arXiv subjects

D. E. Ruiz

Publications and source records attributed to D. E. Ruiz.

At least 19 recordsLinked to original sources

arXiv2025

Asymptotic scaling laws for the stagnation conditions of Z-pinch implosions

Implosions of magnetically-driven annular shells (Z pinches) are studied in the laboratory to produce high-energy-density plasmas. Such plasmas have a wide-range of applications including x-ray generation, controlled thermonuclear fusion, and astrophysics studies. In this work, we theoretically investigate the in-flight dynamics of a magnetically-driven, imploding cylindrical shell that stagnates onto itself upon collision on axis. The converging flow of the Z-pinch is analyzed by considering the implosion trajectory in the $(A, M)$ parametric plane, where $A$ is the in-flight aspect ratio and $M$ is the implosion Mach number. For an ideal implosion in the absence of instabilities and in the limit of $A\gg1$, we derive asymptotic scaling laws for hydrodynamic quantities evaluated at stagnation (e.g., density, temperature, and pressure) and for performance metrics (e.g., soft x-ray emission, K-shell x-ray emission, and neutron yield) as functions of target-design parameters.

physics.plasm-ph↗

arXiv2024

Degradation of performance in ICF implosions due to Rayleigh--Taylor instabilities: a Hamiltonian perspective

The Rayleigh--Taylor instability (RTI) is an ubiquitous phenomenon that occurs in inertial-confinement-fusion (ICF) implosions and is recognized as an important limiting factor of ICF performance. To analytically understand the RTI dynamics and its impact on ICF capsule implosions, we develop a first-principle variational theory that describes an imploding spherical shell undergoing RTI. The model is based on a thin-shell approximation and includes the dynamical coupling between the imploding spherical shell and an adiabatically compressed fluid within its interior. Using a quasilinear analysis, we study the degradation trends of key ICF performance metrics (e.g., stagnation pressure, residual kinetic energy, and aerial density) as functions of initial RTI parameters (e.g., the initial amplitude and Legendre mode), as well as the 1D implosion characteristics (e.g., the convergence ratio). We compare analytical results from the theory against nonlinear results obtained by numerically integrating the governing equations of this reduced model. Our findings emphasize the need to incorporate polar flows in the calculation of residual kinetic energy and demonstrate that higher convergence ratios in ICF implosions lead to significantly greater degradation of key performance metrics.

physics.plasm-ph↗

arXiv2023

Exploring the parameter space of MagLIF implosions using similarity scaling. III. Rise-time scaling

Magnetized Liner Inertial Fusion (MagLIF) is a z-pinch magneto-inertial-fusion (MIF) concept studied on the Z Machine at Sandia National Laboratories. Two important metrics characterizing current delivery to a z-pinch load are the peak current and the current-rise time, which is roughly the time interval to reach peak current. It is known that, when driving a z-pinch load with a longer current-rise time, the performance of the z-pinch decreases. However, a theory to understand and quantify this effect is still lacking. In this paper, we utilize a framework based on similarity scaling to analytically investigate the variations in performance of MagLIF loads when varying the current-rise time, or equivalently, the implosion timescale. To maintain similarity between the implosions, we provide the scaling prescriptions of the experimental input parameters defining a MagLIF load and derive the scaling laws for the stagnation conditions and for various performance metrics. We compare predictions of the theory to 2D numerical simulations using the radiation, magneto-hydrodynamic code HYDRA. For several metrics, we find acceptable agreement between the theory and simulations. Our results show that the voltage near the MagLIF load follows a weak scaling law $\smash{φ_{\rm load} \propto t_φ^{-0.12}}$ with respect to the characteristic timescale $t_φ$ of the voltage source, instead of the ideal $\smash{φ_{\rm load} \propto t_φ^{-1}}$ scaling. This occurs because the imploding height of the MagLIF load must increase to preserve end losses. As a consequence of the longer imploding liners, the required total laser preheat energy and delivered electric energy increase. Overall, this study may help understand the trade-offs of the MagLIF design space when considering future pulsed-power generators with shorter and longer current-rise times.

