Thermal Wave Front Research Articles

Gain performance and thermal effects of Nd:Glass and Nd,Y:SrF2 crystal

The gain performance and thermal effects of Nd:glass (N31) and Nd,Y:SrF2 crystal are investigated and compared. The results show that, under the same pump conditions, Nd,Y:SrF2 can provide a small-signal gain similar to that of N31. The main advantages of Nd,Y:SrF2 are its weaker thermal effects and greater thermal-fracture limitations compared with those of N31. In this paper, the two gain media are compared in the form of rods whose diameter is 5 mm and length is 60 mm. The small-signal gain coefficients of N31 and Nd,Y:SrF2 are 1.39 and 1.46, respectively, at a pump energy of 1.5 J/1 Hz. The pump energy is set at 1.5 J/8 Hz to experimentally investigate their thermal effects. The thermal wavefront of N31 is 0.987λ at a repetition rate of 10 Hz, whereas that of Nd,Y:SrF2 is 0.679λ. In thermal destructive experiments, N31 fractured at an average pump power of 15 W (1.5 J/10 Hz), whereas Nd,Y:SrF2 fractured at a higher power of 27 W (1.5 J/18 Hz) owing to its excellent thermal conductivity, which is 7.28 times that of N31. These results indicate the potential of Nd,Y:SrF2 crystal as a gain medium for high-repetition-rate laser amplifiers.

Diode-pumped high-peak-power nanosecond Nd,Y: SrF2 regenerative laser amplifier

We demonstrate a regenerative laser amplifier based on laser-diode-pumped Nd, Y:SrF2 crystals with an output of approximately 9.78 mJ/10 Hz. A specially designed birefringent filter was inserted into the cavity to compensate the gain narrowing and amplify the seed pulse with a center wavelength of 1053.3 nm. To optimize the design of the resonator, the thermal wavefront of the laser gain module was simulated and experimentally measured. When a laser pulse with a duration of 9 ns and energy of 1 nJ was injected into the regenerative amplifier, the output energy was 9.78 mJ with peak power of 1.1 MW. The energy stability was 0.72 % RMS. The horizontal and vertical beam quality M2 was 1.18 and 1.23 respectively. The results show the potential of the developed amplifier for application in high-power laser facilities.

Реализация бикомпактной схемы для HOLO алгоритма решения задач переноса излучения в среде

Bicompact schemes for the HOLO algorithm for solving the transport equation were applied to solve model problems of radiation transport in a medium (the first and the second Fleck problems). The main idea of HOLO algorithms is to accelerate the convergence of iterative processes due to the joint solving of high order (HO) and low order (LO) kinetic equations. The schemes are constructed by the method of lines on a minimal two-point stencil and have the fourth order of approximation in space. The Runge-Kutta method of the third order of approximation was used for integration over time. Verification and validation of the schemes were carried out. Solutions of the first and the second Fleck problems by the proposed method coincided well with solutions obtained by other methods. A modification of the second Fleck problem was proposed to investigate the dependence of the velocity of the thermal wave front on the absorption coefficient in the optically thick region.

Hyperbolic Conduction and Radiation Heat Transfer in Axisymmetric Cylinders with Variable Properties

This work investigates the combined mode of hyperbolic heat conduction and radiation transfer in a one-dimensional axisymmetric cylinder filled with absorbing, emitting, and scattering media. The volumetric radiation is investigated thanks to the semianalytic solution of the matrix formulation of the spherical harmonics equations PN. The governing hyperbolic energy equation is solved using the finite volume method (FVM) with Roe’s correction of interface fluxes in order to enhance the performances of the method, and the lattice Boltzmann method (LBM) has been designed for comparisons. The effects of the parameters such as constant and spatial-dependent scattering albedos, temperature-dependent thermal conductivity, heat-generated sources, extinction, and the conduction–radiation parameter on both the temperature and heat flux distributions for steady and transient states within the medium are examined. The results of the present work are in excellent agreement with those available in the literature. The PN−FVM results are also compared to those obtained with the PN−LBM combination, and excellent agreement is obtained. These results show that the mentioned parameters have a significant effect on both the temperature profiles and the hyperbolic sharp wave front. This study also shows that the proposed layered approach is an efficient, fast, and accurate solution method for radiative analysis in inhomogeneous media, whereas the Roe’s correction of interface fluxes in the FVM is suitable to accommodate a thermal wave front in non-Fourier analysis.

A Semi-Analytical Description of Radiation Coupled with Thermal Wave Conductive Transfer in Inhomogeneous Solid Cylinder

This study presents the analytical layered solution for thermal radiations coupled with non-Fourier conductive heat transfer, formulated from the Cattaneo-Vernotte flux model in inhomogeneous solid cylinder. This solution is built by combining the spherical harmonics for volumetric thermal radiations with the D1Q3 scheme of lattice Boltzmann method (LBM) for hyperbolic energy equation where the gradient of static particle distribution function was discretized at implicit time. The accuracy of the proposed model for dealing with radiation/conduction problems is investigated by considering a semitransparent radiative transfer in a cylinder with temperature dependent thermal conductivity and space dependent scattering albedo. The effects of different parameters, such as scattering albedo, refractive index, thermal conductivity, emissivity, optical thickness, and the conduction-radiation parameter on both radiations and temperature distributions for steady and transient states are studied. Results of the present work are benchmarked against those available in the literature with accuracy greater than 98.9% for a large interval of parameter sets and therefore, excellent agreement has been obtained. It also establishes from this study that the proposed layered approach is an efficient and accurate method for radiative analysis in inhomogeneous media while the D1Q3 scheme is suitable to accommodate thermal wave front in non-Fourier analysis.

Математическое моделирование динамики тепловых ударных волн в нелинейных локально-неравновесных средах

We performed a mathematical simulation of heat transfer in a local non-equilibrium medium whose transfer characteristics are functions of the temperature distribution. A homogeneous polynomial of arbitrary degree represents nonlinearities in thermal conductivity and thermal diffusivity. The mathematical model consists of a hyperbolic nonlinear heat transfer wave equation, initial conditions and nonlinear boundary conditions of the second and first kind. To solve this problem, we used a conservative homogeneous finite-difference scheme along the upper time grid line (implicitly). We then used the tridiagonal matrix algorithm of the second order in the spatial variable and of the first order in time to solve the resulting system of linearised algebraic equations. A periodic series of rectangular temperature or heat flux pulses form the boundary conditions of the first and second kind. Computation results reveal ultimate propagation rates of temperature and heat fronts featuring pronounced first-kind discontinuities with attenuating magnitudes. As the process unfolds, the initial pulses heat the region between the boundary and the heat wave front, while the subsequent pulses traverse this region at a higher velocity due to thermal diffusivity being a function of temperature, their fronts "catching up" with the previous fronts, increasing the discontinuity magnitude at the initial pulse front, that is, forming a thermal shock wave front similar to that of a shock wave in gas dynamics. We obtained such thermal shock waves for boundary conditions of both the first and the second kind. We also analysed kinematic and dynamic characteristics of thermal waves

Radiation properties of radiative shock in xenon

<sec>Radiative shock is an important phenomenon both in astrophysics and in inertial confinement fusion. In this paper, the radiation properties of X-ray heated radiatve shock in xenon is studied with the simulation method. The radiative shock is described by a one-dimensional, multi-group radiation hydrodynamics model proposed by Zinn [Zinn J 1973 <i> J. Comput. Phys.</i> <b>13</b> 569]. To conduct computation, the opacity and equation-of-state data of xenon are calculated and put into the model. The reliabilities of the model and the physical parameters of xenon are verified by comparing the temperature and velocity of the radiative shock calculated by the model with those measured experimentally. </sec><sec>The evolution of the radiative shock involves abundant physical processes. The core of the xenon can be heated up to 100 eV, resulting in a thermal wave and forming an expanding high-temperature-core. Shortly, the hydrodynamic disturbances reach the thermal wave front, generating a shock. As the thermal wave slows down, the shock gradually exceeds the high-temperature-core, forming a double-step distribution in the temperature profile. </sec><sec>The time evolution of the effective temperature of the radiative shock shows two maximum values and one minimum value, and the radiation spectra often deviate from blackbody spectrum. By analyzing the radiation and absorption properties at different positions of the shock, it can be found that the optical property of the shock is highly dynamic and can generate the above-mentioned radiation characteristics. When the radiative shock is just formed, the radiation comes from the shock surface and the shock precursor has a significant absorption of the radiation. As the shock temperature falls during expansion, the shock precursor disappears and the radiation inside the shock can come out owing to absorption coefficient decreases. When the shock becomes transparent, the radiation surface reaches the outside edge of the high-temperature-core. Then, the temperature of the high-temperature-core decreases further, making this region also optically thin, and the radiation from the inner region can come out. Finally, the radiation strength falls because of temperature decreasing. </sec>

