Simple model of magnetic self-insulation for simulation of non-uniform transmission lines

The vacuum coaxial transmission lines with conducting electrodes and a gap between them of the order of some cm may be used to transport electromagnetic pulses from its generation side to the load. However, the propagation of megavolt-range electromagnetic pulses through vacuum coaxial lines leads to the explosion of microtips and the intense emission of electrons as a result of the high radial electric fields at the surface of the negative electrode. Electrons do not strike a positive electrode in case of sufficiently high magnetic field inside transmission line, thus providing a magnetic insulation effect. Because of the appearance of electrons in the interelectrode gap, the energy transport can be reduced to the simultaneous propagation of electromagnetic fields and electron flows. These processes are accompanied by electron leakage and the current and energy losses. The most simple and effective tool for the description of the magnetic self-insulation wave is the telegraph equations. Some time ago the POS approach was discovered. It gives a possibility to sharpen the wave front of electromagnetic waves (EMW) by current switching during a very short time. The propagation of EMW through the plasma medium is very important for this and other applications. The propagation of the EMW in vacuum and in plasmas is completely analogous from physical point of view. The vacuum self-insulation can be considered as a usual shock wave, because the evolution condition is fulfilled