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Ultraintense Laser-Driven Relativistic Hydrodynamics for Plane Symmetric Systems

Talamo, James M
http://orcid.org/0000-0002-7511-1499
http://rave.ohiolink.edu/etdc/view?acc_num=osu1429866228

Abstract Details

2015, Doctor of Philosophy, Ohio State University, Mathematics.
We consider the relativistic hydrodynamics of a plane symmetric, charged fluid system driven by an ultra-violent, ultra-intense laser. The resulting particle motion will be relativistic due to the strength of the laser. The fluid will accelerate violently with respect to an observer in the laboratory, so although the arena for the evolution is a smooth Minkowski spacetime, methods of general relativity will be invoked. Many systems in relativity can be cast into field theories, and we first extend the variational formulation of special relativity to laser-matter interactions. From this, a full set of four Euler equations arise that govern the hydrodynamics of a general 4-dimensional laser-matter system. The plane symmetry, however, naturally gives rise to two Killing vectors. This allows for a 2+2 reduction process to be used to analyze the system. This will allow for a reformulation of the 4-dimensional system of interacting particles as a 2-dimensional system of interacting plasma sheets. The transverse particle motion is shown to produce a change in the "effective mass" of the plasma sheets, which allows one to consider the sheets as a single entity. To achieve this, we first give the details of this 2+2 formalism and show how it can be used to write the underlying space time as a product of a base manifold and transverse Euclidean planes. We then establish a natural isomorphism between the geometrical objects (vectors, covectors, and tensors) on these manifolds. By examining the effects of this procedure in the LAB and comoving coordinate systems, we establish a coordinate transformation between them. Finally, we apply the results of the 2+2 split to the 4-dimensional Euler equations, which admit two constants of motion. This allows for us to define a plasma sheet as an equivalence class of particles whose spacetime positions differ only longitudinally and define a sheet proper time. Furthermore, the notion of particle thermodynamics can be, and is, generalized to these plasma sheets. The constants of motion along with the plasma sheet thermodynamics allow the 4-dimensional Euler equations to be recast into two equations on the base manifold that refer only to the sheet thermodynamics and sheet velocities. The internal dynamics (transverse motion) within the plasma sheets is modeled by a change in the effective mass of the sheets. Consequently, each sheet can be viewed as a single object and the 4-dimensional Euler equations reduce to a 1+1 dimensional set of equations for a relativistic gas.
Ulrich Gerlach, Ph. D (Advisor)
Barbara Keyfitz, Ph. D (Committee Member)
Fei-Ran Tian, Ph. D (Committee Member)
158 p.
Mathematics
plasma sheet; sheet; laser-driven; ultraintense; sheet thermodynamics; plane symmetric; hydrodynamics; relativistic

Recommended Citations

Citations

  • Talamo, J. M. (2015). Ultraintense Laser-Driven Relativistic Hydrodynamics for Plane Symmetric Systems [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1429866228

    APA Style (7th edition)

  • Talamo, James. Ultraintense Laser-Driven Relativistic Hydrodynamics for Plane Symmetric Systems. 2015. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1429866228.

    MLA Style (8th edition)

  • Talamo, James. "Ultraintense Laser-Driven Relativistic Hydrodynamics for Plane Symmetric Systems." Doctoral dissertation, Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1429866228

    Chicago Manual of Style (17th edition)

osu1429866228
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