Leases - Other information related to leases (Details) - USD ($) $ in Thousands	3 Months Ended
Mar. 31, 2023	Mar. 31, 2022
Lease information:
Operating lease cost	$ 831	$ 831
Operating cash flows from operating leases	876	866
Financing lease cost	393	393
Operating cash flows from financing leases	$ 303	$ 303

Amount of Finance lease costs.

No definition available.

Name:	arch_FinanceLeaseCost
Namespace Prefix:	arch_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount of interest paid on finance lease liability.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 50
-Paragraph 4
-Subparagraph (g)(1)
-URI https://asc.fasb.org/extlink&oid=128292326&loc=SL77918686-209980

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 45
-Paragraph 5
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=123391704&loc=SL77918643-209977

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- References

No definition available.

+ Details

Name:	us-gaap_LeaseCostAbstract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of single lease cost, calculated by allocation of remaining cost of lease over remaining lease term. Includes, but is not limited to, single lease cost, after impairment of right-of-use asset, calculated by amortization of remaining right-of-use asset and accretion of lease liability.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 55
-Paragraph 53
-URI https://asc.fasb.org/extlink&oid=123414884&loc=SL77918982-209971

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 50
-Paragraph 4
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=128292326&loc=SL77918686-209980

+ Details

Name:	us-gaap_OperatingLeaseCost
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount of cash outflow from operating lease, excluding payments to bring another asset to condition and location necessary for its intended use.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 45
-Paragraph 5
-Subparagraph (c)
-URI https://asc.fasb.org/extlink&oid=123391704&loc=SL77918643-209977

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 50
-Paragraph 4
-Subparagraph (g)(1)
-URI https://asc.fasb.org/extlink&oid=128292326&loc=SL77918686-209980

+ Details

Name:	us-gaap_OperatingLeasePayments
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration