Numerical study of the first compression of a cylindrical pinch

In a Plasma Focus discharge after the current sheath reaches the top of the electrodes, its motion becomes radially inward. A shock wave, that travels ahead the magnetic piston, reflects off the axis, starting the first compression phase. The magnetic piston converges, until it is reached by the reflected shock. This is the time of the first maximum compression. The following expansion of the magnetic piston continues until the development of a m = 0 instability produces several compressions (the second compression). Sometimes, the first and the second compression are not clearly resolved in time, due to the relative duration of the first expansion and the growing time of the instability. For studying the first compression phase, we developed a 3-fluid, time-dependent, 1- D code. The code includes three species (atoms, ions and electrons), two temperatures (electrons and heavy particles), radiation (free-free and free-bound, for pure hydrogen or deuterium plasma), ionization (inelastic collisions), thermal conductivity, and electrical conductivity, coupled to an external circuit (a constant magnetic flux is used for the converging phase). At the beginning a cylinder (radius R
_o
, height h) of a neutral gas (filling pressure p
_o
) starts to compress under the action of an external current (I
_o
). A constant external inductance (L
_o
) is assumed. The results of the calculations show that in the range of parameters characteristic of the Plasma Focus devices (I
_o
= 0.1 + 5 MA, p
_o
= 1 + 15 mbar, R
_o
= 1 ÷ 10 cm) ionization and radiation (for pure deuterium), and magnetic difusion plays a secondary rol in this phase.