physics.plasm-ph↗

arXiv2023

Exploring the parameter space of MagLIF implosions using similarity scaling. I. Theoretical framework

Magneto-inertial fusion (MIF) concepts, such as the Magnetized Liner Inertial Fusion (MagLIF) platform [M. R. Gomez et al., Phys. Rev. Lett. 113, 155003 (2014)], constitute a promising path for achieving ignition and significant fusion yields in the laboratory. The space of experimental input parameters defining a MagLIF load is highly multi-dimensional, and the implosion itself is a complex event involving many physical processes. In the first paper of this series, we develop a simplified analytical model that identifies the main physical processes at play during a MagLIF implosion. Using non-dimensional analysis, we determine the most important dimensionless parameters characterizing MagLIF implosions and provide estimates of such parameters using typical fielded or experimentally observed quantities for MagLIF. We then show that MagLIF loads can be "incompletely" similarity scaled, meaning that the experimental input parameters of MagLIF can be varied such that many (but not all) of the dimensionless quantities are conserved. Based on similarity-scaling arguments, we can explore the parameter space of MagLIF loads and estimate the performance of the scaled loads. In the follow-up papers of this series, we test the similar scaling theory for MagLIF loads against simulations for two different scaling "vectors", which include current scaling and rise-time scaling.

physics.plasm-ph↗

arXiv2023

Exploring the parameter space of MagLIF implosions using similarity scaling. II. Current scaling

Magnetized Liner Inertial Fusion (MagLIF) is a magneto-inertial-fusion (MIF) concept, which is presently being studied on the Z Pulsed Power Facility. The MagLIF platform has achieved interesting plasma conditions at stagnation and produced significant fusion yields in the laboratory. Given the relative success of MagLIF, there is a strong interest to scale the platform to higher peak currents. However, scaling MagLIF is not entirely straightforward due to the large dimensionality of the experimental input parameter space and the large number of distinct physical processes involved in MIF implosions. In this work, we propose a novel method to scale MagLIF loads to higher currents. Our method is based on similarity (or similitude) scaling and attempts to preserve much of the physics regimes already known or being studied on today's Z pulsed-power driver. By avoiding significant deviations into unexplored and/or less well-understood regimes, the risk of unexpected outcomes on future scaled-up experiments is reduced. Using arguments based on similarity scaling, we derive the scaling rules for the experimental input parameters characterizing a MagLIF load (as functions of the characteristic current driving the implosion). We then test the estimated scaling laws for various metrics measuring performance against results of 2D radiation--magneto-hydrodynamic HYDRA simulations. Agreement is found between the scaling theory and the simulation results.

physics.plasm-ph↗

arXiv2020

Gravitational spin Hall effect of light

The propagation of electromagnetic waves in vacuum is often described within the geometrical optics approximation, which predicts that wave rays follow null geodesics. However, this model is valid only in the limit of infinitely high frequencies. At large but finite frequencies, diffraction can still be negligible, but the ray dynamics becomes affected by the evolution of the wave polarization. Hence, rays can deviate from null geodesics, which is known as the gravitational spin Hall effect of light. In the literature, this effect has been calculated ad hoc for a number of special cases, but no general description has been proposed. Here, we present a covariant Wentzel-Kramers-Brillouin analysis from first principles for the propagation of light in arbitrary curved spacetimes. We obtain polarization-dependent ray equations describing the gravitational spin Hall effect of light. We also present numerical examples of polarization-dependent ray dynamics in the Schwarzschild spacetime, and the magnitude of the effect is briefly discussed. The analysis reported here is analogous to that of the spin Hall effect of light in inhomogeneous media, which has been experimentally verified.

gr-qc↗

arXiv2019

On a variational formulation of the weakly nonlinear magnetic Rayleigh--Taylor instability

