I'm trying to design a planet with weather conditions similar to the Atacama desert in Chile- mainly in that there's no rain, only fog. From what I understand, in Chile, this is caused by a rain-shadow effect? But I'm not entirely sure. I'd like for the entire planet to be this way, not just on one side of a mountain range, but am not sure if/how this is possible. Thank you!
You simply can't get the right prevailing conditions on an entire planet to get a single weather system worldwide, what you can do is have a world that has very little land suitable for habitation so the few areas that can be colonised all have the same characteristics.
The fog watered west slope of the Andes, which includes but isn't limited to the Atacama, is the result of the fact that sun on the mountains creates a local low pressure system that draws wet air off the sea which forms fog and supplies water in an area where rain bearing wind is blocked by those same mountains.
So the question isn't how to create a world with only fog, it's how to keep people away from areas where it rains. For example the relatively dry conditions of the rain shadow zone, the area that's fog watered, could keep out certain toxic plants, microbes, and/or animals, that would otherwise kill off any colonising effort. Alternatively if the upper atmosphere is toxic, because reasons (as in that's a whole different question), then only areas where rain doesn't fall can support life at all. Such a world would be broken into three types of land; poisonous rain-swept wastes, bone dry deserts, and a few scraps of mountain fringed coastline where rain doesn't fall but fresh water vapour from the ocean supplies enough moisture for life.
Let's toss the rain-shadow effect concept in the bin, since it's reliant upon it raining elsewhere, and thus would have to eliminated. But this isn't actually that hard, if you take a step back and think about it. What is fog? Fog banks are simply surface-level, low-lying cloud formations. Specifically, stratus clouds; the flat or sometimes ragged non-convective stratiform type. Only very weak precipitation can fall from these clouds, usually drizzle or snow grains; and whenever a low stratiform cloud contacts the ground, it's classified as fog, so long as the prevailing surface visibility is less than 1 kilometer (though radiation and advection types of fog tend to form in clear air, rather than from stratus layers). If the visibility increases to 1 kilometer or higher in any kind of fog, the visible condensation is termed mist instead.
So, to achieve this, you simply need to give your planet conditions in which you only have stratiform clouds, in which these stratiform clouds come in contact with the ground across the entire planet's surface at some point, and with visibility reduced to less than a kilometer as a result when they do. These stable stratiform cloud decks, aka as 'fog', tend to form when a cool, stable air mass is trapped underneath a warm air mass. So, there's your answer- give your planet an atmospheric boundary layer at a relatively low altitude, where temperatures are lower below that boundary than they are above it. Unlike on Earth, where the temperature gets colder as the distance above the earth increases, by about 6.5°C per kilometre. How can we do this? By siphoning off a decent portion of the insolation received by this planet at its atmospheric boundary layer, resulting in it never reaching the surface.
The most extreme example of this, which would have resulted in a planet which would have no rain, and would only have fog? That of The Matrix, courtesy of Operation Dark Storm. But there's a relatively simple, far less extreme solution; instead of a shroud of unstoppable, all-consuming self-replicating nanites, why not simply give your planet blooms of buoyant aerial algae instead? These essentially create the atmospheric barrier, at the altitude at which the density of the atmosphere gives them neutral bouyancy- let's say, 0.5-1km above sea level (with your planet smooth enough to lack any peaks tall enough to poke through this layer); and even if 90% of the sun's energy still gets through, that difference'll still be more than enough to turn this layer into a heat sink, trapping the cooler, more stable air mass beneath it.
Thus, limiting your planet's water cycle to only low-lying fog banks, and limiting precipitation on its surface to fog drip. But your planet wouldn't necessarily have to be relatively dry as a result of this, not at all. My advice, if you're building this planet as a setting, and intend it to be an habitable, inhabited world? Abandon the fog desert ecosystem model, and the Atacama desert analogy. Instead, look at cloud forest ecosystems as a better, more realistic and hospitable model to use as your template.