Learn Swedish: Glasyren smälter allteftersom bränningen pågår. - The glaze melts gradually as the firing goes on.

While medan simply means two actions are happening at the same time, allteftersom emphasizes a gradual, proportional change. It tells us that the melting is a continuous process directly tied to the progression of the firing.

Does allteftersom trigger any special word order in the clause that follows it?

No, it acts as a regular subordinating conjunction. It starts a subordinate clause, meaning the subject (bränningen) comes right after it, followed by the verb (pågår). If there were a sentence adverb like inte, it would be placed before the verb according to the standard Swedish BIFF rule.

bränningen literally translates to 'the burning'. Is this the standard word for 'firing' ceramics?

Exactly. It comes from the verb att bränna (to burn). In Swedish, the process of baking clay or melting glaze in a kiln is always referred to as bränning, rather than using a word directly related to fire or baking.

How does the prefix på change the meaning of går (goes) in pågår?

The verb att pågå specifically means to go on, to be in progress, or to last. It turns the physical movement of att gå (to walk or go) into an abstract concept of a process continuing over time, which is perfect for describing an ongoing event like a firing.