As mentioned in an edit to my early lunar mining post, the possibility exists of a 30kWe-class nuclear reactor rated for surface operations on Mars. This would be using a design very similar to the Prometheus project reactor for the canceled JIMO mission. This was developed to a high level including non-nuclear test articles of all major components and irradiance testing of critical components. In other words, this project yielded engineering test data from physical objects; it's not someone's simulation paper slapped together for a hoped-for mission, but the product of a significant amount of time, money and ingenuity. Solid performance data is available. Taking a reactor designed for use on Mars and operating it on the Moon would give NASA a chance to field test the device before committing it to a manned mission; applying it to a mining and ISRU mission would let them test related technologies in a way that yields tangible benefits (lots of useful mass generated on the moon and delivered to LEO) in addition to good engineering data.
Some background information: kWe means kilowatts-electric while kWt means kilowatts-thermal. A nuclear reactor is rated using both values; the efficiency is equal to kWe/kWt. The difference between thermal power and electrical power (kWt - kWe) is the amount of heat that must be dumped to the environment in order to produce that electricity. Normally that means radiators, but for a system on a solid body like the Moon there are useful alternatives. Also important: increasing the power level of a reactor has only a minor effect on its mass. For example, the 30kWe Mars reactor was specified at 7.8t while the 200kWe JIMO reactor was specified at up to 11t. This 41% mass increase yields a 667% power increase, so the base design can be scaled up significantly without a big penalty in mass. This is because most of the mass of a reactor is shielding, coolant, radiators and pumps or turbines. Doubling the amount of fuel only adds a few percent to the structure and the turbines can be scaled up easily (up to a point anyway). Radiators are the main growth point for higher power.
For this lunar mining / Mars surface design (gas Brayton) the efficiency is 18.35%, meaning a 30kWe reactor generates about 163.5kWt, 133.5kW of which is waste and must be disposed of one way or another. The JIMO reactor was meant to be roughly 200kWe. Efficiencies could certainly be higher, but this is a hands-off design intended for a deep space probe with an operational lifetime of 15-20 years. The Mars FSP design is slightly different but still effectively hands-off since it would be absurdly dangerous to expect a flight crew on Mars to perform field reactor surgery.
133kW of heat is a lot of energy, and it is available at a number of different temperatures depending on where in the reactor that heat is tapped.
If relatively pure water ice is available, it can be taken from 90K to 275K (2 °C) for ~334kJ/kg + 334kJ/kg to melt it. The reactor could process 23.9kg of water ice per minute; this application would use heat at the gas cooler, bypassing some or all of the radiator. The radiator return temperature is 106 °C, which could be used to distill any collected water.
Some portion of water is adsorbed onto the surface of soil grains; this water is expected to be recoverable at roughly 600 °C / 873K. Reactor coolant gas just after the turbine is at 920-950K or about 650-670 °C. Lunar soil's specific heat is 0.88 kJ/kg*K at 350K; data is sparse for higher temperatures but can be expected to increase somewhat up to 950K; let's call it double or about 1.7kJ/kg*K. That would mean the available heat could cook soil from 90K to 950K at a rate of 5.46kg per minute. 10 tons processed per day would be 6.94kg per minute, so we are in the right ballpark. A counterflow heat exchanger running between the incoming ore and outgoing ore would only need to recover about 22% of the heat to close the thermal requirements. This processing step would produce water vapor and dry soil for further processing.
The dry soil could be kept hot, separated by a mechanical process into different streams of mineral types and passed into molten oxide electrolysis cells. These cells would use solar reflectors for heat since the operating temperature of the cell is far above that of the reactor, but having preheated material would save time, mass and reflector area. A significant amount of the electricity produced would be consumed by this process in order to make oxygen and mixed metals; each cell would produce a different metal mix based on the mineral stream fed into it; the big three are iron, aluminum and silicon. Theoretically the cells could be operated at night using only internal heating, but the throughput would be much lower and it would require adjustable electrodes. I would prefer to reserve night periods for maintenance and cleaning; molten oxides are chemically very harsh and various components of the cells will need to be scraped out or replaced from time to time. For autonomous or remote operation this means a maintenance robot.
The output of the electroysis cells isn't particularly pure, merely enriched to 80-90% of the target mineral. For single-metal minerals then the pour is 80-90% of the target metal; for multi-metal minerals the purity depends on the chemical formula of the input mineral(s). Separating aluminum-iron-silicon alloys is nontrivial.
In the case of the iron melt, this should be solidified using an atomizing nozzle. Molten metal droplets are sprayed into vacuum to form very small particles, which are collected and then exposed to carbon monoxide to form iron carbonyl. This gas can be forced to deposit very pure iron on any surface that is hot enough, recovering the carbon monoxide for repeated use. This approach has problems; the cooling and collection process is poorly defined and the refining process uses a gaseous reagent that has to be recaptured with high performance. The benefit is very pure iron that can be processed using CVD; in other words, the iron carbonyl gas can be used to 3d-print iron structures as desired without requiring a sintering cycle for the final product. Heat treatment is still required.
Aluminum-rich melts can be processed by heating them above the boiling point of aluminum, roughly 2500 °C. Pure aluminum vapor will be produced while the melt becomes enriched in silicon and other impurities. This is a high energy process but one that can be done with solar heat.
Silicon-rich melts could be processed by the iron method or the aluminum method first, but it may be more useful to go directly to zone refining. The melt is poured into a long trough and a zone is heated to melting; this melted zone is slowly passed along the trough, causing the elements in the melt to concentrate at one end or the other. This is used on Earth in the purification of semiconductor materials. Efficient use of this process requires many zones moving as quickly as can be managed; this is also a batch process unless a relatively low purity is acceptable. I would implement this with a similar magnesia trough as in the electrolysis cell but as thin as possible, with built-in coolant channels in bands or zones. Alternating bands receive coolant or concentrated sunlight, causing alternating melted and solid zones. These are passed along the length of the trough. The result is a bar of material that has specific elements in sequence; there will be a large zone of very pure silicon with smaller zones for each impurity.
An alternative would be to take the bulk, unsorted dry ore from the drying oven, electrolyze it into a mixed metal melt, then process the entire output in batches by zone refining. Each element of interest can be obtained at high purity simply by cutting the bar into pieces at the appropriate points. In between each pure zone is a narrow mixed zone that would be set aside for later processing. There will be several spectrometers available for characterizing each bar. This has an added benefit that trace metals can be accumulated and collected by remelting the mixed zones from several completed bars. The same equipment can produce properly-doped silicon for the manufacture of semiconductor devices once pure silicon, germanium and arsenic are available. Problems with this are that it would take both a large solar reflector area and a large radiator area to handle the tightly-focused heating and cooling. Some method of automating the bar sampling and cutting would also be required. Benefits would be very high purity materials and single-process refining of the entire spectrum of metals and transition metals without the use of chemical reagents.