Stockholders' Equity - Accumulated Other Comprehensive Income (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2018
Increase (Decrease) in Accumulated Other Comprehensive Income [Roll Forward]
Beginning Balance	$ 1,138,954	$ 717,832	$ 607,644
Ending Balance	1,213,614	1,138,954	717,832
Accumulated Other Comprehensive Income (Loss)
Increase (Decrease) in Accumulated Other Comprehensive Income [Roll Forward]
Beginning Balance	3,511	13,587	15,213
Other comprehensive (loss) income before reclassifications	18,379	(9,971)	(1,637)
Amounts reclassified from accumulated other comprehensive income	29	(105)	11
Ending Balance	21,919	3,511	13,587
Currency Translation Adjustments
Increase (Decrease) in Accumulated Other Comprehensive Income [Roll Forward]
Beginning Balance	4,184	13,517	15,168
Other comprehensive (loss) income before reclassifications	18,877	(9,333)	(1,651)
Ending Balance	23,061	4,184	13,517
Unrealized Gains (Losses) on Available-for-Sale Securities
Increase (Decrease) in Accumulated Other Comprehensive Income [Roll Forward]
Beginning Balance	(8)	(112)	(1)
Other comprehensive (loss) income before reclassifications	5	244	(110)
Amounts reclassified from accumulated other comprehensive income	2	(140)	(1)
Ending Balance	(1)	(8)	(112)
Pension Liability Adjustments
Increase (Decrease) in Accumulated Other Comprehensive Income [Roll Forward]
Beginning Balance	(665)	182	46
Other comprehensive (loss) income before reclassifications	(503)	(882)	124
Amounts reclassified from accumulated other comprehensive income	27	35	12
Ending Balance	$ (1,141)	$ (665)	$ 182