A model for plasma-neutral fluid interaction and its application to a study of CT formation in a magnetised Marshall gun

A model for plasma/neutral fluid interaction was developed and included in the DELiTE code framework implementation of non-linear MHD equations. The source rates of ion, electron and neutral fluid momentum and energy due to ionization and recombination are derived using a simple method that enables determination of the volumetric rate of thermal energy transfer from electrons to photons and neutral particles in the radiative recombination reaction. This quantity can not be evaluated with the standard formal procedure of taking moments of the relevant collision operator, and has been neglected in other studies. The plasma/neutral fluid interaction model was applied to study CT formation in the SMRT and SPECTOR magnetized Marshall guns, enabling clarification of the mechanisms behind the significant increases in CT electron density that are routinely observed well after formation on the SPECTOR experiment. Neutral gas, which remains concentrated below the gas valves after CT formation, diffuses up the gun barrel to the CT containment region where it is ionized, leading to the observed electron density increases. This understanding helps account for the exceptionally significant increase in temperature, and markedly reduced density, observed during the electrode edge biasing experiment conducted on SPECTOR. It is thought that edge fueling impediment, a consequence of a biasing-induced transport barrier, is largely responsible for the observed temperature increase and density decrease.

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title: A globally conservative finite element MHD code and its application to the study of compact torus formation, levitation and magnetic compression
abstract: The DELiTE (Differential Equations on Linear Triangular Elements) framework was developed for spatial discretisation of partial differential equations on an unstructured triangular grid in axisymmetric geometry. The framework is based on discrete differential operators in matrix form, which are derived using linear finite elements and mimic some of the properties of their continuous counterparts. A single-fluid two-temperature MHD code is implemented in this framework. The inherent properties of the operators are used in the code to ensure global conservation of energy, particle count, toroidal flux, and angular momentum. The code was applied to study a novel experiment in which a compact torus (CT), produced with a magnetized Marshall gun, is magnetically levitated off an insulating wall and then magnetically compressed through the action of currents in the levitation/compression coils located outside the wall. We present numerical models for CT formation, levitation, and magnetic compression, and comparisons between simulated and experimental diagnostics.

title: Magnetic Compression of Compact Tori, Experiment and Simulation
abstract: The magnetic compression experiment at General Fusion was a repetitive non-destructive test to study plasma physics applicable to magnetic target fusion compression. A compact torus (CT) is formed with a co-axial gun into a containment region with an hour-glass shaped inner flux conserver, and an insulating outer wall. External coil currents keep the CT off the outer wall (radial levitation) and then rapidly compress it inwards. The optimal external coil configuration greatly improved both the levitated CT lifetime and the recurrence rate of shots with good compressional flux conservation. As confirmed by spectrometer data, the improved levitation field profile reduced plasma impurity levels by suppressing the interaction between plasma and the insulating outer wall during the formation process. Significant increases in magnetic field, electron density, and ion temperature were routinely observed at magnetic compression in the final external coil configuration tested, despite the prevalence of an instability, thought be an external kink mode, at compression. Matching the decay rate of the levitation currents to that of the CT currents resulted in a reduced level of MHD activity associated with unintentional compression by the levitation field, and a higher probability of long-lived CTs. The DELiTE (Differential Equations on Linear Triangular Elements) framework was developed for spatial discretisation of partial differential equations on an unstructured triangular grid in axisymmetric geometry. The framework is based on discrete differential operators in matrix form, which are derived using linear finite elements and mimic some of the properties of their continuous counterparts. A single-fluid two-temperature MHD model is implemented in this framework. The inherent properties of the operators are used in the code to ensure global conservation of energy, particle count, toroidal flux, and angular momentum. The development of the discrete forms of the equations solved is presented. The code was applied to study the magnetic compression experiment. The numerical models developed to simulate CT formation, levitation, and magnetic compression are reported. A model for anisotropic thermal diffusion has been formulated and implemented to the code. A method for determining the q profile of the CT was established simulated CT q profiles indicate that the magnetic compression experiment could be improved by modifying the q profile to regimes with increased stability against kink modes. Comparisons between simulated and experimental diagnostics are presented. A model of plasma/neutral fluid interaction was developed and included in the framework. The source rates of species momentum and energy due to ionization and recombination were derived using a simple method that enables determination of the volumetric rate of thermal energy transfer from electrons to photons and neutral particles due to radiative recombination, which has been neglected in other studies. The implementation of the model has enabled clarification of the mechanisms behind the increases in CT electron density that are routinely observed on the SPECTOR plasma injector well after CT formation. This understanding helps account for the exceptionally significant increase in electron temperature, and markedly reduced electron density, observed during the electrode edge biasing experiment conducted on SPECTOR. It is thought that edge fueling impediment, a consequence of a biasing-induced transport barrier, is largely responsible for the observed modifications to temperature and density.

