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Fees and Related Party Transactions (Details) - USD ($)
3 Months Ended 6 Months Ended
Jun. 30, 2022
Jun. 30, 2021
Jun. 30, 2022
Jun. 30, 2021
Advisory Fees [Abstract]        
Advisory fees at annual rate of the Members' Capital     1.50%  
Advisory fees $ 127,699 $ 114,709 $ 242,832 $ 224,618
Sponsor Fees [Abstract]        
Sponsor fees 65,975 59,976 $ 125,158 117,793
Incentive Allocation [Abstract]        
Percentage of incentive allocation     20.00%  
Incentive allocation 673,322 79,082 $ 1,351,960 425,718
Administrator's Fee [Abstract]        
Administrator's fee 10,593 9,724 20,361 19,034
Professional Fees [Abstract]        
Professional fees 55,744 51,976 91,780 69,750
Operating Expenses [Abstract]        
Operating expenses $ 1,725 $ 0 $ 1,725 $ 0
Class 0 Units [Member]        
Sponsor Fees [Abstract]        
Sponsor fees at annual rate of the Members' Capital     0.50%  
Class 2 Units [Member]        
Sponsor Fees [Abstract]        
Sponsor fees at annual rate of the Members' Capital     1.25%