On the fundamental solution of the heat transfer problem in one-dimensional harmonic crystals

The work is devoted to the description of unsteady thermal processes in low-dimensional structures. To obtain the relationship between the microscopic and macroscopic descriptions of solids, it is necessary to understand the heat transfer mechanism at the micro-level. At the latter, in contrast to the macro-level, analytical, numerical, and experimental studies demonstrate significant deviations from the Fourier’s law. The paper bases on the ballistic heat transfer model, according to which the heat is carried by the thermal waves. This effect can be applied, for example, to signal transmission and heat removal problems. The influence of non-nearest neighbors on processes in discrete media, as well as processes in polyatomic lattices, is investigated. To describe the evolution of the initial thermal perturbation, the dispersion characteristics and group velocities in one-dimensional crystal are analyzed for (i) a diatomic chain with variable masses or stiffnesses and for (ii) a monatomic chain with regard for interaction with second neighbors. A fundamental solution to the heat distribution problem for the corresponding crystal models is obtained and investigated. The fundamental solution allows to obtain a description of waves traveling from a point source, and can serve as the basis for constructing all other solutions. In both cases, the solution consists of two thermal fronts moving one after another with different speeds and intensities. Quantitative estimates of the intensity of the thermal wave front are given, and the dynamics of changes in the velocities and intensities of the waves depending on the parameters of the problem is analyzed. Thus, a simple method for estimating the wavefronts intensity is proposed and tested on two models. These results can be used to identify and analyze those parts of the wave processes that are of interest in terms of interpretation of the effects observed in the experiments.

Analysis of laser thermal effect of funnel-shape beam generated by spherical lens pump system

The uniformity of temperature distribution of an end-pumped laser can be improved simply and effectively by introducing the correct amount of spherical aberration into the pump system. An iterative model of optical-thermal coupling is proposed to calculate the temperature distribution of the end-pumped laser amplifier. The results showed that, the thermal effect of the laser gain medium in the coupling system composed of spherical lenses decreased significantly compared with the coupling system composed of aspherical lenses. This is proved by a neodymium-doped yttrium orthovanadate (Nd:YVO4) amplification experimental system, which was end-pumped by a fiber-coupled laser diode (LD) with the optimized wavelength of 878 nm. A comparative study of the two pump systems showed that the decrease in the gain medium thermal wavefront peak-to-valley (PV), the thermal lens effect, and an improvement in beam quality are still observed in the pump amplification experiment with spherical aberration. At last, the relationship between the spherical aberration and the output brightness of the amplifier was established, which provides guidance for further optimization of the spherical aberration of coupling pump systems and improving the beam quality.

Thermally-Compensated High Power Nd: YAG Slab Laser Module With Low Wavefront Distortion

A low-order wavefront aberration self-compensation high power Nd:YAG slab laser module is developed and demonstrated. By numerical simulating the thermal distribution and transmission wavefront of the slab laser medium, a thermally-compensated heat removal geometry is developed to reduce the wavefront distortion. This method allows the non-uniform cooling to flatten the thermal gradient distribution in the width direction of the slab. By using the optimized gain module as an amplifier, the laser output power of 7.8 kW is achieved. Compared to the traditional module, the output power is 7.3 kW, and the peak-to-valley (PV) value of the wavefront distortion is reduced from 17.21 to $2.05~\mu \text{m}$ under full power, the beam quality factor $\beta $ is improved from 12.7 to 3.5 times diffraction limited while without additional correction system.

水冷10 Hz Yb:YAG激光放大器热管理

To control the thermal wavefront distortion of repetition frequency laser, we′ve developed a water-cooled active-mirror laser amplifier, which was uniformly cooled from the rear of crystal disk. The numerical anslysis and experimental study on the characterstics of the amplifier’s thermal distortion were carried out. It was found that the thermal distorition devoted a significiant modulation to the near field of the laser when the average pump power density was as high as 200 W/cm2 with the operation frequency of 10 Hz. Near-field modulation would bring a risk to damage the amplifier. To eliminate the modulation of thermal distortion in the near field, two approaches were taken. Firstly, the pump intensity distribution was homogenized, then the edge thermal balance control was carried out. The near field modulation from thermal wavefront distortion was eliminated by these means, a four-pass amplifier with water-cooled laser heads ran well at 10 Hz. The focal spot of output laser was smaller than 5 diffraction limits without any compensation.

