Scaling Law for Discharges in Z pinch Devices

TL;DR

This paper extends the snowplow model for Z pinch discharges by including outward gas pressure forces, deriving a new scaling law that relates gas temperature to experimental setup parameters.

Contribution

It introduces a modified snowplow model accounting for gas pressure forces and derives a scaling law linking gas temperature to device size and energy.

Findings

Derived a new scaling law for Z pinch gas temperature.

Included gas pressure forces in the snowplow model.

Provided formulas for internal energy and temperature calculation.

Abstract

We consider the snowplow model for studying discharges in Z pinch devices. In this context, to obtain a complete picture on the physics of those discharges, we replenish the term disregarded in the original formulation of the snowplow equations. This is, we now consider not only the magnetic force inward on the current sheath but we take into account also a force outward on it. Such a force results from the kinetic pressure of the gas occluded by the current sheath. The internal energy gained by the gas towards the end of the discharge depends on the full history of the dynamical variables of the system. In other terms, the internal energy is a functional of the dynamical variables of the system. We write down the expression for evaluating that internal energy and we present also the formula for computing the temperature of the gas. On this basis, we derive a scaling law that relates the temperature the gas in a Z pinch experiment would attain with the energetic and spatial wingspan of the corresponding experimental setup.