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Fees and Related Party Transactions (Details) - USD ($)
3 Months Ended 9 Months Ended
Sep. 30, 2022
Sep. 30, 2021
Sep. 30, 2022
Sep. 30, 2021
Advisory Fees [Abstract]        
Advisory fees at annual rate of the Members' Capital     1.50%  
Advisory fees $ 126,730 $ 109,009 $ 369,562 $ 333,627
Sponsor Fees [Abstract]        
Sponsor fees 66,399 56,389 $ 191,557 174,182
Incentive Allocation [Abstract]        
Percentage of incentive allocation     20.00%  
Incentive allocation 449,740 0 $ 1,801,700 425,718
Administrator's Fee [Abstract]        
Administrator's fee 10,613 9,279 30,974 28,313
Professional Fees [Abstract]        
Professional fees 54,594 67,204 146,374 136,954
Operating Expenses [Abstract]        
Operating expenses $ 5,944 $ 0 $ 7,669 $ 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%