Correction for the radiation quality of the beam, k Q,Qo

When a dosimeter is used in a beam of quality Q different from that used in its calibration, Q_o, the absorbed dose to water is given by

D_w,Q= M_QN_D,w,Qok_Q,Qo (2)

where the factor k_Q,Qocorrects for the effects of the difference between the reference beam quality Q_oand the actual user quality Q, and the dosimeter reading M_Qhas been corrected to the reference values of influence quantities, other than beam quality, for which the calibration factor is valid.

The beam quality correction factor k_Q,Qois defined as the ratio, at the qualities Q and Q_o, of the calibration factors in terms of absorbed dose to water of the ioniza-tion chamber

(3)

The most common reference quality Q_oused for the calibration of ionization chambers is ⁶⁰Co gamma radiation, in which case the symbol k_Qis used in this Code of Practice for the beam quality correction factor. In some PSDLs high energy photon and electron beams are directly used for calibration purposes and the symbol k_Q,Qois used in those cases.

Ideally, the beam quality correction factor should be measured directly for each chamber at the same quality as the user beam. However, this is not achievable in most standards laboratories. Such measurements can be performed only in laboratories with access to the appropriate beam qualities. For this reason the tech-nique is at present restricted to a few PSDLs in the world. The procedure requires the availability of an energy independent dosimetry system, such as a calorimeter, operating at these qualities. A related problem is the difficulty in reproducing in a standards laboratory beam qualities identical to those produced by clinical accelerators [53].

When no experimental data are available, or it is difficult to measure k_Q,Qo directly for realistic clinical beams, in many cases the correction factors can be calculated theoretically. Where Bragg–Gray theory can be applied, an expression for k_Q,Qocan be derived comparing Eq. (2) with the N_D,air formalism used in the IAEA Codes of Practice [17, 21] and other dosimetry protocols. A general expression for k_Q,Qohas been given in Refs [20, 54]

(4)

which is valid for all types of high energy beams and includes ratios, at the qualities Q and Q_o, of Spencer–Attix water/air stopping-power ratios, s_w,air, of the mean energy expended in air per ion pair formed, W_air,⁹ and of the perturbation factors p_Q. The

( )

9It should be noticed that W_air, as well as s_w,air, should be averaged over the complete spectra of particles present. This is an important limitation in the case of heavy charged parti-cles, where the determination of all possible particle spectra is a considerable undertaking.

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overall perturbation factors p_Q and p_Qo include all departures from the ideal Bragg–Gray detector conditions, i.e. p_wall, p_cav, p_cel and p_dis. These perturbation factors have been defined in Section 1.6.

In therapeutic electron and photon beams, the general assumption of (W_air)_Q= (W_air)_Qo¹⁰yields the simpler equation for k_Q,Qo

(5)

which depends only on quotients of water to air stopping-power ratios and perturba-tion factors at the beam qualities Q and Q_o. The only chamber specific factors involved are the perturbation correction factors p_Qand p_Qo. It should be emphasized, however, that when comparing experimental and theoretical determinations of k_Q,Qo it is the full Eq. (4) that is relevant, rather than the approximate Eq. (5). The possible energy variation of W_air, as suggested by some experimental evidence (cf. Ref. [55]), makes it necessary to use the approximate symbol (≈) in the latter expression.

When the reference quality Q_ois ⁶⁰Co gamma radiation, values of the product (s_w,air)_Qop_Qoin the denominator of Eq. (4) are given in Appendix II for cylindrical ionization chambers listed in this Code of Practice. These values have been used in the calculation of all k_Q,Qo factors given in the different sections of this Code of Practice when they are normalized to ⁶⁰Co; the symbol k_Qis used in those cases.

In the case of low and medium energy X ray beams, Bragg–Gray conditions do not apply and therefore Eq. (4) can not be used. In addition, the chamber to chamber variation in response is usually rather large (see Sections 8 and 9). For these radiation qualities the formalism is based exclusively on the use of directly measured N_D,w,Qor k_Q,Qofactors for individual user chambers.

3.2.1. A modified k_Q,Qofor electron beam cross-calibrations

For dosimeters that are used in electron beams, when the calibration quality Q_o is ⁶⁰Co, the situation is the same as discussed previously. For a user electron beam quality Q, the beam quality correction factor k_Qis given by Eq. (4).

An alternative to this is the direct calibration of chambers in electron beams, although this option has little application at present because of the limited availability

( )

10Note that this is the same assumption as for the non-dependence of N_D,airon the quality of the beam (see Ref. [17]).

of such calibrations. However, the ongoing development of electron beam primary standards will enable calibration at a series of electron beam qualities. From these calibration factors, a series of measured k_Q,Qofactors may be derived following the procedure given in Section 7.5.2 (the same procedure is used for chambers calibrated directly in high energy photons and in low and medium energy X rays).

A third possibility, which in the absence of direct calibration in electron beams is the preferred choice, is the cross-calibration of a plane-parallel chamber against a calibrated cylindrical chamber in a high energy electron beam of quality Q_cross. The factors k_Q,Qcross, which allow the subsequent use of this chamber in an electron beam of quality Q, are non-trivial because the cross-calibration quality Q_crossis not unique and so for each chamber type a two dimensional table of k_Q,Qcrossfactors is required.

However, it is possible to present the required data in a single table by intro-ducing an arbitrary electron beam quality Q_intwhich acts as an intermediate between the cross-calibration quality Q_crossand the user quality Q (no measurements are made at Q_int, it is a tool to simplify the presentation of the data). The required k_Q,Qcross factor is evaluated as the ratio of the factors k_Q,Qintand kQcross,Qint:

(6)

The factor (kQcross,Qint)^–1 corrects the actual chamber calibration factor N_D,w,Qcrossinto a calibration factor which applies at the intermediate quality Q_int. The factor k_Q,Qintcorrects this latter calibration factor into one which applies at Q so that the general Eq. (2) for D_w,Qcan be applied.

The expressions for k_Q,Qintand kQcross,Qintfollow from Eq. (5), from which it is clear that the stopping-power ratios and perturbation factors at Q_intwill cancel in Eq. (6). Thus the value chosen for Q_int is arbitrary and in this Code of Practice is chosen as R₅₀= 7.5 g/cm², where R₅₀is the beam quality index in electron beams (see Section 7). Values for k_Q,Qint and kQcross,Qint calculated on this basis are given in Table 19 of Section 7.6.1 for a series of chamber types.

The data of Table 19 highlight another advantage of this approach. For a given Q and Q_cross, the value for kQcross,Qintis the same for all well guarded plane-parallel chamber types. For cylindrical chamber types it depends only on the chamber radius r_cyl. The chosen value for Q_int minimizes the differences for cylindrical chambers of different r_cylover the range of beam qualities for which cylindrical chambers are used. This value for Q_int (R₅₀ = 7.5 g/cm²) is also consistent with Ref. [51], so that the same measured or calculated values for k_Q,Qint and kQcross,Qint may be used in Eq. (6).

Note that the above method may also be used for plane-parallel or cylindrical chambers calibrated at a standards laboratory at a single electron beam quality Q_o.

int

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