Ray-tracing Code Research Articles

The Polarization of X-Rays from Warped Black Hole Accretion Disks

Abstract It is commonly assumed that in black hole (BH) accretion disks the angular momenta of the disk and the BH are aligned. However, for a significant fraction of stellar-mass BHs and supermassive BHs, the momenta may not be aligned. In such systems, the interplay of disk viscosity and general relativistic frame dragging can cause the disk to warp or break into two (or more) distinct planes; this is called the Bardeen–Petterson effect. We have developed a general relativistic ray-tracing code to find the energy spectra and polarization of warped accretion disks, accounting for the emission from the disk and for photons reflecting one or multiple times off the warped accretion disk segments. We find that polarization angle can be used to give a lower limit on the misalignment angle when a previous measurement of the jet, which is thought be aligned with the BH angular momentum, can be spatially resolved.

Real-time control of the deposition location of ECRH in the LHD

A real-time control system for the deposition location of electron cyclotron resonance heating (ECRH) has been newly developed and applied to experiments on the Large Helical Device (LHD). Appropriate settings for a steerable launcher for ECRH were obtained by evaluating the deposition location and the absorption power for various electron density profiles using a ray-tracing code. The real-time deposition location control system adjusts launcher settings to improve the first-pass absorption of the refracted electron cyclotron wave, based on the ray-tracing calculations. The control system was designed to use a fast field programmable gate array (FPGA). The FPGA processes in real time the calculation of characteristic parameters regarding the density profile and the calculation of target positions requested for rotation control of a steering mirror of the launcher. The real-time deposition location control during ECRH discharges on the LHD functioned successfully in maintaining the absorption power higher than that without the control, which resulted from the deposition location maintained in the plasma core region.

Two-scale Monte Carlo ray tracing for canopy-leaf vector radiative transfer coupling

Canopy reflectance simulation was widely developed using Monte Carlo (MC) ray tracing. Nevertheless, the proposed models assume leaf as Bi-Lambertian medium. Based on the recently developed leaf MC ray tracing code, this study proposes to couple MC ray tracing simulations on leaf and canopy levels. Firstly, at the first level, the bidirectional scattering distribution function (BSDF) is computed for unpolarized incoming rays as well as some common states of polarization producing together a polarization decomposition basis, allowing to derive the Stokes phase function. Moreover, discretizing both incident and scattering angles over the sphere allows to produce a database of all possible Stokes phase functions. Secondly, at the canopy level, the reflectance is simulated using ray tracing technique, when ray is intercepted, the scattering is done considering the appropriate Stokes phase function in the leaf database. Simulation of multiple wavelengths is accelerated based on a new MC weighted sampling technique permitting to consider the same tracing for all the wavelengths together. Simulation results show the relevance of such modeling compared to traditional models. Indeed, from one side the canopy bidirectional reflectance depends on the leaf BSDF thus if leaves are assumed Bi-Lambertian surfaces leads to inaccurate results, and from the other side, the reflectance is sensitive to polarization and neglecting it affects the results mainly when the incident light is polarized. Comparison with actual polarized reflectance measurements presented in literature shows good agreement with same trends and variation ranges. Quantitative validation of our canopy level model is done using the ROMC web-tool. Reflectance RMSE between our simulations and the ROMC reference is lower than 0.02.

MPRAD: A Monte Carlo and ray-tracing code for the proton radiography in high-energy-density plasma experiments.

Proton radiography is used in various high-energy-density (HED) plasma experiments. In this paper, we describe a Monte Carlo and ray-tracing simulation tool called multimegaelectronvolt proton radiography (MPRAD) that can be used for modeling the deflection of proton beams in arbitrary three dimensional electromagnetic fields as well as the diffusion of the proton beams by Coulomb scattering and stopping power. The Coulomb scattering and stopping power models in cold matter and fully ionized plasma are combined using interpolation. We discuss the application of MPRAD in a few setups relevant to HED plasma experiments where the plasma density can play a role in diffusing the proton beams and affecting the prediction and interpretation of the proton images. It is shown how the diffusion due to plasma density can affect the resolution and dynamical range of the proton radiography.

Modeling non-thermal emission from the jet-launching region of M 87 with adaptive mesh refinement

Context. The galaxy M 87 harbors a kiloparsec-scale relativistic jet, whose origin coincides with a compact source thought to be a supermassive black hole. Observational millimeter very long baseline interferometry campaigns are capable of resolving the jet-launching region at the scale of the event horizon. In order to provide a context for interpreting these observations, realistic general-relativistic magnetohydrodynamical (GRMHD) models of the accretion flow are constructed. Aims. Electrons in the jet are responsible for the observed synchrotron radiation, which is emitted in frequencies ranging from radio to near-infrared (NIR) and optical. The characteristics of the emitted radiation depend on the shape of the electrons’ energy-distribution function (eDF). The dependency on the eDF is omitted in the modeling of the first Event Horizon Telescope results. In this work, we aim to model the M 87 spectral-energy distribution from radio up to optical frequencies using a thermal-relativistic Maxwell–Jüttner distribution, as well as a relativistic κ-distribution function. The power-law index of the eDF is modeled based on sub-grid, particle-in-cell parametrizations for sub-relativistic reconnection. Methods. A GRMHD simulation in Cartesian–Kerr–Schild coordinates, using eight levels of adaptive mesh refinement (AMR), forms the basis of our model. To obtain spectra and images, the GRMHD data was post-processed with the ray-tracing code RAPTOR, which is capable of ray tracing through GRMHD simulation data that is stored in multi-level AMR grids. The resulting spectra and images maps are compared with observations. Results. We obtain radio spectra in both the thermal-jet and κ-jet models consistent with radio observations. Additionally, the κ-jet models also recover the NIR and optical emission. The images show a more extended structure at 43 GHz and 86 GHz and more compact emission at 228 GHz. The models recover the observed source sizes and core shifts and obtain a jet power of ≈1043 ergs s−1. In the κ-jet models, both the accretion rates and jet powers are approximately two times lower than the thermal-jet model. The frequency cut-off observed at ν ≈ 1015 Hz is recovered when the accelerator size is 106 − 108 cm, this could potentially point to an upper limit for plasmoid sizes in the jet of M 87.

Radiometry for the vertical electron cyclotron emission from the runaway electrons at the COMPASS tokamak.

Due to an increased interest in runaway electron (RE) phenomena in tokamak research, the need for diagnostics of runaway electron population in plasma has emerged. A novel diagnostic of the nonthermal electron cyclotron emission from runaway electrons can be utilized for this purpose. It was designed and installed at the COMPASS tokamak based on the available heterodyne radiometer. The vertical ECE (V-ECE) system uses a 16-channel heterodyne radiometer with a vertically placed E2-band horn antenna with a 76.5-90 GHz frequency range front-end. Simulations with the ray-tracing SPECE code have shown a measurement feasibility of the runaway electrons with energies up to 1 MeV. Due to a low optical depth of the plasma in COMPASS during RE discharges, reflected waves from the tokamak wall can be detected as well. First results show strong connection with other RE diagnostics at COMPASS. The V-ECE can obtain important information about RE population evolution and primary generation mechanism.

The particle tracking code BBCNI for large negative ion beams and their diagnostics

Heating and current drive in the next generation tokamak ITER requires the use of large and powerful neutral beams, generated by a precursor ion beam from an ion source around 1 m × 2 m in cross-section. To avoid energy losses and component damage, strict requirements are placed on the divergence and uniformity of this ion beam, which is comprised of many individual beamlets. Understanding, controlling, and predicting the behaviour of these large ion beams requires knowledge of these individual beamlets and their interactions with one another. This is hindered by available experimental diagnostics on these large beams typically only having access to volume averaged information. A forward simulation of beam diagnostics would allow the connection of experimental results with otherwise unobtainable individual beamlet properties. The particle tracking and ray tracing code Bavarian Beam Code for Negative Ions was developed for this reason, and takes into account the interaction of individual component beamlets with whole-beam diagnostics to produce synthetic data that can be compared with experimental results. In this work a significantly reworked and upgraded version of the code is presented and example results are given and analysed for the ITER relevant test facility BATMAN Upgrade. It is shown how the simulation can recreate experimental results, and that one must consider the whole beam in order to do so. The impact of beamlet mixing on beam emission spectroscopy results is shown, as is the importance of long range magnetic fields on the beam transport. The capabilities and limitations of the code are discussed with a view toward application to ITER size ion sources.

