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DOE OSTI2026

Low-Pressure Diffusion Bonding of Vanadium to Commercially Pure Titanium and Ti-6Al-4V

Modern technology increasingly requires components to be made from specific high-performance materials. To support complex multi-metal structures, a variety of techniques are required to join dissimilar metal parts with precise shapes. This study evaluates vacuum diffusion bonding as a method for joining titanium and vanadium, focusing on both pure titanium and the common alloy Ti-6Al-4V. We employ modest pressure provided by a weight and simple surface preparation to simulate the most commercially applicable process. Here, we show that Ti-6Al-4V alloy bonds readily to V, forming a continuous, clearly defined interdiffusion layer with predictable kinetics. Conversely, commercially pure Ti forms a crack-prone bond with V that fails to improve at higher bonding temperatures or longer times. We attribute this failure to the concentration of stress caused by the ß-to-α phase transformation in Ti. The contrasting bonding efficacy between pure Ti and the alloy provides insight into the crystallographic interactions that occur at the interface during bonding and cooling. These results provide surprising insight into a new method for bonding Ti alloys to V and possibly other metals that share the body-centered cubic crystal structure.

36 MATERIALS SCIENCE↗

DOE OSTI2024

ExaDigiT/RAPS

ExaDigiT is a framework for developing comprehensive digital twins of liquid-cooled supercomputers, which has three main modules: (1) a python-based Resource Allocator and Power Simulator (RAPS), (2) a Modelica-based Thermo-Fluidic cooling model, and (3) a C++-based augmented reality model built on Unreal Engine 5. RAPS either simulates workloads or replays historical workloads from system telemetry, and is able to predict dynamic energy consumption, as well as interact with the cooling model to predict cooling system behavior. Such a tool can be used together with reinforcement learning algorithms to provide an end-to-end optimization tool for data centers.

Brewer, Wesley [Oak Ridge National Laboratory (ORN↗

DOE OSTI2023

Molecules Functionalized with Cycling Centers for Quantum Information Science

The ability for a single molecule to produce enough laser-induced fluorescence to control and detect its quantum state is known as optical cycling. This property has been used to great effect in atoms, where the relatively small number of states promotes their ability to repeatedly fluoresce, for applications such as laser cooling, precision measurement, atomic clocks, and quantum information processing. The extension of this capability to molecular species, however, has been difficult, primarily due to their propensity to become vibrationally excited during illumination. This project brought together experts from atomic physics, physical chemistry, and computational quantum chemistry to develop means to create molecules capable of optical cycling. In particular, this program sought to produce an optical cycling center (OCC), a quantum functional group capable of chemical attachment to a wide variety of molecular hosts while retaining (and thereby furnishing to its host) the ability to optically cycle. Following our team’s theoretical identification of promising species, including alkaline-earth phenoxides, we then created these species and in many cases confirmed their optical cycle closure. We now not only know of the existence of a handful of large, molecular species that can be deployed for applications in quantum technologies and measurement, but have improved our knowledge of the molecular mechanisms leading to this discovery, which will enable generalization in the future. The extension of these ideas for informed chemical design of cycling molecules with bespoke properties is now being pursued by multiple groups.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Anisotropic magnetism and electronic structure of trigonal EuAl 2 Ge 2 single crystals

Understanding the interplay between magnetic and electronic degrees of freedom is of profound recent interest in different Eu-based magnetic topological materials. Here, we studied the magnetic and electronic properties of the layered Zintl-phase compound EuAl 2 Ge 2 crystallizing in the trigonal CaAl 2 Si 2 -type structure. We report zero-field neutron diffraction, temperature T - and magnetic-field H-dependent magnetic susceptibility χ(T, H), isothermal magnetization M(T, H), heat capacity C p (T, H), and electrical resistivity ρ(T, H) measurements, together with T-dependent angle-resolved photoemission spectroscopy (ARPES) measurements complemented with first-principle calculations. EuAl 2 Ge 2 undergoes second-order A-type antiferromagnetic (AFM) ordering below T N = 27.5(5) K, with the Eu moments (Eu 2+ , S = 7/2) aligned ferromagnetically in the ab plane while these layers are stacked antiferromagnetically along the c axis. The critical fields at which all moments become parallel to the field are 37.5(5) and 52.5(5) kOe for H ∥ ab and H ∥ c, respectively. The H = 0 magnetic structure consists of trigonal AFM domains associated with ab-plane magnetic anisotropy and a field-induced reorientation of the Eu spins in the domains is also evident at T = 2 K below the critical field H c1 = 2.5(1) kOe. The ρ(T) measurements reveal metallic behavior transforming into a slight resistivity increase on cooling towards T N . A pronounced loss of spin-disorder scattering is observed below T N . The ARPES results show that EuAl 2 Ge 2 is metallic both above and below T N , and the Fermi surface is anisotropic with two hole pockets at the zone center and one small electron pocket at each M point. In the AFM phase, we directly observe folded bands in ARPES due to the doubling of the magnetic unit cell along the c axis with an enhancement of quasiparticle weight due to the complex change in the coupling between the magnetic moments and itinerant electrons on cooling below T N . The observed electronic structure is well reproduced by first-principle calculations, which also predict the presence of nontrivial electronic states near the Fermi level in the AFM phase with Z 2 topological numbers 1;(000)

