Time-dependent Rate Equations Research Articles

Evolution of level population in Ar interacting with XFEL pulses: impact of resonant absorptions

Theoretical exploration of the population dynamics at fine-structure levels of Ar atoms interacting with ultrafast ultraintense x-ray free electron laser (XFEL) pulses is conducted. A time-dependent rate equation based on a detailed-level accounting approach is applied for tracking population levels, encompassing microscopic atomic processes such as photoexcitation, radiative decay, photoionization and Auger decay. A Monte Carlo algorithm is implemented to solve large-scale rate equations efficiently. The primary investigation centers on generating Ar17+ through resonant absorption by the second-harmonic radiation of the x-ray pulse. The calculated population ratios of Ar17+ to Ar16+ align well with the experimental measurements (LaForge et al 2021 Phys. Rev. Lett. 127 213202). In comparison to the transition energy of the strongest line, (1s2)0→(1s1/22p3/2)1 of Ar16+, there is a distinct ∼25 eV red shift in the peak ratio, which is attributed to the presence of intricate resonant channels in the lower ionization stages. The results demonstrate the sensitivity of the population ratio Ar17+/Ar16+ to the laser pulse parameters such as x-ray pulse duration, bandwidth and the contribution of second-harmonic radiation, indicating their potential as diagnostic tools in future experiments.

The Impact of Effective Matter Mixing Based on Three-dimensional Hydrodynamical Models on the Molecule Formation in the Ejecta of SN 1987A

To investigate the impact of matter mixing on the formation of molecules in the ejecta of SN 1987A, time-dependent rate equations for chemical reactions are solved for one-zone and one-dimensional (1D) ejecta models of SN 1987A. The latter models are based on the 1D profiles obtained by angle-averaging of the three-dimensional (3D) hydrodynamical models, which effectively reflect the 3D matter mixing; the impact is demonstrated, for the first time, based on 3D hydrodynamical models. The distributions of initial seed atoms and radioactive 56Ni influenced by the mixing could affect the formation of molecules. By comparing the calculations for spherical cases and for several specified directions in the bipolar-like explosions in the 3D hydrodynamical models, the impact is discussed. The decay of 56Ni, practically 56Co at later phases, could heat the gas and delay the molecule formation. Additionally, Compton electrons produced by the decay could ionize atoms and molecules and could destroy molecules. Several chemical reactions involved with ions such as H+ and He+ could also destroy molecules. The mixing of 56Ni plays a nonnegligible role in both the formation and destruction of molecules through the processes above. The destructive processes of carbon monoxide and silicon monoxide due to the decay of 56Ni generally reduce the amounts. However, if the molecule formation is sufficiently delayed under a certain condition, the decay of 56Ni could locally increase the amounts through a sequence of reactions.

Relaxation of Ne1+ 1s02s22p6 np produced by resonant excitation of an ultraintense ultrafast x-ray pulse

The creation and relaxation of double K-hole states 1s02s22p6 np (n ≥ 3) of Ne1+ in the interaction with ultraintense ultrafast x-ray pulses are theoretically investigated. The x-ray photon energies are selected so that x-rays first photoionize 1s22s22p6 of a neon atom to create a single K-hole state of 1s2s2p6 of Ne1+, which is further excited resonantly to double K-hole states of 1s02s22p6 np (n ≥ 3). A time-dependent rate equation is used to investigate the creation and relaxation processes of 1s02s22p6 np, where the primary microscopic atomic processes including photoexcitation, spontaneous radiation, photoionization and Auger decay are considered. The calculated Auger electron energy spectra are compared with recent experimental results, which shows good agreement. The relative intensity of Auger electrons is very sensitive to the photon energy and bandwidth of x-ray pulses, which could be used as a diagnostic tool for x-ray free electron laser and atom experiments.

The study on the gain of signal pulse in gain fibers and its application in simulation of mode-locked fiber lasers

The effect of the signal pulse on the population densities of upper-level particles of doped ions in gain fibers is studied. The population densities of upper-level particles decrease gradually after encountering the signal pulse in both the two-level system and the three-level system, and the decreasing degree is related to the power of the pulse. Since the power of the signal will change greatly in a short time in a pulsed laser, the time dependent rate equations are more suitable for describing the interaction between the pulse signal and doped particles than the steady state rate equations. Based on this, a simulation method of passively mode-locked fiber lasers, in which the gain of the signal is calculated by time dependent rate equations, is proposed. An erbium doped mode-locked fiber laser at 1564nm is simulated as an example, and the pulse width and spectral width in the simulation results are close to the experimental results. By adding noise to the initial pulse, the stability of the model is verified, and the mode competition between different modes in the process of mode locking can be studied. This method can not only provide a reference for building mode-locked fiber lasers, but also provide a method for studying the mechanism of mode locking.