IonoSeis: A Package to Model Coseismic Ionospheric Disturbances

We present the framework of the modeling package IonoSeis. This software models Global Navigation Satellite System (GNSS) derived slant total electron content (sTEC) perturbations in the ionosphere due to the interaction of the neutral atmosphere and charged particles in the ionosphere. We use a simplified model to couple the neutral particle momentum into the ionosphere and reconstruct time series of sTEC perturbations that match observed data in both arrival time and perturbation shape. We propagate neutral atmosphere disturbances to ionospheric heights using a three-dimensional ray-tracing code in spherical coordinates called Windy Atmospheric Sonic Propagation (WASP3D), which works for a stationary or non-stationary atmospheric models. The source of the atmosphere perturbation can be an earthquake or volcanic eruption; both couple significant amounts of energy into the atmosphere in the frequency range of a few Millihertz. We demonstrate the output of the code by comparing modeled sTEC perturbation data to the observed perturbation recorded at GNSS station BTNG (Bitung, Indonesia) immediately following the 28 September 2018, Sulawesi-Palu earthquake. With this framework, we provide a software to couple the lithosphere, atmosphere, and ionosphere that can be used to study post-seismic ionospherically-derived signals.

Modeling the electron cyclotron emission below the fundamental resonance in ITER

The electron cyclotron emission (ECE) in fusion devices is non-trivial to model in detail at frequencies well below the fundamental resonance where the plasma is optically thin. However, doing so is important for evaluating the background for microwave diagnostics operating in this frequency range. Here we present a general framework for estimating the ECE levels of fusion plasmas at such frequencies using ensemble-averaging of rays traced through many randomized wall reflections. This enables us to account for the overall vacuum vessel geometry, self-consistently include cross-polarization, and quantify the statistical uncertainty on the resulting ECE spectra. Applying this to ITER conditions, we find simulated ECE levels that increase strongly with frequency and plasma temperature in the considered range of 55–75 GHz. At frequencies smaller than 70 GHz, we predict an X-mode ECE level below 100 eV in the ITER baseline plasma scenario, but with corresponding intensities reaching keV levels in the hotter hybrid plasma scenario. Benchmarking against the SPECE raytracing code reveals good agreement under relevant conditions, and the predicted strength of X-mode to O-mode conversion induced by wall reflections is consistent with estimates from existing fusion devices. We discuss possible implications of our findings for ITER microwave diagnostics such as ECE, reflectometry, and collective Thomson scattering.

Model-based real-time plasma electron density profile estimation and control on ASDEX Upgrade and TCV

Real-time plasma electron density profile estimation and control are essential in the operation of future tokamaks. In particular, the robustness against diagnostics failure and disturbances is important for long pulse operation.A model-based approach to profile estimation is implemented on the control systems of ASDEX Upgrade and TCV, which is able to merge information from various diagnostics for both core and edge density, as well as systematically handling diagnostic failure. The model used for profile estimation is employed to tune a feedback controller before an experiment, thereby reducing the experimental time required for tuning.Subsequently, this observer and controller have been employed in scientific experiments on ASDEX Upgrade and TCV. On ASDEX Upgrade, the density profile estimator was used in high-density pellet-fuelled discharges, providing a more reliable real-time estimate of the core density for feedback control than previously achieved. On TCV, in experiments on integrated pressure and safety factor profile control, the density profile estimator and feedback controller provide a constant density despite disturbances from time-varying ECCD power. Additionally, the real-time density profiles provide an essential input for other real-time plasma state estimation codes including Electron Cyclotron ray tracing codes, contributing to a complete real-time estimation of the entire plasma state.

