Halliday & Matthiessen (2004: 123):
An Adjunct is an element that has not got the potential of being Subject; that is, it cannot be elevated to the interpersonal status of modal responsibility. This means that arguments cannot be constructed around those elements that serve as Adjuncts; in experiential terms, they cannot be constructed around circumstances, but they can be constructed around participants, either actually, as Subject, or potentially, as Complement … .
Halliday & Matthiessen (2004: 132-3):
The two types of Adjuncts are also similar both in their own composition (as adverbial groups and prepositional phrases) and in how they may be differentiated from circumstantial Adjuncts. Whereas circumstantial Adjuncts fall most naturally at the end of the clause, where they carry the unmarked tonic (intonational) prominence, modal and conjunctive Adjuncts occur finally only as Afterthought and can never carry the only tonic prominence in the clause. … And while they all can occur thematically, only the circumstantial Adjuncts can normally occur as predicated Theme …
Halliday & Matthiessen (2004: 133):
What is common to the modal and conjunctive Adjuncts, as distinct from the circumstantials, is that they are both constructing a context for the clause. Thus even though the same semantic feature may be involved, for example time, it has a different significance in each case. A modal Adjunct of time, such as just, yet, already, relates closely to the primary tense, which is the ‘shared time’ of speaker and listener; a conjunctive Adjunct of time, such as next, meanwhile, locates the clause in time with respect to the preceding textual environment; and both are different from time as circumstance, such as in the afternoon. And the same item may function sometimes circumstantially and sometimes conjunctively; for example, then, at that moment, later on, again.