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Wavefront reconstruction is a critical component in various optical systems, including adaptive optics, interferometry, and phase contrast imaging. Traditional reconstruction methods often employ either the Cartesian (pixel) basis or the Zernike polynomial basis. While the Cartesian basis is adept at capturing high-frequency features, it is susceptible to overfitting and inefficiencies due to the high number of degrees of freedom. The Zernike basis efficiently represents common optical aberrations but struggles with complex or non-standard wavefronts such as optical vortices, Bessel beams, or wavefronts with sharp discontinuities. This paper introduces a novel approach to wavefront reconstruction using an over-complete phase dictionary combined with sparse representation techniques. By constructing a dictionary that includes a diverse set of basis functions - ranging from Zernike polynomials to specialized functions representing optical vortices and other complex modes - we enable a more flexible and efficient representation of complex wavefronts. Furthermore, a trainable affine transform is implemented to account for misalignment. Utilizing principles from compressed sensing and sparse coding, we enforce sparsity in the coefficient space to avoid overfitting and enhance robustness to noise.

There is ample evidence for magnetic reconnection in the solar system, but it is a nontrivial task to visualize, to determine the proper approaches and frames to study, and in turn to elucidate the physical processes at work in reconnection regions from in-situ measurements of plasma particles and electromagnetic fields. Here an overview is given of a variety of single- and multi-spacecraft data analysis techniques that are key to revealing the context of in-situ observations of magnetic reconnection in space and for detecting and analyzing the diffusion regions where ions and/or electrons are demagnetized. We focus on recent advances in the era of the Magnetospheric Multiscale mission, which has made electron-scale, multi-point measurements of magnetic reconnection in and around Earth's magnetosphere., Comment: submitted to Space Science Reviews (116 pages, incl. 31 figures, 7 tables)

Models for collisionless magnetic reconnection in near-Earth space are distinctly characterized as 2D or 3D. In 2D kinetic models, the frozen-in law for the electron fluid is usually broken by laminar dynamics involving structures set by the electron orbit size, while in 3D models the width of the electron diffusion region is broadened by turbulent effects. We present an analysis of in situ spacecraft observations from the Earth's magnetotail of a fortuitous encounter with an active reconnection region, mapping the observations onto a 2D spatial domain. While the event likely was perturbed by low-frequency 3D dynamics, the structure of the electron diffusion region remains consistent with results from a 2D kinetic simulation. As such, the event represents a unique validation of 2D kinetic, and laminar reconnection models., Comment: Accepted for publication in Geophysical Research Letters. Copyright 2022 American Geophysical Union. Further reproduction or electronic distribution is not permitted. 11 pages. 5 figures

Magnetic wave perturbations are observed in the solar wind and in the vicinity of Earth's bow shock. For such environments, recent work on magnetic pumping with electrons trapped in the magnetic perturbations have demonstrated the possibility of efficient energization of superthermal electrons. Here we also analyze the energization of such energetic electrons for which the transit time through the system is short compared to time scales associated with the magnetic field evolution. In particular, considering an idealized magnetic configuration we show how trapping/detrapping of energetic magnetized electrons can cause effective parallel velocity diffusion. This parallel diffusion, combined with naturally occurring mechanisms known to cause pitch angle scattering, such as Whistler waves, produces enhanced heating rates for magnetic pumping. We find that at low pitch angle scattering rates the combined mechanism enhances the heating beyond the predictions of the recent theory for magnetic pumping with trapped electrons.

