Plasma Temperature Profiles Research Articles

Thermalization and hotspot formation around small primordial black holes

We quantitatively analyze a basic question: what is the stationary solution of the background plasma temperature profile around a black hole (BH)? One may naively expect that the temperature profile continuously decreases from the Hawking temperature at the surface of the BH towards an outer region. We show analytically and numerically that this is not the case because local thermal equilibrium cannot be maintained near the surface of the BH and also because the high-energy particles emitted from Hawking radiation cannot be instantaneously thermalized into the background plasma. The temperature profile has a plateau within a finite distance from the BH, and even the overall amplitude of background temperature at a distance far away from the BH is significantly suppressed compared with the naive expectation. The main reason for these counterintuitive results comes from the fact that the size of the BH is too small that particles of Hawking radiation goes far away within the typical time scale of interactions.

Modelling and Experimental Validation of the Flame Temperature Profile in Atmospheric Plasma Coating Processes on the Substrate

This work presents a characterisation model for the temperature distribution at different substrate depths during the atmospheric plasma spray (APS) coating process. The torch heat flow in this model is simulated as forced convection defined by a surface, a temperature profile, and a convection coefficient. The simulation model considers three plasma temperature profiles of the Al2O3 coating on a 5 mm thickness flat aluminium substrate. The simple and low-cost experimental procedure, based on a thermocouple, measures the plasma plume temperature distribution of the APS coating system, and their results are used to obtain the parameter values of each of the three proposed plasma temperature profiles. The experimental method for in situ non-contact temperature measurements inside the substrate is based on an infrared pyrometry technique and validates the simulation results. The Gaussian temperature profile shows excellent accuracy with the measured temperatures. The Gaussian approach could be a powerful tool for predicting residual stress through a coupled one-way thermal-mechanical analysis of the APS process.

Concept of a Diagnostic System for Measuring the Electron Temperature Profile of Plasma from the Intensity of Electron Cyclotron Emission for the TRT Facility

Concept of a Diagnostic System for Measuring the Electron Temperature Profile of Plasma from the Intensity of Electron Cyclotron Emission for the TRT Facility

Large-database cross-verification and validation of tokamak transport models using baselines for comparison

State-of-the-art 1D transport solvers ASTRA and TRANSP are verified, then validated across a large database of semi-randomly selected, time-dependent DIII-D discharges. Various empirical models are provided as baselines to contextualize the validation figures of merit using statistical hypothesis tests. For predicting plasma temperature profiles, no statistically significant advantage is found for the ASTRA and TRANSP simulators over a baseline empirical (two-parameter) model. For predicting stored energy, a significant advantage is found for the simulators over a baseline empirical model based on confinement time scaling. Uncertainty in the results due to diagnostic and profile fitting uncertainties is approximated and determined to be insignificant due in part to the large quantity of discharges employed in the study. Advantages are discussed for validation methodologies like this one that employ (1) large databases and (2) baselines for comparison that are specific to the intended use-case of the model.

Observation of laser ablation of silicon as a function of pulse length at constant fluence via time-resolved x-ray spectroscopy

We investigate the ablation of silicon as a function of laser pulse length at a constant fluence using time-resolved x-ray spectroscopy data obtained from OMEGA EP experiments at the University of Rochester's Laboratory for Laser Energetics. Our targets consisted of three-layer planar structures composed of Si (50 μm), Cu (25 μm), and SiO2 (500 μm) layers. The Si layer was irradiated by a 351-nm laser with varying pulse widths of 250 ps, 500 ps, 1 ns, and 10 ns while maintaining a constant fluence of ∼27.9 kJ/cm2. Electron temperatures and densities of the ablated plasma were determined by analyzing the time-resolved x-ray spectroscopy data through a comparison of experimental measurements with synthetic results obtained from Si atomic calculations in a steady state and non-local thermodynamic equilibrium. These calculations were computed using PrismSPECT [MacFarlane et al., High Energy Density Phys. 3, 181 (2007)]. Additionally, radiation-hydrodynamics simulations with FLASH are used to generate simulated plasma-density and plasma-temperature profiles, which are then compared with the experimental measurements. Our analyses reveal that increasing the laser pulse length at a constant fluence results in a decrease in electron temperatures and densities. Furthermore, the longer pulses with lower intensities lead to deeper ablation regions before reaching the peak ablation but lower ionization balances in the silicon layer. These findings emphasize the critical role of laser pulse length in plasma ablation and shock generation for laser-impulse studies.

