The Cumulative Energy Budget of a Repeating Fast Radio Burst

This paper keeps the cumulative energy ledger of a repeating fast radio burst, summing a representative three-hundred-burst sample for an FRB 121102-class source at a stated radio efficiency, charging the total against a magnetar magnetic reservoir, and deriving the active lifetime and field requirements the budget implies. The headline results are as follows. Total isotropic radio energy of 300 bursts at the stated mean: 9e+41 erg; Source energy required at a radio efficiency of one percent: 9e+43 erg; Fraction of the magnetar magnetic reservoir consumed by the full sample at one percent efficiency: 0.000135; Mean burst rate energy output during an active year at 300 bursts: 2.85e+34 erg s-1; Years of activity the reservoir supports at the observed mean rate and one percent efficiency: 3.7e+04 yr; Isotropic energy of a burst with the sample mean fluence scaled to the FRB 180916 distance ratio: 9.18e+37 erg. All values are computed from the stated assumptions and published inputs; the study is simulated and computed, not measured.