The magnetic-Rayleigh--Taylor (MRT) instability is a ubiquitous phenomenon that occurs in magnetically-driven Z-pinch implosions. It is important to understand this instability since it can decrease the performance of such implosions. In this work, I present a theoretical model for the weakly nonlinear MRT instability. I obtain such model by asymptotically expanding an action principle, whose Lagrangian leads to the fully nonlinear MRT equations. After introducing a suitable choice of coordinates, I show that the theory can be cast as a Hamiltonian system, whose Hamiltonian is calculated up to sixth order in a perturbation parameter. The resulting theory captures the harmonic generation of MRT modes. In particular, it is shown that the saturation amplitude of the linear MRT instability grows as the stabilization effect of the magnetic-field tension increases. Overall, the theory provides an intuitive interpretation of the weakly nonlinear MRT instability and provides a systematic approach for studying this instability in more complex settings.

physics.plasm-ph↗

arXiv2019

Quasioptical modeling of wave beams with and without mode conversion: I. Basic theory

This work opens a series of papers where we develop a general quasioptical theory for mode-converting electromagnetic beams in plasma and implement it in a numerical algorithm. Here, the basic theory is introduced. We consider a general quasimonochromatic multi-component wave in a weakly inhomogeneous linear medium with no sources. For any given dispersion operator that governs the wave field, we explicitly calculate the approximate operator that governs the wave envelope $ψ$ to the second order in the geometrical-optics parameter. Then, we further simplify this envelope operator by assuming that the gradient of $ψ$ transverse to the local group velocity is much larger than the corresponding parallel gradient. This leads to a parabolic differential equation for $ψ$ ("quasioptical equation") in the basis of the geometrical-optics polarization vectors. Scalar and mode-converting vector beams are described on the same footing. We also explain how to apply this model to electromagnetic waves in general. In the next papers of this series, we report successful quasioptical modeling of radiofrequency wave beams in magnetized plasma based on this theory.

physics.plasm-ph↗

arXiv2019

Variational nonlinear WKB in the Eulerian frame

Nonlinear WKB is a multiscale technique for studying locally-plane-wave solutions of nonlinear partial differential equations (PDE). Its application comprises two steps: (1) replacement of the original PDE with an extended system separating the large scales from the small, and (2) reduction of the extended system to its slow manifold. In the context of variational fluid theories with particle relabeling symmetry, nonlinear WKB in the mean Eulerian frame is known to possess a variational structure. This much has been demonstrated using, for instance, the theoretical apparatus known as the generalized Lagrangian mean. On the other hand, the variational structure of nonlinear WKB in the conventional Eulerian frame remains mysterious. By exhibiting a variational principle for the extended equations from step (1) above, we demonstrate that nonlinear WKB in the Eulerian frame is in fact variational. Remarkably, the variational principle for the extended system admits loops of relabeling transformations as a symmetry group. Noether's theorem therefore implies that the extended Eulerian equations possess a family of circulation invariants parameterized by $S^1$. As an illustrative example, we use our results to systematically deduce a variational model of high-frequency acoustic waves interacting with a larger-scale compressible isothermal flow.

math-ph↗

arXiv2019

Wave kinetic equation for inhomogeneous drift-wave turbulence beyond the quasilinear approximation

The formation of zonal flows from inhomogeneous drift-wave (DW) turbulence is often described using statistical theories derived within the quasilinear approximation. However, this approximation neglects wave--wave collisions. Hence, some important effects such as the Batchelor--Kraichnan inverse-energy cascade are not captured within this approach. Here we derive a wave kinetic equation that includes a DW collision operator in the presence of zonal flows. Our derivation makes use of the Weyl calculus, the quasinormal statistical closure, and the geometrical-optics approximation. The obtained model conserves both the total enstrophy and energy of the system. The derived DW collision operator breaks down at the Rayleigh--Kuo threshold. This threshold is missed by homogeneous-turbulence theory but expected from a full-wave quasilinear analysis. In the future, this theory might help better understand the interactions between drift waves and zonal flows, including the validity domain of the quasilinear approximation that is commonly used in literature.

