Introduction to gyrokinetic theory with applications in magnetic confinement research in plasma physics

The present lecture provides an introduction to the subject of gyrokinetic theory with applications in the area of magnetic confinement research in plasma physics--the research arena from which this formalism was originally developed. It was presented as a component of the ''Short Course in Kinetic Theory within the Thematic Program in Partial Differential Equations'' held at the Fields Institute for Research in Mathematical Science (24 March 2004). This lecture also discusses the connection between the gyrokinetic formalism and powerful modern numerical simulations. Indeed, simulation, which provides a natural bridge between theory and experiment, is an essential modern tool for understanding complex plasma behavior. Progress has been stimulated in particular by the exponential growth of computer speed along with significant improvements in computer technology. The advances in both particle and fluid simulations of fine-scale turbulence and large-scale dynamics have produced increasingly good agreement between experimental observations and computational modeling. This was enabled by two key factors: (i) innovative advances in analytic and computational methods for developing reduced descriptions of physics phenomena spanning widely disparate temporal and spatial scales and (ii) access to powerful new computational resources

IAEA Theory Summary 1998 IAEA Meeting, Yokohama, Japan - Oct. 17--24, 1998

This is a summary of the advances in magnetic fusion energy theory research presented at the 17th International Atomic Energy Agency Fusion Energy Conference from 17--24 October, 1998 in Yokohama, Japan. Theory and simulation results from this conference provided encouraging evidence of significant progress in understanding the physics of thermonuclear plasmas. Indeed, the grand challenge for this field is to acquire the basic understanding that can readily enable the innovations which would make fusion energy practical. In this sense, as depicted in Fig. 1, research in fusion energy is increasingly able to be categorized as fitting well the ''Pasteur's Quadrant'' paradigm, where the research strongly couples basic science (''Bohr's Quadrant'') to technological impact (''Edison's Quadrant''). As supported by some of the work presented at this conference, this trend will be further enhanced by advanced simulations. Eventually, realistic three-dimensional modeling capabilities, when properly combined with rapid and complete data interpretation of results from both experiments and simulations, can contribute to a greatly enhanced cycle of understanding and innovation. Plasma science theory and simulation have provided reliable foundations for this improved modeling capability, and the exciting advances in high-performance computational resources have further accelerated progress

Electron energy transport and magnetic curvature driven modes

A transport coefficient for anomalous electron thermal conduction is constructed on the basis of the so-called Principle of Profile Consistency. It is assumed that the relevant modes in plasma where a substantial fraction of the electron population is magnetically trapped produce magnetic reconnection at a microscopic level and are driven by the combined effects of the plasma pressure gradient and the magnetic field curvature. Consequently, the scaling for the electron energy confinement time exhibits a strongly favorable dependence on the radius of magnetic curvature

Measurement of the Bottom contribution to non-photonic electron production in p+pp+p collisions at s\sqrt{s} =200 GeV

The contribution of $B$ meson decays to non-photonic electrons, which are mainly produced by the semi-leptonic decays of heavy flavor mesons, in $p+p$ collisions at $\sqrt{s} =$ 200 GeV has been measured using azimuthal correlations between non-photonic electrons and hadrons. The extracted $B$ decay contribution is approximately 50% at a transverse momentum of $p_{T} \geq 5$ GeV/$c$. These measurements constrain the nuclear modification factor for electrons from $B$ and $D$ meson decays. The result indicates that $B$ meson production in heavy ion collisions is also suppressed at high $p_{T}$.Comment: 6 pages, 4 figures, accepted by PR

Pullback Transformations in Gyrokinetic Theory

The Pullback transformation of the distribution function is a key component of the gyrokinetic theory. In this paper, a systematic treatment of this subject is presented, and results from applications of the uniform framework developed are reviewed. The focus is on providing a clear exposition of the basic formalism which arises from the existence of three distinct coordinate systems in gyrokinetic theory. The familiar gyrocenter coordinate system, where the gyromotion is decoupled from the rest of particle's dynamics, is non-canonical and non-fabric. On the other hand, Maxwell's equations, which are needed to complete a kinetic system, are initially only defined in the fabric laboratory phase space coordinate system. The pullback transformations provide a rigorous connection between the distribution functions in gyrocenter coordinates and Maxwell's equations in laboratory phase space coordinates. This involves the generalization of the usual moment integrals originally defined on the cotangent fiber of the phase space to the moment integrals on a general 6D symplectic manifold, is shown to be an important step in the proper formulation of gyrokinetic theory. The resultant systematic treatment of the moment integrals enabled by the pullback transformation. Without this vital element, a number of prominent physics features, such as the presence of the compressional Alfven wave and a proper description of the gyrokinetic equilibrium, cannot be readily recovered

Partonic flow and ϕ\phi-meson production in Au+Au collisions at sNN\sqrt{s_{NN}} = 200 GeV

We present first measurements of the $\phi$-meson elliptic flow ($v_{2}(p_{T})$) and high statistics $p_{T}$ distributions for different centralities from $\sqrt{s_{NN}}$ = 200 GeV Au+Au collisions at RHIC. In minimum bias collisions the $v_{2}$ of the $\phi$ meson is consistent with the trend observed for mesons. The ratio of the yields of the $\Omega$ to those of the $\phi$ as a function of transverse momentum is consistent with a model based on the recombination of thermal $s$ quarks up to $p_{T}\sim 4$ GeV/$c$, but disagrees at higher momenta. The nuclear modification factor ($R_{CP}$) of $\phi$ follows the trend observed in the $K^{0}_{S}$ mesons rather than in $\Lambda$ baryons, supporting baryon-meson scaling. Since $\phi$-mesons are made via coalescence of seemingly thermalized $s$ quarks in central Au+Au collisions, the observations imply hot and dense matter with partonic collectivity has been formed at RHIC.Comment: 6 pages, 4 figures, submit to PR

Measurement of open charm production in dd+Au collisions at sNN\sqrt{s_{NN}}=200 GeV

We present the first comprehensive measurement of $D^{0}, D^{+}, D^{*+}$ and their charge conjugate states at mid-rapidity in $d$+Au collisions at $\sqrt{s_{_{NN}}}$=200 GeV using the STAR TPC. The directly measured open charm multiplicity distribution covers a broad transverse momentum region of 0$<p_{T}<11$ GeV/$c$. The measured $dN/dy$ at mid-rapidity for $D^{0}$ is $0.0265\pm 0.0036 (stat.) \pm 0.0071 (syst.)$ and the measured $D^{*+}/D^{0}$ and $D^{+}/D^{0}$ ratios are approximately equal with a magnitude of $0.40\pm 0.09(stat.) \pm 0.13(syst.)$. The total $c\bar{c}$ cross section per nucleon-nucleon collision extracted from this study is $1.18 \pm 0.21(stat.) \pm 0.39(syst.)$mb. The direct measurement of open charm production is consistent with STAR single electron data. This cross section is higher than expectations from PYTHIA and other pQCD calculations. The measured $p_{T}$ distribution is harder than the pQCD prediction using the Peterson fragmentation function.Comment: Quark Matter 2004 Proceeding