arXiv subjects

Fulvio Militello

Publications and source records attributed to Fulvio Militello.

13 recordsLinked to original sources

arXiv2024

The impact of non-local parallel electron transport on plasma-impurity reaction rates in tokamak scrape-off layer plasmas

Plasma-impurity reaction rates are a crucial part of modelling tokamak scrape-off layer (SOL) plasmas. To avoid calculating the full set of rates for the large number of important processes involved, a set of effective rates are typically derived which assume Maxwellian electrons. However, non-local parallel electron transport may result in non-Maxwellian electrons, particularly close to divertor targets. Here, the validity of using Maxwellian-averaged rates in this context is investigated by computing the full set of rate equations for a fixed plasma background from kinetic and fluid SOL simulations. We consider the effect of the electron distribution as well as the impact of the electron transport model on plasma profiles. Results are presented for lithium, beryllium, carbon, nitrogen, neon and argon. It is found that electron distributions with enhanced high-energy tails can result in significant modifications to the ionisation balance and radiative power loss rates from excitation, on the order of 50-75% for the latter. Fluid electron models with Spitzer-H\"arm or flux-limited Spitzer-H\"arm thermal conductivity, combined with Maxwellian electrons for rate calculations, can increase or decrease this error, depending on the impurity species and plasma conditions. Based on these results, we also discuss some approaches to experimentally observing non-local electron transport in SOL plasmas.

physics.plasm-ph↗

arXiv2024

ReMKiT1D -- A framework for building reactive multi-fluid models of the tokamak Scrape-Off Layer with coupled electron kinetics in 1D

In this manuscript we present the recently developed flexible framework for building both fluid and electron kinetic models of the tokamak Scrape-Off Layer in 1D - ReMKiT1D (Reactive Multi-fluid and Kinetic Transport in 1D). The framework can handle systems of non-linear ODEs, various 1D PDEs arising in fluid modelling, as well as PDEs arising from the treatment of the electron kinetic equation. As such, the framework allows for flexibility in fluid models of the Scrape-Off Layer while allowing the easy addition of kinetic electron effects. We focus on presenting both the high-level design decisions that allow for model flexibility, as well as the most important implementation aspects. A significant number of verification and performance tests are presented, as well as a step-by-step walkthrough of a simple example for setting up models using the Python interface.

physics.plasm-ph↗

arXiv2023

Scaling laws for electron kinetic effects in tokamak scrape-off layer plasmas

Tokamak edge (scrape-off layer) plasmas can exhibit non-local transport in the direction parallel to the magnetic field due to steep temperature gradients. This effect along with its consequences has been explored at equilibrium for a range of conditions, from sheath-limited to detached, using the 1D kinetic electron code SOL-KiT, where the electrons are treated kinetically and compared to a self-consistent fluid model. Line-averaged suppression of the kinetic heat flux (compared to Spitzer-Harm) of up to 50% is observed, contrasting with up to 98% enhancement of the sheath heat transmission coefficient, $γ_e$. Simple scaling laws in terms of basic SOL parameters for both effects are presented. By implementing these scalings as corrections to the fluid model, we find good agreement with the kinetic model for target electron temperatures. It is found that the strongest kinetic effects in $γ_e$ are observed at low-intermediate collisionalities, and tend to increase at increasing upstream densities and temperatures. On the other hand, the heat flux suppression is found to increase monotonically as upstream collisionality decreases. The conditions simulated encompass collisionalities relevant to current and future tokamaks.

physics.plasm-ph↗

arXiv2020

Blob interaction in 2D scrape off layer simulations

Interaction of coherent structures known as blobs in the scrape-off layer of magnetic confinement fusion devices is investigated. Isolated and interacting seeded blobs as well as full plasma turbulence are studied with a two dimensional fluid code. The features of the blobs (size, amplitude, position) are determined with a blob tracking algorithm, which identifies them as coherent structures above a chosen density threshold and compared to a conventional center of mass approach. The agreement of these two methods is shown to be affected by the parameters of the blob tracking algorithm. The benchmarked approach is then extended to a population of interacting plasma blobs with statistically distributed amplitudes, sizes and initial positions for different levels of intermittency. As expected, for decreasing intermittency, we observe an increasing number of blobs deviating from size-velocity scaling laws of perfectly isolated blobs. This is found to be caused by the interaction of blobs with the electrostatic potential of one another, leading to higher average blob velocities. The degree of variation from the picture of perfectly isolated blobs is quantified as a function of the average waiting time of the seeded blobs.

