Flux Loss Research Articles

Establishing a high-performance anti-fouling PEI-ZIF-PAA membrane with improved Lewis acid-base interactions and hydrophilicity

Membrane fouling and the trade-off between membrane permeability and selectivity restrict the potential applications of membrane filtration for water treatment. ZIF-8 was found having great permeability and antibiofouling performance, but with issue on particle aggregation makes it difficult to achieve high ZIFs loading and fabricate a defect-free molecular sieving membrane in previous research. In this study, we formed a scalable antibiofouling surface with improved permeability and fouling resistance on a PEI-ZIF-PAA membrane using a layer-by-layer assembly technique. The synergistic effects of being sandwiched between two different polyelectrolyte layers with opposite charges endowed the ZIF nanoparticles with improved stability and scalability for membrane modification. The PEI-ZIF-PAA membrane exhibited a satisfactory water flux of 120.78 LMH, which was 46.97% higher than that of the pristine PES membrane. The normalized water flux loss was serious in the absence of ZIF-8, and the flux increased with the ZIF-8 concentration. Antifouling tests suggested that the PEI-ZIF-PAA membrane possessed good antifouling performance due to the much higher surface hydrophilicity and positive Lewis acid-base interactions with foulants. The HA rejection increased with the ZIF-8 concentration and reached a maximum of 92.1% in the presence of 1.00% (w/v) ZIF-8. The membrane regeneration was tested under physical and chemical cleaning with flux recovery rates of about 85% and 95%. XDLVO analysis showed that the total interaction energy between HA and the PEI-ZIF-8-PAA membrane was 26.45 mJ/m2, and the superior antifouling performance was mainly attributed to Lewis acid-base interactions. This study indicates that ZIF-8 nanocrystals are promising materials for fabricating novel membranes for sewage treatment.

Effect of Temperature Cycling Pretreatment on the Thermal Stability of Sm2(Co, Fe, Zr, Cu)17 Magnets in the Mild Temperature Range.

The irredeemable magnetic losses of Sm(Co, Fe, Zr, Cu)7.8 permanent magnets caused by oxidation are very important for their practical application. In this work, the simulated results with R2 ≥ 98% based on the data of the temperature cycling test and the long-term isothermal test for the original samples confirmed that the magnetic flux losses reached 9.38% after the 5000th cycle in range R.T.-300 °C, and 7.15% after oxidated at 180 °C for 10 years, respectively. Demagnetization curves showed that the low-temperature oxidation mainly led to the remanence attenuation, while the coercivity remained relatively stable. SEM observation and EDS analysis revealed that an oxide outer layer with a thickness of 1.96 μm was formed on the surface of the original sample at 180 °C for 180 days, in which there was no enrichment or precipitation of metal elements. However, once a Cu, O-rich outer layer with a thickness of 0.72 μm was grown by using a temperature cycling from -50-250 °C for three cycles, the attenuation of magnetic properties could be inhibited under the low-temperature oxidation. This work suggested that the magnetic attenuation of Sm2Co17-type permanent magnets in the low-temperature field could not be ignored, and provided a simple method to suppress this attenuation of magnetic properties below 300 °C.

Toroidal Flux Loss due to Flux Emergence Explains why Solar Cycles Rise Differently but Decay in a Similar Way.

A striking feature of the solar cycle is that at the beginning, sunspots appear around midlatitudes, and over time the latitudes of emergences migrate toward the equator. The maximum level of activity (e.g., sunspot number) varies from cycle to cycle. For strong cycles, the activity begins early and at higher latitudes with wider sunspot distributions than for weak cycles. The activity and the width of sunspot belts increase rapidly and begin to decline when the belts are still at high latitudes. Surprisingly, it has been reported that in the late stages of the cycle the level of activity (sunspot number) as well as the widths and centers of the butterfly wings all have the same statistical properties independent of how strong the cycle was during its rise and maximum phases. We have modeled these features using a Babcock-Leighton type dynamo model and show that the flux loss through magnetic buoyancy is an essential nonlinearity in the solar dynamo. Our Letter shows that the nonlinearity is effective if the flux emergence becomes efficient at the mean-field strength of the order of 10^{4} G in the lower part of the convection zone.

