Appendix Longitudinal electrodynamic forces Applications

Summary

In this report I have investigated how longitudinal electrodynamic forces (forces in the direction of current flow) manifest themselves in many experiments. When it comes to forces in solid and liquid metal conductors, the phenomena seem to be possible to explain by means of longitudinal Maxwell stresses, given e.g. by:

This stress has its maximum at the periphery of the conductor, and is zero at the center. In addition to this a pinch pressure acts, which by hydraulic action causes a pressure at the center, in liquid conductors.

In dense plasmas, such as ionized water, the situation is more complicated. The forces that appear may be several magnitudes greater than those expected from electrodynamical considerations. Further research is needed. (It has been suggested that chemical bonding energy is released in the process.)

The Ampère electrodynamics approach advanced by Graneau has been analysed, and compared with the Maxwell stress approach. They turn out to be equivalent, one focusing on the charge carriers and the other on the field properties.

The stress in a conductor can be compared to that of magnets stacked side by side in a rectangular pipe. The stress predicted is of the same magnitude as that from the pinch forces, but is acting in different directions. Graneau's `Finite current element' analysis (based on the Ampère electrodynamics) overestimates the forces, due to the mixing of uniform and non-uniform stress in that analysis.

The various 2:nd order relativistic theories involved have been discussed -- the overview hopefully clears out some of the tangles. Forces from relativistic electric fields and from surface charges are minute in comparison to the Maxwell stress, but may be of importance for the charge distribution in plasmas.

The Maxwell stress approach is in good agreement with experimental data in e.g. the railgun and multiarc generator experiments. It is still unclear though if the forces are great enough to cause the fragmentation in Nasi owski's experiment, although it seems as this may well be.

Several applications have been covered -- in metal engineering, propulsion technology and electrodynamic fusion etc. Hopefully these applications show what could be achieved if the thinking is directed along new paths.

Appendix Longitudinal electrodynamic forces Applications