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We outline transient quasi-magnetostatic phenomena associated withWeibel-type instabilities, mainly, the formation and decay of the currentsheets and filaments. We consider a collisionless anisotropic plasma cloud withhot electrons expanding into an inhomogeneous background plasma taking intoaccount an external magnetic field in different geometries entailing (i) ahot-electron spot of a circular or cylindrical form within an initial-valueproblem or a finite-time injection of electrons from a target surface, (ii)inhomogeneous layers of cold background plasma of different densities andspatial scales, (iii) an external magnetic field with three orientations:perpendicular to the target or along it, directed either across or parallel toa long axis of the hot-electron spot. We heed typical laser-plasma experiments.We outline development of the principle current structures linked with distinctforms of the anisotropic electron velocity distribution using particle-in-cellmodeling of the instability process for diverse sets of the attributes(i)--(iii). Applications to the analysis of laboratory and space plasmaproblems involving an explosive development of the small-scale filamentation ofthe electric current and self-consistent magnetic turbulence are discussed.

Electron Weibel instability and~quasi-magnetostatic structures in~an~expanding collisionless plasma