Interplanetary electric fields for extreme magnetic storms

Using a list of sudden-commencement storms, the ring-current index, and 1-h near-Earth solar-wind measurements from solar cycles 20–25, we develop extreme-value statistical models relating storm intensity 𝐷 =max⁡{−𝐷⁢𝑠⁢𝑡} to the storm main-phase maximum duskward interplanetary electric field 𝐸. The conditional relationship 𝐷|𝐸 is demonstrably sublinear—linear models are confidently rejected—indicating saturation of magnetospheric response under extreme solar-wind forcing. An event like that of July 2012 (𝐸 =69.6 mV/m), if Earth-directed, would be associated with a median storm intensity of 𝐷 =49⁢5⁶⁴⁸₃₇₈ nT. Storms comparable to March 1989 (𝐷 =594 nT) correspond to electric fields of 𝐸 =5⁢4⁷⁶₃₉ mV/m, while Carrington-class storms (𝐷 =964 nT) correspond to 𝐸 =9⁢5¹³³₆₈ mV/m—substantially lower than several previous estimates. These results indicate that solar-wind conditions capable of driving extremely intense magnetic storms are less exceptional, and potentially more frequent, than previously thought.