Nonlinear interaction of Alfvénic instabilities and turbulence via the modification of the equilibrium profiles

Nonlinear simulations of Alfvén modes (AMs) driven by energetic particles (EPs) in the presence of turbulence are performed with the gyrokinetic particle-in-cell code ORB5. The AMs carry a heat flux, and consequently they nonlinearly modify the plasma temperature profiles. The isolated effect of this modification on the dynamics of turbulence is studied by means of electrostatic simulations. We find that turbulence is reduced when the profiles relaxed by the AM are used, with respect to the simulation where the unperturbed profiles are used. This is an example of indirect interaction of EPs and turbulence. First, an analytic magnetic equilibrium with circular concentric flux surfaces is considered as a simplified example for this study. Then, an application to an experimentally relevant case of ASDEX Upgrade is discussed.

Characterization of early current quench time during massive impurity injection in JT-60SA

Characteristics of the early current quench (CQ) time in mitigated disruptions are studied for a full-current (5.5 MA) scenario in the JT-60SA superconducting tokamak. Self-consistent evolution of the plasma temperature and current density profiles during the early CQ phase before the plasma moves vertically is simulated using the axisymmetric disruption code INDEX for given impurity source profiles. It is shown that the hollow (flat) impurity density profiles peaks (flattens) the current density, and it causes a temporal change in the internal inductance in this phase. However the resultant CQ time is found to be insensitive to the impurity source profile for the same assimilated quantity. The simulation results are interpreted by the L/R model including the temporal change in the internal inductance as well as the effect of a gap between the plasma and the conducting vessel structures and stabilizing plates. This results will improve the accuracy to estimate the amount of impurity assimilated into plasma from the observed CQ rate in the massive gas injection (MGI) experiment planned in JT-60SA. The accessible range in which the CQ time can be scanned as well as the electron densities to suppress runaway electrons is also shown for different injected amounts of neon, argon, and their deuterium mixture under the limitation of the MGI gas amount. Mitigated disruptions in JT-60SA typically lead to the CQ time shorter than the vessel wall time, which is expected to produce relevant contributions to disruption mitigation in ITER and future reactors.

Atomic collisional data for neutral beam modeling in fusion plasmas

The injection of energetic neutral particles into the plasma of magnetic confinement fusion reactors is a widely-accepted method for heating such plasmas; various types of neutral beam are also used for diagnostic purposes. Accurate atomic data are required to properly model beam penetration into the plasma and to interpret photoemission spectra from both the beam particles themselves (e.g. beam emission spectroscopy) and from plasma impurities with which they interact (e.g. charge exchange recombination spectroscopy). This paper reviews and compares theoretical methods for calculating ionization, excitation and charge exchange cross sections applied to several important processes relevant to neutral hydrogen beams, including H + Be4+ and H + H+. In particular, a new cross section for the proton-impact ionization of H (1s) is recommended which is significantly larger than that previously accepted at fusion-relevant energies. Coefficients for an empirical fit function to this cross section and to that of the first excited states of H are provided and uncertainties estimated. The propagation of uncertainties in this cross section in modeling codes under JET-like conditions has been studied and the newly-recommended values determined to have a significant effect on the predicted beam attenuation. In addition to accurate calculations of collisional atomic data, the use of these data in codes modeling beam penetration and photoemission for fusion-relevant plasma density and temperature profiles is discussed. In particular, the discrepancies in the modeling of impurities are reported. The present paper originates from a Coordinated Research Project (CRP) on the topic of fundamental atomic data for neutral beam modeling that the International Atomic Energy Agency (IAEA) ran from 2017 to 2022; this project brought together ten research groups in the fields of fusion plasma modeling and collisional cross section calculations. Data calculated during the CRP is summarized in an and is available online in the IAEA’s atomic database, CollisionDB.

Core transport modelling of the DTT full power scenario using different fuelling strategies

