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Analysis of equatorial and polar region magnetograms reveals that there is an impulsive injection of energy into the geomagnetic ring current and that the impulsive injection exhibits a temporal behavior similar to DP substorm activity but usually lags it by one or more hours. Based upon observations of Dst at low latitude, a method is developed for the determination of the rate of energy injection into the ring current as a function of time. In obtaining this rate, a knowledge of the rate of decay of the ring current is necessary; a determination of that decay rate is made here. It is found that the magnitude of the main phase of a magnetic storm correlates with the integrated DP activity during the 10 hours preceding the maximum excursion of Dst, independent of whether the magnetic storm commences gradually or is preceded by a storm sudden commencement. The results presented here lead to the conclusion that the energetic particles responsible for the DP activity and the growth of the ring current simultaneously emerge in a burst‐like manner from a source or holding region outside the Van Allen belts; during such injections, some of the particles travel along the magnetic field to the auroral zones to give rise to DP and related activity there, while others diffuse radially inward to the Van Allen belts and arrive there, often with a delay of one or more hours.

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We present calculations for the effective action of string world sheet in R 3 and R 4 utilizing its correspondence with the constrained Grassmannian σ-model. Minimal surfaces describe the dynamics of open strings while harmonic surfaces describe that of closed strings. The one-loop effective action for these are calculated with instanton and anti-instanton background, representing N-string interactions at the tree level. The effective action is found to be the partition function of a classical modified Coulomb gas in the confining phase, with a dynamically generated mass gap.