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This paper provides a summary of recent research connected with the shock ignition (SI) concept of the inertial confinement fusion which was carried out at PALS. In the experiments, Cu planar targets coated with a thin CH layer were used. Two-beam irradiation experiment was applied to investigate the effect of preliminary produced plasma to shock-wave generation. The 1ω or 3ω main beam with a high intensity >1015 W/cm2 generates shock wave, while the other 1ω beam with the intensity below 1014 W/cm2 creates CH pre-plasma simulating the pre-compressed plasma related to SI. Influence of laser wavelength on absorbed energy transfer to shock wave was studied by means of femtosecond interferometry and measuring the crater volume. To characterize the hot electron and ion emission, two-dimensional (2D) Kα-imaging of Cu plasma and grid collector measurements were used. In single 1ω beam experiments energy transport by fast electrons produced by resonant absorption made a significant contribution to shock-wave pressure. However, two-beam experiments with 1ω main beam show that the pre-plasma is strongly degrading the scalelength which leads to decreasing the fast electron energy contribution to shock pressure. In both the single 3ω beam experiments and the two-beam experiments with the 3ω main beam, do not show any clear influence of fast electron transport on shock-wave pressure. The non-monotonic behavior of the scalelength at changing the laser beam focal radius in both presence and absence of pre-plasma reflects the competition of plasma motion and electron heat conduction under the conditions of one-dimensional and 2D plasma expansion at large and small focal radii, respectively.
The experimental study of the plasma projectile acceleration in the laser-induced cavity pressure acceleration (LICPA) scheme is reported. In the experiment performed at the kilojoule PALS laser facility, the parameters of the projectile were measured using interferometry, a streak camera and ion diagnostics, and the measurements were supported by two-dimensional hydrodynamic simulations. It is shown that in the LICPA accelerator with a 200-J laser driver, a 4-μg gold plasma projectile is accelerated to the velocity of 140 km/s with the energetic acceleration efficiency of 15–19% which is significantly higher than those achieved with the commonly used ablative acceleration and the highest among the ones measured so far for any projectiles accelerated to the velocities ≥100 km/s. This achievement opens the possibility of creation and investigation of high-energy-density matter states with the use of moderate-energy lasers and may also have an impact on the development of the impact ignition approach to inertial confinement fusion.
During the Epoch of Reionization (EoR), feedback effects reduce the efficiency of star formation process in small halos or even fully quench it. The galaxy luminosity function (LF) may then turn over at the faint-end. We analyze the number counts of z > 5 galaxies observed in the fields of four Frontier Fields (FFs) clusters and obtain constraints on the LF faint-end: for the turn-over magnitude at z ∼ 6, MUVT ≳-13.3; for the circular velocity threshold of quenching star formation process, vc* ≲ 47 km s−1. We have not yet found significant evidence of the presence of feedback effects suppressing the star formation in small galaxies.
The paper is a continuation of research carried out at Prague Asterix Laser System (PALS) related to the shock ignition (SI) approach in inertial fusion, which was carried out with use of 1ω main laser beam as the main beam generating a shock wave. Two-layer targets were used, consisting of Cu massive planar target coated with a thin polyethylene layer, which, in the case of two-beam irradiation geometry, simulate conditions related to the SI scenario. The investigations presented in this paper are related to the use of 3ω to create ablation pressure for high-power shock wave generation. The interferometric studies of the ablative plasma expansion, complemented by measurements of crater volumes and Kα emission, clearly demonstrate the effect of changing the incident laser intensity due to changing the focal radius on efficiency of laser energy transfer to a shock wave and fast electron emission. The efficiency of the energy transfer increases with the radius of the focused laser beam. The pre-plasma does not significantly change the character of this effect. However, it unambiguously results in the increasing temperature of fast electrons, the total energy of which remains very small (<0.1% of the laser energy). This study shows that the optimal radius from the point of view of 3ω radiation energy transfer to the shock wave is the maximal one used in these experiments and equal to 200 µm that corresponds to the minimal effect of two-dimensional (2D)-expansion. Such a result is typical for the ablation process determined by electron conductivity energy transfer under the conditions of one-dimensional or 2D matter expansion without any appreciable effect due to energy transfer by fast electrons. The 2D simulations based on application of the ALANT-HE code and an analytical model that includes generation and transport of hot electrons has been used to support of experimental data.
