Term for words that are modified by prefixing the word with "a" (e.g. anew, aplenty)

It occurred to me that there are quite a large number of words - many of them archaic - that are existing words prefixed with the letter 'a' to create a new word. For example: anew, aplenty, atwitter, apace, etc.

1) Is there a term for this particular modifier , or if not, what's the origin of the term (were these words formerly separate words - e.g. 'a new' - that later became one, thereby fossilising the 'phrase'?

2) Is there any way of working out a list of such words?

Thanks!

As suggested by @dotsamuelswan, you might want to check out this page on the prefix a-. See the first definition. It points out that there are a few different sources for the a- prefix. The linked page quotes the OED as follows:

[I]t naturally happened that all these a- prefixes were at length confusedly lumped together in idea, and the resultant a- looked upon as vaguely intensive, rhetorical, euphonic, or even archaic, and wholly otiose. [OED]