Main Physical Processes Research Articles

Plastic strain effect on cleavage microcracks propagation in probabalistic statement. Part 1. Formulation of the problem and research methods

The first part considers the main physical and mechanical processes occurring under tension of round bars. The procedure is presented that allows one to describe the plastic strain effect on the critical brittle fracture stress in probabilistic statement. The main statements of Prometey model for prediction of fracture stress are also presented. The investigations are carried out for two materials: 2Cr–Ni–Mo–V steel used for WWER-1000 RPV in the thermally-embrittled state and low-alloyed low-strength steel of St3 grade taken as model material ruptured by cleavage up to plastic strain up to 50%.

Circumlunar Dusty Plasma: Main Physical Processes and Experimental Data Obtained during the “Luna-25” Mission

Circumlunar Dusty Plasma: Main Physical Processes and Experimental Data Obtained during the “Luna-25” Mission

Analytical solutions for the advective–diffusive ice column in the presence of strain heating

Abstract. A thorough understanding of ice thermodynamics is essential for an accurate description of glaciers, ice sheets and ice shelves. Yet there exists a significant gap in our theoretical knowledge of the time-dependent behaviour of ice temperatures due to the inevitable compromise between mathematical tractability and the accurate description of physical phenomena. In order to bridge this shortfall, we have analytically solved the 1D time-dependent advective–diffusive heat problem including additional terms due to strain heating and depth-integrated horizontal advection. Newton's law of cooling is applied as a Robin-type top boundary condition to consider potential non-equilibrium temperature states across the ice–air interface. The solution is expressed in terms of confluent hypergeometric functions following a separation of variables approach. Non-dimensionalization reduces the parameter space to four numbers that fully determine the shape of the solution at equilibrium: surface insulation, effective geothermal heat flow, the Péclet number and the Brinkman number. The initial temperature distribution exponentially converges to the stationary solution. Transient decay timescales are only dependent on the Péclet number and the surface insulation, so higher advection rates and lower insulating values imply shorter equilibration timescales, respectively. In contrast, equilibrium temperature profiles are mostly independent of the surface insulation parameter. We have extended our study to a broader range of vertical velocities by using a general power-law dependence on depth, unlike prior studies limited to linear and quadratic velocity profiles. Lastly, we present a suite of benchmark experiments to test numerical solvers. Four experiments of gradually increasing complexity capture the main physical processes for heat propagation. Analytical solutions are then compared to their numerical counterparts upon discretization over unevenly spaced coordinate systems. We find that a symmetric scheme for the advective term and a three-point asymmetric scheme for the basal boundary condition best match our analytical solutions. A further convergence study shows that n≥15 vertical points are sufficient to accurately reproduce the temperature profile. The solutions presented herein are general and fully applicable to any problem with an equivalent set of boundary conditions and any given initial temperature distribution.

SPECIFICS OF DESIGNING AN INFRARED PYROMETER-REFLECTOMETER FOR SEMICONDUCTOR HETEROSTRUCTURE FABRICATION

There are general technical requirements for all types of reactors for chemical vapour deposition technology using AIII- BV metalorganic compounds. Among them, it is worth highlighting the large temperature gradients that cause the origin of convection loops, which in turn, taking into account the high speed of the gas flow, lead to turbulence in the reactor instead of the expected laminar flow. It is also important to take into account the change in parameters of the wafer surface during the growth process and the need for signal separation between the useful signal from the wafer surface and the background signal from the wafer carrier, which rotates at fixed speed for uniform deposition of compounds. To obtain high-quality heterostructures with reproducible parameters, it is important to have a system of precise temperature control on the wafer surface directly in the deposition area, since the deposition process for many complex semiconductor devices (for example, laser diodes, LEDs, photodiodes, transistors on heterojunctions) is very sensitive to temperature changes. The method of optical pyrometry is a non-contact method that allows to precisely determine the temperature of the wafer surface and meets the technical requirements of CVD epitaxy growth reactors. This article is devoted to the analysis of the features of the development of optoelectronic systems for precise temperature measurement during epitaxial growth in order to determine the criteria for the selection or development of components of the optoelectronic system of the pyrometer-reflectometer. The main physical processes, electro-optical characteristics of Si photodiode, AlGaAs/GaAs LED and parameters of bandpass interference filters were investigated. Based on the analysis of the obtained research and measurement results, scientific recommendations have been developed. The recommendations aimed at the selection and optimization of the parameters of the components of the pyrometer-reflectometer (photodetectors, light emitting diodes, optical filters) in order to improve the accuracy and temperature stability of measurements in the pyrometer’s operation conditions, which take into account the compensation of emissivity change from the surface of the wafer.