Spectral and Timing Analysis of the Accretion-powered Pulsar 4U 1626–67 Observed with Suzaku and NuSTAR

Abstract We present an analysis of the spectral shape and pulse profile of the accretion-powered pulsar 4U 1626−67 observed with Suzaku and Nuclear Spectroscopic Telescope Array (NuSTAR) during a spin-up state. The pulsar, which experienced a torque reversal to spin-up in 2008, has a spin period of ∼7.7 s. Comparing the phase-averaged spectra obtained with Suzaku in 2010 and with NuSTAR in 2015, we find that the spectral shape changed between the two observations: the 3–10 keV flux increased by ∼5%, while the 30–60 keV flux decreased significantly by ∼35%. Phase-averaged and phase-resolved spectral analysis shows that the continuum spectrum observed by NuSTAR is well described by an empirical negative and positive power law times exponential continuum with an added broad Gaussian emission component around the spectral peak at ∼20 keV. Taken together with the observed value obtained from the Fermi/gamma-ray burst monitor data, we conclude that the spectral change between the Suzaku and NuSTAR observations was likely caused by an increase in the accretion rate. We also report the possible detection of asymmetry in the profile of the fundamental cyclotron line. Furthermore, we present a study of the energy-resolved pulse profiles using a new relativistic ray tracing code, where we perform a simultaneous fit to the pulse profiles assuming a two-column geometry with a mixed pencil- and fan-beam emission pattern. The resulting pulse profile decompositions enable us to obtain geometrical parameters of accretion columns (inclination, azimuthal and polar angles) and a fiducial set of beam patterns. This information is important to validate the theoretical predictions from radiation transfer in a strong magnetic field.

Public Release of RELXILL_NK: A Relativistic Reflection Model for Testing Einstein’s Gravity

Abstract We present the public release version of relxill_nk, an X-ray reflection model for testing the Kerr hypothesis and general relativity. This model extends the relxill model that assumes the black hole (BH) spacetime is described by the Kerr metric. We also present relxilllp_nk, the first non-Kerr X-ray reflection model with a lamppost corona configuration, as well as all other models available in the full relxill_nk package. In all models the relevant relativistic effects are calculated through a general relativistic ray-tracing code that can be applied to any well-behaved, stationary, axisymmetric, and asymptotically flat BH spacetime. We show that the numerical error introduced by using a ray-tracing code is not significant compared with the observational error present in current X-ray reflection spectrum observations. In addition, we present the reflection spectrum for the Johannsen metric as calculated by relxill_nk.

Numerical design approval of W7-X port liners

The world’s largest operating stellarator, Wendelstein 7-X (W7-X) is operating since 2015. One of its final goals is the demonstration of steady-state operation capabilities with pulse-lengths of up to 30 min. Such pulses require a constant heating of the plasma due to losses by plasma-wall interactions, particle drift and radiation. The latter are assumed to occur with resulting loads of up to 10 MW in total on the surfaces of plasma-facing components (PFC) and ports. Thus, a shielding is required for the port walls, in order to avoid wall temperatures above 80 °C in average, which otherwise would cause unsustainable heat loads on the superconducting magnetic coil system of W7-X.Furthermore, it is necessary to protect the sensitive weld seam, connecting ports and PV from direct thermal radiation. Plasma radiation would directly expose this weld, due to the gap between port and in vessel components. The paper presents the determination of the relevant heat loads, based on the 1-way ray-tracing code of S. Bozhenkov for the whole W7-X. On an exemplarily chosen port, the capability of the port-liner design to maintain the steady-state operation under the computed heat loads is demonstrated.

