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An analytical expression for the focal intensity of a laser pulse was obtained for an asymmetric out-of-plane compressor with gratings of arbitrary surface shape. The focal intensity is most strongly affected by the linear angular chirp caused by the spatial shift of different frequencies on the second and third gratings. The chirp can be eliminated by simply rotating the fourth grating by an optimal angle, which significantly reduces the requirements for the grating quality. It is shown that the decrease in the focal intensity depends on the product of the grating surface root mean square and pulse spectrum bandwidth. With low-quality gratings, spectrum narrowing would not reduce focal intensity; contrariwise, it may even slightly increase it.
An optical spectrometer system based on 60 channels of fibers has been designed and employed to diagnose light emissions from laser–plasma interactions. The 60 fiber collectors cover an integrated solid angle of $\pi$, enabling the measurement of global energy losses in a symmetrical configuration. A detecting spectral range from ultraviolet to near-infrared, with angular distribution, allows for the understanding of the physical mechanisms involving various plasma modes. Experimental measurements of scattered lights from a conical implosion driven by high-energy nanosecond laser beams at the Shenguang-II Upgrade facility have been demonstrated, serving as reliable diagnostics to characterize laser absorption and energy losses from laser–plasma instabilities. This compact diagnostic system can provide comprehensive insights into laser energy coupling in direct-drive inertial confinement fusion research, which are essential for studying the driving asymmetry and improving the implosion efficiencies.
Optimising stellarators for quasisymmetry leads to strongly reduced collisional transport and energetic particle losses compared with unoptimised configurations. Although stellarators with precise quasisymmetry have been obtained in the past, it remains unclear how broad the parameter space is where good quasisymmetry may be achieved. We study the range of aspect ratios and rotational transform values for which stellarators with excellent quasisymmetry on the boundary can be obtained. A large number of Fourier harmonics is included in the boundary representation, which is made computationally tractable by the use of adjoint methods to enable fast gradient-based optimisation and by the direct optimisation of vacuum magnetic fields, which converge more robustly compared with solutions from magnetohydrostatics. Several novel configurations are presented, including stellarators with record levels of quasisymmetry on a surface, three field period quasiaxisymmetric stellarators with substantial magnetic shear, and compact quasisymmetric stellarators at low aspect ratios similar to tokamaks.
We present a framework for analysing plasma flow in a rotating mirror. By making a series of physical assumptions, we reduce the magnetohydrodynamic (MHD) equations in a three-dimensional cylindrical system to a one-dimensional system in a shallow, cuboidal channel within a transverse magnetic field, similar to the Hartmann flow in ducts. We then solve the system both numerically and analytically for a range of values of the Hartmann number and calculate the dependence of the plasma flow speed on the thickness of the insulating end cap. We observe that the mean flow overshoots and decelerates before achieving a steady-state value, a phenomenon that the analytical model cannot capture. This overshoot is directly proportional to the thickness of the insulating end cap and the external electric field, with a weak dependence on the external magnetic field. Our simplified model can act as a benchmark for future simulations of the supersonic mirror device CMFX (centrifugal magnetic fusion experiment), which will employ more sophisticated physics and realistic magnetic field geometries.
We study the first contact of an emulsion drop impacting on a smooth solid surface. The lubricating air layer causes rapid deceleration of the bottom tip of the drop as it approaches first contact, causing a dimple in the drop surface. When the dispersed emulsion droplets are of higher density than the drop's continuous phase, the rapid deceleration (${\sim }10^5$ m s$^{-2}$) induces the formation of narrow spikes extruding out of the free surface. These spikes form when the impact Weber number exceeds a critical value ${\simeq }10$. Time-resolved interferometric imaging, at rates up to 7 million frames per second, shows the emergence and shape of these spikes leading to the local contacts with the solid. We characterize the tip curvature and capillary pressure affecting their dynamics as they emerge and can touch the substrate before the main outer ring of contact.
We study the tearing instability of a current sheet in a relativistic pair plasma with a power-law distribution function. We first estimate the growth rate analytically and then confirm the analytical results by solving numerically the dispersion equation, taking into account all exact particle trajectories within the reconnecting layer. We found that the instability is suppressed when the particle spectrum becomes harder.