Successive Interacting Coronal Mass Ejections: How to Create a Perfect Storm

Coronal mass ejections (CMEs) are the largest type of eruptions on the Sun and the main driver of severe space weather at the Earth. In this study, we implement a force-free spheromak CME description within 3D magnetohydrodynamic simulations to parametrically evaluate successive interacting CMEs within a representative heliosphere. We explore CME–CME interactions for a range of orientations, launch time variations, and CME handedness and quantify their geo-effectiveness via the primary solar wind variables and empirical measures of the disturbance storm time index and subsolar magnetopause standoff distance. We show how the interaction of two moderate CMEs between the Sun and the Earth can translate into extreme conditions at the Earth and how CME–CME interactions at different radial distances can maximize different solar wind variables that induce different geophysical impacts. In particular, we demonstrate how the orientation and handedness of a given CME can have a significant impact on the conservation and loss of magnetic flux, and consequently B z , due to magnetic reconnection with the interplanetary magnetic field. This study thus implicates the identification of CME chirality in the solar corona as an early diagnostic for forecasting geomagnetic storms involving multiple CMEs.

Preparation of chlorine-resistant and regenerable antifouling nanofiltration membrane through interfacial polymerization using beta cyclodextrin monomers

Constructing membrane with good chlorine resistance and antifouling properties is considered to be important challenges confronting membrane applications. In this study, a composite nanofiltration (NF) membrane (β-CDx/y/PES) was prepared by interfacial polymerization using beta cyclodextrin (β-CD) monomers. Subsequently, the β-CD-based (AZ-β-CDx/y/PES) membrane was prepared by assembling azobenzene labeled zwitterions into the hydrophobic internal cavity of β-CD via host-guest interaction. The optimized membrane exhibited slight change in water flux and rejection under chlorine environment. The AZ-β-CDx/y/PES membrane also displayed an evidently lower loss in water flux in the antifouling test in comparison with the β-CDx/y/PES membrane. More interestingly, the trans azo groups in azobenzene labeled zwitterions can turn into the cis isomers as the visible light irradiation converted to the UV light irradiation, breaking the interaction between azobenzene labeled zwitterions and β-CD. Hence, the contaminants upon the membrane surface can be simply eliminated by water washing under UV light irradiation. The antifouling membrane can be regenerated via immersing the reacquired β-CD2/10/PES membrane into fresh azobenzene labeled zwitterions solution again.

Pool boiling experiment with Novec-649 in microchannels for heat flux prediction

Boiling dissipates significant amounts of heat as a result of small temperature differences between a wall and a fluid. For this reason, the heat transfer process is widely used across many industries, e.g. for cooling electronic devices, power sources, etc. In practice, heat dissipation from an electronic device occurs mainly during the controlled heat flux loss through the wall to the coolant. This mechanism was studied for boiling Novec-649 (GWP = 1) at atmospheric pressure on copper surfaces with 0.2 to 0.5 mm deep grooves milled in parallel. The resultant microchannels and the spaces between them were 0.2 mm, 0.3 mm, and 0.4 mm wide. The maximum heat flux for the surface with 0.4 mm deep and 0.3 mm wide microchannels was 274 kW/m2. The highest heat transfer coefficient, 22.3 kW/m2K, was obtained for the surface with a 0.5 mm deep and 0.3 mm wide microchannel. A twofold increase in the maximum heat flux and a fivefold increase in heat transfer coefficient were obtained compared to the smooth surface. The effect of geometric parameters on the heat exchange process was investigated for the heat flux density range of 6.6–274 kW/m2. Diameters and frequencies of departing vapor bubbles were determined experimentally with the use of a high-speed camera. A simplified model was proposed to determine the diameters, frequencies, and heat fluxes at different superheats. The model provided a heat flux prediction with a maximum mean deviation of 35 %.

Heat transfer enhancement by a flexible inverted flag with an inclination angle

The heat transfer system, including an inclined inverted flag that plays a role of a vortex generator, is proposed in the present study. A two-dimensional simulation is performed to analyze the effects of the inclination angle and the bending rigidity of the inverted flag on thermal performance. To consider the fluid-flexible body–thermal interaction, an immersed boundary method is adopted. The four regimes are observed depending on the inclination angle and the bending rigidity, that is, large-amplitude flapping (LAF), small-amplitude flapping (SAF), deflected (D), and straight (S) modes. The SAF and LAF modes are observed to be favorable in terms of the heat transfer efficiency, which considers the heat flux and mechanical energy loss. A scaling analysis is performed to explain the correlation between the flapping kinematics and the thermal quantities. A scaling parameter is newly defined based on the momentum transfer to the inverted flag due to a vortical impulse and shows a proportional relation to the mean drag force with a slope of 0.166. The heat transfer efficiency is observed to be proportional and inversely proportional to the parameter in the SAF and LAF modes, respectively. The optimized heat transfer system is obtained at the angle of 12° and the bending rigidity of 0.7, where the efficiency is enhanced up to 112.8% over the baseline flow.

