A More Realistic Z-pinch Snowplow Model
We introduce an extended snowplow model for Z-pinch experiments that accounts for partial particle entrainment and current loss during contraction. We applied the methods to a specific case.
physics.plasm-ph↗
arXiv subjects
Miguel Cárdenas
Publications and source records attributed to Miguel Cárdenas.
Dimensional Analysis Approach to Experiments in Z pinch Devices
The physical behavior of discharges in Z pinch devices can be completely deciphered in terms of only three dimensionless parameters. These parameters can be arranged in a way that draw a surface in 3D space. This surface compiles all the accessible information on the macroscopic physical behavior of each possible Z pinch discharge. We analyze the practical problems the drawing of this surface encounters and in view of the situation, we devote the remainder of the article to outline a feasible method for estimating the plasma temperature in Z pinch discharges.
physics.plasm-ph↗
Lagrangian Formulation of the Snowplow Model and Operating Point for Z pinch Devices
We write down the lagrangian for the snowplow model of the Z pinch system. Then, we develop the Euler-Lagrange equations to find out the corresponding equations of motion. Next, we set a criterion for quantitatively estimating the performance of Z pinch devices. Finally, we apply this criterion to a specific Z pinch system.
physics.plasm-ph↗
Snowplow Model Predictions for Plasma Temperature in Z pinch Discharges
Using the general framework of the snowplow model, we introduce the equations for computing plasma temperature in Z pinch discharges. We also present expressions to quantify energy transfers in Z pinch discharges. We then apply this methodology to estimate the temperature and energy transfers of a real prototypical experiment and analyze how the plasma temperature behaves under various modifications of the parameters of the prototypical experiment. Among our discoveries we highlight that the temperature of the plasma in the discharges grows linearly with the initial voltage at the capacitor bank. We summarize this and other findings through a single, fairly compact formula.
physics.plasm-ph↗
Scaling Law for Discharges in Z pinch Devices
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.
physics.plasm-ph↗