# Z pinch at equilibrium

1. May 27, 2008

### bman!!

"An imploding Z-pinch is comprised of a thin-walled hollow cylinder of plasma with very low
resistivity. A constant axial current of 1MA is applied to the plasma and it starts to implode. An
additional axial field of 1 Tesla is also generated which exists only on the inside of the cylinder.
The cylinder stops imploding when which three pressures are all equal ? Why is there no
magnetic tension force involved ? If the initial radius of the cylinder is 1cm, what is its final
radius and what is the final value of Bz ?"

normally equilibrium is when the magnetic pressure due to the toroidal field pressure is equal to the thermal pressure gradient (i.e. the magnetic feild causes the zpinch to contract until the compressional heating results in thermal pressure pushing outwards to counteract this effect)

however i seem to get the impression from the answers that the total equilibrium is due to the thermal pressure AND the internal (Bz) magnetic field pressure counteracting the inwards force.

or can i just calculate when the fields are equal using flux surface conservation? is so why (i think this is what my instructor shows me in the answers.....)

cheers