A review of Vlasov–Fokker–Planck numerical modeling of inertial confinement fusion plasma

The interaction of intense lasers with solid matter generates a hot plasma state that is well described by the Vlasov–Fokker–Planck equation. Accurate and efficient modeling of the physics in these scenarios is highly pertinent, because it relates to experimental campaigns to produce energy by inertial confinement fusion on facilities such as the National Ignition Facility. Calculations involving the Vlasov–Fokker–Planck equation are computationally intensive, but are crucial to proper understanding of a wide variety of physical effects and instabilities in inertial fusion plasmas. In this topical review, we will introduce the background physics related to Vlasov–Fokker–Planck simulation, and then proceed to describe results from numerical simulation of inertial fusion plasma in a pedagogical manner by discussing some key numerical algorithm developments that enabled the research to take place. A qualitative comparison of the techniques is also given.     

Isotope separation of Potassium with a magneto–optical combined method

Due to the similar physical and chemical properties, isotopes are usually hard to separate. On the other hand, the isotope shifts are very well separated in a high-resolution spectrum, making them possible to be addressed individually by lasers, thus separated. Here we report such an isotope separation experiment with Potassium atoms. The isotopes are independently optical pumped to the desired spin states, and then separated with a Stern–Gerlach scheme. A micro-capillary oven is used to collimate the atomic beam, and a Halbach-type magnet array is used to deflect the desired atoms. Finally, the ⁴⁰K is enriched by two orders of magnitude. This magneto–optical combined method provides an effective way to separate isotopes and can be extended to other elements if the relevant optical pumping scheme is feasible.     

Assessment of a composite CC2/DFT procedure for calculating 0–0 excitation energies of organic molecules

The task to assess the performance of quantum chemical methods in describing electronically excited states has in recent years started to shift from calculation of vertical (ΔE_ve) to calculation of 0–0 excitation energies (ΔE₀₀). Here, based on a set of 66 excited states of organic molecules for which high-resolution experimental ΔE₀₀ energies are available and for which the approximate coupled-cluster singles and doubles (CC2) method performs particularly well, we explore the possibility to simplify the calculation of CC2-quality ΔE₀₀ energies using composite procedures that partly replace CC2 with more economical methods. Specifically, we consider procedures that employ CC2 only for the ΔE_ve part and density functional theory methods for the cumbersome excited-state geometry optimisations and frequency calculations required to obtain ΔE₀₀ energies from ΔE_ve ones. The results demonstrate that it is indeed possible to both closely (to within 0.06–0.08 eV) and consistently approximate ‘true’ CC2 ΔE₀₀ energies in this way, especially when CC2 is combined with hybrid density functionals. Overall, the study highlights the unexploited potential of composite procedures, which hitherto have found widespread use mostly in ground-state chemistry, to also play an important role in facilitating accurate studies of excited states.     

Optimization of a magneto–optic trap using nanofibers

We experimentally demonstrate a reliable method based on a nanofiber to optimize the number of cold atoms in a magneto–optical trap(MOT) and to monitor the MOT in real time.The atomic fluorescence is collected by a nanofiber with subwavelength diameter of about 400 nm.The MOT parameters are experimentally adjusted in order to match the maximum number of cold atoms provided by the fluorescence collected by the nanofiber.The maximum number of cold atoms is obtained when the intensities of the cooling and re-pumping beams are about 23.5 mW/cm~2 and 7.1 mW/cm~2,respectively; the detuning of the cooling beam is-13.0 MHz, and the axial magnetic gradient is about 9.7 Gauss/cm.We observe a maximum photon counting rate of nearly(4.5 ± 0.1) × 10~5 counts/s.The nanofiber–atom system can provide a powerful and flexible tool for sensitive atom detection and for monitoring atom–matter coupling.It can be widely used from quantum optics to quantum precision measurement.     

Spatial structure of a Bose–Einstein condensate in a combined trap

We study the spatial structure of a Bose–Einstein condensate(BEC) with a space-dependent s-wave scattering length in a combined trap. There exists a space-dependent nonlinear atomic current in the system. The atomic current has an important influence on the spatial structure of the BEC. Research findings reveal that a large chemical potential can effectively suppress the chaotic spatial structure in the BEC system. Due to the large chemical potential, a strong atomic current is necessary to make...     