Intense lateral intrusion of offshore sub-surface waters in Halifax Harbour

The main physical processes affecting the circulation variability in Halifax Harbour (HH), including the intense lateral intrusion of offshore sub-surface waters into Bedford Basin (BB), are studied using a nested-grid modelling system (NGMS). The annual and monthly mean circulation in HH are characterized by a typical two-layer estuarine circulation, with seaward currents in the upper layer and landward currents in the lower layer, both showing strong temporal and spatial variability. The intense lateral intrusion of offshore sub-surface waters into BB occurs at time scales of a few days. The intense intrusion, in combination with winter connection, is important for the renewal of deep waters in BB. The model sensitivity experiments suggest that the persistent northwesterly winds strengthen the near-surface seaward currents and the lateral intrusion of offshore sub-surface waters into BB. The persistent southwesterly winds can also trigger the lateral intrusion, but are less effective than the northwesterly winds. The southeasterly winds, on the contrary, reduce significantly the seaward currents in the surface layer and prevent the lateral intrusion. The accumulative effects of winds and tides on the 3D hydrodynamics in HH are also examined. Local winds have dominant effects on the 3D currents and temperature/salinity, through driving vertical mixing and coastal upwelling. By comparison, tides play a secondly role in affecting the currents and temperature/salinity in BB but are important in the Narrows.

Simple 3D PIC Analysis for Beam Phase Space Oscillation in RF Driven Negative Hydrogen Ion Source

Temporal oscillation of the negative hydrogen ion (H−) beam in the Radio Frequency (RF) ion source is investigated by a simple 3D3V Particle-In-Cell (PIC) model. The model solves electron, proton, and H− transport processes in the extraction region. The calculation domain is from the vicinity of the beam aperture to the ground electrode. To understand the relation between the plasma density oscillation and the extracted H− beam characteristics, the input electron and proton fluxes from the driver region are varied parametrically with the fundamental J-PARC RF frequency (2 MHz). The numerical results give an idea of the main physical processes between the oscillations of the plasma parameters and the extracted H− ion trajectories depending on the plasma meniscus shape in the different RF phases.

Impact of gas hardening on the population properties of hierarchical black hole mergers in active galactic nucleus disks

Hierarchical black hole (BH) mergers in active galactic nuclei (AGNs) are unique among formation channels of binary black holes (BBHs) because they are likely associated with electromagnetic counterparts and can efficiently lead to the mass growth of BHs. Here, we explore the impact of gas accretion and migration traps on the evolution of BBHs in AGNs. We have developed a new fast semi-analytic model, that allows us to explore the parameter space while capturing the main physical processes involved. We find that an effective exchange of energy and angular momentum between the BBH and the surrounding gas (i.e., gas hardening) during inspiral greatly enhances the efficiency of hierarchical mergers, leading to the formation of intermediate-mass BHs (up to 104 M⊙) and triggering spin alignment. Moreover, our models with efficient gas hardening show both an anticorrelation between the BBH mass ratio and the effective spin and a correlation between the primary BH mass and the effective spin. In contrast, if gas hardening is inefficient, the hierarchical merger chain is already truncated after the first two or three generations. We compare the BBH population in AGNs with other dynamical channels as well as isolated binary evolution.

Modifying single-crystal silicon and trimming silicon microring devices by femtosecond laser irradiation

Single-crystal silicon (c-Si) is a vital component of photonic devices and has obvious advantages. Moreover, femtosecond-pulsed laser interactions with matter have been widely applied in micro/nanoscale processing. In this paper, we report the modification mechanisms of c-Si induced by a femtosecond laser (350 fs, 520 nm) at different pulse fluences, along with the mechanism of this technique to trim the phase error of c-Si-based devices. In this study, several distinct types of final micro/nanostructures, such as amorphization and ablation, were analyzed. The near-surface morphology was characterized using optical microscopy, scanning electron microscopy, and atomic force microscopy. The main physical modification processes were further analyzed using a two-temperature model. By employing Raman spectroscopy, we demonstrated that a higher laser fluence significantly contributes to the formation of more amorphous silicon components. The thickness of the amorphous layer was almost uniform (approximately 30 nm) at different induced fluences, as determined using transmission electron microscopy. From the ellipsometry measurements, we demonstrated that the refractive index increases for amorphization while the ablation decreases. In addition, we investigated the ability of the femtosecond laser to modify the effective index of c-Si microring waveguides by either amorphization or ablation. Both blue and red shifts of resonance spectra were achieved in the microring devices, resulting in double-direction trimming. Our results provide further insight into the femtosecond laser modification mechanism of c-Si and may be a practical method for dealing with the fabrication errors of c-Si-based photonic devices.