Unravelling the roles of Indian Ocean Dipole and El-Niño on winter primary productivity over the Arabian Sea

The Northern Arabian Sea (NAS) is a highly productive basin in the Indian Ocean. The marked seasonal variation of surface winds has the major control on the oceanic primary productivity in the NAS. A regional physical and biogeochemical coupled model was used to examine the control of marine physical processes on the primary productivity in the NAS. It is found that the pure positive Indian Ocean Dipole (PPIOD) has positive anomalies, whereas a co-occurrence of El-Niño and positive IOD (CEPIOD) events leads to negative anomalies in winter-time Chlorophyll-a (Chl-a) concentration during 2000–2018. The CEPIOD events are characterized by weaker winter convective mixing than PPIOD events. The evolution of this discrepancy in the convective mixing process is sufficiently explained by the presence of weaker northeasterly (dry and cold) winds (<2.4 m/s) and a lower net heat flux loss (<- 47 W/m2) during CEPIOD as compared to the PPIOD events. Higher convective mixing results in intense convective cooling, a deeper mixed layer depth (MLD), increased nutrients’ injection through entrainment, and a stronger winter bloom, whereas weak convective mixing causes warming and a shallow MLD, resulting in weak winter bloom. The higher-mixing and surface-cooling condition was observed more often in PPIOD than in CEPIOD years. These conditions promote vertical convective mixing that maintains nutrients’ supply in the near-surface layers and supports primary productivity in PPIOD years.

Dependence of radiation belt flux depletions at geostationary orbit on different solar drivers during intense geomagnetic storms

The loss of electron flux of the outer radiation belt has been widely studied in terms of the mechanism that brings in these losses. There are a few studies which have attempted to explain the interplanetary conditions that favor the depletions. As the Sun is the prime cause of any change happening in the magnetosphere, it is important to look at the solar drivers that bring in such changes. In this study, we attempt to understand the effect of solar structures and substructures on the loss of radiation belt high-energy electrons during intense geomagnetic storms. The superposed epoch analysis is used to observe any peculiar changes in GOES electron flux data during the storms that are associated with solar structures such as CME and CIR, ICME substructures such as the magnetic cloud, magnetic cloud with sheath, ejecta, ejecta with sheath, and only sheath. The long-term data also give an opportunity to compare the flux decrease during solar cycles 23 and 24. It has been observed that 1) CIR-associated storms cause a comparatively higher flux decrease than CME-associated storms, 2) sheath-related storms bring out a higher flux decrease, and 3) there is no significant change in flux for the storms of both the solar cycles. The flux decrease in intense storms at the geostationary orbit is essentially triggered by the “Dst effect.” Apart from this, the minimum IMF Bz and northward IMF Bz before turning southward add to the flux decrease. These results hold true for the electron depletions occurring only during intense geomagnetic storms and may alter otherwise.

Study of a High-Power Medium Frequency Transformer Using Amorphous Magnetic Material

A shell-type medium frequency transformer (MFT) using amorphous alloy material is designed for high-power electronic applications. The optimal area product design method is adopted to design an MFT, which maximizes the high efficiency and power density, minimizes the loss and volume, and meets the limitations of insulation and temperature rise. Then, a 20 kVA/10 kHz MFT is designed. To ensure the rationality of the MFT design, the magnetic properties of the amorphous alloy material are measured, and finite element simulations are carried out based on measured magnetic properties. The magnetic flux density, loss, and temperature rise of the designed MFT are analyzed. Finally, a 20 kVA/10 kHz MFT prototype is fabricated, and experimental tests are carried out. The loss and temperature rise of the MFT prototype are within reason, which verifies the effectiveness of the proposed scheme.

