arXiv subjects

N. A. Lopez

Publications and source records attributed to N. A. Lopez.

13 recordsLinked to original sources

arXiv2026

Collisional whistler instability and electron temperature staircase in inhomogeneous plasma

High-beta magnetized plasmas often exhibit anomalously structured temperature profiles, as seen from galaxy cluster observations and recent experiments. It is well known that when such plasmas are collisionless, temperature gradients along the magnetic field can excite whistler waves that efficiently scatter electrons to limit their heat transport. Only recently has it been shown that parallel temperature gradients can excite whistler waves also in collisional plasmas. Here we develop a Wigner--Moyal theory for the collisional whistler instability starting from Braginskii-like fluid equations in a slab geometry. This formalism is necessary because, for a large region in parameter space, the fastest-growing whistler waves have wavelengths comparable to the background temperature gradients. We find additional damping terms in the expression for the instability growth rate involving inhomogeneous Nernst advection and resistivity. They (i) enable whistler waves to re-arrange the electron temperature profile via growth, propagation, and subsequent dissipation, and (ii) allow non-constant temperature profiles to exist stably. For high-beta plasmas, the marginally stable solutions take the form of a temperature staircase along the magnetic field lines. The electron heat flux can also be suppressed by the Ettingshausen effect when the whistler intensity profile is sufficiently peaked and oriented opposite the background temperature gradient. This mechanism allows cold fronts without magnetic draping, might reduce parallel heat losses in inertial fusion experiments, and generally demonstrates that whistler waves can regulate transport even in the collisional limit.

physics.plasm-ph↗

arXiv2025

Geometrical optics in phase space

Geometrical optics (GO) is widely used for reduced modeling of waves in plasmas but fails near reflection points, where it predicts a spurious singularity of the wave amplitude. We show how to avoid this singularity by adopting a different representation of the wave equation. Instead of the physical space $x$ and the wavevector $k$, we use the ray time $τ$ as the new canonical coordinate and the ray energy $h$ as the associated canonical momentum. To derive the envelope equation in the $τ$-representation, we construct the Weyl symbol calculus on the $(τ, h)$ space and show that the corresponding Weyl symbols are related to their $(x, k)$ counterparts by the Airy transform. This allows us to express the coefficients in the envelope equation through the known properties of the original dispersion operator. When necessary, solutions of this equation can be mapped to the $x$-space using a generalised metaplectic transform. But the field per se might not even be needed in practice. Instead, knowing the corresponding Wigner function usually suffices for linear and quasilinear calculations. As a Weyl symbol itself, the Wigner function can be mapped analytically, using the aforementioned Airy transform. We show that the standard Airy patterns that form in regions where conventional GO fails are successfully reproduced within MGO simply by remapping the field from the $τ$-space to the $x$-space. An extension to mode-converting waves is also presented. This formulation, which we call generalised metaplectic GO (MGO) offers a promising tool, for example, for reduced modeling of the O--X conversion in inhomogeneous plasma near the critical density, an effect that is important for fusion applications and also occurs in the ionosphere. Aside from better handling reflection, MGO is similar to GO and can replace it for any practical purposes.

physics.plasm-ph↗

arXiv2024

Regarding the extension of metaplectic geometrical optics to modelling evanescent waves in ray-tracing codes

Metaplectic geometrical optics (MGO) is a recently developed ray-tracing framework to accurately compute the wavefield behavior near a caustic (turning point or focal point), where traditional ray-tracing breaks down. However, MGO has thus far been restricted to having real-valued wavevectors. This is disadvantageous because often upon crossing a caustic from the `illuminated' region to the `shadow' region, two real-valued rays coalesce into one complex-valued ray corresponding to the transition from propagating to evanescent behavior. One can distinguish caustics as having either `illuminated shadows' or `proper shadows' -- the former corresponds to when the shadow still contains real-valued rays (albeit in a fewer quantity than in the illuminated region), while the latter corresponds to when the shadow contains no real-valued rays. Here, by means of examples, we show how MGO can be used to model both types of shadows. First, for illuminated shadows we show that MGO can actually be used `as is', provided a corrected quadrature-angle bias is used compared to that proposed in the original references. This is then implemented and demonstrated in a recently developed MGO ray-tracing code. Second, we show that for proper shadows, the MGO formalism can still be used if the symplectic rotation matrix that removes caustics along rays is allowed to be complex-valued. In both cases, strong agreement is seen between the MGO and the exact solution, demonstrating the potential of MGO for improving the predictive capability of ray-tracing codes and laying the foundations for modeling more complicated evanescent phenomena such as tunnelling with MGO.