physics.plasm-ph↗

arXiv2018

Wave kinetics of drift-wave turbulence and zonal flows beyond the ray approximation

Inhomogeneous drift-wave turbulence can be modeled as an effective plasma where drift waves act as quantumlike particles and the zonal-flow velocity serves as a collective field through which they interact. This effective plasma can be described by a Wigner-Moyal equation (WME), which generalizes the quasilinear wave-kinetic equation (WKE) to the full-wave regime, i.e., resolves the wavelength scale. Unlike waves governed by manifestly quantumlike equations, whose WMEs can be borrowed from quantum mechanics and are commonly known, drift waves have Hamiltonians very different from those of conventional quantum particles. This causes unusual phase-space dynamics that is typically not captured by the WKE. We demonstrate how to correctly model this dynamics with the WME instead. Specifically, we report full-wave phase-space simulations of the zonal-flow formation (zonostrophic instability), deterioration (tertiary instability), and the so-called predator-prey oscillations. We also show how the WME facilitates analysis of these phenomena, namely, (i) we show that full-wave effects critically affect the zonostrophic instability, particularly, its nonlinear stage and saturation; (ii) we derive the tertiary-instability growth rate; and (iii) we demonstrate that, with full-wave effects retained, the predator-prey oscillations do not require zonal-flow collisional damping, contrary to previous studies. We also show how the famous Rayleigh-Kuo criterion, which has been missing in wave-kinetic theories of drift-wave turbulence, emerges from the WME.

physics.plasm-ph↗

arXiv2018

Wave kinetic equation in a nonstationary and inhomogeneous medium with a weak quadratic nonlinearity

We present a systematic derivation of the wave kinetic equation describing the dynamics of a statistically inhomogeneous incoherent wave field in a medium with a weak quadratic nonlinearity. The medium can be nonstationary and inhomogeneous. Primarily based on the Weyl phase-space representation, our derivation assumes the standard geometrical-optics ordering and the quasinormal approximation for the statistical closure. The resulting wave kinetic equation simultaneously captures the effects of the medium inhomogeneity (both in time and space) and of the nonlinear wave scattering. This general formalism can serve as a stepping stone for future studies of weak wave turbulence interacting with mean fields in nonstationary and inhomogeneous media.

physics.optics↗

arXiv2017

Mode conversion in cold low-density plasma with a sheared magnetic field

A theory is proposed that describes mutual conversion of two electromagnetic modes in cold low-density plasma, specifically, in the high-frequency limit where the ion response is negligible. In contrast to the classic (Landau--Zener-type) theory of mode conversion, the region of resonant coupling in low-density plasma is not necessarily narrow, so the coupling matrix cannot be approximated with its first-order Taylor expansion; also, the initial conditions are set up differently. For the case of strong magnetic shear, a simple method is identified for preparing a two-mode wave such that it transforms into a single-mode wave upon entering high-density plasma. The theory can be used for reduced modeling of wave-power input in fusion plasmas. In particular, applications are envisioned in stellarator research, where the mutual conversion of two electromagnetic modes near the plasma edge is a known issue.

