It's hard to get through a post or paper on lunar exploration these days without hearing about microwave sintering. Let's take a look at what it is and why so many people are excited about it.
In short, the unique properties of lunar soil make microwave heating very efficient. Strong concrete-like ceramic blocks can be made without water or other materials, just regolith. No material needs means very low mass shipped to the surface for building structures. This takes either a lot of power or a lot of patience.
Details after the break.
Let's start with the basics. If you already understand how and why microwaves work, skip ahead.
Microwaves are electromagnetic radiation in the 1.6 to 30 GHz range, a bit above FM and TV broadcast frequencies and a bit below infrared. Many of us are familiar with the microwave oven, a device that heats water very efficiently. Similar equipment is used in radar and wireless power transmission.
Microwaves heat dielectric materials (such as water). Molecules will try to line up with the electromagnetic field; since the field is rapidly changing direction the molecules end up spinning and colliding. This converts the microwave energy into rotational energy and then into heat. The microwave field can penetrate through most materials to a few cm or more. Water is generally the best at absorbing this energy. As long as the material in a microwave oven still has water, the available energy will be applied to making steam; microwaved food rarely gets hotter than the boiling point of water unless it runs dry or has a lot of fats or oils.
Metals can either absorb or reflect microwaves depending on geometry. The oven compartment of a microwave oven is a resonant cavity made of metal (usually steel) that is designed to reflect microwave energy around the inside repeatedly until it can be absorbed by food. If there is nothing inside the oven cavity to do this then all that energy gets dumped back into the magnetron (the source of microwave energy), usually destroying it.
Other metal objects can absorb microwaves efficiently, leading to very high temperatures and sometimes to electrical arcs or sparks. I suggest a review of Youtube videos on the subject ("Is it a good idea to microwave this?" for example); there's a lot of interesting effects to see and watching a video won't destroy your microwave oven. Or your face.
Microwaves can be produced by several methods, but the common choice is a cavity magnetron. These devices are only 55-70% efficient in common use, though the application of brainpower could improve on that somewhat for dedicated space hardware. Other devices (klystron, traveling wave tube, cyclotron) are less efficient but have other desirable properties for things like particle accelerators and microwave transmitters.
A magnetron is a vacuum tube with complex metal shapes that form several cavities, often resembling the cylinder on a revolver. Electrons from a high voltage power supply stream through an open space next to these cavities, causing a 'ringing' effect that results in microwaves of a specific frequency being produced. The wikipedia article has a lot of additional information if you're interested.
Sintering means to heat a material enough for it to stick together, but not quite enough for it to melt. This process is used in powder metallurgy, ceramics, cement and some composites (carbon-carbon for example). Firing a clay pot is a form of sintering, as are ice cubes in a glass of water that get stuck together. This is a complex topic that dives deep down the rabbit hole where physics and chemistry meet, but it is reasonable to think of it as a way to form solid objects out of powder with heat and pressure.
Now for the application.
Everyday microwave ovens work best on water. One might then wonder why a microwave device would be useful on the moon, where the exposed soil is extremely dry. The reason is that lunar soil is nothing like earth soil; it was not produced by erosion via wind and water. Instead, lunar soil (or regolith) is made up of tiny jagged fragments of glass and metals formed from meteor impacts. The fragments are then bombarded by solar wind, increasing surface area and forming nanoparticles of free iron.
These iron nanoparticles are extremely effective at trapping microwave energy. It takes only a tiny fraction of free iron content in this form to make the soil act like metal foil. The metal absorbs most of the energy, focusing most of the heat into tiny areas. This concentrated heat starts melting the surrounding material, which often then becomes microwave-absorbing and increases heat gain. This is called thermal runaway, normally a very bad thing but in this case it works to our advantage. We can get incredibly high temperatures (thousands of degrees C) without needing any extreme materials. To some extent that means high-power microwaving of regolith can go beyond sintering into making slag or molten rock if necessary.
Most resource harvesting concepts plan to use magnetic rakes or separators to collect free nickel-iron nodules. These are pieces of meteors or drops of metallic ejecta large enough to see with the naked eye. The nanoparticles of iron I mentioned above can't be extracted this way; they are generally trapped in the crystal structure of the surrounding material. That means raked regolith can still be used to form blocks, so sintering is compatible with most other resource extraction schemes.
There are two general approaches depending on the desired outcome.
Paving a road or a landing site doesn't require specific blocks or shapes, so after the area is leveled a rover can scan a microwave emitter across the space to be sintered. A smooth single sheet of ceramic material is the result. This is a very straightforward process and can be done in one pass if desired, very similar to bulk asphalt paving methods on Earth.
Assembling buildings and other structures generally means making blocks of some kind. That means collecting regolith, processing it (removing bulk metal and lumps), pressing it into a shape or form and then microwaving to bind the block together. Similar techniques are used in powder metallurgy to form tungsten parts, among other things. Perhaps a better model would be slipcast ceramics: clay powder or slurry is blown or poured into a mold, dried and/or pressed, then fired in a kiln.
On Earth, heating dirt to high temperatures and keeping it that way for long enough to fuse would be difficult. There is trapped water to evaporate and carry away heat, plenty of air to do the same through convection and the dirt itself conducts heat fairly well. (Sand, however, appears to work quite nicely.) In a vacuum, only conduction and radiation are effective. For a loose powdery regolith surface, radiation is the primary means of heat loss; that means once the material is heated it stays hot for much longer than it would in an atmosphere. This is one reason for pressing the powder: it helps conduct heat throughout the block for more even sintering.
What does it all mean?
Magnetrons are robust and very well understood devices. We can build them for high power output (1 to 100 kW), relatively high efficiency (60-80%) and long life (decades). They require high voltage electricity, powerful magnets and robust cooling but otherwise work in microgravity or in any orientation, resist vibration, have no moving parts and can be made easy to replace as a modular unit. They even generally survive abuse by college students so long as they don't intentionally burn them out.
Turning regolith into solid building materials without needing a binder (water, cement, sulfur, etc.) means the output of the system depends only on available power, not on how much binder mass can be shipped. Importantly, the same microwave power unit can be used for a range of processes and target temperatures. Low-level heating to drive off volatiles, moderate heat for sintering or high heat for outright melting (gas-tight surface layer) are all possible.
In sum, a magnetron would be a very useful and versatile tool for material processing. That's the big deal.