physics.plasm-ph↗

arXiv2024

Application of the Scrape-Off-Layer Fast Ion (SOLFI) code to assess particle motion in mirrors and tokamaks

This paper introduces the Scrape-Off-Layer Fast Ion (SOLFI) code, which is a new and versatile full-orbit Monte Carlo particle tracer developed to follow fast ion orbits inside and outside the separatrix in tokamaks. SOLFI is benchmarked in a simple straight mirror geometry, showing that the code conserves particle energy and magnetic moment, obtains the correct passing boundary for particles moving in the magnetic mirror field with an imposed electrostatic field, and correctly observes equal ion and electron current at the ambipolar potential predicted from analytical theory. This result has consequences for collisionless scrape-off-layers in spherical tokamaks. We then utilize SOLFI for fundamental physics studies in novel tokamak geometries, exploring the effect of shaping on the trapped particle fraction and bounce locations in tokamaks and demonstrating that negative triangularity can be used to maximize the fraction of particles bouncing in the good-curvature region, potentially leading to enhanced confinement.

physics.plasm-ph↗

arXiv2024

Exact boundary-value solution for an electromagnetic wave propagating in a linearly-varying index of refraction

The propagation of electromagnetic waves in a linearly-varying index of refraction is a fundamental problem in wave physics, being relevant in fusion science for describing certain wave-based heating and diagnostic schemes. Here, an exact solution is obtained for a given incoming wavefield specified on the boundary transverse to the direction of inhomogeneity by performing a spectral, rather than asymptotic, matching. Two case studies are then presented: a Gaussian beam at oblique incidence and a speckled wavefield at normal incidence. For the Gaussian beam, it is shown that when the waist $W$ is sufficiently large, oblique incidence manifests simply as rigid translation and focal shift of the corresponding diffraction pattern at normal incidence. The destruction of the hyperbolic umbilic caustic (corresponding to a critically focused beam) as $W$ is reduced is then demonstrated. The caustic disappears once $W \lesssim δ_a \sqrt{L}$ ($L$ being the medium lengthscale normalized by the Airy skin depth $δ_a$), at which point the wave behavior is increasingly described by Airy functions, but experiences less focusing as a result. To maximize the intensity of a launched Gaussian beam at a turning point, one should therefore minimize the imaginary part of the launched complex beam parameter while having the real part satisfy critical focusing. For the speckled wavefield, it is shown that the transverse speckle pattern only couples to the Airy longitudinal pattern when the coupling parameter $η= \sqrt{L}/f_\#$ is large, with $f_\#$ being the f-number of the launching aperture. When $η\ll 1$, a reduced description of the total wavefield can be obtained by simply multiplying the incoming speckle pattern with the Airy swelling.

physics.optics↗

arXiv2023

New solution to Airy's equation for modeling beams near turning points

Here I present a summarised description of the general behavior of waves near turning points. I show that when asymptotic matching to a prescribed incident wavefield is performed, the solution changes from being the Airy function to being more generally the hyperbolic umbilic function. This solution accounts for (de-)focusing of the incident wavefield due to gradient-index lensing in addition to the familiar Airy physics, which importantly do not superimpose. Possible applications to fusion research are discussed.

