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Reports of spontaneously generated magnetic fields in laser-created plasmas are briefly reviewed and theoretical explanations mentioned. Observations which indicate that a dynamo effect might be operative are pointed out. Standard plasma equations are proved to imply an Einstein-de Haas effect, i.e. magnetically induced mass rotation, and a Barnett effect, i.e. a dynamo mechanism. The experimental support for these two effects is discussed. A theorem concerning rotation of theta-pinches and denying the effects is shown to be based on a too simplified continuum plasma description. Indications are presented that the dynamo magnetic field may have plasma confining properties.