Although some have suggested building dedicated nuclear plants to do desalination at scale, there may be a cheaper way. At the equator, a gigawatt of solar energy arrives per square kilometre, for free. First, assume we have a reservoir of fresh water, which we start vaporizing with a large field of solar mirrors, producing low-pressure steam. Feed the low pressure steam through a turbine where the steam is pressurized, not by burning jet fuel, but by further heating by the solar mirror array, producing large volumes of high pressure steam moving along a pipe. This arrangement can be used to move large volumes of water great distances, re-pressurizing the steam with solar-powered turbines every few kilometres.
In order to desalinate water at scale, inject sea water into the fast-moving high-pressure steam. The water flashes to steam, yielding somewhat lower-pressure steam with suspended salt crystals. The salt can now be removed from the steam mechanically, perhaps by passing the steam through a vortical separator. Some of the resulting fresh water goes back to the source reservoir, the rest continues inland. Once the steam arrives at its destination, it can be converted back to water by going through a heat exchanger or perhaps doing useful work.