Giacomo Grasso

Subversion is a free/open-source version control system. That is, Subversion manages all data contained in a project over time, remembering every change ever made to your files and directories. This allows you to recover older versions of your data, or examine the history of how your data changed.

Per la generazione di una popolazione di numeri pseudocasuali campionati da una funzione di distribuzione Maxwelliana sono comunemente utilizzati due diversi algoritmi: il primo di questi è piuttosto semplice e per questo didatticamente valido, ma, come spesso accade, piuttosto inefficiente e poco performante, mentre il secondo, noto come algoritmo di Johnk, è più complesso ma sicuramente più elegante e performante.

The Structured Adaptive Mesh Refinement (SAMR) is a numerical technique for the solution of spatial dependent problems via dynamic creation of a multi scale hierarchy of structured grids. This approach leads to a faster and finer solution, and to the damping of numerical noise at different wave lengths.

Particle In Cell simulation codes were showed to be a suitable tool for modelling collisional plasmas, in particular self-sustained discharges and breakdown in gases. For this purpose, they have to be coupled with a Monte Carlo Collisional module able to model charged particle interaction with a background gas via random numbers. Argon is deeply used as background gas in such simulations, but numerical data or interpolation formula of electron and ion impact cross section are not so easy to collect. In this short report, interpolating formulae and energy range of validity will be presented, as extracted from XOOPIC sources.

Particle In Cell (PIC) simulations require large machine-time to process particles charge assignment and motion. Moreover coupling such methods with Monte Carlo Collisional (MCC) modules causes another expensive computational cost to simulate particle multiple collisions with background gas and domain boundaries. Merging many particles in few particles with increased weights is a widely used accelerating technique. A merging procedure based on charge conservation on a spatial 2D domain is here proposed to avoid an exponentially increasing number of particles per cell during the simulation. Two different strategies are here presented, based on first and second order charge moments conservation. If coupled with a splitting technique, the technique should increase performances of both PIC and MCC module reducing noise in electric field solution and increasing samples representativeness in stochastic calculations.

In a previous work [2] two different merging techniques were presented to reduce the number of simulation particles in Paticle In Cell Monte Carlo Collisional (PIC-MCC) codes. At least two particles are needed to replace a set of N > 2 particles in a single cell preserving the charge fractions on the nodes. Few preliminary results will be here presented and algorithm listings will be enclosed to show the main differences between the two techniques.

The effectiveness of Particle In Cell (PIC) codes in plasma dynamics simulation requires the ability to artificially change the number of particles during the calculation. The local number of particles per cell generally increases during the simulation and can be kept controlled in order to avoid exponentially increasing computation time ans to mantain a high enough local accuracy. The adopted technique is a spatial and energetic merging of the particles in the phase space based on conservation laws of total charge and energy and momentum of the two particles sets. In [2] a detailed description of the spatial merging was dealt with: particles inside the same cell can be merged together into two new particles positioned in order to conserve the charge fractions on the four cell nodes. Unfrtunately this is not enough: the new particles should conserve also the total energy and momentum of the starting ones and, in total, they should reproduce the same distribution function in the phase space. Few theoretical considerations will be given here about this topic.

Usually, Particle In Cell-Monte Carlo Collisional (PIC-MCC) codes are equipped with technique aimed to reduce the total number of simulation particles in order to limit computation time. This approach is not always effcient from the point of view of both the Particle In Cell (PIC) and Monte Carlo (MC) modules. PIC methods are affected by charge spatial distribution on the grid; when this fluctuates rapidly, usually because of a not high enough number of particles per cell, the solution of the electric field introduces numerical noise. Moreover, it's widely known that Monte Carlo techniques effectiveness depends on the number of sample: the statistical approach of the method requires a representative enough ensemble. This means that a depletion of simulation particles due to absorbing events or charge neutralization could compromise the correctness of the results, biasing the solution towards a casual direction. A splitting technique, succesfully emploied in Monte Carlo simulations, will be adapted to hybrid PIC-MCC codes in order to reduce noise and to improve representativeness in the phase-space domain.

Particle-In-Cell (PIC) simulation codes were shown to be a suitable tool for modeling collisional plasmas, in particular self-sustained discharges and breakdown in gases. For this purpose, they have to be coupled with a Monte Carlo Collisional (MCC) module able to model charged particle interaction with a background gas via random numbers. Molecular Hydrogen is often used as background gas in such simulations, but numerical data or inter polation formula of electron and ion impact cross section are not so easy to collect. In this short report, both interpolating formulae and tabulated data will be presented, as collected from a wide variety of literature sources.

In Plasma Focus (PF) devices electrical breakdown, the first avalanche ionization phase leads the system to the formation of a plasma seed by the cathode-insulator junction: this results only in a pre-breakdown mechanism. In order to simulate the evolution of the system towards the final plasma sheath configuration, a further mechanism of free charges production is needed, leading to a greater ionization degree of the filling gas. Such a mechanism was found to be supplied by secondary electrons photoemission from cathode: during the plasma seed formation, electrons colliding with gas neutral molecules produce an excited molecules spatial distribution. The de-excitation process of this population leads to a photons production rate delayed in time, which is responsible of the secondary emission of electrons from cathode.

A description of the photoemission mechanism is briefly presented, together with a detailed study of the excited molecules distribution and of a spatial map for cathode sight factor.

The es-cPIF (electrostatic-collisional Particle In cell for plasma Focus devices) code has been developed with High Performance Computing (HPC) wills. To achieve this goal, the code writing has been deeply analyzed on two levels: a direct one of program main blocks, functions and operations architecture optimization, and an indirect second one of cache memory access optimization by means of advanced particles management techniques. The developed es-cPIF code efficiency has then been tested by low level profiling by means of the IBM's Hardware Performance Monitor (HPM) tool. The obtained results are here presented and compared with the ones of a BLAS benchmarking code suitably written.