Nuclear Power is a method of energy generation. It uses nuclear fuel to produce heat, which is usually transformed into electricity. Nuclear power is considered the preferred energy source for most plans for medium- to long-term human expeditions to Mars.
Usage On Mars
The generation of electricity from nuclear fuel does not depend on weather conditions so would be useful for maintaining a reliable source of power on Mars. However, due to the unclear availability of radioactive resources on Mars and the difficulty in preparing the fuel (the nuclear enrichment process) any nuclear fuel will have to be brought from Earth for the foreseeable future. This would significantly prevent the settlement from being independent from Earth.
Molten Salt Energy Storage
Molten Salt Energy Storage  is a process used in Concentrated Solar Thermal  that allows storing large amounts of heat energy in the form of high temperature molten salt. This reserve can be tapped for direct use in colony heating, Evaporative water purification, and Rodriguez Wells.
Rodriguez Well (RODWELL)
RODWELLS Are a form of well melted into Antarctic Ice to provide a constant source of water for use on a base, this lowers a heat source deep into the ice melting an area of ice that is partially pumped out as the ice cave grows 
In a Light Water Reactor, heat caused by the radioactivity boils water to steam. Turbines are driven by the steam's pressure, spinning a dynamo to generate electric energy. In a Molten Salt Reactor the heat generated from the core is redirected for use in Molten Salt Thermal Storage, structural heating, Stirling Generators to provide electricity, Evaporative Water Purification, and to melt water in RODWELLS.
Heating greenhouses and other buildings may be done indirectly by the heat of the nuclear fission. The heat can be transported in pipes from the reactor to the buildings. Heat exchangers avoid nuclear pollution of the buildings.
Types of Nuclear Generation
Radioisotope thermoelectric generators (abbr.: RTG) are simple devices. They produce a heat difference, transformed by a thermocouple to electrical energy. The maintenance effort is low. However, RTGs do not provide enough power for a base.
Nuclear Heatpipe Reactor
Megawatt Level Heat-Pipe Reactors  offer stable, safe power that requires no outside support system or personnel and is immune to meltdown, it can be scaled from .5kw to 50mw for remote bases, small cities, and forward operating bases here on Earth, these reactors could power a Colony or a Spaceship for between 5 and 40 years with no maintenance, with no in-situ resources needed. Heatpipe Reactors are inherently stable meaning if no energy is removed as heat the system stabilises to s constant temperature. Heat-Pipe Reactors are inherently "Walk-Away Safe" meaning if an emergency happens and the reactor is left alone it will not melt doen or change state.  
Molten Salt Reactor
Molten Salt Reactors use a liquid salt fuel that suspends a nuclear fuel in the salt at atmospheric pressure as opposed to a solid fuel reactor that uses high pressure water as a cooling agent that can turn into a steam explosion. If the salt temperature rises it will separate the suspended nuclear fuel and slow the reaction, as a safety feature at the lowest point in the core a pipe is cooled forcing the salt in that section of pipe to freeze and create a plug of salt, if that external cooling is lost the plug melts and the liquid salt contents of the core dump into a storage tank, when the salt is separated from the graphite moderator the salt becomes sub-critical and cools down. In the unlikely event of a leak of the Salt solidifies quickly allowing for far easier cleanup vs liquid water seeping into the environment. Since no pressurized steam is involved there is no need for a large domed pressure building around the core. For a more detailed explanation from Dr. Kirk Sorensen please see https://youtu.be/D3rL08J7fDA
- What sort of nuclear fuel is needed?
- How long can the described nuclear power stations work without replenishment of nuclear fuel?
- What is known about nuclear resources on Mars?
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- Idaho National Labs, Dr. K.P Annath, Dr. Michael Kellar, Mr. James Werner, Dr James Sterbentz Portable Special Purpose Nuclear Reactor (2 MW) for Remote Operating Bases and Microgrids , https://ndiastorage.blob.core.usgovcloudapi.net/ndia/2017/power/Ananth19349.pdf, May 2017.
- NASA Kilopower Project, Dr. David Poston Small Nuclear Reactors for Mars - 21st Annual Mars Society Convention , https://www.youtube.com/watch?v=NLE5YFuCmhw, Sep 2018.
- Safety assessment of molten salt reactors in comparison with light water reactors, Badawy M.Elsheikh Safety assessment of molten salt reactors in comparison with light water reactors , https://www.sciencedirect.com/science/article/pii/S1687850713000101, Oct, 2013.
- How Molten Salt Reactors Might Spell a Nuclear Energy Revolution, Stephen Williams How Molten Salt Reactors Might Spell a Nuclear Energy Revolution , https://www.zmescience.com/ecology/what-is-molten-salt-reactor-424343/, Feb 2019.