The subject of this chapter is the quantum mechanical analysis of the interaction of electromagnetic radiation with atomic transitions. The analysis is based on the Schrödinger wave equation, and in the first section, the gauge-invariant form of the external electromagnetic field is introduced. The electric dipole interaction and the long-wavelength approximation for the analysis of this interaction are discussed. The perturbative analysis of both single-photon and two-photon electric dipole interactions is presented, and density matrix analysis is introduced. The interaction of radiation with the resonances of atomic hydrogen is then discussed. The analysis is performed for both coupled and uncoupled representations. In the last section of the chapter, the radiative interactions for multielectron atoms are discussed. The Wigner–Eckart theorem and selection rules for transitions between levels characterized by coupling are developed. The effect of hyperfine splitting on radiative transitions is also briefly discussed.
It is critical to evaluate whether the flow has transitioned into turbulence because most of the impact of large-scale mixing occurs when the flow becomes fully developed turbulence. Hydrodynamic instability flows are even more complex because of their time-dependent nature; therefore, both spatial and temporal criteria will be introduced in great detail to demonstrate the necessary and sufficient conditions for the flow to transition to turbulence. These criteria will be extremely helpful for designing experiments and numeric simulations with the goal to study large-scale turbulence mixing. One spatial criterion is that the Reynolds number must achieve a critical minimum value of 160,000. In addition, the temporal criteria suggest that flows need to be given approximately four eddy-turnover-times. This chapter will expand on these issues.
The chapter begins with the introduction of the two-particle Schrödinger wave equation (SWE) and the solution of this equation for the hydrogen atom. The orbital angular momentum of the electron results from the SWE solution. The Pauli spinors are introduced, and the SWE wavefunctions are modified to account for the spin of the electron. The structure of multielectron atoms is then discussed. The discussion is focused on low-Z atoms for which Russell–Saunders or LS coupling is appropriate. Alternate coupling schemes are briefly discussed. Angular momentum coupling algebra, the Clebsch–Gordan coefficients, and 3j symbols are then introduced. The Wigner–Eckart theorem is discussed, and the use of irreducible spherical tensors for evaluation of quantum mechanical matrix elements is discussed in detail.
Introduces Nernst potentials for bacterial cells, simple Hodgkin–Huxley models for action potentials and describes experimental methods to measure membrane potentials.
The stability of Taylor–Couette flow modulated by oscillatory wall suction/blowing is investigated using Floquet linear stability analysis. The growth rate and stability mode are obtained by numerical calculation and asymptotic expansion. By calculating the effect of wall suction/blowing on the critical mode of steady Taylor–Couette flow, it is found that for most suction/blowing parameters, the maximum disturbance growth rate of the critical mode decreases and the flow becomes more stable. Only in a very small parameter region, wall suction/blowing increases the maximum disturbance growth rate of the critical mode, resulting in flow instability when the gap between the cylinders is large. The asymptotic results for small suction/blowing amplitudes indicate that the change of flow instability is mainly due to the steady correction of the basic flow induced by the modulation. A parametric study of the critical inner Reynolds number and the associated critical wavenumber is performed. It is found that the flow is stabilized by the modulation for most of the parameter ranges considered. For a wide gap between the cylinders, it is possible for the system to be mildly destabilized by weak suction/blowing.
We focus on three integrated measures of the mixing: the mixed-width, mixedness, and mixed mass. I will also examine the dependence of these mixing parameters on density disparities, Mach numbers, and other flow properties. It is shown that the mixed mass is nondecreasing. The asymmetry of the bubble and spike is also discussed.
Experimental research into the control of particle charge in dusty plasmas conducted at Auburn University indicates that photocurrents generated by exposing dust to intense, near-ultraviolet light can provide a reliable and novel method of independently controlling dust charge without radically altering the background plasma; the experiment also showed that some particles may respond differently to this photo-discharge, with some exhibiting highly periodic responses to the discharge and others exhibiting chaotic behaviour. Since the dust particles in the experiment were a polydisperse sample of different sizes and shapes, particle geometry may play a role in explaining this difference. Simulations of particle discharge and dynamics are used in an attempt to reproduce experimental results and investigate a possible correlation between particle symmetry and dynamic periodicity.