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Fees and Related Party Transactions (Details) - USD ($)
3 Months Ended 9 Months Ended
Sep. 30, 2021
Sep. 30, 2020
Sep. 30, 2021
Sep. 30, 2020
Advisory Fees [Abstract]        
Advisory fees at annual rate of the Members' Capital     1.50%  
Advisory fees $ 109,009 $ 110,261 $ 333,627 $ 314,493
Sponsor Fees [Abstract]        
Sponsor fees 56,389 58,023 $ 174,182 165,889
Incentive Allocation [Abstract]        
Percentage of incentive allocation     20.00%  
Incentive allocation 0 238,422 $ 425,718 315,624
Administrator's Fee [Abstract]        
Administrator's fees $ 9,279 $ 9,466 $ 28,313 $ 27,083
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%