Stress-Strain State of a Welded Joint in Welding a Saddle Branch to a Polyethylene Pipe under Low Temperatures

Purpose of research. The aim of the study is a comparative analysis of the stress-strain states of welded joints during welding of saddle branches to existing gas pipelines under normal conditions using standard technology and low temperatures using the proposed technology.Methods. To achieve the goal, a numerical implementation of the mathematical model of the thermoelastic state by the finite element method in the Python programming environment using the Fenics computing package was performed. The computational grid was built using the GMSH program. Visualization of the obtained results was implemented using the Paraview package.Results. On the basis of computational experiments of welding a saddle branch to an existing gas pipeline at permissible and low ambient temperatures, the dynamics of the temperature fields, stresses and strains in the heataffected zone are almost identical.Conclusion. The calculation results showed that when welding saddle branches to polyethylene pipes of existing gas pipelines at low temperatures using the proposed technology, the main physical and mechanical processes will proceed as in welding under normal conditions and provide the necessary strength.

Using a Combination of High-Frequency Coastal Radar Dataset and Satellite Imagery to Study the Patterns Involved in the Coastal Countercurrent Events in the Gulf of Cadiz

This study exploits the combination of High-Frequency Coastal Radar (HFR) information with satellite-derived observations to characterize the patterns involved in the coastal countercurrents (CCCs) events in the Gulf of Cadiz (GoC), which is situated in the SW of the Iberian Peninsula. The westward alongshore currents are observed throughout the year, but the main drivers necessary to develop this flow and its extension in both parts of the basin are not fully clear. In order to identify the main physical processes (both local and remote) that induce the development of these countercurrents and to evaluate the connection of the circulation patterns between the eastern and the western part of the GoC, we make use of several data sources available for the region. First of all, a land-based system of HFR antennas located at four different sites of the GoC provides the velocity field of the surface circulation of the basin. To achieve a significant characterization of the CCCs in the Gulf, the dataset analyzed is processed by means of a series of operations, including the Empirical Orthogonal Functions (EOFs) analysis used to identify spatial and temporal variability of the flow, a low-pass filter used to isolate the sub-inertial signal of the current and temporal interpolation to fill in the missing values. Secondly, given the known importance of the zonal component of the local winds combined with the variations in the mean pressure at sea level over the Western Mediterranean during these events, time series of meteorological data are processed and correlated with the current velocity series via a statistical analysis. Finally, sea surface temperature fields and chlorophyll-a distribution patterns are used as tracers to obtain information on the extension of the countercurrents where HFR data are missing in four cases studied during the year 2017. The conducted analysis revealed the consistent occurrence of westward coastal currents throughout the year, driven in the most intense cases by a combination of the zonal component of the local wind and atmospheric pressure fluctuations over the Western Mediterranean Sea. During those events, CCCs reached the Portuguese side of the Gulf and facilitated the advection of biological material and warmer waters.

Investigation of thermal behavior of powder stream and molten pool during laser-based directed energy deposition