The Kelvin-Helmholtz (KH) instability of a shear layer with an initially-uniform magnetic field in the direction of flow is studied in the framework of 2D incompressible magnetohydrodynamics with finite resistivity and viscosity using direct numerical simulations. The shear layer evolves freely, with no external forcing, and thus broadens in time as turbulent stresses transport momentum across it. As with KH-unstable flows in hydrodynamics, the instability here features a conjugate stable mode for every unstable mode in the absence of dissipation. Stable modes are shown to transport momentum up its gradient, shrinking the layer width whenever they exceed unstable modes in amplitude. In simulations with weak magnetic fields, the linear instability is minimally affected by the magnetic field, but enhanced small-scale fluctuations relative to the hydrodynamic case are observed. These enhanced fluctuations coincide with increased energy dissipation and faster layer broadening, with these features more pronounced in simulations with stronger fields. These trends result from the magnetic field reducing the effects of stable modes relative to the transfer of energy to small scales. As field strength increases, stable modes become less excited and thus transport less momentum against its gradient. Furthermore, the energy that would otherwise transfer back to the driving shear due to stable modes is instead allowed to cascade to small scales, where it is lost to dissipation. Approximations of the turbulent state in terms of a reduced set of modes are explored. While the Reynolds stress is well-described using just two modes per wavenumber at large scales, the Maxwell stress is not., Comment: 39 pages, 17 figures, preprint format

A new optimized quasihelically symmetric configuration is described that has the desir-able properties of improved energetic particle confinement, reduced turbulent transportby 3D shaping, and non-resonant divertor capabilities. The configuration presented in thispaper is explicitly optimized for quasihelical symmetry, energetic particle confinement,neoclassical confinement, and stability near the axis. Post optimization, the configurationwas evaluated for its performance with regard to energetic particle transport, idealmagnetohydrodynamic (MHD) stability at various values of plasma pressure, and iontemperature gradient instability induced turbulent transport. The effect of discrete coilson various confinement figures of merit, including energetic particle confinement, aredetermined by generating single-filament coils for the configuration. Preliminary divertoranalysis shows that coils can be created that do not interfere with expansion of thevessel volume near the regions of outgoing heat flux, thus demonstrating the possibilityof operating a non-resonant divertor., Comment: 13 figures, 3 tables

Conceptually, a rough number is a positive integer with no small prime factors. Formally, for real numbers $x$ and $y$, let $\Phi(x,y)$ denote the number of positive integers at most $x$ with no prime factors less than $y$. In this paper we establish the lower bound $\Phi(n,p)\geq \lfloor 2n/p \rfloor +1$ when $p\geq 11$ is prime and $n\geq 2p$., Comment: 16 pages, appendix with 11 tables

Turbulence in space and astrophysical plasmas is governed by the nonlinear interactions between counterpropagating Alfven waves. Here we present the theoretical considerations behind the design of the first laboratory measurement of an Alfven wave collision, the fundamental interaction underlying Alfvenic turbulence. By interacting a relatively large-amplitude, low-frequency Alfven wave with a counterpropagating, smaller-amplitude, higher-frequency Alfven wave, the experiment accomplishes the secular nonlinear transfer of energy to a propagating daughter Alfven wave. The predicted properties of the nonlinearly generated daughter Alfven wave are outlined, providing a suite of tests that can be used to confirm the successful measurement of the nonlinear interaction between counterpropagating Alfven waves in the laboratory., Comment: 14 pages, 4 figures, accepted to Physics of Plasmas

Turbulence is a phenomenon found throughout space and astrophysical plasmas. It plays an important role in solar coronal heating, acceleration of the solar wind, and heating of the interstellar medium. Turbulence in these regimes is dominated by Alfven waves. Most turbulence theories have been established using ideal plasma models, such as incompressible MHD. However, there has been no experimental evidence to support the use of such models for weakly to moderately collisional plasmas which are relevant to various space and astrophysical plasma environments. We present the first experiment to measure the nonlinear interaction between two counterpropagating Alfven waves, which is the building block for astrophysical turbulence theories. We present here four distinct tests that demonstrate conclusively that we have indeed measured the daughter Alfven wave generated nonlinearly by a collision between counterpropagating Alfven waves., Comment: 9 pages, 7 figures (12 panels), accepted for publication in Physics of Plasmas

Two-dimensional spatial solitonic lattices are generated and investigated experimentally and numerically in an SBN:Ce crystal. An enhanced stability of these lattices is achieved by exploiting the anisotropy of coherent soliton interaction, in particular the relative phase between soliton rows. Manipulation of individual soliton channels is achieved by use of supplementary control beams., Comment: 4 pages, 7 figures, submission to PRE-R, Correction: Replacement due to incorrect figure placement