## How do AC and DC fields relate to each other?

We live in a DC magnetic field, the earth's geomagnetic field, and any AC field is superimposed on it.

The AC field is often less than the DC field. In fact it's often very much less. This example, not drawn to scale, shows the 0.4 µT AC field implicated in the epidemiology of childhood leukaemia with the typical 48 µT geomagnetic field in the UK. (0.4 µT is the rms value, the peak is slightly higher, see a tutorial on ways of characterising AC fields.)

When the AC field is less than the DC field, it doesn't change the average value of the total field. The AC fluctuations average to zero, and the average field is still 48 µT in this example.

## What does this mean for mechanisms?

Let's consider proposed mechanisms for how an AC magnetic field might produce effects in living systems. Clearly, if a mechanism depends just on the AC component, the DC field and the total field are irrelevant. Induced currents, for example, are produced only by AC fields.

But some mechanisms depend on the total field. The free radical mechanism is one example. It operate on such a fast timescale - tens of nanoseconds - that it just "sees" the instantaneous total field without knowing whether that is an AC field or a DC field.

If these mechanisms that depend on the total field were strictly linear - the effects they produced was exactly proportional to the field - any effects of the AC field produced would also average to zero. On the positive half cycle there would be a positive effect, on the negative half cycle an equal and opposite negative effect, and the two cancel. For free radicals, it might be an increase in the concentration on the positive half cycle and an equal and opposite decrease on the negative half cycle. The average concentration of free radicals is unchanged.

The only way these mechanisms can produce an overall effect from an AC field is if they are not strictly linear. Then the effect on the positive half cycle might be slightly larger than the effect on the negative half cycle, and the two would not exactly cancel, leaving a small overall effect.

This has two consequences.

- because the effect arises from the imperfect cancellation of two opposite effects, it is expected to be a smaller effect; and
- mathematically, we are saying that the linear component still averages to zero, and the net effect comes from the non-linearity, which is expressed as a quadratic or square term. So any effect of AC fields from these mechanisms will dependent not on the field but on the field squared (or, in principle, an even higher power).

We also predict, for mechanisms that depend on the total field, that if the AC field produces effects, then so would changes in the DC field, for example as we move from one lattitude to another on the earth. See one test of the implications of this for epidemiology.