We (ham radio ops) use a reference to a half wave dipole in free space and label it as 'dBd', as opposed to 'dBi', gain over an isotropic model.120113-1633 EST
One needs a basic reference. Ultimately an isotropic radiator is a basic reference. Such a practical device does not exist for most radio measurements. A dipole can be defined relative to an isotropic radiator, and thus many measurements are referenced to a dipole.
As you narrow the width of a radiated beam of energy for a given input power you will increase the power density, but unless you can perfectly collimate a beam, the energy density of the narrowed beam will diminish as the square of the radial distance.
When I was referring to the atmosphere having no effect I specified very low frequency radiation.
It is interesting that the results of the values given in the question produced a power density of 10 microwatts per sq-meter.
Yes, I see you addressed ELF, but the question about HAARP involved HF. Either way, until you get to the ionosphere, HF pretty much travels through the atmosphere with impunity, as does MW and ELF.