Precise modeling of radiofrequency (RF) wave propagation and absorption in magnetized plasmas is an important practical problem in fusion science. Because ab initio simulations in realistic geometries can be prohibitively expensive, significant effort has been invested by the plasma community in the development of various reduced algorithms. Still, most of these algorithms rely on the geometrical-optics (GO) ordering and, in particular, assume that the wavelengths of interest are smaller than the characteristic scales of the amplitude evolution and plasma in general. This assumption is used to simplify the hot-plasma dielectric response (even in full-wave codes) and also Maxwell's equations per se (in ray-tracing, beam-tracing, and quasioptical codes). In either case, the approximations involved are typically ad hoc and can be significantly improved by modern asymptotic theory based on Weyl symbol calculus. Furthermore, the modern, symplectically invariant reformulation of GO, called metaplectic geometrical optics (MGO), allows for reduced wave models even when the local wavelength is not small. This can help model wave transformations near reflection points and caustics (for example, O-X conversion), where traditional GO fails and ab initio simulations are typically considered necessary. We strive to develop a rigorous and comprehensive analytical theory of MGO and apply it to improve reduced modeling of RF waves, including mode conversion, in fusion plasmas and beyond.

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Selected papers: [1], [2], [3], [4]
Dissertations: D. E. Ruiz (2017), N. A. Lopez (2022)

As a factor that can significantly affect the transport of particles and energy-momentum, plasma turbulence has been attracting attention in many contexts, from fusion to astrophysics. What makes this problem particularly challenging is that turbulence often tends to self-organize and produce coherent structures, such as zonal flows and large-scale magnetic fields (plasma dynamo). These effects cannot be modeled adequately within the classic homogeneous-turbulence theory à la Kolmogorov and, instead, are often described in terms of mean-field theories. However, traditional mean-field theories are typically limited in that they assume a significant separation between the mean-field scales and the scales of turbulent fluctuations. Since this assumption is often invalid for mean fields that form self-consistently at plasma self-organization, there has been a growing interest in understanding mean-field formation without relying on scale separation. We work on "quantumlike" formulations of plasma turbulence, where turbulent fluctuations are described as effective quantumlike plasma. Mean fields govern collective interactions within this effective plasma much like electromagnetic fields govern collective interactions of electrons and ions, while eddy-eddy interactions serve as collisions. We have applied this formalism to elucidate the interaction of drift-wave turbulence with zonal flows, including the so-called Dimits shift, and also to better understand magnetohydrodynamic dynamo.

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Selected papers: [1] [2]
Dissertations: S. Jin (2025), H. Zhu (2020), D. E. Ruiz (2017)

Wave-particle interactions are commonly described within the quasilinear theory (QLT), which predicts diffusion of resonant particles in the momentum space with the diffusion coefficient determined by the wave energy spectrum. However, this classic theory misses (oversimplifies) the adiabatic ponderomotive effects caused by the slow evolution of the wave parameters in time and space. As a result, the classic QLT also fails to conserve the action of waves that are not resonant to any particles yet still evolve adiabatically in response to the background-plasma parameters' changing in time and (or) space. Postulating action conservation undermines QLT's exact energy-momentum conservation, which is a significant part of the classic QLT's appeal. Dewar's "oscillation-center QLT" reinstates both action and energy-momentum conservation ad hoc, but a general first-principle QLT has been lacking. We have developed a more rigorous formulation of QLT based on the Weyl symbol calculus. This formulation captures both adiabatic and nonadiabatic dynamics and leads to an exactly conservative model for any Hamiltonian wave-plasma interactions. Effects of plasma inhomogeneity and Balescu-Lenard collisions are also accommodated, and the known results for electrostatic, relativistic electromagnetic, and gravitational interactions are reproduced as special cases. Extensions of this improved QLT can help better understand transport in fusion plasmas, in particular, interactions of energetic particles with plasma turbulence.

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Like quasilinear theory, models of nonlinear waves are also prone to exhibiting nonphysical effects (e.g. spurious dissipation) when approximated ad hoc. To address this issue and study new effects, we have developed variational methods for several classes of nonlinear-wave problems, in contexts ranging from intense laser-plasma interactions to parametric instabilities of radiofrequency waves in fusion plasmas. Particularly interesting in this regard are waves with trapped particles, which, counterintuitively, can exhibit nonlinearities that involve fractional and even negative powers of the wave amplitude (as long as the trapped particles actually remain trapped).

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Selected papers: [1], [2], [3], [4], [5], [6]

Quantum computers were originally proposed as a means of simulating quantum systems but may also be applicable to modeling classical plasmas. Particularly fitting for quantum simulations are linear plasma problems such as modeling of radiofrequency-wave propagation in fusion plasmas. We have developed several algorithms for modeling such waves on a quantum computer. They can potentially outperform classical algorithms in sufficiently large simulations, although hardware requirements for such algorithms remain far beyond the reach of modern technology. Quantum simulations of nonlinear classical physics of plasmas are even more challenging. Due to the no-cloning theorem, such simulations require embedding of nonlinear systems to linear ones. This tends to increase the problem size exponentially, thus negating the potential quantum speedup. How to truncate linear embeddings efficiently without losing essential physics remains an open problem. This is a research frontier where fresh ideas can readily change the whole field.

Selected presentations: [1]
Selected papers: [1], [2], [3], [4]

Recently, emission of gravitational waves was detected simultaneously with electromagnetic (EM) emission supposedly produced by the same source. This might indicate a significant coupling between GWs and EM waves near the compact objects where GWs are produced, so EM radiation could be used as an additional source of information about these objects. The interaction of gravitational and WM waves, mediated by gases or plasmas, has been hypothesized for a long time, but a systematic theory of GWs in the presence of matter has been lacking. The standard approach to study GW--matter coupling is to solve Einstein-Vlasov equations, but this has proven to be prohibitively cumbersome and typically involves oversimplifications. We used an alternative, variational formulation to derive gauge-invariant wave equations for collective oscillations of the self-consistent metric, EM fields, and plasma. This forms a foundation for studying GW-plasma interactions rigorously. For example, we have discovered a new ponderomotive effect that is analogous to the ponderomotive effect of EM waves but relies entirely on gravitational interactions.

Dissertation: D. Garg (2023)