Answer to Question #12535 Submitted to "Ask the Experts"

Portable battery operated x-ray devices are becoming more and more popular, for example, Golden Engineering's XRS4 is a 370 kVp x-ray generator. These devices do not provide a continuous high voltage electron beam to create x rays, but rather they use the charging and discharging of a capacitor to create a train of short x-ray pulses to create a radiograph. The individual pulse width is typically 10 nanoseconds (ns) long, with up to nine pulses provided per second (pulses s^-1), and up to 3,000 pulses per battery charge. Given the very high instantaneous dose rate during the individual pulse, can a pencil dosimeter accurately measure exposure, or will there be recombination of the ions in the pencil dosimeter leading to an under response? For instance, the x-ray device reportedly produces about 5 milliroentgen¹ approximately 1 × 10^-6 (coulombs per kilogram [C kg^-1] in air) per pulse (mR pulse^-1) at approximately 30 centimeters (cm). If the pulse is only 10 ns long, this would correspond to an instantaneous dose rate of 500,000 roentgens per second (R s^-1) or 1.8 × 10⁹ roentgens per hour (R h^-1), which greatly exceeds the 10,000 R h^-1limit typically advertised for pencil dosimeters.  

When pulsed radiations are involved in potential exposures, there may be concerns for losses in instrument response associated with ion recombination, as your concerns imply.  For the particular instance you cite, I do not believe the recombination effects will be very impactful. I shall attempt to describe why I have so concluded. The manufacturer's warning not to use the dosimeters under field exposure rates greater than 10,000 R h^-1 are presumably based on continuous exposure conditions. The critical parameter to be evaluated, regardless of how high the theoretical exposure rate appears for a single pulse is the charge density produced by a given pulse, and we shall review this below.

The extent to which recombination effects are significant depends on the individual pulse intensity as well as the pulse frequency and the detector characteristics. For the conditions you specify, a pulse width of 10 nanoseconds and a maximum pulse rate of 9 pulse s^-1, the on-time of the unit is very low with about 125 milliseconds (ms) between pulses. For a typical air-filled pencil type dosimeter most all of the negative charges produced by ionization will appear as negative ions, electrons attached to oxygen molecules. The mobility of such ions is much less than that for free electrons, probably being on the order of 100 cm s^-1. However, considering the rather small diameter of most pocket ion chamber device, the ion clearance time will then be a few to several milliseconds, much less than the time between pulses. Consequently, any ion losses associated with recombination will be associated with individual pulses and not with charge-density effects associated with overlapping pulses. It then becomes necessary only to estimate the recombination losses associated with each pulse.

Much of the meaningful analytical work in this regard has been done by J.W. Boag in the 1960s, 1970s, and 1980s. I will not cite references here, but you can readily find them cited by searching the internet. The work is also referenced and used in International Commission on Radiation Units and Measurements (ICRU) Report 34, The Dosimetry of Pulsed Radiation, 1982, and I will primarily follow that approach. For low linear energy transfer (LET) radiation, as of concern in your case, we will not have to attempt any corrections for what is referred to as initial (or sometimes columnar) ion recombination which relates to recombination along the track of an ionizing particle and which is most notable for densely ionizing particles such as alpha particles or protons. It is primarily the general, volume type recombination that we will consider.

For a cylindrical ionization chamber with a central electrode, similar to our concern here, a quantity referred to as u, related to the charge collection efficiency, f, by

f = (1/u) ln(1 + u)

is given by

u = µ{q [K_cyl (a – b)]²/V},

where µ is a constant related to ion mobilities and the recombination coefficient; q is the charge density produced by radiation in the chamber; a is the radius of the ion chamber; b is the radius of the central electrode; V is the applied voltage, and K_cyl is given by

K_cyl = {[(a/b + 1) ln(a/b)]/[2(a/b – 1)]}^0.5 .

For a typical pocket ion chamber the voltage is 150 to 200 volts (V). I shall assume the lower voltage of 150 V. Naturally the voltage of these pocket devices decreases with increasing exposure and recombination losses will increases somewhat as the voltage decreases. I do not know the specific characteristics of the devices you are using, and I have used a ratio a/b = 10, with a = 0.005 meters (m) and b = 0.0005 m, yielding a K_cyl value of 1.19. The value of µ recommended by Boag for air ionization chambers with electrode separations greater than about 2.5 mm is 3.02 × 10¹⁰ volt meters per coulomb (V-m C^-1); this value is not an absolute constant and can vary somewhat among different chamber types. You note that the generator produces a pulse exposure of 5 mR at about 30 cm. The calculated charge density in the air of the ion chamber at an assumed temperature of 22^o C is then

q = (5 × 10^-3 R) [2.58 × 10^-4 (C kg^-1R^-1)] (1.20 kg m^-3) = 1.55 × 10^-6 C m^-3.

The calculated value of u then is (3.02 × 10¹⁰){1.55 × 10^-6[1.19(0.005 – 0.0005)]²}/150 = 8.9 × 10^-3, and

f = (1/8.9 × 10^-3) ln(1 + 8.9 × 10^-3 ) = 0.996.

This result would indicate only a small loss of 0.4% of ions due to recombination. This would not be a concern from a health physics perspective.

Keep in mind that these calculations are only exemplary, being based on assumptions regarding the pencil chambers in question. You may be able to refine them somewhat if you have more specific details.

George Chabot, PhD, CHP

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¹ The exposure units are given here in roentgens (R) and milliroentgens (mR), called traditional units, because those are the measurement units used by the instrument. However, the Health Physics Society has adopted the SI (International System) of units and the corresponding SI units are given in parentheses.