Measurement of stray millimeter-wave radiation from a 70-GHz ECH/ECCD system in Heliotron J

Stray millimeter-wave radiation from a 70-GHz electron cyclotron heating and current drive (ECH/ECCD) system has been measured in the Heliotron J helical device. Two rotatable diode detectors located at the outboard side ports are used to pick up the stray radiation: one is installed at the ECH launcher port and the other is installed at a toroidal angle of 135 deg far from the ECH launcher port. Both detectors are rotated to measure the polarization of the stray radiation. The results show that at the toroidal position far from the ECH launcher, the polarization is not fully randomized before plasma breakdown, whereas the polarization is uniform after a quasi-stationary plasma is generated. The polarization near the ECH launcher is not uniform even in a quasi-stationary plasma. Plasma experiments scanning the electron density indicate that the EC power absorption estimated from the stray radiation at the toroidal position far from the ECH launcher is correlated with the single-pass absorption rate calculated by the TRAVIS ray-tracing code. These results indicate that the diagnostic using a simple diode detector can be used as a real-time monitor of EC power absorption only when the plasma with finite density is produced and the detector is placed far from the ECH launcher port.

Rossby wave instability and high-frequency quasi-periodic oscillations in accretion discs orbiting around black holes

Context. The rather elusive high-frequency quasi-periodic oscillations (HFQPOs) observed in the X-ray light curve of black holes have been seen in a wide range of frequencies, even within one source. Also notable is the detection of “pairs” of HFQPOs with a close-to-integer ratio between the frequencies. Aims. The aim of this paper is to investigate some of the possible observables that we could obtain from the Rossby wave instability (RWI) active in the accretion disc surrounding the compact object. Methods. Using the newly developed GR-AMRVAC code able to follow the evolution of the RWI in a full general relativistic framework, we explore how RWI can reproduce observed HFQPO frequency ratios and whether or not it is compatible with observations. In order to model the emission coming from the disc we have linked our general relativistic simulations to the general relativistic ray-tracing GYOTO code and delivered synthetic observables that can be confronted with actual data from binary systems hosting HFQPOs. Results. We demonstrate that some changes in the physical conditions prevailing in the part of the disc where RWI can be triggered lead to various dominant RWI modes whose ratio recovers frequency ratios observed in various X-ray binary systems. In addition we also show that when RWI is triggered near to the last stable orbit of a spinning black hole, the amplitude of the X-ray modulation increases with the spin of the black hole. Revisiting published data on X-ray binary systems, we show that this type of relationship actually exists in five systems where an indirect measurement of the spin of the black hole is available.

Interferometric observations of SiO thermal emission in the inner wind of M-type AGB stars IK Tauri and IRC+10011.

Asymptotic giant branch (AGB) stars go through a process of strong mass loss that involves pulsations of the atmosphere, which extends to a region in which the conditions are adequate for dust grains to form. Radiation pressure acts on these grains which, coupled to the gas, drive a massive outflow. The details of this process are not clear, including which molecules are involved in the condensation of dust grains. We seek to study the role of the SiO molecule in the process of dust formation and mass loss in M-type AGB stars. Using the IRAM NOEMA interferometer we observed the 28SiO and 29SiO J = 3 - 2, v = 0 emission from the inner circumstellar envelope of the evolved stars IK Tau and IRC+10011. We computed azimuthally averaged emission profiles to compare the observations to models using a molecular excitation and ray-tracing code for SiO thermal emission. We observe circular symmetry in the emission distribution. We also find that the source diameter varies only marginally with radial velocity, which is not the expected behaviour for envelopes expanding at an almost constant velocity. The adopted density, velocity, and abundance laws, together with the mass-loss rate, which best fit the observations, give us information concerning the chemical behaviour of the SiO molecule and its role in the dust formation process. The results indicate that there is a strong coupling between the depletion of gas-phase SiO and gas acceleration in the inner envelope. This could be explained by the condensation of SiO into dust grains.