Analytical layered solution of radiation and non–Fourier conduction problems in optically complex media

The analytical layered solution for radiative transfer through participating optically complex media is developed. The angular processing of radiation is based on double spherical harmonics method (DPN) which split up the radiative intensity into two stream components before expanding in Legendre polynomial basis. The proposed layered radiative solution assumes that the optically complex media is a set of thin layers dealing with homogeneous properties. Therefore, the analytical solution for radiative transfer is performed and then coupled to the finite volume method (FVM), to solve the non – linear hyperbolic thermal conduction problems, formulated thanks to Cattaneo–Vernotte flux. In developing the FVM, the Roe′s corrections of interface fluxes is adopted in order to enhance the performances of the method. The accuracy of the proposed model for dealing with inhomogeneous radiation/conduction problems is investigated by considering participating media such as slab, solid or hollow spheres, with temperature – dependent thermal conductivity. The effects of different parameters, known as scattering albedo, graded index function, thermal conductivity, boundary emissivity and the conduction–radiation parameter on both temperature and heat flux distributions for purely radiation, steady and transient states are studied. Results of the present work compare well with those available in the literature with maximum relative error less than 1%. These results show that the listed parameters have a significant effect on both temperature profiles and hyperbolic sharp wave front. It also comes from this study that the proposed layered approach is an efficient, robust, and accurate method for radiative flow analysis in inhomogeneous media while the Roe′s correction of interface fluxes in FVM is suitable to accommodate thermal wave front in non – Fourier analysis.

On the fundamental solution of the heat transfer problem in one-dimensional harmonic crystals

Unsteady thermal processes in low-dimensional structures are considered. Understanding the heat transfer at the micro-level is necessary to obtain a link between micro- and macroscopic descriptions of solids. At the macroscopic level, heat propagation is described by the Fourier law. However, at the microscopic level, analytical, numerical and experimental studies show significant deviations from this law. The previously created model of heat transfer at the microlevel, which has a ballistic character, is used in the work. The influence of non-nearest neighbors on the thermal processes in discrete media is studied, as well as the heat distribution in polyatomic lattices is considered. To describe the evolution of the initial thermal perturbation, the analysis of dispersion characteristics and group velocities in a one-dimensional crystal for a diatomic chain with alternating masses or stiffnesses and a monoatomic chain with regard for interaction with second neighbors is carried out. The fundamental solution of the heat propagation problem for the corresponding crystal models is obtained and studied. The fundamental solution allows us to obtain a description of the waves running from a point source and to use it as a basis for the construction of all other solutions. For both chains, the solution consists of two fronts moving one after another with different velocities and intensity characteristics. Quantitative estimations of the thermal wavefront intensity coefficients are given, and the dynamics of changes in speeds and intensities of the waves depending on the parameters of the problem is analyzed. Two mechanisms of evolution of the heat wavefront in one-dimensional discrete systems are revealed. The presented results can be used for correct interpretation of experiments on unsteady ballistic heat transfer in crystals.

Numerical analysis of temperature field and thermal stress associated with dual-phase-lag heat conduction

A numerical method for generalized dual-phase-lag (DPL) heat conduction is proposed. Differential equations including the third-order derivative in time are obtained by using finite element space discretization and are solved by the finite difference method. The backward difference has less numerical oscillation but the central difference can better describe the sharp temperature change near the thermal wave front. In generality, the backward difference is an ideal method for the transient solution of the temperature field associated with the DPL model. However, the time step must be small enough so that the temperature field near the thermal wave front can be obtained accurately.

Numerical studies on the radiation uniformity of Z-pinch dynamic hohlraum

Radiation uniformity is important for Z-pinch dynamic hohlraum driven fusion. In order to understand the radiation uniformity of Z-pinch dynamic hohlraum, the code MULTI-2D with a new developed magnetic field package is employed to investigate the related physical processes on Julong-I facility with drive current about 7–8 MA. Numerical simulations suggest that Z-pinch dynamic hohlraum with radiation temperature more than 100 eV can be created on Julong-I facility. Although some X-rays can escape out of the hohlraum from Z-pinch plasma and electrodes, the radiation field near the foam center is quite uniform after a transition time. For the load parameters used in this paper, the transition time for the thermal wave transports from r = 1 mm to r = 0 mm is about 2.0 ns. Implosion of a testing pellet driven by cylindrical dynamic hohlraum shows that symmetrical implosion is hard to achieve due to the relatively slow propagation speed of thermal wave and the compression of cylindrical shock in the foam. With the help of quasi-spherical implosion, the hohlraum radiation uniformity and corresponding pellet implosion symmetry can be significantly improved thanks to the shape modulation of thermal wave front and shock wave front.