Calculations of operating schemes for a passive harmonic cavity in HLS-Ⅱ

A passive higher harmonic cavity (HHC) will be used in the Hefei Light Source II Project (HLS-Ⅱ) to lengthen the bunch and consequently increase the beam lifetime dominated by Touschek scattering. The effects of constant voltage and constant detuning have been calculated and compared over the operating current from 0.4 to 0.2 A on the bunch lengthening for the passive normal conducting harmonic cavity system in HLS-Ⅱ. The results show that the bunch shape has less change and the lifetime improvement factors are not less than 2.7 over the beam currents for the constant voltage case. The constant voltage operating scheme may be applied to our machine.     

Evaluation of the neutron production rate using D–D and D–T fuel in an inertial electrostatic confinement fusion device

The correlation between the neutron production rate and fuel species in a spherical inertial electrostatic confinement fusion (IECF) device is investigated by solving the Poisson equation for various ion and electron distribution functions. The fuel ion energy distribution function is determined at each radial point. The fusion reaction rate is evaluated from the energy distribution function. The dependence of the neutron production rate (NPR) on some important parameters, like the ion convergence, the broadening of the distributions in the energy space, working pressure and fuel species, are also investigated. Compared with the IECF device with D–D, numerical calculations show that by increasing the percentage of tritium in the D–T mixture fuel the neutron production rate grows significantly.     

Accurate interface-tracking of surfaces in three dimensions for arbitrary Lagrangian–Eulerian schemes

We extend the computational method presented in [1] for tracking an interface immersed in a given velocity field to three spatial dimensions. The proposed method is particularly relevant to the simulation of unsteady free surface problems using the arbitrary Lagrangian–Eulerian framework, and has been constructed with two goals in mind: (i) to be able to accurately follow the interface; and (ii) to automatically maintain a good distribution of the grid points along the interface. The method combines information from a pure Lagrangian approach with information from an ALE approach. The new method offers flexibility in terms of how an “optimal” point distribution should be defined, and relies on the solution of two-dimensional surface convection problems. We verify the new method by solving model problems both in the single and multiple spectral element case, and we compare this method with other traditional alternatives. We have been able to verify first, second, and third order temporal accuracy for the new method by solving these three-dimensional model problems.     

On the determination of energy fluxes at plasma–surface processes

A summary is given of different methods for the determination of the energy influx and its influence on the thermal balance and energetic conditions of substrate surfaces during plasma processing. The discussed mechanisms include heat radiation and kinetic and potential energy of charged particles and sputtered neutrals. For a few examples such as magnetron sputtering of a-C:H films, sputter deposition of aluminum on microparticles, and titanium deposition in a hollow-cathode arc evaporation device the energetic balance of substrates during plasma processing is presented. Received: 6 July 2000 / Accepted: 12 December 2000 / Published online: 3 April 2001     

Quark potential in a quark–meson plasma

We investigate the effect of the restoration of chiral symmetry on the quark potential in a quark–meson plasma by considering meson exchanges in the two flavor Nambu–Jona-Lasinio model at finite temperature and density. There are two possible oscillations in the chiral restoration phase; one is the Friedel oscillation due to the sharp quark Fermi surface at high density, and the other is the Yukawa oscillation driven by the complex meson poles at high temperature. The quark–meson plasma is strongly coupled in the temperature region 1≤T/T _c≤3, with T _c being the critical temperature of the chiral phase transition. The maximum coupling in this region is located at the phase transition point.     

Spectroscopic estimation of plasma parameters,in the 100–400 ns stage,of a laser-induced plasma in vacuum

This work is focused on the interpretation of the emission spectra in laser-induced plasma observed in the phase at 100–400?ns from after the laser pulse, when the discrete emission lines prevail on the continuum emission, can be important to retrieve the initial stage of expansion. A Q-switched neodymium-doped yttrium aluminum garnet laser has been used for the ablation of a lead sample in vacuum. The observed line profiles, corresponding to different species of lead, were analyzed in terms of delay time. Measurements of parameters of the produced plasmas are performed. The results obtained corroborate the importance of considering nonequilibrium effects in the initial stage of plasma expansion. Also, Stark width for two spectral lines of triply ionized lead is given.     

Suppression of elliptic flow in a minimally viscous quark–gluon plasma

We compute the time evolution of elliptic flow in non-central relativistic heavy-ion collisions, using a (2+1$2+1$)-dimensional code with longitudinal boost-invariance to simulate viscous fluid dynamics in the causal Israel–Stewart formulation. We show that even “minimal” shear viscosity η/s=?/(4π)$\eta /s=?/(4\pi )$ leads to a large reduction of elliptic flow compared to ideal fluid dynamics, raising questions about the interpretation of recent experimental data from the Relativistic Heavy Ion Collider.     

Electro–magneto interaction in fractional Green-Naghdi thermoelastic solid with a cylindrical cavity

A unified mathematical model of Green–Naghdi’s thermoelasticty theories (GN), based on fractional time-derivative of heat transfer is constructed. The model is applied to solve a one-dimensional problem of a perfect conducting unbounded body with a cylindrical cavity subjected to sinusoidal pulse heating in the presence of an axial uniform magnetic field. Laplace transform techniques are used to get the general analytical solutions in Laplace domain, and the inverse Laplace transforms based on Fourier expansion techniques are numerically implemented to obtain the numerical solutions in time domain. Comparisons are made with the results predicted by the two theories. The effects of the fractional derivative parameter on thermoelastic fields for different theories are discussed.     

Hydrodynamic analysis of electrostatic counter-streaming instability in a spin-polarized electron–positron–ion plasma

In this study, we present linear analysis of electrostatic counter-streaming instability in spin-polarized electron–positron–ion (e-p-i) plasma. With the aid of the separate spin evolution-quantum hydrodynamic (SSE-QHD) model, we derive the dispersion relation of counter-streaming instability. We numerically solve the dispersion and find four wave solutions: Langmuir wave, positron acoustic mode, and two electron and positron spin-dependent waves. It is noted that coupling of streaming and spin effects excites Langmuir instability and positron acoustic mode instability. However, in the absence of spin effect, only Langmuir instability will survive in e-p-i plasma. We have also discussed the effects of positron concentration, streaming speed, and spin polarization on the real frequency of waves and the growth rate. The present study may be helpful for understanding longitudinal wave propagation and instabilities in dense magnetized environments.     

Simulation research on effect of magnetic nanoparticles on physical process of magneto–acoustic tomography with magnetic induction

Magneto–acoustic tomography with magnetic induction(MAT-MI) is a multiphysics coupled imaging technique that is combined with electrical impedance tomography and ultrasound imaging. In order to study the influence of adding magnetic nanoparticles as a contrast agent for MAT-MI on its physical process, firstly, we analyze and compare the electromagnetic and acoustical properties of MAT-MI theoretically before and after adding magnetic nanoparticles, and then construct a two-dimensional(2 D) planar model. Under the guidance of space-time separation theory, we determine the reasonable simulation conditions and solve the electromagnetic field and sound field physical processes in the two modes by using the finite element method. The magnetic flux density, sound pressure distribution, and related one-dimensional(1 D), 2 D, and three-dimensional(3 D) images are obtained. Finally, we make a qualitative and quantitative analysis based on the theoretical and simulation results. The research results show that the peak time of the time item separated from the sound source has a corresponding relationship with the peak time of the sound pressure signal. At this moment, MAMPTMI produces larger sound pressure signals, and the sound pressure distribution of the MAMPT-MI is more uniform, which facilitates the detection and completion of sound source reconstruction. The research results may lay the foundation for the MAT-MI of magnetically responsive nanoparticle in subsequent experiments and even clinical applications.     

Simulation of laser–plasma interactions and fast-electron transport in inhomogeneous plasma

A new framework is introduced for kinetic simulation of laser–plasma interactions in an inhomogeneous plasma motivated by the goal of performing integrated kinetic simulations of fast-ignition laser fusion. The algorithm addresses the propagation and absorption of an intense electromagnetic wave in an ionized plasma leading to the generation and transport of an energetic electron component. The energetic electrons propagate farther into the plasma to much higher densities where Coulomb collisions become important. The high-density plasma supports an energetic electron current, return currents, self-consistent electric fields associated with maintaining quasi-neutrality, and self-consistent magnetic fields due to the currents. Collisions of the electrons and ions are calculated accurately to track the energetic electrons and model their interactions with the background plasma. Up to a density well above critical density, where the laser electromagnetic field is evanescent, Maxwell’s equations are solved with a conventional particle-based, finite-difference scheme. In the higher-density plasma, Maxwell’s equations are solved using an Ohm’s law neglecting the inertia of the background electrons with the option of omitting the displacement current in Ampere’s law. Particle equations of motion with binary collisions are solved for all electrons and ions throughout the system using weighted particles to resolve the density gradient efficiently. The algorithm is analyzed and demonstrated in simulation examples. The simulation scheme introduced here achieves significantly improved efficiencies.     

Analytical formulas for calculating the blocking probability of a dynamic star network

Routing and wavelength assignment (RWA) has becomeone of the key problems for today's complicated wave-length division multiplexing (WDM) networks. In gen-eral, RWA can be classified either into the dynamiccase and the static case according to the wavelengthallocation[1], or into the star, ring and mesh networksaccording to the topology. Although extensive researchworks[2,3] have been done on the RWA and many al-gorithms have been developed for the case of dynamicrings[4], little has been …     

Role of glueballs in non-perturbative quark–gluon plasma

Discussed is how non-perturbative properties of quark gluon plasma, recently discovered in RHIC experiment, can be related to the change of properties of scalar and pseudoscalar glueballs. We set up a model with the Cornwall–Soni's glueball–gluon interaction, which shows that the pseudoscalar glueball becomes massless above the critical temperature of deconfinement phase transition. This change of properties gives rise to the change of sign of the gluon condensate at T>Tc$T>T_c$. We discuss the other physical consequences resulting from the drastic change of the pseudoscalar glueball mass above the critical temperature.     

Nonlinear propagation of an intense Laguerre–Gaussian laser pulse in a plasma channel

The nonlinear propagation of an intense Laguerre–Gaussian(LG) laser pulse in a parabolic preformed plasma channel is analyzed by means of the variational method. The evolution equation of the spot size is derived including the effects of relativistic self-focusing, preformed channel focusing, and ponderomotive self-channeling. The parametric conditions of the LG laser pulse and plasma channel for propagating with constant spot size, periodically focusing and defocusing oscillation,catastrophic focusing, and solitary waves are obtained. Compared with the laser pulse with fundamental Gaussian(FG)mode, it is found that the effect of vacuum diffraction is reduced by half and the effects of relativistic and wakefield focusing are decreased by a quarter due to the hollow transverse intensity profile of the LG laser pulse, while the effect of channel focusing is the same order of magnitude with that of the FG laser pulse. Thus, the matched condition for the intense LG laser pulse with constant spot size is released obviously, while the parameters of the laser and plasma for the existence of solitary waves nearly coincide with those of the FG laser pulse.     

Atomic motion in the magneto–optical trap consisting of partially spatially coherent laser

Rb atom motion in a magneto–optical trap(MOT) consisting of a partially spatially coherent laser(PSCL) is investigated theoretically. The spatial coherence of the laser is controlled by the electro–optic crystal. The instantaneous spatial distribution of the dissipative force induced by the PSCL on an Rb atom is varying with time stochastically. The simulated results indicate that compared with a fully coherent laser, the spatial coherent laser has effects on the atomic trajectories;however, the capture velocity and the escape velocity are kept the same. The main reason is that the spatial coherence of the laser fluctuates temporally and spatially, but the average photon scattering rate varies little, which makes the total number of atoms and the atomic density distribution unchanged.