Dan Dubin (University of California, San Diego)
I will present a brief overview of the physics of long range and short range Coulomb
collisions in strong magnetic fields and in strongly-coupled plasmas.
Alain J. Brizard (Saint Michaels College)
Given the importance of the collisionless gyrokinetic formalism in the analytical and numerical investigations of magnetized plasmas, the inclusion of self-consistent collisional effects in the neoclassical and collisionless regimes within the gyrokinetic formalism (when the collisional mean-free-path is far longer than the background magnetic field non-uniformity length scale) is of crucial importance in our ability to understand the complex nonlinear dynamics of magnetized fusion plasmas over long time scales. The exact energy-momentum conservation laws of a guiding-center Fokker-Planck collision operator, expressed in terms of the Landau form, are investigated in the limits of arbitrary magnetic-field non-uniformity. These exact conservation laws play fundamental roles in understanding the numerical accuracy of particle simulations.
HAMILTONIAN AND ACTION FORMULATIONS
Phil Morrison (University of Texas at Austin)
Theory ranges broadly, from the description and prediction of phenomena to the understanding of the mathematical structure of physical laws. At one end of the spectrum is phenomenology, as epitomized by Landau's mastery, while on the other is theory, as epitomized by Dirac's theoretical ingenuity, which for want of a better term we will call basic. The discipline of plasma physics has accrued generations of impressive phenomenology while, despite an early budding in the 1960s and occasional development in latter years, it will be argued that basic theory has been largely underdeveloped and under appreciated in plasma physics in comparison to other disciplines of physics. Examples will be given to illustrate how basic theory can serve as fertile ground for advancement of our discipline.
I. Y. Dodin (Princeton University, PPPL)
Plasma wave theory remains full of surprises and challenges, such as improving the modeling of linear radio frequency (RF) waves and advancing the understanding of intense laser-plasma interactions. However, theoretical methods of studying plasma waves have been fundamentally unchanged for many decades. A revision is long overdue, not only for the sake of pure theory, but also for practical applications, pedagogical purposes, and strengthening connections between plasma physics and other disciplines. An attractive alternative to the standard "ab initio" Maxwell-Vlasov formulation is a more abstract, universal, and yet also simple and robust field-theoretical approach, which actually makes use of the specific properties that waves have as opposed to other electromagnetic fields. The talk will present some recent examples of how variational methods lead to new insights in basic wave theory and also facilitate calculations. Potential applications are envisioned, for instance, in ray-tracing and full-wave simulations of RF wave propagation, advanced understanding of ponderomotive and quantum effects, and wave kinetics . Much of this current work is stimulated by previous advances in the area [Tracy et al, Ray Tracing and Beyond: Phase Space Methods in Plasma Wave Theory (Cambridge Univ. Press, 2014)]. However, a lot is yet to be done, so fundamental theory of plasma waves remains an open frontier.
***** 20 MIN VIRTUAL COFFEE BREAK *****
STRUCTURE PRESERVING COMPUTATIONS
Josh Burby (Princeton University, PPPL)
An essential part of designing structure-preserving algorithms for various plasma phenomena is developing structure-preserving reduced models at the continuum level. The continuum model doesn't only identify conservation laws the algorithm should preserve - it can be crafted to optimize the algorithm's parallel scaling efficiency. I will present an example of this principle's application in the context of collisionless magnetized plasma microturbulence. Here the most precise continuum model is the Vlasov-Maxwell system. However, a reduced model that does not require resolving particle gyromotion, i.e. a gyrokinetic model, is desireable. Conventional variational formulations of gyrokinetics preserve the basic Vlasov-Maxwell conservation laws, but not the hyperbolic nature of the Vlasov-Maxwell system; the electromagnetic field is governed by elliptic equations. The replacement of hyperbolic field equations with elliptic approximations introduces a global communication problem into any simulation algorithm that can ruin the algorithm's parallel scaling efficiency. By correctly modifying a conventional gyrokinetic Lagrangian, Vlasov-Maxwell's hyperbolic nature can be preserved in gyrokinetics. In so doing, the global communication problem is eliminated, and the potential for parallel scaling efficiency is greatly improved. The cost of retaining hyperbolic field equations is the reintroduction of light waves into gyrokinetics. However, due to the large dielectric constant of the gyrokinetic vacuum, the speed of light is significantly reduced, which offsets this cost.
Hong Qin (Princeton University, PPPL)
Conventional simulation studies of plasma physics are based on numerically solving the underpinning differential (or integro-differential) equations. The algorithms used in general do not preserve the geometric structures of the physical systems, such as the local energy-momentum conservation law and the symplectic structure (phase space volume). As a consequence, numerical errors accumulate coherently with time and long-term simulation results are not reliable. Recently, a series of geometric algorithms, which preserve the geometric structures of theoretical models in plasma physics have been developed. The superiorities of these geometric algorithms have been demonstrated. For example, symplectic integrators for the guiding-center dynamics are constructed to preserve the noncanonical symplectic structures and bound the energy-momentum errors for all simulation time-steps; variational and symplectic algorithms have been discovered and successfully applied to the Vlasov-Maxwell system and MHD equations as well. It is our vision that future numerical capabilities in plasma physics will be based on the structure-preserving geometric algorithms. This should not be surprising because geometric algorithms are built on the more fundamental field-theoretical formalism, and are directly linked to the perfect form, i.e., the variational principle of physics. The fact that the most elegant form of theory is also the most effective algorithm is philosophically satisfactory. We emphasize that the geometric (Lagrangian/Hamiltonian) formalism and the geometric algorithms suitable for plasma physics studies cannot be adapted from existing mathematical literature. They
have to be discovered and worked out by theoretical plasma physicists.
Timothy Stoltzfus-Dueck (Princeton University, PPPL)
Exploration of the fundamental structure of turbulence in plasmas is a grand challenge for plasma physics, rich both in scientific content and in potential application, requiring the interaction of basic theory, computation, and experiment. Although plasma turbulence occurs in many different environments and parameter ranges in astrophysical, laboratory, and industrial plasmas, there is a common underlying structure (Krommes Phys. Rep. 360, 1, 2002), which allows fundamental research to enable advances across diverse applications. As in neutral fluid turbulence, quadratic nonlinearities redistribute conserved quantities across different scales, typically via an incompressible flow. Unlike in 2- or 3-D neutral fluid turbulence, the flow and its incompressibility are usually situated in a 5- or 6-dimensional phase space. Also, waves and instabilities can contribute energy sources and sinks across many scales, modifying or eliminating the inertial range and suggesting nonuniversality. As examples of promising directions in fundamental plasma turbulence research, we consider three topics: i) the interaction of waves and instabilities with turbulence, ii) the interaction of turbulence with large-scale flows and fields, and iii) structure of the energy cascade in 5- or 6-D phase space. Since plasma turbulence is ubiquitous in the lab and in nature, its study can be undertaken at relatively low cost using existing devices and codes. For this to be successful, we must focus the experimental and numerical work with input from dedicated theoretical studies at the analytical and semi-analytical levels.
Paul Terry (University of Wisconsin, Madison)
Instabilities in magnetically confined fusion devices, particularly microinstabilities, saturate through a turbulent state with multiple constituents that interact in a complex fashion. The constituents include the instability, damped modes in the wavenumber range of the instability, zonal flows, and magnetic fluctuations. Their interactions set fluctuation levels, spectra, and fundamentally nonlocal transport in magnetic fusion experiments. Understanding this process and validating models for it represents a frontier in plasma science.