A modified Green–Lindsay thermoelasticity with strain rate to eliminate the discontinuity

Probing the mechanism of ultrafast thermoelastic processes is becoming increasingly important with the development of laser-assisted micro/nano machining. Although thermoelastic models containing temperature rate have been historically proposed, the strain rate has not been considered yet. In this work, a generalized thermoelastic model is theoretically established by introducing the strain rate in Green–Lindsay (GL) thermoelastic model with the aid of extended thermodynamics. Numerically, a semi-infinite one-dimensional problem is considered with traction free at one end and subjected to a temperature rise. The problem is solved using the Laplace transform method, and the transient responses, i.e. displacement, temperature and stresses are graphically depicted. Interestingly, it is found that the strain rate may eliminate the discontinuity of the displacement at the elastic and thermal wave front. Also, the present model is compared with Green–Naghdi (GN) models. It is found that the thermal wave speed of the present model is faster than GN model without energy dissipation, and slower than GN model with energy dissipation. In addition, the thermoelastic responses from the present model are the largest. The present model based upon GL model is free of the jump of GL model in the displacement distribution, and is safer in engineering practices than GN model. The present work will benefit the theoretical modeling and numerical prediction of thermoelastic process, especially for those under extreme fast heating.

Wavefront correction by target-phase-locking technology in a 500 TW laser facility

We demonstrate a novel approach termed target-phase-locking that could improve the entire beam wavefront quality of a 500 TW Nd3+:phosphate glass laser facility. The thermal and static wavefront from front-end to target is corrected by using one deformable mirror that receives feedback from both the focal-spot sensor and wavefront sensor, and only the main laser of the laser system is employed in the correction process, with auxiliary calibration light no longer necessary. As a result, a static focal spot with full width at half maximum of 8.87 × 5.74 µm is achieved, the thermal wavefront induced by flash-lamp-pumped Nd3+:phosphate glass is compensated with PV from 3.54–0.43 µm, and a dynamic focal spot with intensity exceeding 1020 W cm−2 is precisely predicted at the target with such an approach.

Thermal wave: from nonlocal continuum to molecular dynamics

To accommodate effects of thermomass and size-dependency of thermophysical properties on heat transport and to remove the theoretical singularity of temperature gradients across the thermal wavefront NL FTPL heat conduction, corroborated with MD simulation, is introduced.

Role of heat generation and thermal diffusion during frontal photopolymerization

Frontal photopolymerization (FPP) is a rapid and versatile solidification process that can be used to fabricate complex three-dimensional structures by selectively exposing a photosensitive monomer-rich bath to light. A characteristic feature of FPP is the appearance of a sharp polymerization front that propagates into the bath as a planar traveling wave. In this paper, we introduce a theoretical model to determine how heat generation during photopolymerization influences the kinetics of wave propagation as well as the monomer-to-polymer conversion profile, both of which are relevant for FPP applications and experimentally measurable. When thermal diffusion is sufficiently fast relative to the rate of polymerization, the system evolves as if it were isothermal. However, when thermal diffusion is slow, a thermal wavefront develops and propagates at the same rate as the polymerization front. This leads to an accumulation of heat behind the polymerization front which can result in a significant sharpening of the conversion profile and acceleration of the growth of the solid. Our results also suggest that a novel way to tailor the dynamics of FPP is by imposing a temperature gradient along the growth direction.

Numerical simulation of 30-kW class liquid-cooled Nd:YAG multi-slab resonator.

A numerical modeling is developed for 30-kW class liquid-convection-cooled elastically-mounted Nd:YAG multi-slab laser resonator configuration. The modeling exhibits the thermal effects and resultant wavefront aberration of the gain module under flow cooling and CW pumping at 100-kW level, the self-reproducing oscillating mode within the large-aperture cavity, as well as the beam quality enhancement by adaptive optics. The simulation results predict a CW output power of 31 kW with the optical-optical efficiency of 26.1% obtained from a modified resonator configuration with dual gain modules that have opposite flow directions, while the beam quality can be improved to β<2 after the correction of a deformable mirror.