Leases - Other information related to leases (Details) - USD ($) $ in Thousands	3 Months Ended	9 Months Ended
Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Lease information:
Operating lease cost	$ 831	$ 841	$ 2,492	$ 2,533
Operating cash flows from operating leases	876	865	2,562	2,551
Financing lease cost	393	393	1,179	1,179
Operating cash flows from financing leases	$ 303	$ 303	$ 908	$ 909

Amount of Finance lease costs.

No definition available.

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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 http://asc.fasb.org/extlink&oid=123408670&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 http://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

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Balance Type:	na
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- 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 http://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 http://asc.fasb.org/extlink&oid=123408670&loc=SL77918686-209980

+ Details

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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 http://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 http://asc.fasb.org/extlink&oid=123408670&loc=SL77918686-209980

+ Details

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Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration