A.Piermattei*, S. delle Canne*, L. Azario*, A. Russo*, A. Fidanzio*, R. Miceli*,

A. Soriani **, A. Orvieto** , M. Fantini **.

* Istituto di Fisica, Università Cattolica del S.Cuore, Roma, Italy

**Hitesys S.p.A., Aprilia (LT), Italy

Short title: Saturation loss for ion -chambers

The use of plane parallel ionization chambers with electron beams with high dose per pulse entails dose uncertainties due to the overestimation of the ion recombination factor, k, up to 20% if conventional dosimetric protocols are used. In this work MD-55-2 radiochromic films have been used as reference dosimeters to obtain absolute dose to water per pulse for three Novac7 (Hitesys) electron beams of E₀=5.8 MeV. However, the beam calibration by MD-55-2 films is time consuming and the use of plane parallel chambers is fundamental for periodic quality control procedure. Three plane parallel chambers have been used and the general formula for the k determination has been tested using the calibration doses, . In particular coherent ion recombination factors k_sat(V₀) (with the ion chamber polarized at V₀), that follow the Boag theory, have been estimated at different dose per pulse values for the three plane parallel ionization chambers. This means that at present any ion chamber needs a specific k_sat(V₀) determination by using a reference dosimeter that present an independent response to the dose rate. An accurate determination of k_sat(V₀) using a reference quality beam, can be used to determine the dose to water per pulse for electron beams of different quality and geometrical configuration.

1. Introduction

 

The intraoperative radiation therapy (IORT) by using high dose values per pulse ranging from 3 cGy/pulse to 6 cGy/pulse is available by using the linac Novac7 (Hitesys) that supplies energy beams ranging from 4 MeV to 9 MeV.

Electron beam calibration is generally carried out by using plane parallel chambers that, however, present some complications in the accurate determination of the ion recombination factor when the dose rate per pulse is many times higher than the typical 0.01 cGy/pulse supplied by conventional clinical accelerators. Moreover, for these detectors there is a threshold polarizing voltage below which the chambers follow the Boag theory (Boag and Currant 1980). The existence of a deviation from the theory gives a limitation of the Boag two-voltage (TV) method (Boag and Currant 1980, Weinhous and Meli 1984). Indeed for dose per pulse values, in the range between 0.007 and 1.2 cGy/pulse, Burns and McEwen (1998) suggested, for a correct plane parallel chamber commissioning, the application of the graphical method, based on the extrapolation of the reciprocal signal, 1/M, as a function of the reciprocal voltage, 1/V.

As a result of this, GAF-Chromic films have been selected as reference dosimeters for the Novac7 electron beam calibrations. In particular, the radiochromic MD-55-2 films present high spatial resolution, low response dependence on the electron beam energy and independence for incidence beam angle. Moreover, the MD-55-2 films are made of water-equivalent material and can be used directly in water phantom. In this work the dose per pulse independence for MD-55-2 films has been tested by using chemical Fricke dosimeters.

Dose in water per pulse values at the reference point, for 5.8 MeV (Novac7) electron beams, were obtained by MD-55-2 films and compared with the dose in water per pulse determined by three plane parallel ionization chambers, Markus 23343, NACP-02 and Roos 34001. The results confirmed the overestimation of the ion-recombination factor, when the TV method was used for the three chambers.

Moreover, the dose in water per pulse, determined by MD-55-2 films, were used to obtain adequate values of saturation signals, M_S, for the three chambers. The signals M_V obtained at different polarizing voltage values, V, were used to obtain M_S/M_V ratios as a function of the 1/V. This way, the formula for the ion recombination factor, k, for pulsed radiation, which included the free-electron component (Boag et al. 1996, Hochhauser and Balk 1986), was tested for the three ionization chambers.

 

2. Materials and methods

2.1 Novac7 linac electron beams

Novac7 (Figure 1) is a dedicated IORT linac robot developed to perform radiotherapy treatment during surgery to avoid moving the patient from the surgery room to the radiotherapy bunker. An articulated arm allows to vary the source-patient distance. The linac lays in a structure connected to the microwave source by a flexible waveguide. The pulse repetition frequency (prf) of 5 Hz has been optimized for the 4 ms electron pulses. However, the frequency can be changed from 1 Hz to 29 Hz to vary treatment times.

