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D. S. Oliveira

Publications and source records attributed to D. S. Oliveira.

15 recordsLinked to original sources
arXiv2025

Comparison of filament properties in real-size GBS simulations and experiments of TCV-X21

A direct quantitative comparison of Scrape-Off Layer (SOL) filament properties from fluid turbulence simulations using the GBS code and from experiments on the TCV tokamak is performed within the TCV-X21 validation case. This comparison is made possible by extending the open TCV-X21 dataset with 2D turbulence measurements obtained with Gas Puff Imaging (GPI), providing critical information on the size, velocity, and other key characteristics of turbulent filaments at the outboard midplane and in the divertor region. For the comparison, GBS simulations of TCV-X21 are analyzed using a dedicated synthetic GPI diagnostic that models the neutral helium-plasma interaction and emission processes and accounts for line-integration effects. Poloidal and radial filament velocities are found to be in good agreement between simulations and experiments, while the simulations overestimate the filament radial and poloidal sizes and underestimate the relative fluctuation levels. The simulations further indicate that filaments in the SOL are predominantly represented by density perturbations rather than temperature perturbations, consistent with previous assumptions in experimental analyses of cross-field turbulent transport from GPI data. The poloidal velocity direction of the filaments agrees with the time-averaged $\boldsymbol{E}\times\boldsymbol{B}$ direction at the outboard midplane and X-point region, but not in the divertor leg. Possible explanations are proposed and discussed, highlighting the influence of the instantaneous $\boldsymbol{E}\times\boldsymbol{B}$ velocity components in both poloidal and radial directions. This study provides new insights into turbulent filament behavior and contributes to guiding future efforts to improve first-principles simulations of the boundary plasma.

physics.plasm-ph↗
arXiv2023

Validation of SOLPS-ITER Simulations against the TCV-X21 Reference Case

This paper presents a quantitative validation of SOLPS-ITER simulations against the TCV-X21 reference case and provides insights into the neutral dynamics and ionization source distribution in this scenario. TCV-X21 is a well-diagnosed diverted L-mode sheath-limited plasma scenario in both toroidal field directions, designed specifically for the validation of turbulence codes [D.S. Oliveira, T. Body, et al 2022 Nucl. Fusion 62 096001]. Despite the optimization to reduce the impact of the neutral dynamics, the absence of neutrals in previous turbulence simulations of TCV-X21 was identified as a possible explanation for the disagreements with the experimental data in the divertor region. This motivates the present study with SOLPS-ITER that includes kinetic neutral dynamics via EIRENE. Five new observables are added to the extensive, publicly available TCV-X21 dataset. These are three deuterium Balmer lines in the divertor and neutral pressure in the common and private flux regions. The quantitative agreement metric is combined with the conjugate gradient method to approach the SOLPS-ITER input parameters that return the best overall agreement with the experiment. A proof-of-principle of this method results in a modest improvement in the level-of-agreement; shortcomings of the method and how to improve it are discussed. Alternatively, a scan of the particle and heat diffusion coefficients shows an improvement of 10.4% beyond the agreement level achieved by the gradient method. The result is found for an increased transport coefficient compared to what is usually used for TCV L-mode plasmas, suggesting the need for accurate self-consistent turbulence models for predictive boundary simulations. The simulations indicate that ~65% of the total ionization occurs in the SOL, motivating the inclusion of neutrals in future turbulence simulations towards improved agreement with the experiment.

physics.plasm-ph↗
arXiv2023

Existence and multiplicity for fractional Dirichlet problem with $γ(ξ)$-Laplacian equation and Nehari manifold

This paper is divided in two parts. In the first part, we prove coercivity results and minimization of the Euler energy functional. In the second part, we focus on the existence and multiplicity of a positive solution of fractional Dirichlet problem involving the $γ(ξ)$-Laplacian equation with non-negative weight functions in $\mathcal{H}^{α,β;χ}_{γ(ξ)}(Λ,\mathbb{R})$ using some variational techniques and Nehari manifold.

math.GM↗
arXiv2023

Self-consistent multi-component simulation of plasma turbulence and neutrals in detached conditions