A theory-based integrated modelling work of plasma response to deuterium fuelling in the new Divertor Tokamak Test facility (DTT) is performed, using the 1.5D transport code JETTO with the quasi-linear anomalous transport model QuaLiKiz for the core region. The full power DTT scenario E1 is investigated. It is characterised by 28.8 MW of Electron Cyclotron Resonance Heating, 10 MW of Neutral Beam Injection and 6 MW of Ion Cyclotron Resonance Heating to the plasma. Plasma density and temperature profile evolution is calculated up to the separatrix using two different fuelling methods, gas puffing and pellet injection, and two different seeding gases, argon and neon. To sustain the desired pedestal density level with gas puffing a big amount of neutral flux at the separatrix is needed. The feasibility limits of the pumping system are exceeded, regardless of the type of impurity introduced, thus making the use of pellets mandatory. The simulations performed with pellet injection as fuelling method predict that the pedestal density is well sustained with realistic parameters foreseen for the DTT pellet injector. Strong dependence of the core density on the electron cyclotron resonance (ECR) power deposition profile is found. Trapped Electron Modes dominance, low outward flux and strongly hollow density in the inner core region are foreseen with central peaked ECR power deposition profile. Ion Temperature Gradient modes dominance, inward flux and robust density sustainment on the whole radial interval are predicted for spread ECR power deposition, though with central density close to the ECR cut-off limit and with peaked impurity densities. An intermediate deposition extension is found to sustain the whole density profile and to obtain flatter core densities, as previously predicted for the reference full power DTT scenario by fixed pedestal simulations. The ECR deposition is negligibly modified by refraction changes both during a single pellet cycle and after several pellet cycles, indicating full compatibility between the ECR system and the pellet injection system.

Emission characteristics of bulk aerosols excited by externally focused femtosecond filaments.

The bulk aerosol emissions excited by externally focused femtosecond laser filaments are characterized using time-resolved plasma imaging and spectroscopy. Images of N2 and N2+ plasma fluorescence are used to characterize the filament dimensions. Emission profiles from bulk Sr aerosols are studied, showing that several localized emission regions in the filament begin to develop for lower repetition rates and higher pulse energies. Plasma temperature and electron density profiles are determined using particle emissions along the length of short- and long-focused filaments, and results are compared for on-axis and side-collected spectra. The use of on-axis collection enables the sampling of light emitted over the entire length of the filament; however, the necessary back-propagation of light makes on-axis collection susceptible to self-absorption as the optical path is extended through the filament plasma column formed in bulk aerosols.

Global gyrokinetic simulations of electromagnetic turbulence in stellarator plasmas

Global electromagnetic turbulence is simulated in stellarator geometry using the gyrokinetic particle-in-cell code EUTERPE. The evolution of the turbulent electromagnetic field and the plasma profiles is considered at different values of the plasma beta and for different magnetic configurations. It is found that turbulence is linearly driven at relatively high toroidal mode numbers. In the nonlinear regime, lower toroidal mode numbers, including zonal flows, are excited resulting in a quench of the linear instability drive. The turbulent heat flux is outward and leads to the nonlinear relaxation of the plasma temperature profile. The particle flux is inward for the parameters considered. The effect of the parallel perturbation of the magnetic field on the stellarator turbulence is addressed.

Effects of collisional ion orbit loss on tokamak radial electric field and toroidal rotation in an L-mode plasma

Ion orbit loss has been used to model the formation of a strong negative radial electric field E r in the tokamak edge, as well as edge momentum transport and toroidal rotation. To quantitatively measure ion orbit loss, an orbit-flux formulation has been developed and numerically applied to the gyrokinetic particle-in-cell code XGC. We study collisional ion orbit loss in an axisymmetric DIII-D L-mode plasma using gyrokinetic ions and drift-kinetic electrons. Numerical simulations, where the plasma density and temperature profiles are maintained through neutral ionization and heating, show the formation of a quasisteady negative E r in the edge. We have measured a radially outgoing ion gyrocenter flux due to collisional scattering of ions into the loss orbits, which is balanced by the radially incoming ion gyrocenter flux from confined orbits on the collisional time scale. This suggests that collisional ion orbit loss can shift E r in the negative direction compared to that in plasmas without orbit loss. It is also found that collisional ion orbit loss can contribute to a radially outgoing (counter-current) toroidal-angular-momentum flux, which is not balanced by the toroidal-angular-momentum flux carried by ions on the confined orbits. Therefore, the edge toroidal rotation shifts in the co-current direction on the collisional time scale.

Neutral Beams for Neutron Generation in Fusion Neutron Sources

Neutral beam injection is supposed to be the main source of high-energy particles, driving non-inductive current and generating primary neutrons in fusion neutron sources design based on tokamaks. Numerical simulation of high-energy particles’ thermalization in plasma and fusion neutron emission is calculated by novel dedicated software (NESTOR code). The neutral beam is reproduced statistically by up to 109 injected particles. The beam efficiency and contribution to primary neutron generation is shown to be dependent on the injection energy, input current, and plasma temperature profile. A beam-driven plasma operation scenario, specific for FNS design, enables the fusion rate and neutron generation in plasma volume to be controlled by the beam parameters; the resultant primary neutron yield can be efficiently boosted in plasma maintained at a relatively low temperature when compared to ‘pure’ fusion reactors. NESTOR results are applicable to high-precision nuclear and power balance estimations, neutron power loads distribution among tokamak components, tritium generation in hybrid reactors, and for many other tasks critical for FNS design.

A Genetic Algorithm to Model Solar Radio Active Regions From 3D Magnetic Field Extrapolations

In recent decades our understanding of solar active regions (ARs) has improved substantially due to observations made with better angular resolution and wider spectral coverage. While prior AR observations have shown that these structures were always brighter than the quiet Sun at centimeter wavelengths, recent observations at millimeter and submillimeter wavelengths have shown ARs with well defined dark umbrae. Given this new information, it is now necessary to update our understanding and models of the solar atmosphere in active regions. In this work, we present a data-constrained model of the AR solar atmosphere, in which we use brightness temperature measurements of NOAA 12470 at three radio frequencies: 17, 100 and 230 GHz. The observations at 17 GHz were made by the Nobeyama Radioheliograph (NoRH), while the observations at 100 and 230 GHz were obtained by the Atacama Large Millimeter/submillimeter Array (ALMA). Based on our model, which assumes that the radio emission originates from thermal free-free and gyroresonance processes, we calculate radio brightness temperature maps that can be compared with the observations. The magnetic field at distinct atmospheric heights was determined in our modelling process by force-free field extrapolation using photospheric magnetograms taken by the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO). In order to determine the best plasma temperature and density height profiles necessary to match the observations, the model uses a genetic algorithm that modifies a standard quiet Sun atmospheric model. Our results show that the height of the transition region (TR) of the modelled atmosphere varies with the type of region being modelled: for umbrae the TR is located at 1080 ± 20 km above the solar surface; for penumbrae, the TR is located at 1800 ± 50 km; and for bright regions outside sunspots, the TR is located at 2000 ± 100 km. With these results, we find good agreement with the observed AR brightness temperature maps. Our modelled AR can be used to estimate the emission at frequencies without observational coverage.

Numerical investigation on the influence of current waveform on droplet transfer in pulsed gas metal arc welding

A numerical model for pulsed gas metal arc welding (P-GMAW) was established to investigate the influence of the welding current on the fluid flow of arc plasma and filler metal in P-GMAW. Three sets of welding current waveforms with identical peak and base current but different median currents at the drop stage of current were used to conduct the experiment and numerical simulation. Bead-on-plate welding experiments under different current waveforms were conducted and the results showed that the waveform with a median current of 140 A had the best tolerance of the welding speed amongst the three current waveforms. Based on the mathematical modelling, the temperature profile and fluid flow of arc plasma and filler metal under different current waveforms were obtained and compared. The results showed that the waveform with a median current of 140 A could lead to lower droplet temperature and velocity when the droplet reached the workpiece compared with the other two waveforms. The simulated droplet shapes at different moments were compared with the captured images by a high-speed camera and they exhibited good agreements.

Quantification of the effect of uncertainty on impurity migration in PISCES-A simulated with GITR

A Bayesian inference strategy has been used to estimate uncertain inputs to global impurity transport code (GITR) modeling predictions of tungsten erosion and migration in the linear plasma device, PISCES-A. This allows quantification of GITR output uncertainty based on the uncertainties in measured PISCES-A plasma electron density and temperature profiles (n e, T e) used as inputs to GITR. The technique has been applied for comparison to dedicated experiments performed for high (4 × 1022 m−2 s−1) and low (5 × 1021 m−2 s−1) flux 250 eV He–plasma exposed tungsten (W) targets designed to assess the net and gross erosion of tungsten, and corresponding W impurity transport. The W target design and orientation, impurity collector, and diagnostics, have been designed to eliminate complexities associated with tokamak divertor plasma exposures (inclined target, mixed plasma species, re-erosion, etc) to benchmark results against the trace impurity transport model simulated by GITR. The simulated results of the erosion, migration, and re-deposition of W during the experiment from the GITR code coupled to materials response models are presented. Specifically, the modeled and experimental W I emission spectroscopy data for a 429.4 nm line and net erosion through the target and collector mass difference measurements are compared. The methodology provides predictions of observable quantities of interest with quantified uncertainty, allowing estimation of moments, together with the sensitivities to plasma temperature and density.

Two-Dimensional Simulations of Laser Shock Peening of Aluminum With Water Confinement

Nowadays, advanced surface improvement techniques are required, due to continuously rising demands in aerospace and automotive productions. Laser shock peening (LSP) is a widely known modern surface enhancement method. LSP usually deals with nanosecond laser pulses with high intensities exceeding 1 GW/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . Due to very short time scales, all the occurring physical phenomena and processing parameters are extremely difficult to measure and study just based on experimental investigations. Therefore, multidimensional computer simulations of the processes within LSP are required for further optimization. In this work, a 2-D hydrodynamic simulation of water-confined nanosecond laser shock peening of an aluminum target is performed applying the open-source code MULTI2D. Circular laser beam with a pulse energy of 1 J, 20-ns duration, a diameter of 1 mm, and a uniform spatial distribution is used. Spatial profiles of the laser-induced plasma pressure and temperature are determined together with the shock wave parameters. It is shown that the plasma is highly confined and a temperature-affected region is very thin. Radial expansion of the surface pressure profile and the shock wave propagation can be observed, indicating that radial effects have to be considered during the industrial application of LSP. The obtained results are in good agreement with available simulations and measurements, validating the proposed simulation approach. In addition, temporal and spatial distributions of the pressure at the surface of the target material can be applied in finite-element simulations to predict residual stresses distributions.

Analysis of the New Thomson Scattering Diagnostic System on WEST Tokamak

The French tokamak WEST supports the ITER design and operation. IRFM is designing a new Thomson scattering diagnostic to measure plasma density and temperature profiles. The diagnostic system consists of an endoscope inside a vacuum vessel, composed of actively cooled optical components. In order to validate and guarantee the diagnostic performances during normal operations, mechanical, thermal, hydraulic and vibratory behavior must be checked. Moreover, perpendicular displacement of the optical surface shall not be higher than 40 µm. Since this diagnostic operates in near infrared light, the temperature of all components must stay lower than 200 °C as not to bias the measurements. The differences in water temperature and pressure between the inlet and outlet of the diagnostic must be lower than 50 °C and 5.6 bar, respectively. The natural frequencies of the structure must be higher than 20 Hz and far enough from the frequency of external components. In this study, the worst radiative plasma scenario was chosen. The results of this study validate the accuracy of the measurements. Before manufacturing, electromagnetic disruption events must also be considered.

Investigation of the density shoulder formation by using self-consistent simulations of plasma turbulence and neutral kinetic dynamics

Simulations of plasma turbulence in a lower single-null magnetic configurations are presented. The plasma dynamics is modelled by the drift-reduced two-fluid Braginskii equations that are coupled with a kinetic model for a single neutral species that considers ionization, charge–exchange, recombination and elastic collisions. The effect of increased core fuelling on the plasma scrape-off layer (SOL) density and temperature profile is investigated. The increase in core fuelling leads to an increase of the e-folding length in the near SOL and, in the far SOL, to an increase of the plasma density. These results are in agreement with experimental measurements, and in particular with the observations of the formation of a density shoulder in high-fuelling scenarios. The physical mechanisms underlying the increase of the far SOL density are analysed comparing parallel and perpendicular fluxes in the SOL and considering also simulations with similar parameters but without neutrals. Despite the increase of the blob size, the increase of the far SOL density observed at high-fuelling rates is found to be mainly caused by the strong decrease of parallel transport, due to the cooling of electrons resulting from ionization events.

Plasma Stability in a Tokamak with Reactor Technologies Taking into Account the Pressure Pedestal

Studying stationary regimes with high plasma confinement in a tokamak with reactor technologies (TRT) [1] involves calculating the plasma stability taking into account the influence of the current density profiles and pressure gradient in the pedestal near the boundary. At the same time, the operating limits should be determined by the parameters of the pedestal, which, in particular, are set by the stability limit of the peeling–ballooning modes that trigger the peripheral disruption of edge localized modes (ELM). Using simulation of the quasi-equilibrium evolution of the plasma by the ASTRA and DINA codes, as well as a simulator of magnetohydrodynamic (MHD) modes localized at the boundary of the plasma torus based on the KINX code, stability calculations are performed for different plasma scenarios in the TRT with varying plasma density and temperature profiles, as well as the corresponding bootstrap current density in the pedestal region. At the same time, experimental scalings for the width of the pedestal are used. The obtained pressure values are below the limits for an ITER-like plasma due to the lower triangularity and higher aspect ratio of TRT plasma. For the same reason, the reversal of magnetic field shear in the pedestal occurs at a lower current density, which causes the instability of modes with low toroidal wave numbers and reduces the effect of diamagnetic stabilization.