adverbial particle
Definition - A particle that functions as an adverb (i.e. it modifies a verb or another adverb).

Example -

(1) He gave up.
(2) I turned the radio on.

Etymology -
The word particle derives from the Latin particula, little bit or part.

Example Usages -

1. "Among individual words commonly so classed are the negative particle not (and its contraction n't), the infinitival particle to (to go; to run), the imperative particles do, don't (Do tell me; Don't tell me) and let, let's (Let me see now; Let's go). There is also a set of adverbial and prepositional particles that combine with verbs to form phrasal verbs (out in look out; up in turn up) and prepositional verbs (at in get at; for in care for)."
(Source: (Sidney Greenbaum, "Particle," Oxford Companion to the English Language. Oxford Univ. Press, 1992) )

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