The linac Novac7 supplies electron beams of high values of dose per pulse ranging from 3 cGy/pulse to 6 cGy/pulse. The electron beams are collimated by 6 cm, 8 cm and 10 cm diameter perspex cylindrical collimators. Source-surface distances (SSD) equal to 80 cm and 100 cm can be used. Four nominal electron energy levels, 4 MeV, 5 MeV, 7 MeV and 9 MeV, allow performing treatments at different depths. In this work the electron beam, 7 MeV of nominal energy (an incident energy E₀ = 5.8 MeV) was used. The ratio between the signal measured by an ionization chamber in water phantom and the pulse number was constant within 1%, in the range of 100 and 2000 pulses.

 

2.2 Radiochromic film

2.2.1. MD-55-2 film characteristics

MD-55-2 radiochromic films, ISP Technologies Inc. (LOT #38055), are supplied in sheets of 12.7x12.7 cm² surface, made of a double-layer radiochromic sensor dispersion 30 mm in total thickness (AAPM 1998). The presence of the waterproof polyester bases make the film suitable to be irradiated directly in water. Due to the high spatial resolution (600 cycles / mm) (AAPM 1998) the MD-55-2 films can be used both for dose beam calibration as well as to obtain dose distributions (Piermattei et al. 1999).

The physical characteristics of these films are well reported in literature (AAPM 1998, Piermattei et al. 1998, Zhu et al. 1997). However, it is necessary to underline that the optical density (OD) depends on reading temperature (up to 1 % °C^-1, at a reading temperature of about 14°C) and postirradiation reading time (up to 15% in the first 10 days and less then 1% per week in the following days) (Piermattei et al. 1998). To reduce uncertainties in dose determination, the films used for OD calibration and dose measurements were irradiated within a two hour interval time and the readout temperature was maintained constant between ± 0.25 °C. Due to the non-uniformity in the film emulsion layer, a ‘double irradiation technique’ (Zhu et al. 1997) was performed.

Software was developed to analyze the OD values of MD-55-2 film pieces 2x2 cm² in size. OD readouts were carried out by using a 100 PeC microdensitometer mod. CCD100 (Photoelectron Corporation). The CCD100 incorporates a stable, uniform, monochromatic light source, obtained by an array of 60 gallium-aluminum arsenide LEDs, with a wavelength of 665 nm, closely matched to the absorption peak of the film maximum sensitivity (670 nm), and a high resolution camera for image acquisition. The acquired digital image is sent by a serial interface RS232 to an external computer to be analyzed. The distance between the CCD camera and the light box was fixed at 43 cm, to obtain an adequate pixel dimension, 0.3x0.4 mm².

The OD interfilm precision or reproducibility (defined as the standard deviation of the mean OD values on separate film pieces, irradiated to the same dose) resulted lower than 1% (1s).

The energy independence test of the MD-55-2 films was reported in a recent work (Piermattei et al. 1999), where the films were calibrated in water by using an electron beam of incident energy E₀ = 4.4 MeV, 5.6 MeV and a 7.2 MeV supplied by a Saturne 43 conventional linac. The OD values obtained by the same dose values, supplied by the above electron beams, were well in agreement within the interfilm precision.

Figure 2 reports the OD values as a function of the absorbed dose to water for the E₀=6.2 MeV electron beam supplied by the Saturne 43. The dose values were determined using the ENEA ESC/87 reference cylindrical ionization chamber. Figure 2 reports the film calibration curve obtained by fitting experimental values by a third degree polynomial curve, with a regression coefficient, R²=0.999. The OD=0.347 refers to the first irradiation at 10 Gy, while the second irradiation was carried out in the dose range between 14.6 Gy and 26.6 Gy.

 

2.2.2 MD-55-2 dose per pulse independence

The dose per pulse independence of the MD-55-2 film (irradiated at doses equal to 20 Gy) was checked by using chemical Fricke dosimeters that presented a radiation chemical yield independent of the dose per pulse up to 10 Gy per pulse (ICRU 1982). Ferrous sulphate in glass ampoules with inner dimensions equal to 7 mm in diameter and 20 mm in length were irradiated in a water phantom at the reference depths (IAEA 1987) of two electron beams. The one supplied by a conventional linac Saturne 43 (6.2 MeV) with a prf = 200 Hz and the other supplied by the linac Novac7 (5.8 MeV and prf=5 Hz). Dose to water per pulse determined by the Fricke dosimeters, , were supplied by ENEA-INMRI (Ente per le Nuove tecnologie, Energia Ambiente , Istituto Nazionale Metrologia Radiazioni Ionizzanti), while the dose to water per pulse at the same reference depths were determined by MD-55-2 Gaf-Chromic films following the procedure reported in section 2.2.1.