The influence of final aging temperature on thermal stability of microstructure and magnetic properties in Sm(Co,Fe,Cu,Zr)z high temperature magnets

The change of microstructure and magnetic properties after heated to high temperature remains a critical concern for the application of SmCo magnets. In this work, the influence of final aging temperature on thermal stability of microstructure and magnetic properties in Sm(Co0.777Fe0.1Cu0.09Zr0.033)7.61 high temperature magnets is studied. Meanwhile, the main structure determining the magnetic loss and underlying mechanism are discussed. The results show that the flux loss mainly stems from the reversed domain structure at grain boundaries, which are defects with incomplete cellular nanostructures. Thus, grain size is the key factor determining the flux loss. When the final aging temperature increases from 400 to 600 °C, the grain size decreases monotonically, leading to higher flux loss. On the other hand, the microstructure and magnetic properties tend to reach the equilibrium state at the operating temperature. Therefore, the thermal stability of microstructure and magnetic properties can be enhanced by reducing the temperature difference between final aging temperature and operating temperature. This work offers in-depth insights into the fundamental understanding of magnetic loss and provides methods to reduce magnetic loss in 2:17-type SmCo magnets. The flux loss can be reduced by increasing the grain size, while irredeemable magnetic properties loss can be reduced by increasing the thermal stability of microstructure.

Simulation of solar neutron flux in the Earth's atmosphere for three selected flares

We performed simulations of the solar neutron (ns) flux in the Earth's atmosphere associated with three significant flares (X17 of September 07, 2005, X1.3 of September 07, 2017 and M2.9 of September 08, 2017). The input of the simulations was calculated on the basis of ns signals detected at ground level by the Solar Neutron Telescope of Sierra Negra (SNT-SN), in Mexico, and by the FIB scintillator of the Space Environment Data Acquisition-Attached Payload on board of the International Space Station. Since ns can produce Extensive Air Showers (EAS) in the Earth's atmosphere, we used the CORSIKA code and FLUKA subroutines to simulate the particle fluxes associated with the X17, X1.3 and M2.9 flares. We studied the average longitudinal variations of particle flux and energy loss through the atmosphere to estimate the ns flux impinging on the SNT-SN. The results of the simulated interactions and multiplicities of the particles, as a function of their energy, showed that 11–13% of the ns, released by the X17 flare, could overcome the atmospheric attenuation and propagate from the top of the atmosphere to the SNT-SN (4580 m a.s.l.) without producing EAS. On the other hand, ns associated with the X1.3 and M2.9 flares were lost due to atmospheric attenuation and the production of new particles; therefore, they were not detected at ground level by the SNT- SN. The characterization of these events allowed to develop an automatic tool for the analysis of ns emissions associated with solar flares.

The Influence of Forward Osmosis Module Configuration on Nutrients Removal and Microalgae Harvesting in Osmotic Photobioreactor

Microalgae have attracted great interest recently due to their potential for nutrients removal from wastewater, renewable biodiesel production and bioactive compounds extraction. However, one major challenge in microalgal bioremediation and the algal biofuel process is the high energy cost of separating microalgae from water. Our previous studies demonstrated that forward osmosis (FO) is a promising technology for microalgae harvesting and dewatering due to its low energy consumption and easy fouling control. In the present study, two FO module configurations (side-stream and submerged) were integrated with microalgae (C. vulgaris) photobioreactor (PBR) in order to evaluate the system performance, including nutrients removal, algae harvesting efficiency and membrane fouling. After 7 days of operation, both systems showed effective nutrients removal. A total of 92.9%, 100% and 98.7% of PO4-P, NH3-N and TN were removed in the PBR integrated with the submerged FO module, and 82%, 96% and 94.8% of PO4-P, NH3-N and TN were removed in the PBR integrated with the side-stream FO module. The better nutrients removal efficiency is attributed to the greater algae biomass in the submerged FO-PBR where in situ biomass dewatering was conducted. The side-stream FO module showed more severe permeate flux loss and biomass loss (less dewatering efficiency) due to algae deposition onto the membrane. This is likely caused by the higher initial water flux associated with the side-stream FO configuration, resulting in more foulants being transported to the membrane surface. However, the side-stream FO module showed better fouling mitigation by simple hydraulic flushing than the submerged FO module, which is not convenient for conducting cleaning without interrupting the PBR operation. Taken together, our results suggest that side-stream FO configuration may provide a viable way to integrate with PBR for a microalgae-based treatment. The present work provides novel insights into the efficient operation of a FO-PBR for more sustainable wastewater treatment and effective microalgae harvesting.

