Generalized Plasma Dispersion Function: One-Solve-All Treatment, Visualizations, and Application to Landau Damping

A unified, fast, and effective approach is developed for numerical calculation of the well-known plasma dispersion function with extensions from Maxwellian distribution to almost arbitrary distribution functions, such as the $\delta$, flat top, triangular, $\kappa$ or Lorentzian, slowing down, and incomplete Maxwellian distributions. The singularity and analytic continuation problems are also solved generally. Given that the usual conclusion $\gamma\propto\partial f_0/\partial v$ is only a rough approximation when discussing the distribution function effects on Landau damping, this approach provides a useful tool for rigorous calculations of the linear wave and instability properties of plasma for general distribution functions. The results are also verified via a linear initial value simulation approach. Intuitive visualizations of the generalized plasma dispersion function are also provided.Comment: Accepted by Physics of Plasmas, 9 pages, 14 figures, see arXiv "Other formats" link for supplementary materia

PDRF: A General Dispersion Relation Solver for Magnetized Multi-Fluid Plasma

A general dispersion-relation solver that numerically evaluates the full propagation properties of all the waves in fluid plasmas is presented. The effects of anisotropic pressure, external magnetic fields and beams, relativistic dynamics, as well as local plasma inhomogeneity are included. [Computer Physics Communications, (2013); doi: 10.1016/j.cpc.2013.10.012; code: http://cpc.cs.qub.ac.uk/summaries/AERF\_v1\_0.html]Comment: 10 pages, 5 figures, see also arXiv "Other formats" link for the cod

Some Mathematical Models for ELM Signal

There is no wide accepted theory for ELM (Edge Localized Mode) yet. Some fusion people feel that we may never get a final theory for ELM and H-mode, since which are too complicated (also related to the unsolved turbulence problem) and with at least three time scales. The only way out is using models. (This is analogous to that we believe quantum mechanics can explain chemistry and biology, but no one can calculate DNA structure from Schrodinger equation directly.) This manuscript gives some possible mathematical approaches to it. I should declare that these are just math toys for me yet. They may inspire to good understandings of ELM and H-mode, may not. Useful or useless, I don't know. One need not take too much care of it. Just for fun and enjoying different interesting ideas

Pure Monte Carlo Method: a Third Way for Plasma Simulation

We bring a totally new concept for plasma simulation, other than the conventional two ways: Fluid/Kinetic Continuum (FKC) method and Particle-in-Cell (PIC) method. This method is based on Pure Monte Carlo (PMC), but far beyond traditional treatments. PMC solves all the equations (kinetic, fluid, field) and treats all the procedures (collisions, others) in the system via MC method. As shown in two paradigms, many advantages have found. It has shown the capability to be the third importance approach for plasma simulation or even completely substitute the other two in the future. It's also suitable for many unsolved problems, then bring plasma simulation to a new era.Comment: 8 pages, 4 figures, draft, to submit for PRL or CPC o

Half Spectral, an Another General Method for Linear Plasma Simulation

There are two usual computational methods for linear (waves and instabilities) problem: eigenvalue (dispersion relation) solver and initial value solver. In fact, we can introduce an idea of the combination of them, i.e., we keep time derivative dt term (and other term if have, e.g., kinetic dv term), but transform the linear spatial derivatives dx term to ik, which then can reduce the computational dimensions. For example, most (fluid and kinetic) normal mode problems can be reduced from treating cumbersome PDEs to treating simple ODEs. Examples for MHD waves, cold plasma waves and kinetic Landau damping are given, which show to be extremely simple or even may be the simplest method for simulating them. [I don't know whether this idea is new, but it seems very interesting and useful. So, I choose making it public.]Comment: 7 pages, 5 figures, with code

A Full-Matrix Approach for Solving General Plasma Dispersion Relation

A hitherto difficult and unsolved issue in plasma physics is how to give a general numerical solver for complicated plasma dispersion relation, although we have long known the general analytical forms. We transform the task to a full-matrix eigenvalue problem, which allows to numerically calculate all the dispersion relation solutions exactly free from convergence problem and give polarizations naturally for arbitrarily complicated multi-scale fluid plasma with arbitrary number of components. Attempt to kinetic plasma via $N$-point Pad\'e approximation of plasma dispersion function also shows good results.Comment: 4 pages, 3 figure

Linear Kinetic Coupling of Firehose (KAW) and Mirror Mode

A general gyrokinetic dispersion relation is gotten and is applied to analysis linear kinetic coupling of anisotropic firehose (or, kinetic Alfven wave) and mirror mode. Nyquist stability analysis is also given.Comment: 8 pages, 7 figure

Generation of dipole squeezing in a two-mode system with entangled coherent states of a quantized electromagnetic field

Two-mode quantized electromagnetic fields can be entangled and admit a large number of coherent states. In this paper, we consider a two-mode system that consists of a two-level atom interacting with a two-mode quantized electromagnetic field, which is initially prepared in an entangled two-mode coherent state, via a nondegenerate two-photon process in a lossless cavity. We study the quantum fluctuations in the two-mode system and investigate in detail the effects of detuning, Stark shift and atomic coherence on atomic dipole squeezing (ADS). We show that ADS strongly depends on the atomic coherence. It is found that the stronger the correlations between the two modes are involved, the more the ADS could be generated. The detuning or Stark shift has a destructive effect on ADS, but the combined effect of the detuning and Stark shift may lead to a regular, periodical and strong ADS pattern.Comment: 10 figure

Perturbation Analysis and Randomized Algorithms for Large-Scale Total Least Squares Problems

In this paper, we present perturbation analysis and randomized algorithms for the total least squares (TLS) problems. We derive the perturbation bound and check its sharpness by numerical experiments. Motivated by the recently popular probabilistic algorithms for low-rank approximations, we develop randomized algorithms for the TLS and the truncated total least squares (TTLS) solutions of large-scale discrete ill-posed problems, which can greatly reduce the computational time and still keep good accuracy.Comment: 27 pages, 10 figures, 8 table

A relaxation time model for efficient and accurate prediction of lattice thermal conductivity

Prediction of lattice thermal conductivity is important to many applications and technologies, especially for high-throughput materials screening. However, the state-of-the-art method based on three-phonon scattering process is bound with high computational cost while semi-empirical models such as the Slack equation are less accurate. In this work, we examined the theoretical background of the commonly-used computational models for high-throughput thermal conductivity prediction and proposed an efficient and accurate method based on an approximation for three-phonon scattering strength. This quasi-harmonic approximation has comparable computational cost with many widely-used thermal conductivity models but had the best performance in regard to quantitative accuracy. As compared to many models that can only predict lattice thermal conductivity values, this model also allows to include Normal processes and obtain the phonon relaxation time.Comment: The supplementary materials exceed the size limit of arXiv and could be available after this paper is publishe