Where will the energy come from?

Fossil fuels are running out (that's a founding assumption), so they're out of the question. There's no hydro potential in the Malian desert, and geothermal doesn't seem to hold much promise, either. Bootstrapping with biomass in a desert is a non-starter. Wind is abundant on the West coast of the Sahara, but much less so inland. Therefore, the obvious, and perhaps only, options are solar and nuclear. (Niger, next door, is a well-known source of "yellow cake", as raw uranium from the Earth is known.)

The City Corporation that has been established to develop this project has only a few billion budgeted to kick-start the city, and it is naturally reluctant to spend the whole sum on a nuclear power station. Therefore, solar is all that's left. The alternatives are between solar thermal and solar photovoltaics.

At the moment, photovoltaics are much more expensive and use much more land than solar thermal. Regardless of whether we choose photovoltaics or solar thermal, land could be saved by building high scaffolds and suspending either thermal concentrators or photovoltaic panels off them (taking care to arrange the panels or dishes so they cast little or no shadow on each other). Towers containing dishes or panels arranged radially or spirally like leaves on a stem could reduce the amount of land needed for a given amount of power by as much as 90%. It's a question of trading land costs for infrastructure costs. If we grow desperate for land, we'll build those towers. For now, though, we'll just arrange our panels or concentrators on the ground in the conventional manner.

Based on an installation in Brockton, Massachusetts, in which 500kW are generated on a 27 acre plot, I calculate that a photovoltaic array will yield 4.576 MW per sq. km. Meanwhile, from news of a big project in California, we can get 27.45 MW per sq. km. if we employ thermal concentrators and convert the heat to electricity using Stirling engines. The dishes used in the California project each have a capacity of 25kW.
If we assume they work at full capacity for eight hours a day, 365 days a year, each will generate 73MWh per year. (Actually, they'll probably work for more like 11 hours a day at full capacity in the Sahara, and while a photovoltaic system will stop generating as soon as the light drops below a certain level, a thermal system will continue working for a while after it gets dark, because of the heat stored in the system.)

Solar thermal concentrator facing the sun — Image from Sterling Energy Systems

The city needs 1100 TWh plus a further 800 TWh of electricity to replace the use of petrol-driven vehicles -- 1,900 TWh in all.

To generate 1,900 TWh in a year -- the sum needed by 100 million people to enjoy the high standard of living they feel they deserve, we'll need 26 million dishes, giving a total capacity of 650 gigawatts. The California project indicates that we can fit 1100 such dishes in one square kilometre. Therefore, we need to cover 23,700 sq. km. (9,266 sq. miles) in order to produce the power we need. If the dishes are all organized into one big, square field, it will be 153 km (94 miles) on each side.
Since Desertopolis is 40,000 sq. km., if we reserve the land exclusively for the solar collectors, we'll lose 40% of our land to solar dishes, and have just 26,300 sq. km left, unless we put the dishes on the roofs of buildings, or put other useful things in the ground under them. In that case, we'd lose almost no land. Either way, we've seen that there's enough land available to generate all the power desired.

How much will it cost? Stirling Engineering systems say that if their solar dishes are mass produced, they can make them for $80,000, "or possibly $50,000", apiece. If we assume $70,000 as a compromise, we need $1,820 billion to acquire the 11 million dishes needed to power the city. However, we don't have to get them all at once. If we buy 520,000 units (6.25 GW capacity) a year, at a cost of $36.4 billion, as we grow the city, we'll have it all done in fifty years.

Expensive, but doable, if you have the budget of a fairly large country, which you have to have, if you're planning to equip the population of a fairly large country with all its energy needs.

Are there enough materials in the world to make so many solar dishes? Certainly, yes. They're not made from any exotic materials -- just boring stuff like steel and aluminium, and each uses about as much material as a couple of motor cars, or perhaps one large car. All we need is metal equivalent to 52 million cars -- about a third the number of cars there are in the USA.

It looks as if we may have the energy supply cracked, apart from one small problem, namely that solar energy doesn't work at night. We'll have to look into that. Meanwhile, there's still the food and water supply to deal with.