Figure 3 shows the / ratios obtained at three different dose per pulse values determined by Fricke dosimeters at 0.0390 cGy/pulse (6.2 MeV Saturne 43) and 2.89, 5.68 cGy/pulse (5.8 MeV Novac7). The dose values obtained by MD-55-2 films for Novac7 electron beams resulted independent of the dose per pulse within experimental errors.

When the were converted in average dose rate values (468 cGy/min, 866 cGy/min and 1704 cGy/min) the dose rate independence was in agreement with the data reported in literature (AAPM 1998) for MD-55-2 films irradiated (by a ⁶⁰Co beam with dose rate values of 44, 2400 and 8000 cGy/min) at doses equal to 20 Gy.

 

2.2.3 MD-55-2 films used for Novac7 electron beam calibration

In this paper the MD-55-2 films were used as reference dosimeters to obtain the absolute dose to water per pulse, , of three Novac7 beams of E₀ = 5.8 MeV, 6 cm (with SSD=80 cm), 8 cm (with SSD=80 cm) and 10 cm (with SSD=100 cm) in diameter.

For every beam, six pieces of films (2x2 cm² in size) were placed, two at a time, in water perpendicularly to the beam central axis, at the reference depth, d_ref = 1.2 cm, coincident with the depth of the beam maximum dose. A cylindrical ionization chamber, positioned in water at the edge of the collimated beam, was used to verify the beam stability during the film exposure. By means of the calibration curve, reported in figure 2, the OD values were converted in dose to water per pulse, .

 

2.2.4. Plane parallel ionization chambers

Three different plane parallel ionization chambers, a Markus mod. 23343 (PTW Freiburg), a Roos mod. 34001 (PTW Freiburg) and a NACP-02 (Scanditronix), connected to a Keithley mod. 35617 electrometer, were used to determine absolute dose values for the three Novac7 electron beams mentioned in section 2.2.3. The three chambers present a nominal electrode distance, d, equal to 2 mm, a polarity effect less than 0.5% (at low dose per pulse values) and water as recommended phantom material.

For the ionization chambers, the calibration factors, N_D,P , in terms of absorbed dose in air were determined by comparison with the reference ionization chamber ENEA mod.ESC/87. Applying the Italian Protocol (AIFB 1988) (that follows the recommendation of the IAEA (1988)) a 21 MeV electron beam (20x20 cm² in size at SSD=100 cm), supplied by the conventional linac Saturne 43 (with a prf=100 Hz) was selected for the comparison. Table I reports the nominal sensitive volumes, the recommended (by manufacturer) polarizing voltage values, V₁, together with the calibration factor values, N_D,P. These last values were calculated by averaging the calibration factors obtained with polarizing voltage, V, ranging between 50 V and the threshold voltage, V₀ , as determined in the result section. The percentage standard deviations for the N_D,P values (reported in table I), were coincident with the reproducibility of the ionization chamber signal.

 

Ionization chamber Model	Nominal sensitive volume (cm3)	V1 (V)	ND, P (108 Gy/C)
Markus mod.23343	0.055	300	5.043 ± 0.015
NACP-02	0.160	200	1.360 ± 0.005
Roos mod. 34001	0.350	100	0.781 ± 0.003

Table I - Nominal sensitive volumes, recommended polarizing voltage values, V₁, and calibration factors, N_D,P .

 

For the three Novac7 electron beams obtained by collimators 6, 8, and 10 cm in diameter, the ion recombination factors, k_sat (AIFB 1988), for the three chambers, were determined using the two-voltage (TV) method (Weinhous and Meli 1984). The k_sat values were used to determine the absorbed dose to water per pulse, , at the reference point, d_ref = 1.2 cm following the AIFB 1988 protocol. As reported in literature, for high dose per pulse values, the k_sat factors could be overestimated due both to the unattached electrons to oxygen molecules of the gas (Boag 1950, Hochhauser and Balk 1986, Boag et al. 1996, Burns and Burns 1993) as well as to the chamber response dependence on the polarizing voltage (Buns and McEwen 1998, Nisbet and Thwaites 1998). Indeed the use of polarizing voltage values above threshold voltage values, V₀, entails a limitation of the Boag two-voltage analysis. To investigate these phenomena, dose to water per pulse values, d_w(V) , non correct for ion recombination (assuming k_sat=1) were determined using the signals M_V obtained with different polarizing voltages, V, and the N_D,P calibration factors reported in table I (AIFB 1988). Dose values and d_w(V) , were determined from the mean value of the signals (at standard temperature and pressure) obtained inverting the polarization. The d_w(V) values were compared with and values obtained for the three electron beams. As for measurements, the dose per pulse obtained by ionization chambers were carried out testing the beam stability.

