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Comprehensive analytical model of the dynamic Z pinch.

Alejandro Mesa Dame1,2, Eric S Lavine1, David A Hammer1

  • 1Cornell University, Laboratory of Plasma Studies, Ithaca, New York 14850, USA.

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A new analytical model accurately simulates dynamic Z-pinch implosions, predicting key plasma parameters and shock front behavior. This tool aids in designing and analyzing pulsed-power experiments for fusion energy research.

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Area of Science:

  • Plasma Physics
  • Magnetohydrodynamics (MHD)
  • Pulsed Power Science

Background:

  • Dynamic Z-pinches are crucial for inertial confinement fusion research.
  • Accurate modeling of Z-pinch implosions is essential for experimental design and analysis.
  • Existing models may lack the predictive capability for complex scenarios.

Purpose of the Study:

  • To develop an analytical 1D axisymmetric model for dynamic Z-pinch evolution.
  • To predict the behavior of the magnetic piston, shock front, and plasma parameters.
  • To validate the model against experimental data.

Main Methods:

  • Formulated a 1D axisymmetric analytical model based on ideal MHD equations.
  • Described the implosion process in stages using coupled ordinary differential equations.
  • Incorporated time-dependent current, variable initial density, and weak axial fields.

Main Results:

  • The model successfully predicts trajectories of the magnetic piston and shock front.
  • It provides profiles for velocity, pressure, density, and magnetic field.
  • Comparisons with COBRA facility experimental data show promising agreement.

Conclusions:

  • The developed analytical model offers a valuable tool for Z-pinch research.
  • It can aid in the design and analysis of future pulsed-power experiments.
  • The model's predictive accuracy supports its utility in fusion energy studies.