# Radiation's Nonlinear Characteristics

mathematical modeling to predict whether low doses are more or less harmful than assumed.

 In studying health, we frequently test using very high doses then interpolate linearly to make assumptions about lower exposures. But the real effect might not follow the cause linearly. This will lead to very poor estimates. With radiation, some things are considered logarithmic rather than linear. Both of these may be inaccurate for predicting the effects of low exposures to radiation.
If one observes the DC current output of an ion chamber, or photo-multiplier tube, as I did, one will notice that the current output follows square root relationship to the input radiation.
 Over a range of about a decade and a half the square root curve follows closely to the log curve which is normally used to plot radiation's intensity. Might this imply that the square root curve would be a better choice for plotting radiation, or even a better model for understanding the effects of radiation?
So why does current have a square root relation to radiation? The answer shows up in communication theory and simple circuit theory. Radiation produces a random series of ionizations that a detector reads as electrical pulses. A communication theory text will show that random impulse noise has a power spectrum that contains a DC part. From circuit theory, power has a known relationship to current:

P= I2R or I = sqrt(P/R).

As we have observed current from the detector acts as the square root of the incoming power or radiation intensity.

This all seems to raise a few questions:

• Since power has a square relationship to both the ionization pulses in and the current out, would using square root curves be a more natural model for radiation metering?
• Which is the best model for the impact of radiation for any given material such as living tissues: number of ionizations, power absorbed, current generated, power within a certain spectrum range or, other?

Without knowing the answer to the second question, valid interpolations from large doses to small doses of radiation can not be made. Our models for the health impacts of low level radiation may be contain significant errors. Which model is best for interpolations?

The discussion above only considers possible nonlinear effects of the radiation. No consideration is given to the probable nonlinear characteristics of human flesh and other absorbing materials.