 

3. Results and discussion

Following the Boag theory (Boag and Currant 1980, Burns and McEwen 1998) the ion recombination factor, k, for the three plane parallel ionization chambers at low dose per pulse values can be approximated by

where u = C/V, and C is a constant given by the product of m (a constant which depends on gas of the cavity); r (the charge density of positive ions liberated per pulse) and (the square of the chamber electrode distance) (Boag and Current 1980).

Following Burns and McEwen (1998) suggestions the best estimation of the saturation signals, M_S , for a 21 MeV electron beam (Saturne 43) was obtained using the M_V signals (at standard temperature, pressure and constant number of monitor units) that better follow the linear approximation of 1/M_V versus 1/V. Figure 4 shows the ratios M_S/M_V obtained for the three ionization chambers as a function of 1/V for constant monitor units. The solid line is the linear fit of the ratios with a polarizing voltage below a threshold value, V₀, where equation 1 is satisfied. In this way the values, V₀, for the three ionization chambers were determined and reported in table II. The value V₀=140 V less than the V₁=200 V for the NACP-02 ion-chamber is in agreement with the result obtained by Burns and McEwen (1998).

By equation (1) and the data reported in figure 4, the parameters C were determined for the three ionization chambers. The consistence of these values was verified determining the effective plate separation d_eff values of the ionization chambers, that are proportional to the ratios between the C values and the absorbed dose to air per pulse, D_{air,p ,} in the collecting volume of the ionization chambers. Indeed if the charge density, r, is determined by:

where r_air is the air density , W is the average energy required to create an electron-ion pair in air, e is the electronic charge and D_air,p is determined by the product of the saturation signal per pulse, M_S,p , and N_D,P :

the d_eff can be determined by:

Using the values µ=3.02 10¹⁰ V m C^-1 (ICRU 1982), (W_air/e)=33.97 JC^-1 (CCEMRI 1985) and r_air=1.205 Kg m^-3 (at standard temperature and pressure), the d_eff value (this is not necessarily the actual plate separations) for each ion chamber was within 10% in agreement with the nominal plate separation, d, reported by the chamber manufacturers. The d_eff values and the C/D_air,p ratios, obtained for the three ionization chambers, are reported in table II.

Table II – Threshold voltage values, V₀, C/D_air,p ratios and effective plate separation, d_eff, determined for the three plane parallel ionization chambers. The uncertainties for C/D_air,p ratios were estimated as propagation of the M_S,p (0.7%), N_D,P (0.5%) and C (0.5%) uncertainties.

The absorbed dose to water per pulse (at d_ref = 1.2 cm), , of the three Novac7 electron beams were determined and reported in table III. The dose uncertainty of 2.7% (1s ) was estimated combining in quadrature the uncertainty of 2.5% (1s ) due to the MD-55-2 film calibration and the uncertainty of 1% (1s ) due to OD interfilm reproducibility.

The dose per pulse values, , were determined and reported in table III. The dose uncertainty for 2% (1s ) were determined following the protocol AIFB (1988). The percentage polarity effect resulted lower than 1% for both Roos 34001 and NACP-02 ionization chambers while for the Markus chamber it resulted equal to 7%. This last value resulted greater than 4% observed by Nisbet and Thwaites (1998) for conventional dose per pulse values.

Table III – Absorbed doses to water obtained using MD-55-2 films, , and using plane parallel ionization chambers (Markus-23343, NACP-02 and Roos-34001) .

Figure 5 reports, for the three ionization chambers irradiated with the electron beam 10 cm in diameter, the d_w(V) values and two asymptotic lines, the dashed line represents the absorbed dose per pulse, , value, while the dotted line represents the dose per pulse value. A qualitative analysis of the results, reported in figure 5, suggests that the values cannot be considered adequate asymptotic saturation dose values for the three ionization chambers. Moreover the percentage variation of the values, reported in table III, is within ± 7% and these values are up to 20% higher than the values.