physics.plasm-ph↗

arXiv2023

On the intensity of focused waves near turning points

A wave near an isolated turning point is typically assumed to have an Airy function profile with respect to the separation distance. This description is incomplete, however, and is insufficient to describe the behavior of more realistic wavefields that are not simple plane waves. Asymptotic matching to a prescribed incoming wavefield generically introduces a phasefront curvature term that changes the characteristic wave behavior from the Airy function to that of the hyperbolic umbilic function. This function, which is one of the seven classic 'elementary' functions from catastrophe theory along with the Airy function, can be understood intuitively as the solution for a linearly focused Gaussian beam propagating in a linearly varying density profile, as we show. The morphology of the caustic lines that govern the intensity maxima of the diffraction pattern as one alters the density lengthscale of the plasma, the focal length of the incident beam, and also the injection angle of the incident beam are presented in detail. This morphology includes a Goos-Hänchen shift and focal shift at oblique incidence that do not appear in a reduced ray-based description of the caustic. The enhancement of the intensity swelling factor for a focused wave compared to the typical Airy solution is highlighted, and the impact of finite lens aperture is discussed. Collisional damping and finite beam waist are included in the model and appear as complex components to the arguments of the hyperbolic umbilic function. The observations presented here on the behavior of waves near turning points should aid the development of improved reduced wave models to be used, for example, in designing modern nuclear fusion experiments.

physics.plasm-ph↗

arXiv2022

Metaplectic geometrical optics for ray-based modeling of caustics: Theory and algorithms

The optimization of radiofrequency-wave (RF) systems for fusion experiments is often performed using ray-tracing codes, which rely on the geometrical-optics (GO) approximation. However, GO fails at caustics such as cutoffs and focal points, erroneously predicting the wave intensity to be infinite. This is a critical shortcoming of GO, since the caustic wave intensity is often the quantity of interest, e.g. RF heating. Full-wave modeling can be used instead, but the computational cost limits the speed at which such optimizations can be performed. We have developed a less expensive alternative called metaplectic geometrical optics (MGO). Instead of evolving waves in the usual $\textbf{x}$ (coordinate) or $\text{k}$ (spectral) representation, MGO uses a mixed $\textbf{X} \equiv \textsf{A}\textbf{x} + \textsf{B}\textbf{k}$ representation. By continuously adjusting the matrix coefficients $\textsf{A}$ and $\textsf{B}$ along the rays, one can ensure that GO remains valid in the $\textbf{X}$ coordinates without caustic singularities. The caustic-free result is then mapped back onto the original $\textbf{x}$ space using metaplectic transforms. Here, we overview the MGO theory and review algorithms that will aid the development of an MGO-based ray-tracing code. We show how using orthosymplectic transformations leads to considerable simplifications compared to previously published MGO formulas. We also prove explicitly that MGO exactly reproduces standard GO when evaluated far from caustics (an important property which until now has only been inferred from numerical simulations), and we relate MGO to other semiclassical caustic-removal schemes published in the literature. This discussion is then augmented by an explicit comparison of the computed spectrum for a wave bounded between two cutoffs.

physics.plasm-ph↗

arXiv2021

Metaplectic geometrical optics for modeling caustics in uniform and nonuniform media

As an approximate theory that is highly regarded for its computational efficiency, geometrical optics (GO) is widely used for modeling waves in various areas of physics. However, GO fails at caustics, which significantly limits its applicability. A new framework, called metaplectic geometrical optics (MGO), has recently been developed that allows caustics of certain types to be modeled accurately within the GO framework. Here, we extend MGO to the most general case. To illustrate our new theory, we also apply it to several sample problems, including calculations of two-dimensional wavefields near fold and cusp caustics. In contrast with traditional-GO solutions, the corresponding MGO solutions are finite everywhere and approximate well the true wavefield near these caustics.

physics.optics↗

arXiv2021

Exactly unitary discrete representations of the metaplectic transform for linear-time algorithms