Laser-powder interaction and molten pool evolution are two main physical processes in laser-based directed energy deposition (L-DED), which greatly affect the morphology and quality of the deposition layer. In this research, a comprehensive three-dimensional analytical-numerical model which integrates a laser-powder interaction model and material deposition model is developed to study the multi-physics coupling characteristics in L-DED process. The concentration of the powder stream is modeled based on conservation of mass and is in good agreement with the experimental result which is captured by high-speed camera. The effects of main parameters, including laser power, powder feeding rate, powder feeding angle and defocus length on the laser attenuation and the temperature distribution of the in-flight powder particles are analyzed. The results show that the laser attenuation rate increases from 0.72% to 1.36% with the powder feeding angle increasing from 45 deg. to 65 deg-. However, the laser attenuation rate is almost the same with the defocus length of 25 mm, 35 mm and 45 mm. Moreover, the peak powder temperature on the deposition surface increases with the increase of powder feeding angle and decrease of defocus length. Accordingly, the heat and mass input conditions at the molten pool surface for the material deposition model, including powder mass flux, effective laser intensity and powder temperature are obtained from the laser-powder interaction model. The heat transport and fluid dynamics of the molten pool are discussed based on the calculated results from material deposition model. Finally, the calculated molten pool geometry shows good agreement with the experimental results with the relative error <8.5%. This work is helpful in process optimization from the point of view of adjusting the parameters related to the powder stream and deeper understanding of laser-powder interaction and molten pool evolution during the L-DED process.

Criteria for distinguishing heterogeneous from homogeneous conditions for aromatic diisocyanates in water.

Environmental fate and toxicity testing typically requires knowledge of the water solubility of the test substances. Determining the solubility of aromatic diisocyanates in water poses great challenges because of their hydrophobic nature and water-reactivity. The reactive dissolution process is dynamic and the establishment of a steady-state equilibrium cannot readily be observed. In preparation of experimental work, computer simulation was used to derive and evaluate criteria that enable distinguishing homogeneous (i.e., substances would be fully dissolved in water) from heterogeneous (i.e., a separate organic phase would be present) conditions. The simulation utilized available kinetic information and models representing the main physical and chemical processes taking place. It was found that the transition to heterogeneous conditions (i.e., the exceedance of the solubility limit with increasing loading) can be identified by observing either a rapid decline in ultimate yield of the diamine hydrolysis product from near-stoichiometric to much lower values, or a decrease in rate of formation of the diamine hydrolysis product relative to its ultimate yield. The latter criterion is expected to be the more powerful indicator. These criteria can be used in future work to define and interpret an experimental program for determining solubility limits for aromatic diisocyanates or other poorly-soluble, water-reactive substances.

Разработка алгоритма передачи данных по каналу связи в программной среде Matlab

In order to avoid interference both between symbols and between subcarriers, the use of orthogonal frequency division multiplexing (OFDM) is common in communication systems, so the article investigates data transmission over a communication channel using orthogonal frequency multiplexing (OFDM) technology. The features of the orthogonal frequency division multiplexing technology are considered in this work. Also, the algorithm for the process of data transmission over a communication channel has been developed. The development of the software algorithm was carried out using the Matlab programming environment, since Matlab provides for a large number of different mathematical operations, which makes it possible not to write the detailed code of these operations, thereby allowing to highlight the main physical processes in the algorithm, which simplifies its development. And finally, the assessment of the accuracy of the data transmitted using the developed algorithm was carried out because the final stage of the developed algorithm is the image matrix forming from the binary data stream obtained after the demodulation and the results displaying, which are the restored and original images, the signal constellation graph and the BER parameter. In conclusion, a graph of the dependence of the BER parameter on the value of SNR is given.

Physical effects from the powerful Tonga volcanic eruption of January 15, 2022, in the earth–atmosphere–ionosphere–magnetosphere system

The powerful Tonga volcanic explosion and eruption has been reliably determined to cause numerous processes on a global scale; nevertheless, a comprehensive model of these processes is absent in the literature, which remains an urgent scientific objective. The purpose of this paper is to thoroughly analyze and model the main physical processes that accompanied the volcanic explosion within the Earth (lithosphere, tectonosphere, ocean) – atmosphere – ionosphere – magnetosphere (EAIM) system on January 15, 2022. The study attempts, for the first time, to comprehensively model or estimate the magnitude of the main effects arising in the solid Earth, the troposphere, the ionosphere, and in the magnetosphere. The effects include a rich assortment of waves: Lamb, sound, seismic, tsunami, infrasonic, and atmospheric gravity waves, which propagated on a global scale, with the blast wave launching secondary tsunamis and seismic waves. The powerful waves nonlinearly distorted their profiles and suffered nonlinear attenuation, while the electrical processes in the troposphere caused perturbations in the global electric circuit enhancing the strength of the ionospheric electric fields by one to two orders of magnitude that led to the emergence of secondary processes in the magnetosphere and radiation belts. The volcanic explosion excited all resonators in the EAIM system, perturbing their parameters. Resonances occurred in the Earth's solid shell (Rayleigh wave), in the Earth–ionosphere cavity (Schumann resonances), in the atmosphere (acoustic resonance), in the ionosphere (Alfvén resonances), and in the magnetosphere (magnetospheric resonance). The magnetic effect has been estimated of the submarine volcanic explosion and eruption (∼100–1000 nT), the tsunami (∼0.1 nT), of the volcanic plume (∼1–10 nT), and in the ionosphere due to the ionospheric hole (ΔB ∼ 0.1–10 nT) and an external current in the atmospheric wave field (ΔB ∼ 0.1–1 nT). The magnetospheric effects were caused by electromagnetic emissions in the ∼10–100 kHz band generated by lightning in the volcanic plume, which triggered the precipitation of energetic radiation belt particles into the ionosphere. This is the first time that feedback and main coupling processes, positive and negative, have been observed to emerge among the EAIM system components.

