Halliday & Matthiessen (2014: 188):
Adjuncts of intensity fall into two classes, of which again one relates to expectation.
(i) Those of degree may be total, high degree or low degree … These Adjuncts (especially the ‘total’ ones) are typically associated with interpersonally loaded Processes or Attributes; the same adverbs also function regularly as Sub-modifiers within a nominal group.
(ii) Those of counterexpectancy are either ‘limiting’ or ‘exceeding’ what is to be expected: the meaning is either ‘nothing else than, went no further than’ or ‘including also, went as far as’.
Adjuncts of intensity occur medially or finally in the clause, but seldom initially — they cannot be thematic (hence there is no occasion for those containing the feature ‘negative’ to cause inversion of Subject and Finite).*
∞
* Note that the apparent exception scarcely — as in scarcely had they left, when the next lot arrived — serves as a mood Adjunct of temporality ('no sooner'), not intensity.