Study for the microwave interferometer for high densities plasmas on COMPASS-U tokamak

The present COMPASS tokamak at the Institute of Plasma Physics in Prague is equipped with the 2-mm interferometer, which gives a possibility to measure line-average electron densities up to 1.2×1020 m−3. A high magnetic field tokamak COMPASS-U will be designed and built to replace COMPASS. Higher line-average plasma densities in COMPASS-U of about 5×1020 m−3 will require a new design of the interferometer. This will provide measurements in a wide density range and will allow using a real-time gas puff density feedback. A solution based on the solid-state technology is proposed. The system will use two microwave transceivers with close sub-millimeter wavelengths and will fulfill the principle of the unambiguous measurement. An assessment of signal corrections corresponding to non-linearity effects caused by plasma refractive index is performed. The ray-tracing FIESTA-8 code was used to model the propagation of the probing waves through COMPASS-U plasmas.

Ray tracing calculations in simulated propellant flames with detailed chemistry.

Optical measurements in propellant flames are necessary to understand the combustion physics, yet these conditions provide challenges in probing the flame and may introduce uncertainty into the measurement. This work reports the use of simulations of an ammonium perchlorate propellant flame with finite rate chemistry to understand the role of ammonium perchlorate particle size and pressure on the uncertainty of imaging-based measurements on propellant flames. A two-dimensional ray tracing code was developed to incorporate the effects of the species concentration and temperature gradients on ray refraction within propellant flames. It was determined that the effects of the flame structure based upon pressure and oxidizer particle size increases the amount of ray deflection particularly at high pressures explaining a cause for challenges of aluminum agglomerate measurements at elevated pressure. This framework shows promise for understanding limitations and uncertainties of optical measurements for reacting and turbulent flows.

Magnetized accretion disks around Kerr black holes with scalar hair: Constant angular momentum disks

Testing the true nature of black holes - the no-hair hypothesis - will become increasingly more precise in the next few years as new observational data is collected in both the gravitational wave channel and the electromagnetic channel. In this paper we consider numerically generated spacetimes of Kerr black holes with synchronised scalar hair and build stationary models of magnetized thick disks (or tori) around them. Our approach assumes that the disks are not self-gravitating, they obey a polytropic equation of state, the distribution of their specific angular momentum is constant, and they are marginally stable, i.e. the disks completely fill their Roche lobe. Moreover, contrary to existing approaches in the literature, our models are thermodinamically relativist, as the specific enthalpy of the fluid can adopt values significantly larger than unity. We study the dependence of the morphology and properties of the accretion tori on the type of black hole considered, from purely Kerr black holes with varying degrees of spin parameter, namely from a Schwarzschild black hole to a nearly extremal Kerr case, to Kerr black holes with scalar hair with different ADM mass and horizon angular velocity. Comparisons between the disk properties for both types of black holes are presented. The sequences of magnetized, equilibrium disks models discussed in this study can be used as initial data for numerical relativity codes to investigate their dynamical (non-linear) stability and used in tandem with ray-tracing codes to obtain synthetic images of black holes (i.e. shadows) in astrophysically relevant situations where the light source is provided by an emitting accretion disk.

Light scattering from a drop with an embedded particle and its exploitation in the time-shift technique

This study is devoted to light scattering from drops with an embedded particle, as would be expected in an encapsulation/coating process or with spraying of metallic paints. A ray-tracing approach is taken, in which the polarization and intensity of all rays impinging onto a defined detector aperture are documented, allowing the signal generation arising from the drop passing through a plane wave or focused Gaussian beam to be simulated. For validation of the ray-tracing code, comparisons are drawn to scattering from pure liquid drops, obtained using the Lorenz–Mie solution. When using a highly focused incident beam, the scattering corresponds to the optical arrangement of the time-shift technique and allows the capabilities of that technique to measure drops with embedded particles to be explored. The resulting detector signals for a drop with an embedded spherical particle (encapsulated particles) or an embedded circular flake (metallic paint drop) have been simulated. These signals are compared with signals arising from pure liquid drops and features are identified which could be exploited for detecting the embedded particles using the time-shift technique.