Figure 5 shows that at high dose per pulse values the collection efficiency, f, at the polarizing voltage values here used, is lower than 0.95. This means that the saturation signal M_S cannot be estimated by a linear extrapolation of 1/M against 1/V as used by Burns and McEwen (1998) for low dose per pulse values. Moreover, the effect of free electron collection on the evaluation of the ion recombination factor has to be considered. For these reasons the general formula for the ion recombination factor, k=1/f, (Hochhauser and Balk 1986, Boag et al. 1996) has been used:

where:

p is the free-electron fraction, that is a function of the polarizing voltage, p(V); u=C/V is the same parameter reported in equation (1).

By using the dose to water per pulse , the saturation signals per pulse, M_S, (at standard temperature and pressure) for the three plane parallel chambers were estimated as:

where is the ratio of the effective mass collision stopping power of water to that of air, (AIFB 1988) and the N_D,P is the chamber calibration factor (table I). The M_S uncertainty equal to 4% (1s ) was estimated combining in quadrature the uncertainties of the parameters reported in equation (4).

Therefore, the equation (3) can be rewritten as:

By the M_V signals, determined at a different polarizing voltages, V, the ratios M_S/M_V were used in equation (5). A software iterative procedure that minimized the differences between the first and second member of equation (5) was used to optimize the choice of the C and p(V) values. The procedure included two constraints:

1. the C values were selected within a 2s of the C/D_air,p uncertainty, reported in table II (determined at conventional dose per pulse values);
2. the p(V) values selected, increased with the polarizing voltage and were independent of dose per pulse as reported in literature (Boag 1987, Boag et al. 1996, Hochhauser and Balk 1986).

The p(V) values for the three plane parallel ionization chambers (with nominal plate separation d=2 mm) ranged between 0.05 and 0.15 at V=100 V while at V=150 V p(V) values ranged between 0.10 and 0.20. These results were coherent with those determined by Boag (1987) and Boag et al. (1996) for plane parallel ionization chambers with electrodes distances between 1 mm and 6 mm.

The C and p(V) values, determined by the iterative procedure, were used to implement equation (3) for the three plane parallel chambers. Figure 6 reports the M_S/M_V ratios obtained at 5.30 cGy/pulse fitted by equation (3) as a function of the parameter u. Up to the threshold polarizing voltage V₀ values, (determined at conventional dose per pulse values), the differences between M_S/M_V ratios and k values (equation 3) resulted within 3 % for Roos and NACP-02 chambers and 5% for Markus.

The mean C/D_air,p values obtained for the three ionization chambers at conventional and high dose per pulse values resulted 50.6 ± 2.0 ; 53.2 ± 0.5 and 35.5 ± 0.2 (V/cGy) for Markus, NACP and Roos ionization chambers, respectively.

Figure 7 reports, for the three ion chambers, the _dw(V₀) values as a function of (obtained at three high dose per pulse values) fitted by a second degree polynomial curve. The differences between the curve and the bisector line are representative of the ion recombination factor at V₀, k_sat(V₀) that can be obtained by:

In this work, MD-55-2 radiochromic films have been used as reference dosimeters to obtain the dose calibration of three Novac7 electron beams (E₀=5.8 MeV) of high dose per pulse used for the IORT technique. For the MD-55-2 films the OD independence of dose per pulse has been tested by using Fricke chemical dosimeters. The high spatial resolution and the possible use of the film in water phantom makes the radiochromic film attractive for absolute and relative dosimetry of high dose per pulse radiation beams of different configuration and dimension. The dosimetric uncertainty was estimated of about 2.7 % (1s ).

However, the electron beam calibration by radiochromic films results time consuming and this makes the use of such dosimeters unsuitable for periodic quality control procedures, where the use of a plane parallel ionization chamber is fundamental (IAEA 1997). Nevertheless, the use of ionization chambers at high dose per pulse values, entails dose uncertainties due to: a) the overestimation of the ion recombination factor, k , up to 20% if conventional dosimetric protocols are used; b) the percent polarity effect can result greater than 1%. For the dose per pulse values here examined the percentage polarity effect resulted lower than 1% for both Roos 34001 and NACP-02 ionization chambers while for the Markus chamber it reached 7%. It is important to remember that a high polarity effect may increase during the lifetime of the ion chamber (IAEA 1997), this means that it is important to check the polarity effect of the chamber, regularly.

