EFFECTS OF PLASMA JET PARAMETERS, IONIZATION, THERMAL CONDUCTION, AND RADIATION ON STAGNATION CONDITIONS OF AN IMPLODING PLASMA LINER by MILOŠ STANIĆ A DISSERTATION Submitted in partial fulfillment of the requirements For the degree of Doctor of Philosophy in The Department of Mechanical and Aerospace Engineering to The School of Graduate Studies of The University of Alabama in Huntsville HUNTSVILLE, ALABAMA 2013 In presenting this thesis in partial fulfillment of the requirements for a doctor of philosophy degree from The University of Alabama in Huntsville, I agree that the Library of this University shall make it freely available for inspection. I further agree that permission for extensive copying for scholarly purposes may be granted by my advisor or, in his/her absence, by the Chair of the Department or the Dean of the School of Graduate Studies. It is also understood that due recognition shall be given to me and to The University of Alabama in Huntsville in any scholarly use which may be made of ~ this thesis. 03/03/.2013 MILOS STANIC (date) II THESIS APPROVAL FORM Submitted by Milos Stanic in partial fulfillment of the requirements for the degree of Master of Science in Engineering and accepted on behalf of the Faculty of the School of Graduate Studies by the thesis committee. We, the undersigned members of the Graduate Faculty of The University of Alabama in Huntsville, certify that we have advised and/or supervised the candidate on the work described in this thesis. We further certify that we have reviewed the thesis manuscript and approve it in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mechanical Engineering. ylr/l3 Committee Chair (Date) 22 Dee 2012 Committee Member (Dr. Snezhana I. Abarzhi) (Date) I'/.--' 3/8 13 Committee Member (Date) Committee Member Committee Member (Date) Department Chair College Dean ~ ~AJ dku:t tI/Lsil3 Graduate Dean (Df:RllOl1d; Ka ~<-~e""")-=""'''-''''-'''''---------''-I-L--(D-#-a=-t-e) III ABSTRACT School of Graduate Studies The University of Alabama in Huntsville Degree Doctor of Philosophy College/Dept. Mechanical and Aerospace Engineering Name of Candidate Miloš Stanić Title Effects of Plasma Jet Parameters, Ionization, Thermal Conduction, and Radiation Stagnation Conditions of an Imploding Plasma Liner The disciplines of High Energy Density Physics (HEDP) and Inertial Confinement Fusion (ICF) are characterized by hypervelocity implosions and strong shocks. The Plasma Liner Experiment (PLX) is focused on reaching HEDP and/or ICF relevant regimes in excess of 1 Mbar peak pressure by the merging and implosion of discrete plasma jets, as a potentially efficient path towards these extreme conditions in a laboratory. In this work we have presented the first 3D simulations of plasma liner, formation, and implosion by the merging of discrete plasma jets in which ionization, thermal conduction, and radiation are all included in the physics model. The study was conducted by utilizing a smoothed particle hydrodynamics code (SPHC) and was a part of the plasma liner experiment (PLX). The salient physics processes of liner formation and implosion are studied, namely vacuum propagation of plasma jets, merging of the jets (liner forming), implosion (liner collapsing), stagnation (peak pressure), and expansion (rarefaction wave disassembling the target). Radiative transport was found to significantly reduce the temperature of the liner during implosion, thus reducing the thermal iv leaving more pronounced gradients in the plasma liner during the implosion compared with ideal hydrodynamic simulations. These pronounced gradients lead to a greater sensitivity of initial jet geometry and symmetry on peak pressures obtained. Accounting for ionization and transport, many cases gave higher peak pressures than the ideal hydrodynamic simulations. Scaling laws were developed accordingly, creating a non- dimensional parameter space in which performance of an imploding plasma jet liner can be estimated. It is shown that HEDP regimes could be reached with ~ 5 MJ of liner energy, which would translate to roughly 10 to 20 MJ of stored (capacitor) energy. This is a potentially significant improvement over the currently available means via ICF of achieving HEDP and nuclear fusion relevant parameters. Abstract Approval: Committee Chair ( 'S-;z.~-r3 Department Chair (Dr. Keith Hol ings rth) (Date) Graduate Dean ~ ~~ 'i/ts/13 (Dr. Rhonda Kay Ga lie) (Date) v ACKNOWLEDGMENTS I would like to acknowledge all of my family, my beloved spouse and my friends for providing me with constant support during my Ph.D. studies, as well as several individuals and institutions: Dr. J.T. Cassibry – for the enormous amount of knowledge, tips and opportunities he has provided me with. Dr. R.F. Stellingwerf – for “on call” support regarding the SPHC code. Dr. S.I. Abarzhi – for her help and cooperation with RMI, as well as many useful discussions. R. Hatcher and M. Milosevic – for their help regarding programming. The whole PLX team – for being great collaborators. Dr. J.M. Horack and D. Cook – for providing me with lots of professional opportunities and experience. U.S. Department of Energy – for their funding of the PLX project, which made my Ph.D. a reality. vi TABLE OF CONTENTS LIST OF TABLES ............................................................................................................ xi LIST OF FIGURES ......................................................................................................... xii 1. INTRODUCTION ....................................................................................................... 1 1.1 High Energy Density Physics ............................................................................ 1 1.2 Relevance of HEDP ........................................................................................... 3 1.2.1 High Energy Density Astrophysics ........................................................ 5 1.2.2 Laser-Plasma, Beam-Plasma Interactions .............................................. 6 1.2.3 Free Electron Laser Interactions ............................................................ 6 1.2.4 High-Current Discharges ....................................................................... 6 1.2.5 Hydrodynamics and Shock Interactions................................................. 7 1.2.6 Equation of State and Stripped Atom Physics ....................................... 7 1.2.7 Nuclear Fusion ....................................................................................... 7 1.3 Nuclear Fusion: Main concepts .......................................................................... 8 1.3.1 Fundamental Concepts ........................................................................... 8 1.3.2 Nuclear fusion approaches ................................................................... 12 1.4 Primary motivation, objectives and technical approach .................................. 20 2. THEORETICAL CONSIDERATIONS .................................................................... 23 2.1 Smoothed Particle Hydrodynamics .................................................................. 23 2.1.1 Smoothed particle hydrodynamics theory ............................................ 24 2.1.2 Equations of motion ............................................................................. 26 2.1.3 Numerical aspects of the SPH approach .............................................. 29 2.2 Equation of state ............................................................................................... 31 vii 2.2.1 Perfect gas law, gas composition and partial thermodynamic properties .............................................................................................. 32 2.2.2 Classification of gases .......................................................................... 34 2.2.3 The Equilibrium constant and mass action laws .................................. 35 2.2.4 Partition functions and fundamental thermodynamic properties ......... 38 2.3 Energy transport models .................................................................................. 42 2.3.1 Electron-thermal conduction ................................................................ 42 2.3.2 Radiation basics and black body radiation ........................................... 45 2.3.3 Radiation diffusion and conduction approximations and LTE ............ 50 2.3.4 Radiation losses (optically thin radiation model)................................. 53 2.4 Technical implementation of the equation of state (eos) ................................. 56 3. VERIFICATION AND VALIDATION OF THE CODE ......................................... 63 3.1 The Noh problem ............................................................................................. 65 3.2 Interferometry .................................................................................................. 70 3.2.1 Interferometry principles ...................................................................... 70 3.2.2 Overview of the PLX interferometer and the synthetic interferometry tool ............................................................................... 72 3.2.3 Jet Model .............................................................................................. 73 3.2.4 Comparison of Results ......................................................................... 74 3.3 Richtmyer-Meshkov Instability (RMI) ............................................................ 79