Effects of single-photon double photoionization and direct double Auger decay on K-shell ionization kinetics of Ar atoms interacting with XFEL pulses

In studies investigating the interaction of matter with ultraintense, ultrashort x-ray free electron laser (XFEL) pulses, the evolution kinetics are generally described by directly solving a time-dependent rate equation that considers single-photon and single-electron processes. In the present study, we show the effects of single-photon double photoionization and direct double Auger decay in the K-shell ionization kinetics of XFELs interaction with argon atoms. Because a huge number of coupled transition channels are present in the K-shell ionization, we develop a Monte Carlo method to simulate the complex ionization kinetic processes and give the level population evolution of ions and charge state distribution (CSD). The K-shell-dominated ionization dynamics of Ar irradiated by XFEL pulses with photon energies of 5000, 5500 and 6500 eV are investigated and compared with available experimental observations of the CSD. The results show that the population fractions of Ar5+, Ar6+ and Ar9+ are increased by 78%, 152% and 144%, respectively, by these higher-order processes at a photon energy of 5000 eV. Including the direct double-electron processes, the predicted CSDs are in better agreement with the experiments carried out at the photon energies of 5000, 5500 and 6500 eV. It is expected that the developed theoretical formalism can be used to more accurately calibrate the beam profile and intensity of XFELs.

Experimental and Theoretical Study of an Actively Q-Switched Tm:YLF Laser with an Acousto-Optic Modulator.

We report the characteristics of a diode-end-pumped, high-repetition-rate, acoustic-optic (AO) Q-switched Tm:YLF laser operating from 5 kHz to 10 kHz. In the continuous-wave (CW) regime, a maximum average output power of 8.5 W was obtained with a slope efficiency of 30.7%. Under the AO Q-switching regime, a maximum output power of 7.32 W was obtained at a repetition frequency of 5 kHz with a pulse width of 68 ns and a pulse energy of 1.4 mJ, corresponding to a peak power of 21.5 kW. A time-dependent rate equation model is introduced to theoretically analyze the results obtained in the experiment, in which the cross-relaxation phenomenon, upconversion losses and ground-state depletion are taken into account. Additionally, the evolution processes of population inversion density and intracavity photon number density with time are also presented. The theoretical results well predict the dependence of laser output characteristics of Tm:YLF crystal on the incident pump powers.

Picosecond evolution of pulsed and CW alkali vapor lasers: laser oscillation buildup.

Investigation of the kinetic principle of a diode-pumped alkali vapor laser (DPAL) is key to achieve multifunctional DPALs. In this work, we propose a spatiotemporal model, which combines the time-dependent rate equations of population densities and propagation equations of energies to study the dynamic processes from turn-on to steady-state in DPALs. Time evolution of population densities and pump and laser intensity are resolved on a picosecond time scale to study the build-up process of laser oscillations. For nanosecond-pulse pumping, we obtain a laser pulse of 1.6 ns and a delay time of 2.6 ns at an incident pulse width of 2 ns. This pulse can be stretched by increasing the pump pulse width and delayed by applying a more extended cavity. For CW operation, spiking and relaxation oscillations resulting from a dynamic balance of gain and losses are demonstrated to be much faster than other types of lasers.

Impact of Initial Electron Development on Sodium Plasma Generation Using LIBORS Technique: Numerical Modeling

The present work reports an investigation on the role played by Na3+ ions formed through triatomic associative ionization collision of Na(4d) atoms with Na2 ground state molecules during the early phase of sodium plasma generation by laser ionization based on resonance saturation (LIBORS). Such ionization mechanism is observed experimentally for the first time by Tapalian and Smith (1993) [1]. In their experiment, stepwise atomic excitations are created using two CW dye lasers; one laser is tuned to 589 nm to excite the Na(3s) to Na(3p) D2 transition of sodium and the other laser is tuned 569 nm to excite the Na(3p) to Na(4d) transition. The analysis is grounded on a numerical study of the role of seed electron processes on the temporal evolution of sodium plasma formation by laser irradiation. A previously developed numerical model based on LIBORS technique is modified and adopted. In the present study, the sodium atom is treated as an atom comprises 22 levels namely: a ground state, 18 excited states and three ionic states (atomic, molecular and tri-atomic). The model tackled various collisional and radiative processes that act to enhance and deplete the free electrons generated in the interaction region. The contribution of these processes is signified by solving numerically a system of time-dependent rate equations, which couple the generated atomic and ionic species with the laser fields. Meanwhile, it solves the time-dependent Boltzmann equation for the electron energy distribution function (EEDF) of the generated electrons. The computed values of the EEDF, time evolution of both excited states population and the formed ionic species considering the individual effect of associative ionization, Penning, and photo-ionization and triatomic associative ionization justified the important effect of each of these ionizing processes in creating the early stage electrons. These seed electrons are assumed to rapidly gain energy through superelastic collisions leading eventually to plasma development.

