Electromagnetic Waves with Torsion and Spin

New time dependent wave solutions to the classical homogeneous Maxwell equations in the vacuum have been found. These waves are not transverse; they exhibit both torsion and spin; they have finite magnetic helicity, a non-zero Poynting vector, E x H and a non zero second Poincare invariant, E dot B.

Two four component rank 3 tensors, constructed on topological grounds in terms of the Fields and Potentials, are used to define the concepts of torsion and Spin, even in domains with plasma currents. The divergence of the spin pseudo vector generates the Poincare invariant equivalent to the Lagrangian of the field, B dot H -D dot E-(A dot J - rho phi). The divergence of the Torsion pseudo vector generates the second Poincare invariant, E dot B. The Poincare invariants have closed integrals which are deformation invariants, and therefore can be used to define deformable coherent structures in a plasma. When the second Poincare invariant is non-zero, there can exist solutions that are not time-reversal invariant.


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Last update 01/23/2009
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