Snapped exhaust bolts on beta engine

It's going to be the standard procedure then. carefully centre punch the face of the remaining stud, soak for a day or two with whatever penetrating fluid you believe in, carefully drill a small pilot hole and then enlarge it with a larger drill to take a stud extractor and keeping it vertical hope it doesn't snap and starts to turn and remove the stud.
If that doesn't work then it's a matter of using successively larger drills a matter of drilling out the stud, if you are good / lucky and have got the centre well defined you may be able to pick the swarf / remains of the stud from the threads and all will be well. If not then you go and buy a Helicoil kit.
With respect, I think you intended to say “screw extractor” not “stud extractor”, which clamps on stud’s outer diameter. In any case I wouldn’t bother attempting to use a “screw extractor” but move on to your suggestion to drill out the bulk of the stud. I once broke a screw extractor and gave myself a major task removing its remnants from the screw that I was attempting to extract. Had to resort to electro-discharge process.
Mike
 
completely drilling out the stud and re-tapping to take a larger bolt i also an option.
personally ive never had much luck with stud extractors unless the stud has been drilled to almost its full diameter.
snapping an extractor in the stud leads to more problematic issues
 
… never had much luck with stud extractors unless the stud has been drilled to almost its full diameter …

That is exactly how a screw extractor is supposed to be used. Drill out sheared bolt near to diameter, insert screw extractor and as it bites it reverses out remains of bolt and preserves thread.

This article has drill sizes for screw extractors https://uk.rs-online.com/web/content/discovery/ideas-and-advice/screw-extractors-guide

Unlike others, I have had good experience with screw extractors. Don’t just drill out and screw in extractors, without applying heat, soaking in Plusgas, or even 3 in 1 oil.

If the screw extractor does not work, don’t wham up the torque, stop, then drill out at a size compliant with use of a thread insert repair kit and repair back to original.
 
The best stud extractors I’ve ever used were Snap-On ones. They had left handed drill bits (yes really!!!) which helped loosen the broken bolt as you were drilling the pilot hole. Not cheap, but for once I thought that the Snap-On brand was worth the money. I think other brands now have LH drill bits as well. I’d recommend them for this purpose.
 
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