City-wide monitoring and contributing factors to shallow subsurface temperature variability in Nanjing, China

Shallow temperatures down to a depth of 100 m were measured over one year in 19 closed boreholes located in Nanjing, China, to reveal the conditions and factors influencing the subsurface thermal regime. A monitoring concept with distributed temperature sensing, fiber Bragg grating-based sensor, and a type of Resistance Temperature Detectors, is implemented, providing spatial distribution characteristics of subsurface temperatures. The results show that temperatures near the surface are most dynamic, influenced by the air temperature. The temperature remains stable at the depth of 10–20 m. The mean transition temperature is 18.1 °C. Borehole measurements are interpolated by using satellite images and surface temperature records to obtain large-scale surface temperature distributions and temporal variations of subsurface temperature. Geological and hydrological conditions are primary factors by affecting subsurface upward heat flux and heat loss. Urban land cover change and enhanced heat release from urbanization contribute to a subsurface urban heat island with intensities of 1.0–4.4 °C. The altered subsurface thermal regime is of primary concern for the management of shallow geothermal energy use. The monitoring concept in this study can provide spatially-temporally continuous profiles of subsurface temperature and become a reference for city-wide geothermal monitoring in other urban areas.

Antifouling enhancement of thin-film composite polyamide reverse osmosis membrane by surface immersion deposition and in-situ crosslinking method with NaAlg-GA hydrogel

In order to optimize antifouling performance to organic foulants, a commercial polyamide reverse osmosis membrane of composite polyamide material was modified by surface gelation using sodium alginate (NaAlg) as surface coating agent, which was widely known as a natural polymer and environmentally friendly materials. NaAlg-GA hydrogel layer was successfully deposited on commercial membrane surface by combining immersion coating with in-situ crosslinking method and the chemical structure was verified by FT-IR spectroscopy. SEM and AFM was adopted to analyze the changes of morphology and roughness. Zeta potentiometer, and contact Angle analyzer were all used to analyze the hydrophilicity and charge property of relevant NaAlg modified membranes in detail. Specific separation performance was also evaluated by cross-flow filtration tests. Results from above experiments confirmed that NaAlg modified membranes exhibited a surface with more hydrophilic, smoother and more regular, denser negative charge, slightly improved selectivity and lower permeability. Long-term monitored the performance of 100 ppm NaAlg modified membrane, it was found that the rejection rate fluctuated between 98.96% and 99.17%, and the flux ranged from 25.15 ∼ 26.06 L/m2 h during the whole test period, which fully proved that modified membrane had good durability. BSA pollution experiment results showed that the flux attenuation rate of 100 ppm NaAlg modified membrane decreased from 40.87% to 25.01%, and flux recovery rate of contaminated membrane after washing was as high as 90.8%. In addition, the flux of 100 ppm NaAlg modified membrane exceeded that of unmodified membrane after filtrating 20 h. Moreover, with the extension of time, the cumulative flux loss of modified membrane caused by additional resistance at the initial filtration stage would soon be compensated, and it completely exceeded that of unmodified membrane after 40 h. All above results showed that NaAlg-GA hydrogel layer can effectively improve the antifouling performance.

Convective mixing induced by brine rejection and its parameterization using large eddy simulation

Brine rejection is a primary component of deep convection formation, in which the turbulent mixing associated with the convective plume is the key parameter. Large Eddy Simulation (LES) is more suitable for the modeling of convective mixing. In this study, we use LES to investigate the brine rejection-induced convective mixing forced by the loss of salinity flux at the surface. The model domain is set in a stratified, high-latitude location due to brine rejection most often occurring at high latitudes. The control case for the numerical experiments is configured with a horizontal and vertical resolution of 5 m located at 70°N. Results show that the three-dimensional structure of the sinking plume displays an umbrella-like shape with an upward flow along the central axis and downward flows around the central axis, and is associated with a robust anticlockwise vortex below the source of the salinity flux. A series of numerical experiments are conducted to test the sensitivity of three plume characteristic parameters: eddy viscosity, maximum sinking plume depth, and vortex intensity to two environmental variables: negative salinity flux imposed at the surface (SaF) and background stratification (N). Based on the sensitivity experiments, scaling relationships of eddy viscosity and maximum sinking plume depth concerning SaF and N are identified. Additionally, distributions of velocity show that the rotation has a significant inhibition effect on the sinking plume, while the scaling relationship of the sinking plume shows that gravitational force has a much stronger enhancement effect.