Ultrafast nonequilibrium ion and electron dynamics of a neon plasma produced by an ultra-intense x-ray pulse

Ultrafast nonequilibrium ion and electron dynamics of a neon plasma produced in the interaction with an ultra-intense x-ray pulse is investigated theoretically. Electron energy distribution function (EEDF) is obtained by solving Fokker–Planck equation, which is implemented self-consistently in a time-dependent rate equation in the framework of detailed-level-accounting approximation. Evolution dynamics of EEDF are presented at a variety of ion density in interaction with x-ray pulses of different laser intensities. Thermalization of free electrons is demonstrated after the x-ray pulses have turned off. The results are compared with two other simplified models, i.e., one is a relaxation model and the second uses the Maxwellian approach. Large discrepancies in the EEDF are found and the effects of detailed treatment of electron dynamics on population distributions are demonstrated and discussed.

Temporal evolution of electron beam generated Argon plasma in pasotron device

The plasma- assisted slow wave oscillator (PASOTRON) is a high power microwave source in which the electron beam in the interaction region is confined by the background plasma. The plasma is generated by impact ionization of background gas with the electron beam. A model has been developed for temporal evolution of Argon plasma in pasotron device. In this model, we consider electron beam of energy E interacting with Argon gas. The resulting ionization creates quasi neutral argon plasma composed of argon Ar atoms, singly ionized ions Ar+1and electrons having energy from 0 to E. Electron impact excitation, ionization, radiative decay, radiative recombination and three body recombination processes are considered in this model. Population of ground and excited states of argon atom, ground state of argon ion as well as the population of electron energy groups is calculated by solving time dependent rate equations. Temporal evolution of electron beam generated plasma is given.

Single- and double-core-hole ion emission spectroscopy of transient neon plasmas produced by ultraintense x-ray laser pulses

Single-core-hole (SCH) and double-core-hole (DCH) spectroscopy is investigated systematically for neon gas in the interaction with ultraintense x-ray pulses with photon energy from 937 eV to 2000 eV. A time-dependent rate equation, implemented in detailed level accounting approximation, is utilized to study the dynamical evolution of the level population and emission properties of the laser-produced highly transient plasmas. The plasma-density effects on level populations and charge-state distribution are demonstrated with an x-ray photon energy of 2000 eV. It is shown that atomic number density of relevant experiment is about 1 × 1018 cm−3, which is comparable to a recent experiment. At this density, we systematically investigate the emissivity of the transient neon plasmas. For laser photon energy in the range 937–1360 eV, resonant absorptions (RA) of ( 2) transitions play important roles in time evolution of the population and DCH emission spectroscopy. The RA effects are illustrated in detail for an x-ray pulse of 944 eV photon energy, which creates the RA from the SCH states (, 1s2s2p5, and 1s2p6) of Ne3+. After averaging over the space and time distribution of x-ray pulse, DCH emission spectroscopy is studied at x-ray photon energies of 937, 944, 955, 968, 980, and 990 eV, where there exist resonances from SCH states of Ne2+-Ne7+. The processes with producing DCH states are discussed. For x-ray photon energy larger than 1360 eV, no RA exist and transient plasmas show different features in the DCH spectroscopy.

Interplay of gas and ice during cloud evolution

During the evolution of diffuse clouds to molecular clouds, gas-phase molecules freeze out on surfaces of small dust particles to form ices. On dust surfaces, water is the main constituent of the icy mantle in which a complex chemistry is taking place. We aim to study the formation pathways and the composition of the ices throughout the evolution of diffuse clouds. For this purpose, we use time-dependent rate equations to calculate the molecular abundances in both gas phase and on solid surfaces (onto dust grains). We fully consider the gas-dust interplay by including the details of freeze-out, chemical and thermal desorption, as well as the most important photo-processes on grain surfaces. The difference in binding energies of chemical species on bare and icy surfaces is also incorporated into our equations. Using the numerical code FLASH, we perform a hydrodynamical simulation of a gravitationally bound diffuse cloud and follow its contraction. We find that while the dust grains are still bare, water formation is enhanced by grain surface chemistry which is subsequently released into the gas phase, enriching the molecular medium. The CO molecules, on the other hand, tend to freeze out gradually on bare grains. This causes CO to be well mixed and strongly present within the first ice layer. Once one monolayer of water ice has formed, the binding energy of the grain surface changes significantly and an immediate and strong depletion of gas-phase water and CO molecules occur. While hydrogenation converts solid CO into formaldehyde (H$_2$CO) and methanol (CH$_3$OH), water ice becomes the main constituent of the icy grains. Inside molecular clumps formaldehyde is more abundant than water and methanol in the gas phase owing its presence in part to chemical desorption.

Evolution dynamics of charge state distribution in neon interaction with x-ray pulses of variant intensities and durations

The level population and charge state distribution (CSD) of the neon atomic system interacting with x-ray pulses of variant intensities and durations at a central photon energy of 1110 eV are investigated by solving the time-dependent rate equations. The laser beam has a circular spot size with a Gaussian intensity pattern and the time history of the intensity is represented by Gaussian distribution in time. As an example, the CSD as a function of time is given at different distances from the spot center for an x-ray beam of intensity 1.5 × 1017 W/cm2 and duration 75 fs (fs) for a spot size of 1 μm (full width at half maximum). The final CSD after averaging over the space and time is compared with a recent experiment and good agreement is found between the theory and experiment. Then systematic investigations are carried out to study the evolution of CSD with a wide range of intensity from 1.0 × 1015 W/cm2 to 1.0 × 1019 W/cm2 and duration from 30 fs to 100 fs. The results show that at intensities lower than 1.0 × 1015 W/cm2, the CSD shows a typical physical picture of weak x-ray photoionization of the neutral atomic neon. At higher intensity, i.e., larger than 5.0 × 1016 W/cm2, the dominant ionization stages are Ne7+ and Ne8+, while the fractions of ions in the Ne3+–Ne6+ stages are low for all laser durations and intensities.

Demonstration of a 459-nm pulsed, optically pumped cesium vapor laser

We report on the demonstration of a pulsed cesium vapor laser operating in the blue via direct optical excitation of the 7P3/22 state. The cesium laser may be considered a three-level visible analog to the near infrared diode pumped alkali laser (DPAL). The 6S1/22–7P3/22 pump transition is collisionally broadened by helium. Population is rapidly transferred to the 7P1/22 state using ethane and lasing was observed on the 459.3nm 7P1/22–6S1/22 transition. The best results were found with 550Torr of helium and 100Torr of ethane at cell temperatures from 90–110°C. Using this setup, the maximum slope efficiency (0.45%) and lowest threshold pump energy (10μJ/pulse) were obtained. The maximum output energy was 3.3μJ/pulse, comparable to previous two-photon pumped blue laser demonstrations. Weak blue emission at 459nm was also observed using 200–500Torr of helium alone. A time-dependent rate equation model was developed to aid in the discussion of the intermultiplet mixing and strong infrared radiative transitions inherent in this system. A scalable alkali laser system operating in the blue near the Jerlov minimum has several possible communications, optical storage, color display and remote sensing applications.

NON-EQUILIBRIUM IONIZATION EFFECTS ON THE DENSITY LINE RATIO DIAGNOSTICS OF O IV

The dynamic timescales in the solar atmosphere are shorter than the ionization and recombination times of many ions used for line ratio diagnostics of the transition region and corona. The long ionization and recombination times for these ions imply that they can be found far from their equilibrium temperatures, and spectroscopic investigations require more care before being trusted in giving correct information on local quantities, such as density and temperature. By solving the full time-dependent rate equations for an oxygen model atom in the three-dimensional numerical model of the solar atmosphere generated by the Bifrost code, we are able to construct synthetic intensity maps and study the emergent emission. We investigate the method of electron density diagnostics through line ratio analysis of the O IV 140.1 nm to the 140.4 nm ratio, the assumptions made in carrying out the diagnostics, and the different interpretations of the electron density. The results show big discrepancies between emission in statistical equilibrium and emission where non-equilibrium (NEQ) ionization is treated. Deduced electron densities are up to an order of magnitude higher when NEQ effects are accounted for. The inferred electron density is found to be a weighted mean average electron density along the linemore » of sight and has no relation to the temperature of emission. This study shows that numerical modeling is essential for electron density diagnostics and is a valuable tool when the ions used for such studies are expected to be out of ionization equilibrium. Though this study has been performed on the O IV ion, similar results are also expected for other transition region ions.« less

Theoretical and experimental study of the pump pulse width optimization of the Yb-doped fiber amplifier

In order to suppress the amplified spontaneous emission (ASE) in the low repetition rate high energy fiber master oscillator power amplifier (MOPA) system and achieve the best amplification results, it is necessary to optimize the pump pulse width. Based on solving a set of time-dependent rate and power transfer equations, the optimum pump pulse width is obtained by studying the transient response of the upper level population distribution, stored energy and ASE of the Yb-doped fiber amplifier under pulsed pump. The ASE built-up time is measured and the optimum value is found by tuning the width of pump pulse in the experiment, and the results show the validity of the numerical simulation.

Effect of emission wavelength on photo-stability of laser dye: experimental and theoretical study

Photo-stability of laser dyes has been an important consideration for dye lasers. In this work, photo-stability of dye and its effect has been investigated as a function of dye laser wavelengths rather than commonly studied photo-chemical degradation pathways upon excitation with pump laser. Here, we report a significant improvement in photo-stability of the liquid dye laser at peak emission wavelength compared to edge wavelengths of the dye gain curve, which was related with an increase in rate of stimulated emission of dye at peak wavelength. Thus, high laser efficiency harmonizes to high photo-stability of the dye at peak wavelength which is useful for the applications of dye lasers. As a representative case, the photo-stability rates of pyrromethene 567 (PM567) dye at different laser emission wavelengths were studied using a 10-Hz Nd-YAG (532 nm) laser-pumped dye laser set-up under lasing and non-lasing conditions. Deterioration of dye laser efficiency on account of photo-degradation of dye molecules was theoretically simulated using a time-dependent rate equation model, which has been found to be in good agreement with the experimental observations.

Time-dependent radiative transfer calculations for supernovae

In previous papers we discussed results from fully time-dependent radiative transfer models for core-collapse supernova (SN) ejecta, including the Type II-peculiar SN 1987A, the more "generic" SN II-Plateau, and more recently Type IIb/Ib/Ic SNe. Here we describe the modifications to our radiative modeling code, CMFGEN, which allowed those studies to be undertaken. The changes allow for time-dependent radiative transfer of SN ejecta in homologous expansion. In the modeling we treat the entire SN ejecta, from the innermost layer that does not fall back on the compact remnant out to the progenitor surface layers. From our non-LTE time-dependent line-blanketed synthetic spectra, we compute the bolometric and multi-band light curves: light curves and spectra are thus calculated simultaneously using the same physical processes and numerics. These upgrades, in conjunction with our previous modifications which allow the solution of the time dependent rate equations, will improve the modeling of SN spectra and light curves, and hence facilitate new insights into SN ejecta properties, the SN progenitors and the explosion mechanism(s). CMFGEN can now be applied to the modeling of all SN types

掺镱光纤放大器泵浦脉宽优化

In order to suppress the amplified spontaneous emission (ASE) in the low-repetition rate high-energy fiber master-oscillator-power-amplifier (MOPA) system and achieve the best amplification results, it is necessary to optimize the pump pulse width. Based on solving a set of time-dependent rate and power transfer equations, the transient response of the upper level population distribution, stored energy and ASE of the Yb-doped fiber amplifier under pulsed pump are numerically studied. And the numerical optimum pump pulse width is 793 s under specific parameters given in the paper, including the pump power, fiber length, core area, Yb-doped concentration, etc. In the experiment the ASE built-up time is measured, and the optimum value is 800 s which is found by tuning the width of the pump pulse and measuring the amplification results of the fiber amplifier. The experiment shows the validity of the numerical simulation. 

Theoretical and experimental study of transient response of the Yb-doped fiber amplifier

Some analysis of the transient response of the Yb-doped fiber amplifier are performed by solving a set of time-dependent rate and power transfer equations based on finite-difference method. Meanwhile, the variation of time to reach the steady state for upper level population distribution, the forward and backward amplified spontaneous emissions (ASEs) and stored energy on the system parameters including pump power, fiber length, Yb-doped concentration, and core area are numerically simulated, respectively. The results show that, by optimizing pump pulse width, stored energy can reach or even exceed the steady state value of continuous wave (CW) pump. By increasing Yb-doped concentration and core area, stored energy is increased, the ASE is suppressed and the ASE built-up time is postponed. In addition, the experimental results show the validity of the theoretical ASE built-up time. The obtained results can provide important guiding for the optimization of pump pulse width and fiber parameters.