Related papers: Loading a relativistic kappa distribution in parti…
Numerical algorithms to load relativistic Maxwell distributions in particle-in-cell (PIC) and Monte-Carlo simulations are presented. For stationary relativistic Maxwellian, the inverse transform method and the Sobol algorithm are reviewed.…
Numerical procedures for generating non-Maxwellian velocity distributions in particle simulations are presented. First, Monte Carlo methods for an $(r,q)$ distribution that generalizes flattop and kappa distributions are discussed. Then,…
For kinetic modeling of plasma processes in space, a rejection-sampling procedure for generating a Kappa distribution in particle-in-cell (PIC) simulation is proposed. A Pareto distribution is employed as an envelope distribution. The…
Numerical procedures to generate random variates that follow loss-cone velocity distributions in particle simulations are presented. We propose a simple summation algorithm for the Ashour-Abdalla--Kennel-type loss-cone distribution, also…
A simple numerical method for loading of a relativistic Maxwellian-type distribution is proposed based on inverse transform sampling. The relativistic Maxwellian energy distribution is introduced as an alternative to the Maxwell-J\"{u}ttner…
Kappa-distributed velocities in plasmas are common in a wide variety of settings, from low-density to high-density plasmas. To date, they have been found mainly in space plasmas, but are recently being considered also in the modelling of…
The present paper is devoted to the relativistic statistical theory, introduced in Phys. Rev. E {\bf 66} (2002) 056125 and Phys. Rev. E {\bf 72} (2005) 036108, predicting the particle distribution function $p(E)= \exp_{\kappa}…
A random number generator for the Kappa velocity distribution in particle simulations is proposed. Approximating the cumulative distribution function with the q-exponential function, an inverse transform procedure is constructed. The…
We demonstrate that a nonthermal distribution of particles described by a kappa distribution can be accurately approximated by a weighted sum of Maxwell-Boltzmann distributions. We apply this method to modeling collision processes in…
A procedure for generating random variates from a relativistic Maxwellian distribution with arbitrary temperature and drift velocity is presented. The algorithm is based on the rejection method and can be used to initialize particle…
Kappa distributions are widely used in space plasma physics to model velocity distribution functions with heavy tails. Parameter estimation in these distributions is, however, complicated by the fact that the kappa distribution does not…
From the perspective of non-equilibrium statistical mechanics, modeling the velocity distribution of particles in non-equilibrium, steady-state plasmas presents a significant challenge. Under this context, a family of kappa distributions…
In Monte Carlo simulations, proposed configurations are accepted or rejected according to an acceptance ratio, which depends on an underlying probability distribution and an a priori sampling probability. By carefully selecting the…
Simulating from a gamma distribution with small shape parameter is a challenging problem. Towards an efficient method, we obtain a limiting distribution for a suitably normalized gamma distribution when the shape parameter tends to zero.…
Probabilistic principal component analysis (PPCA) is a probabilistic reformulation of principal component analysis (PCA), under the framework of a Gaussian latent variable model. To improve the robustness of PPCA, it has been proposed to…
Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection…
Markov chain Monte Carlo methods have become standard tools in statistics to sample from complex probability measures. Many available techniques rely on discrete-time reversible Markov chains whose transition kernels build up over the…
The kappa distribution of velocities appears routinely in the study of collisionless plasmas present in Earth's magnetosphere, the solar wind among other contexts where particles are unable to reach thermal equilibrium. Originally justified…
For various plasma applications the so-called (non-relativistic) $\kappa$-distribution is widely used to reproduce and interpret the suprathermal particle populations exhibiting a power-law distribution in velocity or energy. Despite its…
Particle in Cell (PIC) simulations have become a vital tool for the investigation of kinetic processes in plasma physics. Many of the systems investigated with PIC simulations contain particles with relativistic velocities. The correct…