A novel conductive carbon-based forward osmosis membrane for dye wastewater treatment

Forward osmosis (FO) membrane fouling is one of the main reasons that hinder the further application of FO technology in the treatment of dye wastewater. To alleviate membrane fouling, a conductive coal carbon-based substrate and polydopamine nanoparticles (PDA NPs) interlayer composite FO membrane (CPFO) was prepared by interfacial polymerization (IP). CPFO-10 membrane prepared by depositing 10 mL of PDA NPs solution exhibited an optimum performance with water flux of 7.56 L/(m2h) for FO mode and 10.75 L/(m2h) for pressure retarded osmosis (PRO) mode, respectively. For rhodamine B and chrome black T dye wastewater treatment, the water flux losses were reduced by 21.6%, and 14.5% under the voltages of +1.5 V, and −1.5 V, respectively, compared with no voltage applied after the device was operated for 8 h. The applied voltage had little effect on the fouling mitigation performance of the CPFO membrane for neutral charged cresol red. After the device was operated for 4 cycles, the rejection rates of dyes wastewater treated by the CPFO membranes with applied voltage were close to 100%. The flux decline rate and flux recovery rate of CPFO membrane for rhodamine B and chrome black T wastewater treatment under application of +1.5 V and −1.5 V voltage after 4 cycles were 11.6%, 99.2%, and 16.7%, 98.9%, respectively. Therefore, the voltage-applied CPFO membrane still maintained good rejection and antifouling performance in long-term operation. This study provides a new insight into the preparation of conductive FO membranes for dye wastewater treatment and membrane fouling control.

Influence of Thickness of Magnetic Shield on Electromagnetic Field and Losses in End Region of Synchronous Condenser

A magnetic shield is widely used in the end region of a synchronous condenser (SC) to decrease the flux densities and losses of the end structural components. In order to investigate the influence of different magnetic shield thicknesses on the distributions of the flux density and loss in the end region, a 300-Mvar SC is selected as the investigation reference in this article. A three-dimensional (3-D) mathematical model used for the calculation of electromagnetic field and loss in the end region of the SC is established. The flux densities and losses of the end structural components are calculated and compared under the different thicknesses of the magnetic shield. From the detailed performance evaluations by the 3-D finite-element analysis, the variation of the flux densities and loss densities in the end region of the SC along with the thickness of the magnetic shield is revealed. The loss distributions of the main end structural components are studied and the end zones where the loss is most significantly affected by the magnetic shield thickness are obtained. The results provide the theoretical basis for the improvement of the loss distribution in the end region of the SC.

Modeling Radiation Belt Electron Dropouts During Moderate Geomagnetic Storms Using Radial Diffusion Coefficients Estimated With Global MHD Simulations

AbstractMain phase flux dropouts often promote depletion of the outer electron radiation belt. The quantification of the contributions of various loss mechanisms to MeV electron dropouts has not yet been elucidated in detailed case studies for moderate geomagnetic storms. This work focuses on quantifying radial diffusion to study relativistic electron flux losses observed by Van Allen Probes during two moderate storms in 2017. The events are identified as Case 1 (27 March), with losses deep in L, and Case 2 (21 November), with less deep losses. Event‐specific radial diffusion coefficients (DLL) were calculated from global magnetohydrodynamic (MHD) fields simulated by the SWMF/BATS‐R‐US. The MHD‐DLL was used as an input to radial diffusion simulations of both events for relativistic electrons. For the outer boundary conditions defined at L* = 6, electron fluxes measured by GOES‐15 at geosynchronous orbit were converted to phase space densities (PSDs) and then calibrated against the Van Allen Probe A measurements. Using these calibrated PSD of GOES‐15 at the outer boundary and event‐specific MHD‐DLL, the main phase dropout is well captured with radial diffusion simulation for Case 2, but not for the deep dropout in Case 1 down to L* &lt; 4.5. Scaling MHD‐DLL based on validations of the MHD waves against in situ wave observations improves the simulation results of Case 1, but still does not fully resolve its deep dropout. However, analyzing the uncertainty of simulated PSD imposed by the uncertainty in the scaled MHD‐DLL, it was found that outward radial diffusion could still account for the losses at L* &lt; 4.5.

Improved electron trajectory and power distribution in APPLE-knot undulator.

The APPLE-Knot undulator has been proposed to reduce the large on-axis heat load of the APPLE-II at very low photon energy. However, the current designs have an inherent non-zero second field integral due to the Knot sections, resulting in a transverse deflection of the electron beam throughout the undulator. For a long device, such a deviation can degrade the brightness and power distribution of the outgoing beam. Here, a new end-Knot section is presented to compensate for the electron trajectory, and the undulator is symmetrized to balance the output power distribution. The performance of the APPLE-Knot with symmetric power distribution is investigated. The partial power, flux, and polarization are compared with the APPLE-II. In the linear mode, APPLE-Knot shows a pronounced reduction of the partial power, with a similar flux to the APPLE-II. The symmetric power density distribution reduces the hotspot by 41%, with a flux loss of less than 5%. In the circular mode and at low photon energies, the flux is limited by the phase error of the symmetric design.