Neau E. L. (1994) Environmental and industrial applications of pulsed power systems. IEEE Trans. Plasma Sci. 22, 2. Regulla D. F. and Definer U. (1982) Dosimetry by ESR spectroscopy of alanine. Appl. Radiat. lsot. 33, 1101. Regulla D. F. and Definer U. (1983) A system of transfer dosimetry in radiation processing. Radiat. Phys. Chem. 22, 305. Regulla D. F. and Definer U. (1985) Progress in alanine/ESR transfer dosimetry. IAEA publication, STI/PUB/671, International Atomic Energy Agency Vienna, pp. 221. Sharpe P. H. G. and Burns D. T. (1995) The relative response of Fricke, dichromate and alanine dosimeters to 6°Co and high energy electron beam radiation. Radiat. Phys. Chem. 46, 1273. Tanaka R., Mitomo S. and Tamura N. (1984) Effects of temperature, relative humidity, and dose rate on the sensitivity of cellulose triacetate dosimeters to electrons and ~,-rays. Appl. Radiat. Isot. 35, 875.