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G. Alberti

Publications and source records attributed to G. Alberti.

6 recordsLinked to original sources
arXiv2026

Stability of the ball in isoperimetric inequalities between two fractional perimeters

We consider the isoperimetric inequality involving the $s$-perimeter and the $t$-perimeter with $0<s<t<1$, and show that the ball is a local minimizer of the (scale-invariant) isoperimetric ratio $\mathcal{F}(E):=P_t(E)^{\frac{1}{n-t}}/ P_s(E)^{\frac{1}{n-s}}$ among sets $E$ that are nearly spherical. To this end, we rewrite $\mathcal{F}$ as a functional of $u$, where $u$ is a scalar function on the unit sphere in $\mathbb{R}^n$ that parametrizes the boundary of $E$, and prove a quantitative stability result for $\mathcal{F}$ around $u=0$ with respect to a suitable Sobolev norm. This parallels known results where the $s$-perimeter is replaced by the volume.

math.AP↗
arXiv2025

Tungsten erosion and scrape-off layer transport modelling in L-mode helium plasma discharges in ASDEX Upgrade

Due to its unavoidable presence in thermonuclear DT plasmas and to its peculiar effects on materials, investigating the role of helium (He) in plasma-wall interaction (PWI) in current tokamaks is fundamental. In this work, PWI in L-mode He plasma discharges in ASDEX Upgrade (AUG) is modelled by exploiting simplified analytical approaches and two state-of-the-art codes. SOLPS-ITER is employed both to provide a suitable background plasma for erosion simulations and to interpret diagnostics measurements in terms of He+/2+ fraction. In particular, a 50-50% concentration of the two He ions is found in the proximity of the strike-points, while He2+ represents the dominant population farther in the scrape-off layer (SOL). The role of He ion fraction on AUG tungsten divertor erosion is first estimated by means of a simple analytical model and, afterwards, by exploiting ERO2.0, showing the major impact of He2+ in common AUG plasma temperatures. ERO2.0 findings are also compared with experimental erosion data in the strike-point region, showing the possible impact of extrinsic impurities on divertor erosion. Finally, the multi-fluid and kinetic approaches employed in this work to simulate W erosion and migration are compared, including W also in SOLPS-ITER modelling. The impact of target boundary conditions on the W source in SOLPS-ITER is investigated, in order to find a good agreement with ERO2.0 estimation. Then, W migration in the two codes is compared, showing a stronger W transport towards the X-point in ERO2.0 compared to present SOLPS-ITER simulations with no drifts. Similar W influx in core could be achieved by reducing anomalous diffusivity in ERO2.0.

physics.plasm-ph↗
arXiv2024

Numerical simulation of a helium Plasma-Material Interaction experiment in GyM linear device through SOLPS-ITER and ERO2.0 codes

Learning how to safely handle Plasma-Material Interaction (PMI) is a key challenge towards the commercialisation of energy from nuclear fusion. In this respect, linear plasma devices are ideal experimental testbeds, and numerical codes play a crucial complementary role. In this paper, a numerical investigation of PMI-relevant helium plasma experimental discharges in GyM linear device is presented, in which SOLPS-ITER and ERO2.0 codes are coupled for plasma background generation and material erosion investigation respectively, with the aim to support the interpretation and complement the available experimental dataset. On the plasma side, simulated profiles are validated against experimental data to provide a realistic plasma background, and the role of He metastable states is assessed for the first time in SOLPS simulations. On the material side, the erosion and deposition effects due to the introduction of the sample-holder in the simulation volume are investigated, now considering also the real stainless steel composition as wall material.

physics.plasm-ph↗
arXiv2024

Modelling of power exhaust in TCV positive and negative triangularity L-mode plasmas

L-mode negative triangularity (NT) operation is a promising alternative to the positive triangularity (PT) H-mode as a high-confinement ELM-free operational regime. In this work, two TCV L-mode lower single null Ohmic discharges with opposite triangularity $\delta \simeq \pm 0.3$ are investigated using SOLPS-ITER modelling. The main focus is the exploration of the reasons behind the experimentally observed feature of NT plasmas being more difficult to detach than similar PT experiments. SOLPS-ITER simulations are performed assuming the same anomalous diffusivity for particles $D_n^{AN}$ and energy $\kappa_{e/i}^{AN}$ in PT and NT. Nonetheless, the results clearly show dissimilar transport and accumulation of neutral particles in the scrape-off layer (SOL) of the two configurations, which consequently gives rise to different ionization sources for the plasma and produces different poloidal and cross-field fluxes. Simulations also recover the experimental feature of the outer target being hotter in the NT scenario (with $T_{e, NT} \gtrsim 5 \, \mathrm{eV}$) than in the PT counterpart.

physics.plasm-ph↗
arXiv2016

Eulerian, Lagrangian and Broad continuous solutions to a balance law with non convex flux I

We discuss different notions of continuous solutions to the balance law \[u_t + (f(u ))_x =g \] with $g$ bounded, $f\in C^{2}$, extending previous works relative to the flux $f(u)=u^{2}$. We establish the equivalence among distributional solutions and a suitable notion of Lagrangian solutions for general smooth fluxes. We eventually find that continuous solutions are Kruzkov iso-entropy solutions, which yields uniqueness for the Cauchy problem. We also establish the ODE reduction on any characteristics under the sharp assumption that the set of inflection points of the flux $f$ is negligible. The correspondence of the source terms in the two settings is matter of a companion work, where we also provide counterexamples when the negligibility on inflection points fails.

math.AP↗