Simulations of high-density deuterium plasmas in a lower single-null magnetic configuration based on a TCV discharge are presented. We evolve the dynamics of three charged species (electrons, D$^{+}$ and D$_{2}^{+}$), interacting with two neutrals species (D and D$_2$) through ionization, charge-exchange, recombination and molecular dissociation processes. The plasma is modelled by using the drift-reduced fluid Braginskii equations, while the neutral dynamics is described by a kinetic model. To control the divertor conditions, a D$_2$ puffing is used and the effect of increasing the puffing strength is investigated. The increase in fuelling leads to an increase of density in the scrape-off layer and a decrease of the plasma temperature. At the same time, the particle and heat fluxes to the divertor target decrease and the detachment of the inner target is observed. The analysis of particle and transport balance in the divertor volume shows that the decrease of the particle flux is caused by a decrease of the local neutral ionization together with a decrease of the parallel velocity, both caused by the lower plasma temperature. The relative importance of the different collision terms is assessed, showing the crucial role of molecular interactions, as they are responsible for increasing the atomic neutral density and temperature, since most of the D neutrals are produced by molecular activated recombination and D$_2$ dissociation. The presence of strong electric fields in high-density plasmas is also shown, revealing the role of the $E \times B$ drift in setting the asymmetry between the divertor targets. Simulation results are in agreement with experimental observations of increased density decay length, attributed to a decrease of parallel transport, together with an increase of plasma blob size and radial velocity.

physics.plasm-ph↗
arXiv2023

Existence, uniqueness and controllability for Hilfer differential equations on times scales

We introduce a new version of $ψ$-Hilfer fractional derivative, on an arbitrary time scale. The fundamental properties of the new operator are investigated and, in particular, we prove an integration by parts formula. Using the Laplace transform and the obtained integration by parts formula, we then propose a $ψ$-Riemann-Liouville fractional integral on times scales. The applicability of the new operators is illustrated by considering a fractional initial value problem on an arbitrary time scale, for which we prove existence, uniqueness and controllability of solutions in a suitable Banach space. The obtained results are interesting and nontrivial even for particular choices: (i) of the time scale; (ii) of the order of differentiation; and/or (iii) function $ψ$; opening new directions of investigation.

math.OC↗
arXiv2022

New insights on divertor parallel flows, ExB drifts, and fluctuations from in situ, two-dimensional probe measurement in the Tokamak à Configuration Variable

In-situ, two-dimensional (2D) Langmuir probe measurements across a large part of the TCV divertor are reported in L-mode discharges with and without divertor baffles. This provides detailed insights into time averaged profiles, particle fluxes, and fluctuations behavior in different divertor regimes. The presence of the baffles is shown to substantially increase the divertor neutral pressure for a given upstream density and to facilitate the access to detachment, an effect that increases with plasma current. The detailed, 2D probe measurements allow for a divertor particle balance, including ion flux contributions from parallel flows and ExB drifts. The poloidal flux contribution from the latter is often comparable or even larger than the former, such that the divertor parallel flow direction reverses in some conditions, pointing away from the target. In most conditions, the integrated particle flux at the outer target can be predominantly ascribed to ionization along the outer divertor leg, consistent with a closed-box approximation of the divertor. The exception is a strongly detached divertor, achieved here only with baffles, where the total poloidal ion flux even decreases towards the outer target, indicative of significant plasma recombination. The most striking observation from relative density fluctuation measurements along the outer divertor leg is the transition from poloidally uniform fluctuation levels in attached conditions to fluctuations strongly peaking near the X-point when approaching detachment.

physics.plasm-ph↗
arXiv2021

Validation of edge turbulence codes against the TCV-X21 diverted L-mode reference case