Sub-daily rainfall patterns in the mountainous regions of the Island of Tahiti: Insights from a one-year rain gauge network expansion

Study regionThe Island of Tahiti in French Polynesia (17.5°S,149.5°W), with a focus on the mountainous regions of the island interior. Study focusThe high topography of Tahiti creates an obstacle for wet air masses traveling along the surface of the South Tropical Pacific Ocean, which forces air flow uplift and triggers orographic rainfall. Although the main physical processes behind orographic rain enhancement on tropical islands were identified, the ways they shape Tahitian rain fields are still not fully understood, particularly due to a lack of observations. To address the limitations posed by this shortage of rain data, this study describes the temporary expansion of the rain gauge network of Tahiti towards the mountainous island interior, and uses the resultant dataset to investigate the spatial and temporal patterns of orographic rainfall at sub-daily resolution. New hydrological insights for the regionThe analysis of the rain gauge observations on daily and shorter time-scales leads to the identification of three main types of rainfall patterns: (1) a Dry Season Trade Winds type linked to a persistent Trade Winds Inversion (TWI) and characterized by moderate orographic rainfall in windward slopes, dry conditions in most leeward areas, and localized mid-afternoon showers in the mountains downwind of the main summit of the island; (2) a Transition Season Trade Winds type linked to atmospheric disturbances weakening the TWI, and characterized by intense orographic rainfall in windward slopes and mountains, and frequent showers in leeward areas by overshoot of the main crest; and (3) a SPCZ-related type occurring when the South Pacific Convergence Zone (SPCZ) crosses Tahiti during the wet season, and characterized by intense and widespread rainfall throughout the island with clear diurnal cycle and peak intensities recorded in the mid-afternoon.

High‐Energy Electron Flux Enhancement Pattern in the Outer Radiation Belt in Response to the Interplanetary Coronal Mass Ejections

AbstractThe high‐energy electron flux enhancement pattern in the outer radiation belt is observed under the influence of the Interplanetary Coronal Mass Ejections (ICMEs). Ten events were selected during the Van Allen Probes era, with the high‐energy electron flux enhancement starting close to L* = 4. A schematic diagram of the main physical processes responsible for this kind of high‐energy electron flux enhancement is presented, considering the energy deposited in the inner magnetosphere under the influence of ICMEs. Superposed Epoch Analysis is applied to the interplanetary medium parameters, the magnetopause standoff distance, the storm‐time geomagnetic activity indices, the Ultra‐Low Frequency (ULF) waves, and the whistler‐mode chorus waves. A compressed magnetopause, Bz component preferentially southward and storm indices considerably high are observed at the beginning of the electron flux enhancements. The modeled parameters of the chorus waves at the dayside/nightside sectors show the high acceleration efficiency at the beginning of the electron flux enhancement pattern II. These results suggest that the local acceleration driven by chorus waves is essential to these electron flux enhancements at low L*. In contrast, although the ULF waves are detected at the beginning of the studied electron flux enhancements, their contribution is insignificant.

