Period of fighting harsh, reflected by American magazine (7)

I believe the answer is:

wartime

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'period of fighting' is the definition.
(period of time involving fighting)

'harsh reflected by american magazine' is the wordplay.
'harsh reflected by american' becomes 'war' (I can't justify this - if you can you should believe this answer much more).
'magazine' becomes 'time' (US magazine).
'war'+'time'='WARTIME'

Can you help me to learn more?

(Another definition for wartime that I've seen is " Eg, nineteen thirty nine to nineteen fourty five".)

I've seen this clue in The Times.

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