Self-consistent full-size turbulent-transport simulations of the divertor and SOL of existing tokamaks have recently become feasible. This enables the direct comparison of turbulence simulations against experimental measurements. In this work, we perform a series of diverted Ohmic L-mode discharges on the TCV tokamak, building a first-of-a-kind dataset for the validation of edge turbulence models. This dataset, referred to as TCV-X21, contains measurements from 5 diagnostic systems -- giving a total of 45 1- and 2-D comparison observables in two toroidal magnetic field directions. The dataset is used to validate three flux-driven 3D fluid-turbulence models: GBS, GRILLIX and TOKAM3X. With each model, we perform simulations of the TCV-X21 scenario, tuning the particle and power source rates to achieve a reasonable match of the upstream separatrix value of density and electron temperature. We find that the simulations match the experimental profiles for most observables at the OMP -- both in terms of profile shape and absolute magnitude -- while a poorer agreement is found towards the divertor targets. The match between simulation and experiment is seen to be sensitive to the value of the resistivity, the heat conductivities, the power injection rate and the choice of sheath boundary conditions. Additionally, despite targeting a sheath-limited regime, the discrepancy between simulations and experiment also suggests that the neutral dynamics should be included. The results of this validation show that turbulence models are able to perform simulations of existing devices and achieve reasonable agreement with experimental measurements. Where disagreement is found, the validation helps to identify how the models can be improved. By publicly releasing the experimental dataset, this work should help to guide and accelerate the development of predictive turbulence simulations of the edge and SOL.

physics.plasm-ph↗
arXiv2020

Properties of fractional integral operators involving the three-parameters Mittag-Leffler function in the kernels with respect to another function

This paper aims to investigate properties associated with fractional integral operators involving the three-parameters Mittag-Leffler function in the kernels with respect to another function. We prove that the Cauchy problem and the Volterra integral equation are equivalent. We find a closed-form to the solution of the Cauchy problem using successive approximations method and $ψ$-Caputo fractional derivative.

math.CA↗
arXiv2020

Analytical solutions for Navier-Stokes equations with $ψ$-Caputo fractional derivative

This work aims to use the homotopy analysis method to obtain analytical solutions of linear time-fractional Navier-Stokes equations with cylindrical coordinates and of a system of nonlinear time-fractional Navier-Stokes equations with Cartesian coordinates. These equations are described in the $ψ$-Caputo time-fractional derivative. The solutions obtained for time-fractional Navier-Stokes equations are graphically presented.

math.AP↗
arXiv2020

Solutions of time-fractional differential equations using homotopy analysis method

We have used the homotopy analysis method to obtain solutions of linear and nonlinear fractional partial differential differential equations with initial conditions. We replace the first order time derivative by $ψ$-Caputo fractional derivative, and also we compare the results obtained by the homotopy analysis method with the exact solutions.

math.AP↗
arXiv2019

Mild and classical solutions for fractional evolution differential equation

Investigating the existence, uniqueness, stability, continuous dependence of data among other properties of solutions of fractional differential equations, has been the object of study by an important range of researchers in the scientific community, especially in fractional calculus. And over the years, these properties have been investigated more vehemently, as they enable more general and new results. In this paper, we investigate the existence and uniqueness of a class of mild and classical solutions of the fractional evolution differential equation in the Banach space $Ω$. To obtain such results, we use fundamental tools, namely: Banach contraction theorem, Gronwall inequality and the $β$-times integrated $β$-times integrated $α$-resolvent operator function of an $(α,β)$-resolvent operator function.

math.CA↗
arXiv2017

Hilfer-Katugampola fractional derivative

We propose a new fractional derivative, the Hilfer-Katugampola fractional derivative. Motivated by the Hilfer derivative this formulation interpolates the well-known fractional derivatives of Hilfer, Hilfer-Hadamard, Riemann-Liouville, Hadamard, Caputo, Caputo-Hadamard, Liouville, Weyl, generalized and Caputo-type. As an application, we consider a nonlinear fractional differential equation with an initial condition using this new formulation. We show that this equation is equivalent to a Volterra integral equation and demonstrate the existence and uniqueness of solution to the nonlinear initial value problem.

math.CA↗
arXiv2017

Gruss-type inequality by mean of a fractional integral

In this paper, using a fractional integral as proposed by Katugampola we establish a generalization of integral inequalities of Gruss-type. We prove two theorems associated with these inequalities and then immediately we enunciate and prove others inequalities associated with these fractional operator.

math.CA↗