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A solution of magnetic Hall equations for plasma filaments in the Coulombgauge is obtained in the non-holonomic frame. Some physical features of thesolution include, the non-conservation of the magnetic helicity and the decayof the magnetic field in the filaments. From the mathematical point of view,thepresence of Frenet torsion in the filament is actually shown to be fundamentalfor the breaking of conservation of magnetic helicity in the case of helicoidalfilaments. Since the magnetic helicity is not conserved even in the Coulombgauge, and the magnetic field decays, one can say that the dynamo action fails.Actually the presence of torsion enhances the breaking of magnetic fieldhelicity conservation. A similar formula of the one obtained here withoutconsidering the Hall effect has been obtained by Moffatt and Ricca (PRSA-1992)in the case of holonomic filaments. It is shown that unknotted magneticfilaments may place a lower bound on the magnetic energy. Discussions on thewrithe number are also discussed.

Topology of magnetic helicity of torsioned filaments in Hall plasmas