title: Magnetic levitation and compression of compact tori
abstract: The magnetic compression experiment at General Fusion was a repetitive non-destructive test to study plasma physics applicable to Magnetic Target Fusion compression. A compact torus (CT) is formed with a co-axial gun into a containment region with an hour-glass shaped inner flux conserver, and an insulating outer wall. External coil currents keep the CT off the outer wall (radial levitation) and then rapidly compress it inwards. The optimal external coil configuration greatly improved both the levitated CT lifetime and the rate of shots with good flux conservation during compression. As confirmed by spectrometer data, the improved levitation field profile reduced plasma impurity levels by suppressing the interaction between plasma and the insulating outer wall during the formation process. Significant increases in magnetic field, density, and ion temperature were routinely observed at magnetic compression despite the prevalence of an instability, thought be an external kink, at compression. Matching the decay rate of the levitation coil currents to that of the internal CT currents resulted in a reduced level of MHD activity associated with unintentional compression by the levitation field, and a higher probability of long-lived CTs. An axisymmetric finite element MHD code that conserves system energy, particle count, angular momentum, and toroidal flux, was developed to study CT formation into a levitation field and magnetic compression. An overview of the principal experimental observations, and comparisons between simulated and experimental diagnostics are presented.

title: A general nonlinear fluid model for reacting plasma-neutral mixtures
abstract: A generalized, computationally tractable fluid model for capturing the effects of neutral particles in plasmas is derived. The model derivation begins with Boltzmann equations for singly charged ions, electrons, and a single neutral species. Electron-impact ionization, radiative recombination, and resonant charge exchange reactions are included. Moments of the reaction collision terms are detailed. Moments of the Boltzmann equations for electron, ion, and neutral species are combined to yield a two-component plasma-neutral fluid model. Separate density, momentum, and energy equations, each including reaction transfer terms, are produced for the plasma and neutral equations. The required closures for the plasma-neutral model are discussed.

title: Modeling Plasmas with Strong Anisotropy, Neutral Fluid Effects, and Open Boundaries
abstract: Modeling Plasmas with Strong Anisotropy, Neutral Fluid Effects, and Open Boundaries

title: The Framework Of Plasma Physics
abstract: * Foreword by David Pines * The Nature of Plasma * Charged Particle Motion * Fluid Description of a Plasma * The Cold Plasma Model and Waves * MHD and the Drift Model * Vlasov Description of a Plasma * Binary Collisions * Collisional Transport * Turbulent Transport

title: Fundamentals of Plasma Physics
abstract: The widespread importance of plasmas in many areas of contemporary physics makes good textbooks in the field that are both introductory and comprehensive invaluable. This new book by Paul Bellen from CalTech by and large meets these goals. It covers the traditional textbook topics such as particle orbits, the derivation of the MHD equations from Vlasov theory, cold and warm plasma waves, Landau damping, as well as in the later chapters less common subjects such as magnetic helicity, nonlinear processes and dusty plasmas. The book is clearly written, neatly presented, and each chapter has a number of exercises or problems at their end. The author has also thankfully steered clear of the pitfall of filling the book with his own research results. The preface notes that the book is designed to provide an introduction to plasma physics for final year undergraduate and post-graduate students. However, it is difficult to see many physics undergraduates now at UK universities getting to grips with much of the content since their mathematics is not of a high enough standard. Students in Applied Mathematics departments would certainly fare better. An additional problem for the beginner is that some of the chapters do not lead the reader gently into a subject, but begin with quite advanced concepts. Being a multi-disciplinary subject, beginners tend to find plasma physics quite hard enough even when done simply. For postgraduate students these criticisms fade away and this book provides an excellent introduction. More senior researchers should also enjoy the book, especially Chapters 11?17 where more advanced topics are discussed. I found myself continually comparing the book with my favourite text for many years, `The Physics of Plasmas' by T J M Boyd and J J Sanderson, reissued by Cambridge University Press in 2003. Researchers would want both books on their shelves, both for the different ways basic plasma physics is covered, and the diversity of more advanced topics. For the undergraduate level, I would find it easier to construct an introductory course from Boyd and Sanderson.

title: Stoletov constant and effective ionization potential of a diatomic gas molecule
abstract: Applying the dimension theory methods to the experimental data on static electric gas breakdown, we established the dependence of the empirical Stoletov constant on gas characteristics. This constant was shown to be 2.72 times larger than the energy expended by electrons to ionization of one gas particle (atom and molecule). Based on the analysis of elementary processes with participation of metastable levels of molecules and atoms under the optimum electron multiplication condition in a diatomic gas we concluded that the mean energy expended by the electrons to ionization of one molecule is the effective ionization potential of a gas molecule.

title: Interaction of the solar wind with the local interstellar medium
abstract: First results from a two-dimensional (axisymmetric) time-dependent gas dynamic model for the interaction of the solar wind with the local interstellar medium are presented. The model includes the mutual influence of the interstellar and interplanetary plasma (protons and electrons) and the neutral interstellar hydrogen atoms. Neutrals created by charge exchange with the solar wind are ignored; this allows us to approximate the dynamical evolution of the system with the isotropic fluid equations. A supersonic interstellar wind is assumed. The global structure of the heliosphere and interaction region is described for both the plasma and neutral gas. The self-consistent model is compared to a noninteracting gas dynamic model, and dramatic differences in the size of the heliosphere are found. The distribution of neutral hydrogen in the heliosphere is also discussed.

title: MULTI-FLUID SIMULATIONS OF CHROMOSPHERIC MAGNETIC RECONNECTION IN A WEAKLY IONIZED REACTING PLASMA
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title: Polarimeter for the General Fusion SPECTOR machine.
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