Possible scientific experiment?
Well, Victor – you right, absolutely - two visible way today – in 2000 was experiments to make Al from Al2O3 in hydrogen plasma (in some blog reference to UDK 541.14 http://hbar.phys.msu.ru/gorm/forum/index.php?t=msg&th=2433&goto=50817&S=8dc2fbb39a516315e8538348f84b2e64#msg_50817 experiments was done in Krasnoiarsk) , and in 2006 was theoretical study on formula 2Al2O3+3C=4AL+3CO2 (http://www.itp.nsc.ru/Laboratory/LAB_2_1/papers/5.pdf ) again in plasma, was done estimates: 12-14 kWt for 1kg of aluminum at 2400K temperature. Both methods require ether hydrogen or carbon. Carbon is preferable to bring from earth. In second method some amount of a carbon react with aluminum and creates Al4C3, that will require carbon extraction from carbide. Second way requires less energy. Recycle CO2-> C + O2 also will be needed. What do you think ?– can we formulate the real task to investigate instead of just bla-bla - “How to restore aluminum from 2Al2O3 → 4Al +3O2 under vacuum conditions and lunar environment”, or to forget all this for a first stage and to try separation of Al metal from a lunar dust (some amount already present in moon rock's samples).
Experiment in that case can involve extraction, by static, Al particles, and distribute it to collector to form a wire, then evaporation of the formed wire can create on a concave (or flat, or prism formed) surface some reflector mirror. Simple, light and effective experiment (instead of bringing laser reflector or optical device from the earth will be possible to print it on the moon surface).