Workers Compensation Expense (Details) - USD ($) $ in Millions		1 Months Ended
Jan. 18, 2023	Feb. 29, 2020
Workers Compensation Expense
Self-insured operators must post security percent	120.00%
Additional collateral amount		$ 71.1
Number of days required to submit additional collateral to retain self-insurance status		30 days

Contingent amount to be paid to retain the self - insure status within specified time limit of 30 days from receipt of letter.

No definition available.

Name:	arch_AdditionalCollateralContingentAmountSelfInsured
Namespace Prefix:	arch_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant