I recently bought a cheap induction heater module from Aliexpress (search for "induction heater module" and you'll see the sort of thing - a simple low-voltage Royer oscillator), and thoughts started going through my head of a vacuum furnace. The typical construction involves a large quartz tube with the crucible (graphite) on the inside under vacuum and the induction coil wrapped around the outside. Unfortunately, large-diameter quartz tubing is rather expensive, assuming it's even available (which it's not, because we're in the stone age as regards suppliers of quartz tubing).
By accident, I came across things called "UV quartz sleeves" (or similar) - these are used in water purification/treatment systems for ponds/swimming pools etc. In these units, a UV bulb is used to zap any bugs/bacteria in the water, and the bulb is protected by a quartz sleeve. Turns out that these are readily available as replacement parts, and are relatively inexpensive. The only problem is they're only marketed as replacements for a particular model of UV treatment system and generally don't say anything about the actual dimensions. Fortunately I did find one supplier who mentioned sizes - http://www.aquatix-2u.co.uk/pif600b-pisces-quartz-sleeves.html - so I bought the largest one they had. Here it is in all its glory:
It's a pretty impressive bit of quartz for the price (£12). Dimensions are 44mm OD, 40mm ID, 300mm long, with one end closed and a flange at the other end. They're also available with both ends open - again, it's a bit of luck what you can actually get.
As luck would have it, it is a perfect fit inside the coil that came with the Chinese induction heater module! That, combined with some little 25mm or 30mm graphite crucibles (widely available on EBay for ridiculous prices) would make a rather neat induction furnace. Yet something else to add to the ever-expanding list of projects...
Regarding suitability for vacuum use, I'm pretty confident. MTI corporation supply quartz tubes for their furnaces and they also have around 2mm wall thickness (for example, they have a 40mm x 36mm tube). The closed end on mine isn't a perfect dome, it's a bit flattened, but should still be fine.
Here's a quick video overview to show it from various angles: