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At least 883 records · Page 49

Development of a Hybrid Single/Two-Phase Capillary-Based Micro-Cooler Using Copper Inverse Opals Wick with Silicon 3D Manifold for High-Heat-Flux Cooling Application: Preprint

Previously, two-phase capillary-based cooling from narrow (200-1,000 micrometer) heater-bridge copper inverse opal (CIO) wicks with heat flux levels exceeding 1,400 watts per square cm with a low superheat of approximately 10 degrees C was demonstrated. Here, we demonstrate the area scaling of the proposed technology to large-area micro-cooler for the high-heat-flux cooling of microprocessors and power electronics. We developed a hybrid single/two-phase micro-cooler that relies on capillary wicking in 25-micrometer-thick CIOs with an open channel silicon 3D-manifold for liquid delivery and vapor extraction, to achieve a high heat flux of approximately 400 watts per square cm over a heated area of 1 square cm. For the range of inlet water (21 degrees C water temperature) flowrates from 5 to 60 mL per min, we achieved total thermal resistances and vapor qualities of 0.68-0.2 square cm Kelvin per watt and 0.55-0.12, respectively. The high heat flux levels are achieved with flowrates that are 10 times smaller than conventional single- or two-phase microchannel cooling technology. The corresponding two-phase thermal resistances are in the range of 0.05 to 0.02 square cm Kelvin per watt with temperature superheat of 8 to 6 degrees C. While the overall performance of the large-area (10 by 10 square millimeter) capillary-based micro-cooler degraded compared to previous demonstration of the technology for a heated area of 5 by 5 square millimeter, preliminary computational fluid dynamics (CFD) modeling indicates that an improved manifold design will be able to achieve comparable performance.

capillary flow↗

Recharge Demand Mitigation for Latent Heat Thermal Energy Storage at Off-peak Hours

The utilization of integrated heat pump thermal energy storage (HP-TES) systems for space conditioning applications can reduce electrical power demand and achieve utility savings resulting from peak shaving and load shifting. However, issues arise when the energy required to recharge the TES exceeds the shifted energy demand, especially in extreme climates where high-temperature lifts between the outdoor air conditions and phase-change materials (PCMs) during recharging may occur. In this work, a single room-temperature (22°C) PCM-TES is integrated into a single-speed heat pump system using a secondary hydronic loop where the TES is recharged using the outdoor unit during off-peak hours. Three recharge strategies were investigated as potential pathways to reduce recharging power demand: (i) considering different heat source/sink temperatures, (ii) using a variable-speed compressor, and (iii) using a variable-speed pump. Simulations were conducted using Modelica for HP-TES recharging at different heat source/sink temperatures from -30 – 20℃ in heating mode and 0 – 30℃ in cooling mode. Results show that the most effective recharge demand reduction strategy is an HP-TES system using a single-speed compressor with a variable-speed pump for the hydronic loop run at preferable heat source/sink temperatures when the temperature lifts were reduced. Utilizing a variable-speed compressor for the HP-TES system reduced recharge time in extreme cases at the cost of additional compressor power input. The findings motivate potential control strategies that minimize recharge energy and maximize peak energy savings, hence reducing overall operating costs and annual energy consumption for HP-TES systems for space conditioning applications.

25 ENERGY STORAGE↗

Experimental Investigation of a Phase Change Material Charged Serpentine Heat Exchanger with Louvered Fins

Phase change material heat exchangers (PCM-HX) can be used as a latent heat thermal energy storage (LHTES) component in heat pump applications to further enhance the efficiency of a heat pump as well as to yield financial savings by peak-load shifting. In this paper, a low-cost commercially available aluminum serpentine heat exchanger with louvered fins was experimentally investigated to check its thermal performance as a PCM-HX. A transparent rectangular box fabricated from acrylic plates served as a PCM container. Two cameras were used to capture the phase change process of the PCM on the front and top sides of the container during the experiment. A total of 88 installed temperature sensors throughout the test setup and a mass flow meter enabled a quantitative analysis of the PCM-HX as well. The energy balance deviation between the estimated theoretical and experimentally calculated PCM storage was ±14% considering the often-neglected heat loss and thermal mass of the PCM-HX. PCM temperature profiles, charge and discharge rates, and energy densities under different test conditions were also investigated.

42 ENGINEERING↗

Multi-physics Modeling of Radiative Heat Transfer and Fluid Flow for the Reactor Cavity Cooling System

High-temperature gas-cooled reactors (HTGRs) are notable for their high thermal efficiency and potential for combined heat and power applications. These reactors are particularly appealing due to their advanced passive safety features. HTGRs utilize passive safety systems that function without requiring active components like pumps or compressors during emergencies. These reactor designs depend on a Reactor Cavity Cooling System (RCCS) to manage decay heat removal from the reactor pressure vessel (RPV) during accident conditions. The RCCS consists of vertical rectangular channels known as "risers" or riser ducts positioned around the RPV. These risers receive heat from the RPV through both convective and radiative heat transfer mechanisms. Understanding the interplay of multiple physical phenomena, such as fluid dynamics, heat transfer, and neutron interactions, is essential for the effective design and operation of nuclear reactors, particularly for systems like the RCCS. Multi-physics simulations provide a comprehensive approach to studying these interactions, offering detailed insights and enhancing accuracy. They are especially important in RCCS designs, where the interaction between radiative and convective heat transfer can significantly impact system performance. By leveraging multi-physics simulations, complex reactor behaviors can be modeled without compromising the fidelity of the underlying physical processes. This work aims to establish a robust methodology for coupling multiple physical processes in an air-cooled RCCS. By focusing on validating this multi-physics approach, the study involves designing test cases that simulate various conditions to verify the numerical models employed. The outcomes of this research will provide critical insights for accurately modeling and optimizing complex nuclear systems like the RCCS.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

The relative importance of building design parameters in reducing energy use and sensible heat release from buildings in light of forecasted future weather data and building coverage ratio

Buildings typically have a 60-to-75-year lifespan before they require significant maintenance or modifications. However, most builders evaluate the performance of their new buildings using whole-building energy simulation tools based on the current typical meteorological year (TMY) file or actual meteorological year. The energy use consumption and sensible heat release pattern observed from buildings could potentially change based on shifting global climates. Therefore, the recommended energy-efficiency design parameters might also change during these periods. In this study, we evaluate the role of different building design parameters, such as material reflectivity, HVAC COP, and insulation values, on building energy usage and sensible heat release from buildings with different building coverage ratios (BCR), based on the current and future weather file TMY (fTMY) for the middle of the century (2040–2060). The role of sensible heat release from buildings is not accounted for accurately while estimating building energy usage in most whole-building energy simulations. The study conducts a series of whole-building energy simulation analyses using EnergyPlus to evaluate the role of different design parameters based on TMY and fTMY weather conditions. The analysis is conducted for two hot desert climatic cities: Phoenix (USA) and Abu Dhabi (UAE). The results show that, for the base case in a future climate, the sensible heat release is reduced by an average of 30% due to the reduced delta T between the surface and ambient air. Further, the results show an increase in total energy consumption by 5% annually. The results also show that, for buildings with traditional coatings, shorter buildings release more heat than taller buildings. On the other hand, for buildings with reflective paints, shorter buildings release less heat than taller buildings. The findings from this study can be used by policymakers, utility companies, and builders to better understand the relative role of different building design parameters while constructing new and retrofitting existing buildings.

Alhazmi, Mansour [King Fahd University of Petroleu↗

Advanced metal hydride heat transfer system utilizing an electrochemical hydrogen compressor

An electrochemical heat transfer device utilizes an electrochemical hydrogen compressor to pump hydrogen into and out of a reservoir having a metal hydride forming alloy therein. The absorption of hydrogen by the metal hydride forming alloy is exothermic, produces heat, and the desorption of the hydrogen from the metal hydride forming alloy is endothermic and draws heat in. An electrochemical hydrogen compressor may be configured between to reservoirs and pump hydrogen back and forth to form a heat transfer device. A heat exchange device may be coupled with the reservoir or may comprise the outer surface of the reservoir to transfer heat to an object or to the surroundings. A closed loop may be configured having two reservoirs and one or two electrochemical hydrogen compressors to pump the hydrogen in a loop around the system.

Bahar, Bamdad↗

Material Selection and Heat Transfer Model for PTUHS Device

The Path to Ultimate Heat Sink Device (PTUHS) is a passive safety system that utilizes a radiative heat transfer valve to control the rate at which heat is removed from a nuclear reactor pressure vessel (RPV) and dispersed into surrounding soil. The material selection for the PTUHS device is investigated, where the thermophysical properties are either maximized or minimized bases on what section of the PTUHS that material is being used for. Final recommendations of material choice are then presented. The heat transfer model of the PTUHS device is solved in ABAQUS, where a normal operating conditions and SCRAM conditions are solved. These temperature maps and heat flux of the system show the system's ability, where minimal heat is lost during normal operating conditions and system failure in a SCRAM scenario due to temperatures that were reached.

42 - ENGINEERING↗

Experimental and Computational Heat Transfer Study of sCO2 Single Jet Impingement

The present study experimentally investigates the heat transfer capability of supercritical carbon dioxide (sCO2) single-jet impingement. The evaluated jet Reynolds number range is between 80,000 and 1,000,000, with a non-dimensional jet-to-target surface spacing of 2.8. CO2- impinging jet stagnation conditions were maintained at approximately 20 MPa and a temperature of 673 K for most experiments. The goal is to understand how changes in the aforementioned parameters influence heat transfer between the working fluid and the heated surface. Additionally, due to the elevated Reynolds numbers and difference in thermodynamic properties between air and CO2, air-derived impingement correlations may not be appropriate for CO2 impingement; these correlations will be evaluated against experimental sCO2 impingement data. At the time of this study, no sCO2 impingement data was available relevant to sCO2 power cycles. The target surface is a 1.5-inch diameter copper block centered on the 3mm jet orifice. A mica heating element bolted to the bottom of the copper block provides a uniform heat flux. Thermocouples embedded in the copper block are used to determine the surface temperature. Nusselt numbers obtained from experimental sCO2 data are compared to area-averaged Nusselt numbers from air-derived correlations. The comparisons showed that air correlations drastically underpredict the heat transfer when sCO2 is used as the working fluid. A modified sCO2 correlation using experimental data at discussed conditions is derived based on an existing air correlation.

Richardson, John↗

Optimizing Heat Recovery with Storage: Control Validation and Sensitivity Analysis of the Time-Independent Energy Recovery Plant Using Modelica

Heat recovery in large building central plants saves energy but traditionally requires simultaneous heating and cooling. The Time-Independent Energy Recovery (TIER) plant shifts this paradigm by integrating thermal energy storage (TES) to enable heat recovery regardless of concurrent demand, offering a highly efficient, space-saving solution to achieve California’s energy goals. However, its integration of heat recovery chillers, cooling-only chillers, cooling towers, and trim air-source heat pumps (ASHPs) creates growing control and sizing complexity. To overcome this, this study employs high-fidelity Modelica dynamic simulation to validate TIER control sequences and optimize equipment sizing. We translated the written Sequences of Operation into executable Control Description Language (CDL) to test logic against sub-hourly loads. This verification workflow successfully identified and resolved critical vulnerabilities, such as thermal storage freezing and equipment short-cycling, in a virtual environment prior to physical deployment. Then, the study analyzes TIER plant performance across three simulated building types in three locations, and a real building load profile, ensuring variety in heating and cooling loads, and simultaneity factors and explores sizing rules for the TES and ASHP capacity. The analysis shows that the TIER plant operates equipment efficiently leading to a plant SCOP of around 7.5 across all scenarios, higher than a traditional ASHP plant, and a viable pathway to de-risk complex system design and control through simulation to identify optimal designs that maximize energy efficiency, minimize operational costs, and ensure robust operation in varied environmental conditions, thereby facilitating the broader adoption of such a solution for large buildings.

Zanetti, Ettore↗

Direct Quantification of Heat Generation Due to Inelastic Scattering of Electrons Using a Nanocalorimeter

Transmission electron microscopy (TEM) is arguably the most important tool for atomic-scale material characterization. A significant portion of the energy of transmitted electrons is transferred to the material under study through inelastic scattering, causing inadvertent damage via ionization, radiolysis, and heating. In particular, heat generation complicates TEM observations as the local temperature can affect material properties. Here, the heat generation due to electron irradiation is quantified using both top-down and bottom-up approaches: direct temperature measurements using nanowatt calorimeters as well as the quantification of energy loss due to inelastic scattering events using electron energy loss spectroscopy. Combining both techniques, a microscopic model is developed for beam-induced heating and to identify the primary electron-to-heat conversion mechanism to be associated with valence electrons. Building on these results, the model provides guidelines to estimate temperature rise for general materials with reasonable accuracy. This study extends the ability to quantify thermal impact on materials down to the atomic scale.

42 ENGINEERING↗

Asymmetric response of cross-equatorial ocean heat transport to latitudinal thermal forcing in CESM

The partitioning of cross-equatorial heat transport between the atmosphere and the ocean is investigated through a series of fully coupled experiments, where external radiative forcing is applied over different latitudinal bands. The modeling results reveal a first-order collaborative relationship between the ocean and the atmosphere. In response to low-latitude perturbations, the cross-equatorial heat transport is realized mainly through the atmosphere, as the total ocean heat transport (OHT) is largely offsets by its horizontal gyre component. However, as perturbations shift to higher latitudes in both hemispheres, the OHT responses become more important. Here, we also find a significant interhemispheric asymmetry in the cross-equatorial heat transport, with the OHT contribution being more important in the Southern Hemisphere. This asymmetry is mainly attributed to different responses in the changes of the ocean circulation. When the radiative forcing is placed over the Southern Ocean, a buoyancy-driven clockwise cell is generated that extends from the Southern Ocean into the tropics in both the Indo-Pacific and Atlantic basins, effectively transporting energy to the northern hemisphere. Conversely, when the radiative forcing is placed over the northern high latitudes, the weakening of the Atlantic Meridional Overturning Circulation is responsible for the anomalous southward heat transport.

54 ENVIRONMENTAL SCIENCES↗

Thermo-Hydro-Mechanical Modeling of Brine Migration in a Heated Borehole Test in Bedded Salt

Abstract This research paper focuses on the thermo-hydro-mechanical (THM) modeling of brine migration in a heated borehole test conducted as part of the ongoing Brine Availability Test in Salt (BATS) at the Waste Isolation Pilot Plant (WIPP) in New Mexico. It is a component of the international collaboration project DECOVALEX-2023 (DEvelopment of COupled models and their VALidation against EXperiments), which aims to understand the THM processes governing brine flow in heated rock salt repositories through collaborative analysis by multiple research teams. Using the TOUGH–FLAC simulator, THM simulations were performed and compared with data from the BATS phase 1a. This experiment involved two identical horizontal-borehole arrays, one heated and one serving as a control, both equipped with sensor arrays. Analysis of measurements revealed water flow rate surges during heater power transitions, with the highest jump observed during cooling. Acoustic emission activity exhibited distinct patterns in response to heater power changes, suggesting that damage to rock salt is particularly pronounced during the cooling phase. The THM simulations successfully captured these phenomena, highlighting the significance of thermal effects, brine migration, and mechanical behavior in predicting brine availability in heated and damaged rock salt. Our modeling also revealed the critical interplay between heating and cooling-induced damage and its influence on flow properties, particularly affecting brine inflow estimation. Notably, we found that cooling-induced brine inflow spikes result from increased permeability due to tensile dilatancy. These findings have important implications for the development of robust containment strategies and enhance our understanding of the complex processes involved in repository performance.

58 GEOSCIENCES↗

A critical review of electrochemical heat pump technologies: Status, challenges, and perspectives

The development of advanced heat pump technologies is critical for reducing global energy consumption in the building sector, where space heating and cooling account for nearly 50% of energy use. Electrochemical heat pumps (EHPs) offer a promising alternative to vapor compression systems by enabling direct electrochemical-to-thermal energy conversion, often with environmentally benign working fluids that exhibit low or zero global warming potential (GWP). Prior literature has predominantly focused on chemically reactive heat pumps, while comprehensive assessments of electrochemical mechanisms remain limited. Here, this review addresses this gap by systematically evaluating the underlying principles, architectures, and performance metrics of EHP systems. Compared to conventional vapor compression systems, EHPs can achieve 10%-30% higher energy efficiency, with reported cooling coefficients of performance (COP c ) ranging from 3.5 to 14.3 under standard operating conditions. Despite these advantages, widespread adoption is hindered by challenges including membrane degradation, electrode fouling, sluggish redox kinetics, and elevated system-level capital costs. To address these limitations, the review outlines three research priorities: (i) the development of advanced membranes, catalysts, and electrode materials with enhanced chemical and mechanical stability; (ii) the application of molecular-level simulations for the rational design of high-performance redox-active working fluids; and (iii) the integration of advanced diagnostic techniques for real-time monitoring and sustained operation of EHPs. By consolidating recent advances and explicitly identifying technological and scientific gaps, this work uniquely contributes a comprehensive framework for guiding future electrochemical heat pump research and facilitating the transition to sustainable thermal management technologies.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Passive cooling designs to improve heat resilience of homes in underserved and vulnerable communities

Disadvantaged communities face a growing threat to staying safe during heat waves, especially during coincident power outages. This study develops a methodology to evaluate the effectiveness of passive cooling measures (those that operate without power) to improve residential building heat resilience. Building performance is simulated for representative homes and on district scales in two disadvantaged communities in Fresno, California. Eleven passive measures are evaluated using four heat resilience metrics with and without grid power. Results show performance of the mitigation measures varies by building characteristics, surrounding environment, and power scenario. The two most effective measures were installing solar-control window films and adding roof insulation. For pre-1978 single-family homes, these two measures can reduce unmet degree-hours (UDH) indoors by 12% and 11% respectively without grid power, or 28% and 37% with grid power. Their respective UDH reductions at district scale typically range 8% — 20% and 4% — 12% without grid power, or 14% — 44% and 8% — 51% with grid power. Top floors have higher overheating risk than lower floors during extreme heat events with coincident power outages. Natural ventilation can help, reducing UDH by 21% — 26%. The methodology and findings from this study can help cities, communities, and utilities develop effective and targeted strategies to promote greater residential heat resilience.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Experimental performance of ejector heat pump operating in the sub-critical mode

Ejector heat pump (EHP) is an efficient-energy technology with a promising potential to replace the vapor compression cycle in heating and cooling applications. It can be powered by low-grade waste heat and uses environmentally friendly working fluids. EHP has also become a viable solution in research seeking cooling applications. However, little attention has been paid to using EHP for heating purposes. In order to investigate this, a steam EHP for domestic water heating was designed and built. The coefficient of performance (COP) is evaluated at various operating and design conditions in sub-critical operational modes to achieve higher condensation temperatures. Two primary nozzles with a throat diameter of 1.5 mm and 2.0 mm were investigated. The primary nozzle is movable along the ejector’s axis, allowing investigation of its positional effects on the EHP’s COP. Further, experimental measurements revealed that using a smaller throat diameter results in a high COP and low back pressure. The EHP COP and back pressure increase when the LTE temperature increases. Using a throat diameter of 1.5 mm, the EHP COP increases as the nozzle exit position (NXP) becomes closer to the constant area section. A COP of 2.42 and a back pressure of 4.28 kPa are achieved at a high-temperature evaporator (HTE) temperature of 130 °C and a low-temperature evaporator (LTE) temperature of 30 °C using a primary nozzle with 1.5 mm.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Dynamic Behavior of Oval-Twisted Helical Tube Heat Exchanger: Numerical Study with RELAP5-3D

Convective heat transfer characteristics and theoretical thermal stress behaviors are numerically calculated using RELAP5-3D for the helical-coiled once-through steam generator (H-OTSG) and the novel heat exchanger design known as the oval-twisted helically coiled heat exchanger (OTHCHX) under (1) fluctuating wall temperature conditions, (2) square-wave pulsating flow conditions, and (3) the combined effects of fluctuating wall temperature and square-wave pulsating flow conditions. Heat transfer coefficient models for the H-OTSG and OTHCHX were developed based on existing data and implemented into RELAP5-3D, successfully capturing the N⁢uavg behavior within 8% to 10% of the reported data. Under fluctuating wall temperature conditions, the OTHCHX displayed higher N⁢u avg behavior than the H-OTSG. As 𝑓 increased, the $𝜎^{𝑚⁢𝑎⁢𝑥}_{𝑡⁢ℎ}$ decreased. The $𝜎^{𝑚⁢𝑎⁢𝑥}_{𝑡⁢ℎ}$ was higher for the OTHCHX than for the H-OTSG under fluctuating wall temperature conditions. Under pulsating flow conditions, the H-OTSG and OTHCHX displayed much higher 𝑁⁢𝑢 𝑎𝑣𝑔 than under constant flow conditions. The H-OTSG displayed a higher $𝜎^{𝑚⁢𝑎⁢𝑥}_{𝑡⁢ℎ}$ over the OTHCHX. Under combined fluctuating wall temperature and pulsating flow conditions, the augmented heat transfer behavior from the pulsating flow was counteracted by the wall temperature fluctuations, producing slightly higher 𝑁⁢𝑢 𝑎𝑣𝑔 over constant wall temperature, constant flow conditions, but much lower than only constant pulsating flow under constant wall temperature conditions. The effects of simultaneous wall temperature fluctuations and square-wave pulsating flow caused higher $𝜎^{𝑚⁢𝑎⁢𝑥}_{𝑡⁢ℎ}$ than that of only wall temperature fluctuations or pulsating flow. As the Reynolds number (Re) increased, $𝜎^{𝑚⁢𝑎⁢𝑥}_{𝑡⁢ℎ}$ increased. However, when 𝑓=𝑓$_{\dot{m}}$, the $𝜎^{𝑚⁢𝑎⁢𝑥}_{𝑡⁢ℎ}$ showed decreasing values as Re increased. In conclusion, the results indicate that thermal-fluid resonance can help mitigate thermal stresses.

Thermal stress↗

Edge localized mode characteristics and divertor heat flux during stationary and transient phase for CFETR hybrid scenario

The study of edge localized mode (ELM) behavior, stationary heat flux and transient heat flux during the ELM crash phase is performed for a China Fusion Engineering Test Reactor (CFETR) 1 GW hybrid mode operation scenario ($R$ = 7.2 m, ${B_{\text{T}}}$ = 6.5 T, ${I_{\text{p}}}$ = 13.78 MA). Modeling and simulation start with a scenario obtained by multi-code integrated modeling on the one modeling framework for integrated tasks framework. Linear stability and nonlinear simulations of ELM dynamics are carried out using the BOUT++ six-field reduced magnetohydrodynamic module, which show a much smaller ELM energy loss (Δ ELM ~ 0.13%) compared to that of a Type-I ELM. Parametric analysis of the weak linear growth rate and small ELM energy loss characteristics shed light on physics corresponding to a grassy ELM regime for CFETR 1 GW hybrid scenario. The transient heat flux on the divertor target during this small ELM phase is investigated using BOUT++. Here we found that upstream radial transport in the scrape-off-layer (SOL) induced by small ELMs is weak, which keeps it in the drift-dominated region. However, the heat flux width is still broadened to ${\lambda _{\text{q}}}$ = 4.64 mm by the increase of separatrix temperature during ELM nonlinear evolution. The impact of transient peak heat load and ELM energy fluence on tungsten melting and net erosion rate of divertor target is evaluated for the first-time using physics-based transport that connects the pedestal with the SOL. Energy fluence caused by a single ELM pulse is below the tungsten melting limit, while tungsten erosion would exceed the material requirements. We conclude that external mitigation methods, such as divertor detachment and advanced divertor geometry are likely needed for the steady state operation of CFETR.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

RF antenna helicity dependent particle heating in a helicon source

Experiments have demonstrated that ion phenomena, such as the lower hybrid resonance, play an important role in helicon source operation. Damping of the slow branch of the bounded whistler wave at the edge of a helicon source (i.e. the Trivelpiece-Gould mode) has been correlated with the creation of energetic electrons, heating of ions at the plasma edge, and anisotropic ion heating. Here we present ion velocity distribution function measurements, electron density and temperature measurements, and magnetic fluctuation measurements on both sides of an m = |1| helical antenna in a helicon source as a function of the driving frequency, magnetic field strength, and magnetic field orientation relative to the antenna helicity. Significant electron and ion heating (up to two times larger) occurs on the side of the antenna consistent with the launch of the m = +1 mode. The electron and ion heating occurs within one electron skin depth of the plasma edge, where slow wave damping is expected. The source parameters for enhanced particle heating are also consistent with lower hybrid resonance effects, which can only occur for Trivelpiece-Gould wave excitation.

wave modes↗