The effect of laser intensity on characteristics of the plasma ablated from a low-Z (CH) planar target irradiated by a 250 ps, 0.438 µm laser pulse with the intensity of up to 1016 W/cm2 as well as on parameters of the laser-driven shock generated in the target for various scale-lengths of preformed plasma was investigated at the kilojoule Prague Asterix Laser System (PALS) laser facility. Characteristics of the plasma were measured with the use of 3-frame interferometry, ion diagnostics, an X-ray spectrometer, and Kα imaging. Parameters of the shock generated in a Cl doped CH target by the intense 3ω laser pulse were inferred by numerical hydrodynamic simulations from the measurements of craters produced by the shock in the massive Cu target behind the CH layer. It was found that the pressure of the shock generated in the plastic layer is relatively weakly influenced by the preplasma (the pressure drop due to the preplasma presence is ~10–20%) and at the pulse intensity of ~1016 W/cm2 the maximum pressure reaches ~80–90 Mbar. However, an increase in pressure of the shock with the laser intensity is slower than predicted by theory for a planar shock and the maximum pressure achieved in the experiment is by a factor of ~2 lower than predicted by the theory. Both at the preplasma absence and presence, the laser-to-hot electrons energy conversion efficiency is small, ~1% or below, and the influence of hot electrons on the generated shock is expected to be weak.
This paper reports on properties of a plasma formed by sequential action of two laser beams on a flat target, simulating the conditions of shock-ignited inertial confinement fusion target exposure. The experiments were performed using planar targets consisting of a massive copper (Cu) plate coated with a thin plastic (CH) layer, which was irradiated by the 1ω PALS laser beam (λ = 1.315 μm) at the energy of 250 J. The intensity of the fixed-energy laser beam was scaled by varying the focal spot radius. To imitate shock ignition conditions, the lower-intensity auxiliary 1ω beam created CH-pre-plasma which was irradiated by the main beam with a delay of 1.2 ns, thus generating a shock wave in the massive part of the target. To study the parameters of the plasma treated by the two-beam irradiation of the targets, a set of various diagnostics was applied, namely: (i) Two-channel polaro-interferometric system irradiated by the femtosecond laser (~40 fs), (ii) spectroscopic measurements in the X-ray range, (iii) two-dimensional (2D)-resolved imaging of the Kα line emission from Cu, (iv) measurements of the ion emission by means of ion collectors, and (v) measurements of the volume of craters produced in a massive target providing information on the efficiency of the laser energy transfer to the shock wave. The 2D numerical simulations have been used to support the interpretation of experimental data. The general conclusion is that the fraction of the main laser beam energy deposited into the massive copper at two-beam irradiation decreases in comparison with the case of pre-plasma. The reason is that the pre-formed and expanding plasma deteriorates the efficiency of the energy transfer from the main laser pulse to a solid part of the targets by means of the fast electrons and the wave of an electron thermal conductivity.
The risks of flooding in rice production include losses that can affect some 13 million ha of rice lands in Southeast Asia. This study integrated social and gender perspectives into the varietal evaluation process to contribute to planned faster uptake of submergence-tolerant rice (Sub1) varieties. In this study, the participatory varietal selection (PVS) process was used in eliciting male and female farmers' opinions with respect to selecting popular varieties with the SUB1 gene introgressed, for added tolerance of flash floods of up to two weeks. Fifteen Sub1 varieties and the farmers' local check were tested under the PVS researcher-managed (PVS-RM) trials, which involved farmers' preference analysis (PA). The farmers tested the pre-selected lines with the SUB1 gene in their own fields to further evaluate their performance under varying conditions. During flooding, farmers experienced lower production depending on water depth, timing with respect to rice growth stage, duration, frequency of occurrence and quality. On-farm PA results showed wide variability in the performance of the Sub1 varieties compared with local popular varieties. This implies the need for further testing of pre-released lines in terms of adaptability and the continuous development of rice genotypes for varying flood-prone rice ecosystems. Women are as knowledgeable as men because of the significant roles they play in rice production and food preparation. Moreover, farmers and breeders have almost the same criteria in choosing the best performing rice lines. Sensory tests revealed the eating and cooking qualities important to farmers. The findings of this study can provide feedback to breeding programmes to ensure a greater likelihood of adoption and ultimately increasing rice productivity in submergence-prone rice areas.
