A number of factors make the rising column of air above the collector significantly narrower than the collector's diameter:
(1) Hot air rises. The hotter the air, relative to the temperature of the surrounding air mass, the faster the air rises. The collector is hotter in its center, making the air in the center also hotter. The air over the center of the collector rises faster, because it is hotter. The hotter air towards the center of the collector rises faster than the air over the perimeter, causing the air over the perimeter to curve inwards as well as upwards. This effect narrows the rising column of air over the collector.
(2) As the cooler air moves inward from the perimeter towards the center of the collector, it gradually increases in temperature as it spends more time over the hot collector. The hotter the air gets, the faster it rises. The cooler air, which moves mostly horizontally while at the perimeter, moves more and more vertically as it moves towards the center and increases in temperature. The result is that the path of the air curves upwards as it moves inwards (see diagram below), and so the rising column of air is much narrower than the collector itself.
Thus there are two factors which make the air hotter over the center of the collector, first, that the center of the collector itself is hotter and, second, that the air in the center has spent more time over the collector.
(3) The rising air in the center meets with less resistance as it rises, because it is surrounded by air that is also rising. This factor causes the air towards the center to rise faster, drawing in air from the perimeter, and again narrowing the rising column of air.
(4) As the hot air over the collector rises, new cooler air must move in from the sides around the collector to replace the rising air. The cooler air at the perimeter moves inward from 360 degrees around the collector. This results in a wind moving inwards towards the center of the collector. Air movement over the perimeter of the collector is more horizontal than vertical. This wind pushes the rising column of air inwards, again making the column of air narrower than the collector itself.
For the above reasons, most of the updraft over the collector occurs around the center of the collector. Therefore, the air pressure will also be lowest towards the center of the collector.