The metaplectic transform (MT), a generalization of the Fourier transform sometimes called the linear canonical transform, is a tool used ubiquitously in modern optics, for example, when calculating the transformations of light beams in paraxial optical systems. The MT is also an essential ingredient of the geometrical-optics modeling of caustics that was recently proposed by the authors. In particular, this application relies on the near-identity MT (NIMT); however, the NIMT approximation used so far is not exactly unitary and leads to numerical instability. Here, we develop a discrete MT that is exactly unitary, and approximate it to obtain a discrete NIMT that is also unitary and can be computed in linear time. We prove that the discrete NIMT converges to the discrete MT when iterated, thereby allowing the NIMT to compute MTs that are not necessarily near-identity. We then demonstrate the new algorithms with a series of examples.

physics.optics↗

arXiv2020

Restoring geometrical optics near caustics using sequenced metaplectic transforms

Geometrical optics (GO) is often used to model wave propagation in weakly inhomogeneous media and quantum-particle motion in the semiclassical limit. However, GO predicts spurious singularities of the wavefield near reflection points and, more generally, at caustics. We present a new formulation of GO, called metaplectic geometrical optics (MGO), that is free from these singularities and can be applied to any linear wave equation. MGO uses sequenced metaplectic transforms of the wavefield, corresponding to symplectic transformations of the ray phase space, such that caustics disappear in the new variables, and GO is reinstated. The Airy problem and the quantum harmonic oscillator are studied analytically using MGO for illustration. In both cases, the MGO solutions are remarkably close to the exact solutions and remain finite at cutoffs, unlike the usual GO solutions.

physics.optics↗

arXiv2019

Pseudo-differential representation of the metaplectic transform and its application to fast algorithms

The metaplectic transform (MT), also known as the linear canonical transform, is a unitary integral mapping which is widely used in signal processing and can be viewed as a generalization of the Fourier transform. For a given function $ψ$ on an $N$-dimensional continuous space $\textbf{q}$, the MT of $ψ$ is parameterized by a rotation (or more generally, a linear symplectic transformation) of the $2N$-dimensional phase space $(\textbf{q},\textbf{p})$, where $\textbf{p}$ is the wavevector space dual to $\textbf{q}$. Here, we derive a pseudo-differential form of the MT. For small-angle rotations, or near-identity transformations of the phase space, it readily yields asymptotic \textit{differential} representations of the MT, which are easy to compute numerically. Rotations by larger angles are implemented as successive applications of $K \gg 1$ small-angle MTs. The algorithm complexity scales as $O(K N^3 N_p)$, where $N_p$ is the number of grid points. We present a numerical implementation of this algorithm and discuss how to mitigate the associated numerical instabilities.

physics.comp-ph↗

arXiv2018

Mode-conversion of the extraordinary wave at the upper hybrid resonance in the presence of small-amplitude density fluctuations

In spherical tokamaks, the electron plasma frequency is greater than the electron cyclotron frequency. Electromagnetic waves in the electron cyclotron range of frequencies are unsuitable for directly heating such plasmas due to their reduced accessibility. However, mode-conversion of the extraordinary wave to the electron Bernstein wave (X-B mode-conversion) at the upper hybrid resonance makes it possible to efficiently couple externally-launched electromagnetic wave energy into an overdense plasma core. Traditional mode-conversion models describe an X-mode wave propagating in a potential containing two cutoffs that bracket a single wave resonance. Often, however, the mode-conversion region is in the edge, where turbulent fluctuations and blobs can generate abrupt cutoffs and scattering of the incident X-mode wave. We present a new framework for studying the X-B mode-conversion which makes the inclusion of these fluctuations analytically tractable. In the new approach, the high-field cutoff is modelled as an infinite barrier, which manifests as a boundary condition applied to a wave equation involving only one cutoff adjacent to the resonance on the low-field side. The new model reproduces the main features of the previous approach, yet is more suitable for analyzing experimental observations and extrapolating to higher dimensions. We then develop an analytical estimate for the effect of small-amplitude, quasi-monochromatic density fluctuations on the X-B mode-conversion efficiency using perturbation theory. We find that Bragg backscattering of the launched X-mode wave reduces the mode-conversion efficiency significantly when the fluctuation wavenumber is resonant with the wavenumber of the incident X-mode wave. These analytical results are corroborated by numerically integrating the mode-conversion equations.

physics.plasm-ph↗