The magnetostatic field of a periodic cylindrical array of perfect conductors of arbitrary x‐y cross section

The magnetic field in an imploding wire array is studied. After the initial explosion of the wires the array starts imploding. The process can be considered quasistatic electromagnetically and the assumption of perfect conduction is made. Under these conditions the driving magnetostatic forces generated by the wires need to be calculated in a series of snapshots, which are stages of the magnetohydrodynamics process. For that purpose a Green’s function technique is developed to solve for the magnetostatic field generated by an array of perfectly conducting wires of arbitrary x‐y cross section, carrying current in the z direction. The wires are enclosed in an outer cylinder, inside of which they are arranged with angular periodicity. This outer cylinder carries all the returning current, and ideally does not permit any magnetic lines to escape from its enclosure. The resulting equations for the magnetic vector potential (A=A?,∇2A=0 in vacuum, A=0 on the outer cylinder, A=const≠0 on the inner conductors) are...