The most common and most likely answer to this crossword clue is the 9 letter word CYCLOTRON
I've seen this crossword clue in The Times
C
Y
C
L
O
T
R
O
N
More clues leading to the result CYCLOTRON
Buddy explains!

The straight part
We know that "Accelerator" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case accelerator = cyclotron.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does CYCLOTRON mean?
CYCLOTRON noun- An early particle accelerator in which charged particles were generated at a central source and accelerated spirally outward through a fixed magnetic field and alternating electric fields.