arXiv subjects

Claudio Di Troia

Publications and source records attributed to Claudio Di Troia.

5 recordsLinked to original sources

arXiv2021

Analysis of the nonlinear dynamics of a chirping-frequency Alfvén mode in a Tokamak equilibrium

Chirping Alfvén modes are considered as potentially harmful in burning Tokamak plasmas. In this paper, the nonlinear evolution of a single-toroidal-number chirping mode is analysed by numerical particle simulation. This analysis can be simplified if the different resonant phase-space structures can be investigated as isolated ones. This can be done adopting a coordinate system that includes two constants of motion. In our simulations, we adopt as constants of motion, the magnetic momentum and the initial particle coordinates. For each resonant structure, a density-flattening region is formed around the respective resonance radius, with radial width that increases as the mode amplitude grows. It is delimited by two large negative density gradients, drifting inward and outward. With constant mode frequency, this density flattening would be responsible for the exhausting of the drive when large negative density gradients leave the resonance region. The frequency chirping, however, causes the resonance radius and the resonance region to drift inward. This drift delays the moment in which the inner density gradient reaches the inner boundary of the resonance region. On the other side, the island reconstitutes around the new resonance radius; as a consequence, the large negative density gradient further moves inward. This process continues as long as it allows to keep the large gradient within the resonance region. When this is no longer possible, the resonant structure ceases to be effective in driving the mode. To further grow, the mode has to tap a different resonant structure, possibly making use of additional frequency variations.

physics.plasm-ph↗

arXiv2018

Non-perturbative guiding center and stochastic gyrocenter transformations: gyro-phase is the Kaluza-Klein 5^th dimension also for reconciling General Relativity with Quantum Mechanics

The non perturbative guiding center transformation is extended to the relativistic regime and takes into account electromagnetic fluctuations. The main solutions are obtained in covariant form: the gyrating particle and the guiding particle solutions, both in gyro-kinetic as in MHD orderings. Moreover, the presence of a gravitational field is also considered. The way to introduce the gravitational field is original and based on the Einstein conjecture on the feasibility to extend the general relativity theory to include electromagnetism by geometry, if applied to the extended phase space. In gyro-kinetic theory, some interesting novelties appear in a natural way, such as the exactness of the conservation of a magnetic moment, or the fact that the gyro-phase is treated as the non observable fifth dimension of the \emph{Kaluza-Klein} model. Electrodynamic becomes non local, without the inconsistency of self-energy. Finally, the gyrocenter transformation is considered in the presence of stochastic e.m. fluctuations for explaining quantum behaviors via Nelson's approach. The gyrocenter law of motion is the \emph{Schrödinger} equation.

physics.gen-ph↗

arXiv2015

From charge motion in general magnetic fields to the non perturbative gyrokinetic equation

The exact analytical description of non relativistic charge motion in general magnetic fields is, apparently, a simple problem but, it has not been solved up to now apart for rare cases. The key feature of the present derivation is to adopt a non perturbative magnetic field description to find new solutions of motion. Among all solutions, two are particularly important: guiding particle and gyro-particle solutions. The guiding particle has been characterized to be minimally coupled to the magnetic field, the gyro-particle has been defined to be maximally coupled to the magnetic field and, also, to move on a closed orbit. The generic charged particle motion is shown to be expressed as the sum of such particular solutions. This non perturbative approach corresponds to the description of the particle motion in the gyro-center and/or guiding center reference frame obtained at all the orders of the modern gyro-center transformation. The Boltzmann equation is analyzed with the described exact guiding center coordinates. The obtained gyrokinetic equation is solved for the Boltzmann equation at marginal stability conditions.

physics.plasm-ph↗

arXiv2015

Bayesian derivation of plasma equilibrium distribution function for tokamak scenarios and the associated Landau collision operator

A class of parametric distribution functions has been proposed in [C.DiTroia, Plasma Physics and Controlled Fusion,54,2012] as equilibrium distribution functions (EDFs) for charged particles in fusion plasmas, representing supra-thermal particles in anisotropic equilibria for Neutral Beam Injection, Ion Cyclotron Heating scenarios. Moreover, the EDFs can also represent nearly isotropic equilibria for Slowing-Down $alpha$ particles and core thermal plasma populations. These EDFs depend on constants of motion (COMs). Assuming an axisymmetric system with no equilibrium electric field, the EDF depends on the toroidal canonical momentum $P_ϕ$, the kinetic energy $w$ and the magnetic moment μ. In the present work, the EDFs are obtained from first principles and general hypothesis. The derivation is probabilistic and makes use of the Bayes' Theorem. The bayesian argument allows us to describe how far from the prior probability distribution function (pdf), e.g. Maxwellian, the plasma is, based on the information obtained from magnetic moment and GC velocity pdf. Once the general functional form of the EDF has been settled, it is shown how to associate a Landau collision operator and a Fokker-Planck equation that ensures the system relaxation towards the proposed EDF.

physics.plasm-ph↗

arXiv2012

From the orbit theory to a guiding center parametric distribution function

This work proposes a parametric equilibrium distribution function F_eq to be applied to the gyrokinetic studies of the Finite Orbit Width behavior of guiding centers representing several species encountered in axisymmetric tokamak plasma, as fusion products, thermal bulk and energetic particles from Ion Cyclotron Radiation Heating and Negative Neutral Beam Injections. After the analysis of the basic results of orbit theory obtained with a particularly convenient orbit coordinates set, it is shown how the proposed F_eq satisfies the two conditions that make it an equilibrium distribution function: (i) it must depend only on the constants of motion and adiabatic invariants, and (ii) the guiding centers must remain confined for suitably long time. Furthermore, the F_eq can be modeled, with a proper choice of its parameters, to reproduce the most common distribution functions. A local Maxwellian distribution function is obtained for the thermal plasma in the Zero Orbit Width approximation. For the fusion αparticles, F_eq can also reproduce the Slowing Down (SD) distribution function. More generally, for supra-thermal particles, when external heatings are present, such as (N)NBI and ICRH, the proposed model distribution function shows similarities with the anisotropic SD and the biMaxwellian distribution functions. F_eq can be used to fit experimental profiles and it could provide a useful tool for experimental and numerical data analysis. Moreover, it could help to develop analytical computations for facilitating data interpretation in the light of theoretical models. This distribution function can be easily implemented in gyrokinetic codes, where it can be used to simulate plasma also in the presence of external heating sources.

physics.plasm-ph↗