In a recent paper, Miller derived a Kummer-type transformation for the generalised hypergeometric function
when pairs of parameters differ by unity, by means of a reduction formula for a certain Kampé de Fériet function. An alternative and simpler derivation of this transformation is obtained here by application of the well-known Kummer transformation for the confluent hypergeometric function corresponding to
The author describes the recently developed theory of Hadamard expansions applied to the high-precision (hyperasymptotic) evaluation of Laplace and Laplace-type integrals. This brand new method builds on the well-known asymptotic method of steepest descents, of which the opening chapter gives a detailed account illustrated by a series of examples of increasing complexity. A discussion of uniformity problems associated with various coalescence phenomena, the Stokes phenomenon and hyperasymptotics of Laplace-type integrals follows. The remaining chapters deal with the Hadamard expansion of Laplace integrals, with and without saddle points. Problems of different types of saddle coalescence are also discussed. The text is illustrated with many numerical examples, which help the reader to understand the level of accuracy achievable. The author also considers applications to some important special functions. This book is ideal for graduate students and researchers working in asymptotics.
In this opening chapter we present a detailed account, together with a series of examples of increasing complexity, of the classical method of steepest descents applied to Laplace-type integrals. Consideration is also given to the common causes of non-uniformity in the asymptotic expansions so produced due to a variety of coalescence phenomena. The chapter concludes with a brief discussion of the Stokes phenomenon and hyperasymptotics, both of which have undergone intense development during the past two decades. Such a preliminary discussion, as well as hopefully being of general interest in its own right, is necessary for the remaining chapters, since the Hadamard expansion procedure can be viewed as an ‘exactification’ of the method of steepest descents yielding hyperasymptotic levels of accuracy. Considerable space in the later chapters is devoted to showing how the Hadamard expansion procedure can be modified to deal with various coalescence problems.
One of the most important methods of asymptotic evaluation of certain types of integral is known as the method of steepest descents. This method has its origins in the observation made by Laplace in connection with the estimation of an integral arising in probability theory of the form (Laplace, 1820; Gillespie, 1997).
The aims of this book are twofold. The first is to present a detailed account of the classical method of steepest descents applied to the asymptotic evaluation of Laplace-type integrals containing a large parameter, and the second is to give a coherent account of the theory of Hadamard expansions. This latter topic, which has been developed during the past decade, extends the method of steepest descents and effectively ‘exactifies’ the procedure since, in theory, the Hadamard expansion of a Laplace or Laplace-type integral can produce unlimited accuracy.
Many texts deal with the method of steepest descents, some in more detail than others. The well-known books by Copson Asymptotic Expansions (1965), Olver Asymptotics and Special Functions (1997), Bleistein and Handelsman Asymptotic Expansion of Integrals (1975), Wong Asymptotic Approximations of Integrals (1989) and Bender and Orszag Advanced Mathematical Methods for Scientists and Engineers (1978) are all good examples. It is our aim in the first chapter to give a comprehensive account of the method of steepest descents accompanied by a set of illustrative examples of increasing complexity. We also consider the common causes of non-uniformity in the asymptotic expansions of Laplace-type integrals and conclude the first chapter with a discussion of the Stokes phenomenon and hyperasymptotics.
The next two chapters present the Hadamard expansion theory of Laplace and of Laplace-type integrals possessing saddle points. A study of these chapters makes it apparent how this theory builds upon and extends the method of steepest descents.
In Chapter 3 we introduced two basic modes of expansion using Hadamard series, namely the forward expansion Scheme A and the forward-reverse expansion Scheme B. The first scheme uses the Hadamard series Sn(z), defined in (3.2.9), and is suitable for isolated saddle points when adjacent saddles or other singularities are sufficiently remote to result in a sequence of well-separated exponential levels. If maximal exponential separation is employed, the resulting convergence of the Hadamard series has to be accelerated through use of the modified form of the series. This involves the computation of coefficients expressed in terms of one-dimensional integrals in (3.2.18) of a common form at each level of the expansion. If one is prepared to accept a reduced exponential separation, however, it is possible, through judicious choice of the expansion points Ωn, to produce Hadamard series that converge rapidly at a geometric rate without the need for the computationally more expensive modified form.
In Scheme B, the zeroth interval is dealt with by forward expansion as in Scheme A, but with forward-reverse expansion about the points Ωn for the intervals with n ≥ 1. This has the advantage of covering a given interval on the integration path with fewer evaluations of the inversion expansions. By careful choice of the Ωn it is similarly possible to arrange for the Hadamard series at all levels to converge at a geometric rate.