Influence of Internal Erosion on Rainfall-Induced Instability of Layered Deposited-Soil Slopes

Layered deposited-soil slopes are widely distributed in mountainous terrain. The rainfall-induced instability of layered deposited-soil slopes is not only controlled by the unsaturated infiltration process but also by the seepage-induced internal-erosion process within the deposited soils. In this paper, the main physical processes within two-layer deposited-soil slopes under rainfall infiltration are summarized, and a coupled seepage–erosion finite element model is established to analyze the interactions between the rainfall infiltration process and the internal-erosion process within layered deposited-soil slopes. This finite element model was validated by simulating the coupled seepage–erosion process in a one-dimensional layered soil column. Then, serials of two-dimensional coupled seepage–erosion simulations were conducted to investigate the rainfall-induced seepage–erosion patterns, as well as their impact on the stability evolution of the layered deposited slopes. It was shown that the rainfall-induced seepage–erosion accelerate the water infiltration into the slope and facilitate the generation of subsurface stormflow near the layer interface, which will weaken the soils around the layer interface and accelerate the slope failure process inevitably. Special attention should be paid to the rainfall-induced seepage–erosion effect when evaluating the stability of layered deposited-soil slopes.

Understanding Surface Air Temperature Cold Bias Over China in CMIP6 Models

AbstractThe systematic simulated cold biases in models for surface air temperature (SAT) over China have been under discussion for a long time, but the related attribution is still unclear. In this study, we investigate the main contributors and relevant physical processes of SAT biases over China based on 31 models participating in the sixth phase of the Coupled Model Intercomparison Project from a surface energy budget perspective. On annual and seasonal scales, less downward clear‐sky longwave radiation in the models, which is due to the underestimated tropospheric temperature and water vapor amount, is the main cause of cold biases over the Tibetan Plateau, Tarim Basin, Sichuan Basin, and most of eastern China. Meanwhile, the simulation biases in surface albedo and sensible heat flux induce cold biases depending on regions and seasons. In winter and spring, the overestimated surface albedo in association with more snow cover leads to prevalent cold biases over the western Tibetan Plateau and Northeast China. Excessive sensible heat release caused by the overestimated ground–air temperature difference facilitates SAT underestimation in the Sichuan Basin during summer and autumn. In addition, the cold biases in winter and spring are larger than those in summer and autumn, due to the stronger snow cover overestimation and tropospheric temperature underestimation.

Dynamical charging of interstellar dust particles in the heliosphere

Interstellar dust (ISD) particles penetrate the solar system due to the relative motion of the Sun and the local interstellar cloud. Before entering the heliosphere, they pass through the heliospheric interface – the region of the solar wind interaction with the interstellar plasma. The size distribution and number density of dust grains are modified in the interface essentially. The modification depends on the charging of the dust particles along their trajectories. In this paper, we present modeling results of the charging of ISD particles passing through the heliospheric interface. The main physical processes responsible for the charging within the heliospheric conditions are the sticking of primary plasma particles, secondary electron emission, photoemission, and the effects of cosmic ray electrons. We consider two methods to calculate the electric charge of ISD particles based on (1) the classic steady-state assumption that the charge depends only on local plasma and radiation conditions and (2) the dynamical computation of charge along the particle trajectory. We demonstrate that the steady-state assumption is quite justified to model trajectories and number density distributions of relatively big ISD grains (radius of 100 nm and larger) penetrating the heliosphere. The estimates show that ISD grains of these sizes require less than 0.25 years (distance of ≈1 au) after transition from the LISM into the heliosphere to reach an equilibrium. For small particles ( radius of 10 nm), the dynamical computation of charge influences the trajectories and modifies the number density substantially. The dust density accumulations are distributed within a more elongated region along the heliopause in case of dynamically changed charge as compared with the use of a steady-state charge approximation. As a result, the magnitudes of number density at the points of density features differ several times between the results obtained by the two considered approaches.

Fundamental limitations on gain of terahertz quantum cascade lasers

We analyze the main physical processes in quantum cascade lasers with a spatial separation between the region of photon radiation and longitudinal optical (LO) phonon emission, which facilitates the depopulation of the lower level of the optical transition. Our objective is to identify the reasons for the reduction of population inversion at low photon energy and explore methods to enhance it. The expression for population inversion is derived from an equation for a simplified density matrix. This approach allows us to consider the coherence of tunneling between different levels and comprehend its influence on transition probabilities in a straightforward manner. We have found out that the energy uncertainty principle is the fundamental factor limiting population inversion in terahertz lasers. By optimizing the tunneling matrix element between the two regions and the LO phonon emission time, it is possible to significantly increase the population inversion. The optimal value for the matrix element is smaller than its maximum possible value, while the optimal LO phonon emission time exceeds the time achieved during LO phonon resonant emission.