physics.plasm-ph↗

arXiv2017

A geometric theory of waves and its applications to plasma physics

Waves play an essential role in many aspects of plasma science, such as plasma manipulation and diagnostics. Due to the complexity of the governing equations, approximate models are often necessary to describe wave dynamics. In this dissertation, waves are treated as geometric objects of a variational theory rather than formal solutions of specific PDEs. This approach simplifies calculations, highlights the underlying wave symmetries, and leads to improved modeling of wave dynamics. This thesis presents two breakthroughs that were obtained in the general theory of waves. The first main contribution is an extension and reformulation of geometrical optics (GO) as a first-principle Lagrangian theory that correctly describes polarization effects, such as polarization precession and the polarization-driven bending of ray trajectories, which appear as leading-order corrections to GO. The theory was applied to several systems of interest, such as relativistic spin-1/2 particles and radio-frequency waves in magnetized plasma. The second main contribution of this thesis is the development of a phase-space method to study basic properties of nonlinear wave--wave interactions. Specifically, I show that waves propagating in modulated media, both classical and quantum, can experience time-averaged refraction caused by effective ponderomotive forces on wave rays. This phenomenon is analogous to the ponderomotive effect encountered by charged particles in high-frequency electromagnetic fields. I also show that phase-space methods can be useful to study problems in the field of wave turbulence, such as the nonlinear interaction of high-frequency waves with large-scale structures. Overall, the results obtained can serve as a basis for future studies on more complex nonlinear wave--wave interactions, such as modulational instabilities in general wave ensembles or wave turbulence.

physics.plasm-ph↗

arXiv2017

Extending geometrical optics: A Lagrangian theory for vector waves

Even when neglecting diffraction effects, the well-known equations of geometrical optics (GO) are not entirely accurate. Traditional GO treats wave rays as classical particles, which are completely described by their coordinates and momenta, but vector-wave rays have another degree of freedom, namely, their polarization. The polarization degree of freedom manifests itself as an effective (classical) "wave spin" that can be assigned to rays and can affect the wave dynamics accordingly. A well-known manifestation of polarization dynamics is mode conversion, which is the linear exchange of quanta between different wave modes and can be interpreted as a rotation of the wave spin. Another, less-known polarization effect is the polarization-driven bending of ray trajectories. This work presents an extension and reformulation of GO as a first-principle Lagrangian theory, whose effective-gauge Hamiltonian governs the aforementioned polarization phenomena simultaneously. As an example, the theory is applied to describe the polarization-driven divergence of right-hand and left-hand circularly polarized electromagnetic waves in weakly magnetized plasma.

physics.plasm-ph↗

arXiv2017

Ponderomotive dynamics of waves in quasiperiodically modulated media

Similarly to how charged particles experience time-averaged ponderomotive forces in high-frequency fields, linear waves also experience time-averaged refraction in modulated media. Here we propose a covariant variational theory of this "ponderomotive effect on waves" for a general nondissipative linear medium. Using the Weyl calculus, our formulation accommodates waves with temporal and spatial period comparable to that of the modulation (provided that parametric resonances are avoided). Our theory also shows that any wave is, in fact, a polarizable object that contributes to the linear dielectric tensor of the ambient medium. The dynamics of quantum particles is subsumed as a special case. As an illustration, ponderomotive Hamiltonians of quantum particles and photons are calculated within a number of models. We also explain a fundamental connection between these results and the commonly known expression for the electrostatic dielectric tensor of quantum plasmas.

physics.plasm-ph↗

arXiv2017

Photon polarizability and its effect on the dispersion of plasma waves

High-frequency photons traveling in plasma exhibit a linear polarizability that can influence the dispersion of linear plasma waves. We present a detailed calculation of this effect for Langmuir waves as a characteristic example. Two alternative formulations are given. In the first formulation, we calculate the modified dispersion of Langmuir waves by solving the governing equations for the electron fluid, where the photon contribution enters as a ponderomotive force. In the second formulation, we provide a derivation based on the photon polarizability. Then, the calculation of ponderomotive forces is not needed, and the result is more general.

physics.plasm-ph↗

arXiv2017

Variational principles for dissipative (sub)systems, with applications to the theory of linear dispersion and geometrical optics

Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables. Here, a different approach is proposed. We show that, for a broad class of dissipative systems of practical interest, variational principles can be formulated using constant Lagrange multipliers and Lagrangians nonlocal in time, which allow treating reversible and irreversible dynamics on the same footing. A general variational theory of linear dispersion is formulated as an example. In particular, we present a variational formulation for linear geometrical optics in a general dissipative medium, which is allowed to be nonstationary, inhomogeneous, nonisotropic, and exhibit both temporal and spatial dispersion simultaneously.

physics.plasm-ph↗