For any newly commissioned chamber, a plot of M_S/M_V ratios against 1/V (figure 4) is recommended. In this work, the general formula for k determination (equation (3)) was used to fit M_S/M_V ratios and the existence of a threshold voltage value, V₀, at high dose per pulse values seems to be also confirmed.

An ion recombination factor k_sat(V₀) coherent with the Boag theory has been estimated at three different dose per pulse values as ratio of the dose to water per pulse measured by GAF-Chromic film, , and the uncorrected dose to water d_w(V₀) (equation 6). However, it is important to observe that the results reported in figure 7 for the three ionization chambers are only indicative for other ionization chambers of the same model. Indeed, as reported by Burns and McEwen [1998], for an NACP-02 ion chamber, differences in the parallel plate separation of 0.16 mm entails differences in the ion recombination factor up to 8%. This means that, at present, any chamber needs a specific k_sat(V₀) vs d_w(V₀) calibration by using a reference dosimeter that presents an independent response to the dose rate. However, it is important to underline that an accurate determination of k_sat(V₀) at a reference quality beam, can be used to determine the dose to water per pulse for electron beams of different quality (Burns and Burns 1993) and different geometrical configuration.

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AIFB 1988 (Associazione Italiana di Fisica Biomedica) Protocollo per la dosimetria di base nella radioterapia con fasci di fotoni ed elettroni con E_max fra 1 e 40 MeV. Notiziario della A.I.F.B. VI(2).

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Hochhauser E and Balk OA 1986 The influence of unattached electrons on the collection efficiency of ionisation chambers for the measurements of radiation pulses of high dose rate. Phys. Med. Biol. 31, 223-233.

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Piermattei A , Delle Canne S , Azario L , Fidanzio A , Soriani A , Orvieto A , Fantini M 1999 , Linac Novac7 electron beam calibration using GAF-Chromic film. Phys. Med. 15(4) In press.

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We gratefully acknowledge D. Di Nucci, P. Di Nicola for their technical assistance. This work was supplied by grants from MURST (Ministero dell’Università e della Ricerca Scientifica e Tecnologica).

Figure 1 – Dedicated IORT linac robot developed to perform radiotherapy treatment during surgery. The external dimensions are 2.55 m in height, 2.3 m in length, 1 m in width and the weight is 600 Kg.

Figure 2 – MD-55-2 film calibration in terms of optical density OD () vs absorbed dose to water, by using an electron beam of E₀ = 6.2 MeV supplied by a conventional linac (Saturne 43). The OD=0.347 refers to the first irradiation at 10 Gy. The fit is obtained by using a third degree polynomial curve. The symbol dimension is representative of OD precision.

Figure 3 – / ratios () at three different dose per pulse values: 0.0390 cGy/pulse, 2.96 cGy/pulse and 5.38 cGy/pulse, are reported. The bars are representative of the uncertainties determined as propagation of dose uncertainties (2.7%, 1s) for and (1.4%, 1s) for .

Figure 4 – M_S/M_V ratios () as a function of 1/V obtained for the three ionization chambers, (a) Markus. Mod. 23334, (b) NACP-02, (c) Roos mod. 34001, irradiated by a 21 MeV (Saturne 43) electron beam. The solid line is the linear fit of the ratios with a polarizing voltage below the value V₀ ().

Figure 5 – The d_w(V) values () and asymptotic lines are reported. The dotted lines represent the value =3.03 cGy/pulse while the dashed lines represent the values obtained by the Markus mod. 23334 (a), NACP-02 (b) and Roos mod. 34001 (c). The result were obtained with the Novac7 electron beam, 10 cm in diameter.

Figure 6 – M_S/M_V ratios () at 5.30 cGy/pulse obtained for the three ionization chambers: Markus mod. 23334 (a), NACP-02 (b), Roos mod. 34001 (c) as a function of parameter u. The continuous curves (equation 3) represent k vs u. The closed symbols () indicate the results obtained at V₀.

Figure 7 – d_w(V0) values as a function of obtained by the Markus mod. 23334 (a), NACP-02 (b), Roos mod. 34001 (c) ionization chambers irradiated at 3.03, 5.30 and 6.20 cGy/pulse. The data are fitted by second degree polynomial curves.