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Brace yourself for a fun challenge: build a photorealistic 3D renderer from scratch! In just a couple of weeks, build a ray tracer that renders beautiful scenes with shadows, reflections, refraction effects, and subjects composed of various graphics primitives: spheres, cubes, cylinders, triangles, and more. With each chapter, implement another piece of the puzzle and move the renderer forward. Use whichever language and environment you prefer, and do it entirely test-first, so you know it's correct.

Lightning strikes generate broadband electromagnetic signals. At Extremely Low Frequencies (ELF), these signals partly leak into the ionosphere and produce so‐called Lightning Generated (LG) whistlers that the Absolute Scalar Magnetometers on board the ESA Swarm satellites can detect. The dispersion of LG whistlers has been empirically described by Eckersley (1935, ): T=D/f$T=D/\\sqrt{f}$ , where T$T$is the group delay of a wave packet, f$f$its frequency and D$D$is called the dispersion of the whistler. Although we find that ELF LG whistlers detected by Swarm generally follow this law, this is not the case for those detected close to the magnetic equator. Modeling ELF LG whistlers with ray‐tracing technique successfully predicts the observed dispersions and allows us to decipher what makes ELF LG equatorial whistlers different. For such whistlers, low frequencies follow rays with shorter paths than high frequencies, partly compensating for the fact that high frequencies travel faster.

Hiss waves play a critical role in shaping Earth's radiation belts and mediating magnetosphere‐ionosphere energy transfer. Intense hiss emissions are frequently generated within dynamic plasmaspheric plumes through linear and nonlinear wave‐particle interactions. However, the contribution of plume hiss to the spatial distribution of hiss throughout the plasmasphere is not yet well quantified. In this study, we perform ray‐tracing simulations to investigate the global propagation of plume hiss under varying plume morphologies, including different widths and levels of density lumpiness. We find that most hiss power is confined near the local time sector of the plume. Narrower plumes with embedded density ducts significantly enhance earthward wave guidance into the plasmaspheric core, compared to wide, smooth plumes. Furthermore, a subset of rays guided azimuthally along the plasmapause can serve as seed waves for intense dayside hiss. Our results highlight the role of plume hiss in shaping the global‐scale distribution of hiss waves.

With the rapid development of X‐ray free‐electron lasers (XFELs) that can generate ultrashort X‐ray pulses with a duration range from attoseconds to femtoseconds, the study of ultrashort XFEL pulse propagation in beamline systems is increasingly important, especially in dispersive beamline systems. We developed a 6D phase space ray‐tracing method to simulate pulse propagation in dispersive soft X‐ray optical systems. We validated this method by simulating a typical dispersive optical system: a grating monochromator. The simulation indicated that the spatiotemporal properties such as pulse front tilt, pulse front rotation and angular dispersion can be described. Using this approach, we performed a start‐to‐end simulation of the Shenzhen Superconducting Soft X‐ray Free Electron Laser (S3FEL) FEL‐1 beamline. Compared with the 3D pulse propagation method based on Fourier optics, this significantly reduces the simulation time. Our work provides a useful tool for X‐ray beamline systems design. This work develops a 6D phase space tracing module in the FURION software. The 6D phase space tracing provides a solution for the rapid simulation of ultrashort pulse propagation in X‐ray beamlines, especially in dispersive beamline systems.

Recent radio frequency (RF) current drive experiments in EAST provide an opportunity to investigate RF synergy effects between electron cyclotron (EC) and lower hybrid (LH) current drive. Synergy current is the excess current that can arise from overlapping two wave-particle resonance bands in the velocity phase space. In this work, a ray-tracing and Fokker–Planck code package, GENRAY/CQL3D, is used to model and investigate the phase space interaction of two waves for EAST. The target plasma features a high central electron temperature of 6.5 keV, promoting Landau damping of the LH power on-axis that overlaps with the EC power resonance region. The GENRAY/CQL3D code evaluates a self-consistent electron distribution function in the presence of two RF quasilinear diffusion coefficients. A systematic scan in collisional dissipative LH power loss and fast-electron radial transport is performed. Including the divertor SOL in GENRAY and fast-electron radial diffusion in CQL3D can quantitatively provide model total RF currents in line with the experimental range. Radial transport operator broadens and smooths the radial region of synergistic current generation. The impact of LH wave scattering on the synergistic interaction is examined by introducing the LH wave scattering angle in a heuristic manner. The sensitivity analysis is presented. Furthermore, a numerical scan of the ECCD injection angles is conducted to evaluate the synergistic interactions. The roles of LH current drive and ECCD in synergistic current generation are further examined through a power scan of both power sources.

Saturn Kilometric Radiation (SKR), being the dominant radio emission at Saturn, has been extensively investigated. The low‐frequency extension of SKR is of particular interest due to its strong association with Saturn's magnetospheric dynamics. However, the highly anisotropic beaming of SKR poses challenges for observations. In most cases, the propagation of SKR is assumed to follow straight‐line paths. We explore the propagation characteristics of SKR across different frequencies in this study. An extended equatorial shadow region for low‐frequency SKR is identified, resulting from the merging of the Enceladus plasma torus and the previously known equatorial shadow zone. Ray‐tracing simulations reveal that low‐frequency (≲$\\lesssim $ 100 kHz) SKR is unable to enter the shadow region and is instead reflected toward high latitudes. In contrast, high‐frequency SKR (≳$\\gtrsim $ 100 kHz) generally propagates without hindrance. Observations suggest that some low‐frequency SKR can enter the shadow region through reflection by the magnetosheath or leakage from the plasma torus. Plain Language Summary Saturn Kilometric Radiation (SKR) is a natural electromagnetic wave generated in Saturn's high‐latitude region along its magnetic field lines. Variations in SKR frequency could offer insights into Saturn's magnetic conditions, especially its interaction with the solar wind. However, the observed frequency characteristics of SKR depend on viewing geometry due to its directional nature. While past studies assumed SKR travels in straight lines, this may not hold true for low‐frequency SKR. These emissions can change direction when they encounter dense plasma, similar to light reflecting off a mirror or bending when entering water. At Saturn's equatorial region, the plasma torus created by Enceladus, one of Saturn's moons, contains dense plasma and significantly affects radio wave propagation. Our study investigates the distribution of SKR at different frequencies and identifies a shadow region where low‐frequency SKR emissions are rarely seen. Using numerical simulations of ray propagation paths, we discover that low‐frequency SKR emissions cannot reach these shadow regions because they are reflected by the dense plasma torus. However, occasionally, we observe low‐frequency SKR in the shadow region, suggesting the possibility of reflection by Saturn's magnetosheath or leakage through the plasma torus. Key Points The propagation characteristics of Saturn Kilometric Radiation (SKR) are established statistically and by ray‐tracing A shadow region of the low‐frequency SKR near the equatorial region at large radial distances is discovered and discussed Low‐frequency SKR may enter the shadow region due to torus leakage or reflection at the magnetosheath

Current GPS positioning accuracy in urban areas is still unsatisfactory for various applications, including pedestrian navigation and autonomous driving. Due to the ineffectiveness of special corrector designs against non-line-of-sight (NLOS) reception, the research regarding NLOS signals has been increasing in the recent years. This study first develops an algorithm to detect NLOS signals from the pseudorange measurements by using a 3D building model, ray-tracing simulation, and known receiver position. According to the analysis of 24 h of collected NLOS data, a new finding is that NLOS pseudorange delay is highly correlated with the elevation angle of satellite instead of the received signal strength. Thus, we further propose an innovative NLOS model using two variables, the elevation angle and the distance between the receiver and building that reflect the NLOS. The proposed model is evaluated in both pseudorange and position domains. Based on the experiment results regarding pseudorange error, the difference between the proposed model and the collected NLOS measurement is very small. Finally, the proposed model is applied to a hypothesis-based positioning method and achieves about 6.3 m in terms of horizontal positioning accuracy, which is only slightly worse than the method applied with ray-tracing simulation.

In complex underground parking scenarios, non-line-of-sight (NLOS) obstructions significantly impede positioning signals, presenting substantial challenges for accurate vehicle localization. While traditional positioning approaches primarily focus on mitigating NLOS effects to enhance accuracy, this research adopts an alternative perspective by leveraging NLOS propagation as valuable information, enabling precise positioning in NLOS-dominated environments. We introduce an innovative NLOS positioning framework based on the generalized source (GS) technique, which employs ray-tracing (RT) to transform NLOS paths into equivalent line-of-sight (LOS) paths. A novel GS filtering and weighting strategy to establish initial weights for the nonlinear equation system. To combat significant NLOS noise interference, a robust iterative reweighted least squares (W-IRLS) method synergizes initial weights with optimal position estimation. Integrating ultra-wideband (UWB) delay and angular measurements, four distinct localization modes based on W-IRLS are developed: angle-of-arrival (AOA), time-of-arrival (TOA), AOA/TOA hybrid, and AOA/time-difference-of-arrival (TDOA) hybrid. The comprehensive experimental and simulation results validate the exceptional effectiveness and robustness of the proposed NLOS positioning framework, demonstrating positioning accuracy up to 0.14 m in specific scenarios. This research not only advances the state of the art in NLOS positioning but also establishes a robust foundation for high-precision localization in challenging environments.

Improvements in electron cyclotron resonance heating (ECRH) and current drive (ECCD) predictions are important issues for the design and control of high-performance fusion plasmas in future devices, where these should play a more important role as actuators than in devices to date. A newly developed EC-prediction package based on the quasioptical ray tracing code PARADE revealed in JT-60SA that (i) the radial profiles of both EC power deposition and driven current are broadened and (ii) the net driven current is increased by a few kA/MW, in comparison with conventional predictions due to dissipative diffractive propagation (DDP). The mechanism of DDP is as follows: EC wave beam obliquely passing through the resonant surface is dissipated non-uniformly on its beam cross section, so that the beam trajectory shifts gradually and thus the resonant position also shifts, resulting in the broadened power deposition profile. This novel ECCD and ECRH prediction package based on PARADE is applicable not only to JT-60SA but other existing devices and even, future devices.