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Critical Literature Review of Low Global Warming Potential (GWP) Refrigerants and their Environmental Impact

Refrigeration and air conditioning currently account for ~20% of the total electricity consumption in buildings around the world. Over the next three decades as global temperatures are projected to increase, urbanization and economic growth will lead to an increased demand for refrigeration and cooling. Most commonly used refrigerants belong to the five following classes: (i) chlorofluorocarbons, (ii) hydrochlorofluorocarbons, (iii) hydrofluorocarbons (HFCs), (iv) hydrofluoroolefins (HFOs), and (v) natural refrigerants. Over the past century, there have been shifts in which compounds were used for refrigeration to improve safety and durability, allow for ozone protection, and, most recently, to reduce global warming potential (GWP). Although technological advances have led to increased cooling capacity and safer refrigerants, emissions from refrigeration systems can affect the environment by contributing to greenhouse gas emissions or by depleting the ozone layer, depending on the gas emitted. The focus is increasingly on adopting compounds that are both efficient at cooling and effective for reducing emissions and other adverse environmental impacts. Because of policy and regulatory changes to avert ozone depletion and global climate change, much discussion has centered on the environmental impacts of next-generation refrigerants. Of particular interest are the fluorinated refrigerants, HFCs and HFOs, most of which are defined as per- and polyfluoroalkyl substances (PFAS) and their breakdown products (especially trifluoroacetic acid). The US Environmental Protection Agency in 2021 drafted a Strategic Roadmap for PFAS, which has already resulted in an increase in investment in research on these compounds and has restricted the release of PFAS into the environment through the implementation of monitoring and reporting requirements. A critical evaluation of fluorinated refrigerants and their breakdown products with respect to persistence, biodegradation and toxicity, and global warming potential is needed to guide environmental regulations. This document aims to perform a critical review of the relevant scientific data on the most common refrigerants currently used, their degradation products, and their alternatives. Where available, estimates of precursor production quantities and existing environmental regulatory information are reviewed. Key data of interest for the evaluation include physicochemical properties, environmental fate parameters, ecological or human health toxicity/risk information, and GWP for compounds of interest.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

CLEAP Project: OR-SAGE Analysis for MT, UT, and CO States

The OR-SAGE tool is designed to use industry-accepted practices in screening sites and then employ the proper array of data sources through the considerable computational capabilities of GIS technology available at ORNL. The tool was developed to screen the potential for NPP siting on a national and regional basis. However, because of the tool granularity, it is often focused specifically on the immediate area around user sites of interest. If data center siting parameters can be added to OR-SAGE, the ability to evaluate data center siting on a localized scale will be beneficial.1 More than 60 data sets have been collected and processed by ORNL to develop exclusionary, avoidance, and suitability criteria for screening sites for a variety of power generation types, including nuclear power plants. Available site evaluation parameters include population density, slope, seismic activity, proximity to cooling-water sources, proximity to hazard facilities, avoidance of protected lands and floodplains, susceptibility to landslide hazards, and many others. All siting parameters should be considered as flags to inform siting decisions and should not be used to rule in or rule out any NPP site. Once data center siting parameters are identified, appropriate data sets will be collected and processed. The OR-SAGE process is very versatile. Essentially, OR-SAGE is a visual, relational database. The database partitions the contiguous United States, a total of 720 million hectares (~1.8 billion acres), into 100-m by 100-m (1 hectare or ~2.5 acre) cells. The database is tracking just under 700 million individual land cells. Successive suitability criterion is applied to each cell in the database. User-specified thresholds can be applied to each siting parameter data layer. In this manner, a variety of scenarios can be quickly and thoroughly evaluated. Data can be added and/or revised within OR-SAGE to address user interests. Siting security assessment capability is currently being added to OR-SAGE. Security is expected to be of concern at data centers whether it is collocated with a nuclear power generating technology or not. If data center is collocated with a nuclear power generating source, the security threat attractiveness level of both will likely increase. It will be of additional benefit if a potential data center site is also assessed for security vulnerability.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Holistic energy analysis method for thermal management architectures of data centers

Modern high-performance computing (HPC) data centers (DCs), particularly those supporting energy-intensive artificial intelligence (AI) workloads, face escalating thermal management challenges that degrade performance through thermal throttling and drive up cooling power consumption and operational costs. To address this challenge, many have developed a wide variety of thermal management solutions (single-phase, two-phase, direct, indirect, hybrid, and more) which attempt to cool HPC DCs effectively while attempting to minimize overall system power consumption. However, the analysis of these solutions and methods to effectively compare one with another is lacking. Overall power usage effectiveness (PUE) and total-power usage effectiveness (TUE) provide a metric to quantify power consumption but fail to identify components in the system which require further optimization. To address this, we propose a holistic analytical framework – the waterfall diagram (WFD) – which leverages a waterfall chart methodology, offering a comprehensive visualization of both the thermal management system loop and heat flow pathways from individual server components to the outdoor ambient. Use of the WFD enables graphical estimations of power efficiency and cooling performance across each component of a DC cooling system and complements Sankey-style energy flow visualizations by additionally resolving stage-wise temperature changes and incremental TUE contributions. The framework is used in conjunction with simulation-based approaches, to conduct a detailed pressure drop and flow distribution analysis aimed at identifying the optimal coolant distribution architecture for a single-phase direct-to-chip water-cooled DC, which serves as the baseline for subsequent WFD analysis. Among the evaluated architectures, the 3 U modular coolant distribution architecture is found to demonstrate the best performance, considering minimal pressure drop and uniform flow distribution. In addition, TUE is calculated for each cooling loop component based on its associated pressure drop and corresponding pumping power, which are integrated into the WFD. This correlation between TUE and local temperature offers immediate insight into the power efficiency and thermal performance contributions of individual components, facilitating further development and optimization. Examples of WFD applications are presented under varying thermal loads and ambient conditions, demonstrating reasonable cooling strategies. Notably, the 3 U modular architecture maintains a consistent chip case temperature of 85°C, achieving a TUE of 1.016 at ambient temperature of 47°C, and a TUE of 1.026 at ambient temperature of 52°C. The WFD methodology provides an efficient, holistic, and streamlined framework for DC thermal management architecture assessment and enables design optimization which is important for addressing the thermal-fluidic energy challenges of current and next-generation DCs.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2021

Magnetic Field Measurements of First Pre-series Full -Length 4.2 m Quadrupole MQXFA03 Using PCB Rotating Coils for the Hi Hi-Lumi LHC Project

The U.S. Hi-Lumi LHC Accelerator Upgrade Project (AUP) and CERN have joined efforts to develop high field quad-rupoles for the Hi-Lumi LHC upgrade. The US national laborato-ries in the AUP project will deliver 10 magnets and each cryostat has two 4.2 m high gradient quadrupoles in it. These magnets are made of Nb3Sn conductors, with large aperture (150 mm) and in-tegrated gradient of 556.9 T. This paper reports on magnetic measurements performed during the vertical test at Brookhaven National Laboratory (BNL) in 2019-2020. A warm measurement Z-Scan (+/- 15 A) with 42 Z-positions before cool-down was per-formed at BNL. The results were directly compared to field data measured at LBNL during magnet assembly. Measured harmonics and magnetic center offsets (ΔX and ΔY) have provided timely and informative diagnostics on the magnet structure’s shape at both warm and cold temperatures. A new centering fixture was de-signed and added to better center the warm bore tube which con-tains the rotating coil probe. After the quench training to 16.47 kA was achieved, a complete set of cold measurements (Z-Scan at 16.47 kA and I-Scan from 960 A to 16.47 kA and back to 960 A) was made. Periodic axial variation of allowed and nonallowed harmonics was observed which is related to the coil radial and/or mid-plane variations along the magnet axis. Overall, the average harmonics in the straight section are within the required field boundaries.

43 PARTICLE ACCELERATORS↗

DOE OSTI2024

NEXUS-DC: Nuclear Energy eXpedition for US Data Centers [Slides]

This presentation covers the growing interest in utilizing nuclear power to satisfy the increasing energy demands of data centers in the United States, emphasizing the factors that accelerate reactor deployment. It addresses clean and reliable energy needs, highlights the importance of power supply redundancy for reliability, and discusses challenges and solutions related to cooling, waste heat reuse, and techno-economics. Additionally, it includes a strength, weakness, opportunities and threat analysis and emphasizes community engagement and collaboration for accelerating regulatory approvals and reactor deployment.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2021

Production and Persistence of Extreme Two-temperature Plasmas in Radiative Relativistic Turbulence

Turbulence is a predominant process for energizing electrons and ions in collisionless astrophysical plasmas, and thus is responsible for shaping their radiative signatures (luminosity, spectra, and variability). To better understand the kinetic properties of a collisionless radiative plasma subject to externally driven turbulence, we investigate particle-in-cell simulations of relativistic plasma turbulence with external inverse Compton cooling acting on the electrons. We find that ions continuously heat up while electrons gradually cool down (due to the net effect of radiation), and hence the ion-to-electron temperature ratio T i /T e grows in time. Furthermore, we show that Ti/Te is limited only by the size and duration of the simulations (reaching ${T}_{i}/{T}_{e}\sim {10}^{3}$), indicating that there are no efficient collisionless mechanisms of electron–ion thermal coupling. This result has implications for models of radiatively inefficient accretion flows, such as observed in the Galactic center and in M87, for which so-called two-temperature plasmas with ${T}_{i}/{T}_{e}\gg 1$ have been invoked to explain their low luminosity. Additionally, we find that electrons acquire a quasi-thermal distribution (dictated by the competition of turbulent particle energization and radiative cooling), while ions undergo efficient nonthermal acceleration (acquiring a harder distribution than in equivalent nonradiative simulations). There is a modest nonthermal population of high-energy electrons that are beamed intermittently in space, time, and direction; these beamed electrons may explain rapid flares in certain high-energy astrophysical systems (e.g., in the Galactic center). These numerical results demonstrate that extreme two-temperature plasmas can be produced and maintained by relativistic radiative turbulence.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Thermal Performance of a Conduction-Cooled CCT Dipole ReBCO Magnet: Several Cycles of Cool-Down and Thermal Gradient Measurements

Here, this paper presents experimental results from conduction-cooled thermal testing of a ReBCO canted cosine theta (CCT) magnet (C2), originally designed and fabricated at LBNL using CORC cables. While the performance of the coil under liquid helium and nitrogen environments has been previously established, this study explores its behavior under conduction cooling using a large test cryostat at The Ohio State University. The magnet, measuring 613 mm in length and weighing ∼75 kg, consists of four helical layers wound with ReBCO-based CORC wire and was thermally anchored to a copper cold ring supported by a G-10 strongback. Cooling was provided by two Sumitomo RDK-415D cryocoolers, offering a combined 3 W at 4.2 K and 150 W at 77 K. Multiple thermal cycles were performed, with cooldown durations of up to 45 hours. Final base temperatures of approximately 10.8 K (at the coil edge) and 12.0 K (at the coil center) were achieved, with an axial temperature difference of approximately 1.2 K. The warm-up period extended over approximately 24.6 hours. Voltage measurements from all four layers were recorded during cooldown and warmup. The system demonstrated stable cooldown performance, repeatable gradients, and good thermal anchoring. These results support the feasibility of conduction cooling in large-scale HTS magnets, aligning with broader goals for “green” cryogen-free accelerator technologies and paving the way for more sustainable, scalable, and energy-efficient high-field magnet systems in next-generation particle accelerators.

Canted cosine theta magnets↗

DOE OSTI2025

Thermal stress in degraded forests in the Brazilian Amazon Arc of Deforestation

Understanding thermal stress in tropical forests has taken on new urgency in light of accelerating climate change and expansion of deforestation and forest degradation. Degraded tropical forests in particular may be approaching critical temperature thresholds even more rapidly than intact forests, with implications for tree survival and ecosystem recovery. We investigate thermal stress in degraded tropical forests within the Brazilian Amazon Arc of Deforestation. Using land surface temperature data from the ECOsystem Spaceborne Thermal Radiometer Experiment on the international Space Station (ECOSTRESS), we compared canopy temperatures of intact, selectively logged, and burned forests in Feliz Natal, Mato Grosso, Brazil. Upper canopy temperatures in previously burned forests were 4.1% higher (mean = 36.5 °C) and 50.9% more variable compared to intact and logged forests, which showed remarkably similar temperature distributions (means of 34.9 °C and 35.1 °C, respectively). Modeled leaf temperature distributions based on canopy temperature measurements from one of the warmest days in a 2 year dry season record indicated that 87% of leaves in the warmest burned forest patches exceeded the temperature threshold where respiration surpasses photosynthesis, compared to approximately 72%–74% in intact and logged forests, respectively, in the same time period. After controlling for environmental factors, burned forests were predicted to be 2.6 °C warmer on average [1.39 °C–3.96 °C, 95% credible interval] than intact forests across a 5–40 m canopy height range. Burned forests showed modest thermal recovery over time, with temperatures decreasing by approximately 1.2 °C over a 30 year recovery period. In contrast, logged forests showed minimal thermal differences from intact forests (−0.353 on average, [−1.125–0.274, 95% credible interval]) and negligible change (0.15 °C) over the same timeframe. While the absolute probabilities of exceeding damaging thermal thresholds remain low across all forest types under current climate conditions, the probability of leaves exceeding temperatures that cause permanent leaf damage was ten times higher in burned forests, with implications for the future of burned forest regeneration in water-limited regions of the Amazon basin. In particular, the combination of higher mean temperatures, greater temperature variability, and more frequent exposure to damaging thermal thresholds implies that burned tropical forests will experience substantially higher mortality rates and slower biomass recovery compared to intact and selectively logged forests, especially in water-limited regions where trees cannot rely on evaporative cooling to moderate canopy temperatures.

Brazilian Amazon Arc of Deforestation↗

DOE OSTI2026

Quantum-State-Controlled Collisions of Ultracold Polyatomic Molecules

Collisions between ultracold calcium monohydroxide (CaOH) molecules are realized and studied. Inelastic collision rate constants are measured for CaOH prepared in ground and excited vibrational states, and the electric field dependence of these rates is measured for molecules in single quantum states of the parity-doubled bending mode. Theoretical calculations of collision rate coefficients are performed and found to agree with measured values. The lowest collisional loss rates are for states with repulsive long-range potentials that shield ultracold molecules from loss channels at short distance. These results unveil the collisional behavior of parity-doublet molecules in the ultracold regime and lay the foundation for future experiments to evaporatively cool polyatomic molecules to quantum degeneracy.

Vilas, Nathaniel B. [Harvard University, Cambridge↗

DOE OSTI2022

Public – Private Partnership to Promote Efficient Manufacturing and Workforce Development (IAC Final Technical Report)

Through delivering ninety (90) energy assessments to small- and medium-sized manufacturing facilities in and around Tennessee, significant understandings were gained through providing detailed energy assessment reports to manufacturers and training seventy-seven (77) engineering students in which thirty-five (35) certified IAC students were recognized by DOE. The robust involvement of Tennessee Valley Authority (TVA), local utility and Tennessee Tech’s Cybersecurity Education, Research, and Outreach Center (CEROC) in majority of assessments made the technical operation very effective where leaded to 40.5% implementation rate of energy recommendations. Other benefits of the award to the public are a dynamic modeling tool capable of analyzing existing cooling towers for energy use optimization was developed and presented to DOE IAC, providing technical assistance to non-participating manufacturers in the form of workshop and training, publishing fifteen (15) peer-reviewed conference and journal papers as well as a book chapter in the area of industrial energy efficiency field, assisting the TVA Magnolia Combined Cycle Power Plant to become the First 50001 Ready Certified Power Plant in the U.S. through briefing them on ISO 50001 and 50001 Ready as well as providing an energy assessment to the plant, assisted the new IAC center at Clemson University with on-site and remote support, and provided assessment and training in unique areas of water, waste water, cyber security and smart manufacturing to our clients, students and community.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2020

Summary of Results for Idaho Accelerator Center (IAC) Experiments with Compact Electron Permanent Magnet Spectrometer (CEPMS)

The Compact Electron Permanent Magnet Spectrometer (CEPMS) shown in Figure 2 consists of collimation at the electron beam entrance, a vacuum chamber for beam transport and a removable 60 degree sector magnet constructed by SABR Enterprises (Ref 2) that is used to momentum analyze the incoming electron beam. There are electron detection planes located perpendicular to straight through and the 60 degree trajectory ports. The planes are designed to accept phosphor screens for time integrated measurements. The screens can be replaced by scintillator for time resolved measurements using gated or streak cameras. The length of the spectrometer along the beamline without the collimator is about 400mm (14”). The spectrometer requires no power supply with controls for cycling or cooling for the magnet. The entire assembly, with magnet installed, weighs about 35kg (75lbs) Figure 3 depicts central and extreme trajectories through the spectrometer for various electron energies. The chamber accommodates a +/-50mm wide detection field relative to the center trajectory. Trajectories with larger momentum (energy) are bent the least. Since the permanent magnet slides off and on with reference to the upstream edge of the vacuum chamber, it can be adjusted to various positions to slightly increase or decrease the central energy thereby changing the range of available energies. Figure 4 shows the effect of changing the location of the permanent magnet on the electron trajectory. A small inward change in r produces a longer trajectory in the magnet therefore, the same energy trajectory is bent more.

43 PARTICLE ACCELERATORS↗

DOE OSTI2022

Investigation of the effect of structural defects from hydride precipitation on superconducting properties of high purity SRF cavity Nb using magneto-optical and electron imaging methods

Abstract Nb is an elemental superconductor with a critical temperature of 9.3 K and is widely used to fabricate superconducting radiofrequency (SRF) cavities for particle accelerators. However, microstructural defects in Nb, such as grain boundaries (GBs) and dislocations, can act as pinning centers for magnetic flux that can degrade SRF cavity performance. Hydrogen contamination is also detrimental to SRF cavity performance due to the formation of normal conducting hydrides during cool down. In this study, disc shaped Nb bi-crystals extracted from high-purity large-grain Nb slices were investigated to study the effects of GBs, hydrogen, and dislocations on superconducting properties. Grain orientation and GB misorientation were measured using Laue x-ray diffraction and electron backscattered diffraction (EBSD) analyses. Cryogenic magneto-optical imaging was used to directly observe magnetic flux penetration below T c = 9.3 K. Damage caused by low temperature precipitation of hydrides and their dissolution upon reheating after cryogenic cycles was examined using electron channeling contrast imaging, and EBSD. The relationships between hydride formation, dislocation content, GBs, cryo-cooling, heat treatment (HT), and flux penetration indicate that both GB character and hydrogen content affect magnetic flux penetration. Such flux penetration could be facilitated by dislocation structures and low angle GBs resulting from hydride precipitation and HT.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Critical Literature Review of Low Global Warming Potential (GWP) Refrigerants and their Environmental Impact

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

On the Stability Analysis of Astrophysical Cooling Functions

To model the temperature evolution of optically thin astrophysical environments at MHD scales, radiative and collisional cooling rates are typically either pretabulated or fit into a functional form and then input into MHD codes as a radiative loss function. Thermal balance requires estimates of the analogous heating rates, which are harder to calculate, and due to uncertainties in the underlying dissipative heating processes these rates are often simply parameterized. The resulting net cooling function defines an equilibrium curve that varies with density and temperature. Such cooling functions can make the gas prone to thermal instability (TI), which will cause departures from equilibrium. There has been no systematic study of thermally unstable parameter space for nonequilibrium states. Motivated by our recent finding that there is a related linear instability, catastrophic cooling instability, that can dominate over TI, here we carry out such a study. We show that Balbus instability criteria for TI can be used to define a critical cooling rate, Λ c , that permits a nonequilibrium analysis of cooling functions through the mapping of TI zones. We furthermore illustrate how thermal conduction modifies the shape of TI zones. Upon applying a Λ c -based stability analysis to coronal loop simulations, we find that loops undergoing periodic episodes of coronal rain formation are linearly unstable to catastrophic cooling instability, while TI is stabilized by thermal conduction.

79 ASTRONOMY AND ASTROPHYSICS↗