physics.plasm-ph↗

arXiv2020

Dynamics of scrape-off layer filaments in detached conditions

The here presented work studies the dynamics of filaments using 3D fluid simulations in the presence of detached background profiles. It was found that evolving the neutrals on the time-scale of the filament did not have a significant impact on the dynamics of the filament. In general a decreasing filament velocity with increasing plasma background density has been observed, with the exception of detachment onset, where a temporarily increase in radial velocity occurs. The decreasing trend with temporary increase was found for filaments around the critical size and larger, while smaller filaments where less affected by detachment. With detachment the critical filament size increased, as larger filaments were faster in detached conditions. This breaks the trend of attached conditions, where the critical size decreases with increasing density.

physics.plasm-ph↗

arXiv2020

SOL-KiT -- fully implicit code for kinetic simulation of parallel electron transport in the tokamak Scrape-Off Layer

Here we present a new code for modelling electron kinetics in the tokamak Scrape-Off Layer (SOL). SOL-KiT (Scrape-Off Layer Kinetic Transport) is a fully implicit 1D code with kinetic (or fluid) electrons, fluid (or stationary) ions, and diffusive neutrals. The code is designed for fundamental exploration of non-local physics in the SOL and utilizes an arbitrary degree Legendre polynomial decomposition of the electron distribution function, treating both electron-ion and electron-atom collisions. We present a novel method for ensuring particle and energy conservation in inelastic and superelastic collisions, as well as the first full treatment of the logical boundary condition in the Legendre polynomial formalism. To our knowledge, SOL-KiT is the first fully implicit arbitrary degree harmonic kinetic code, offering a conservative and self-consistent approach to fluid-kinetic comparison with its integrated fluid electron mode. In this paper we give the model equations and their discretizations, as well as showing the results of a number of verification/benchmarking simulations.

physics.comp-ph↗

arXiv2019

Dependence on ion temperature of shallow-angle magnetic presheaths with adiabatic electrons

The magnetic presheath is a boundary layer occurring when magnetized plasma is in contact with a wall and the angle $α$ between the wall and the magnetic field $\vec{B}$ is oblique. Here, we consider the fusion-relevant case of a shallow-angle, $α\ll 1$, electron-repelling sheath, with the electron density given by a Boltzmann distribution, valid for $α/ \sqrt{τ+1} \gg \sqrt{m_{\text{e}}/m_{\text{i}}}$, where $m_{\text{e}}$ is the electron mass, $m_{\text{i}}$ is the ion mass, $τ= T_{\text{i}}/ZT_{\text{e}}$, $T_{\text{e}}$ is the electron temperature, $T_{\text{i}}$ is the ion temperature, and $Z$ is the ionic charge state. The thickness of the magnetic presheath is of the order of a few ion sound Larmor radii $ρ_{\text{s}} = \sqrt{m_{\text{i}} \left(ZT_{\text{e}} + T_{\text{i}} \right) } / ZeB$, where $e$ is the proton charge and $B = |\vec{B}|$ is the magnitude of the magnetic field. We study the dependence on $τ$ of the electrostatic potential and ion distribution function in the magnetic presheath by using a set of prescribed ion distribution functions at the magnetic presheath entrance, parameterized by $τ$. The kinetic model is shown to be asymptotically equivalent to Chodura's fluid model at small ion temperature, $τ\ll 1$, for $|\ln α| > 3|\ln τ| \gg 1$. In this limit, despite the fact that fluid equations give a reasonable approximation to the potential, ion gyro-orbits acquire a spatial extent that occupies a large portion of the magnetic presheath. At large ion temperature, $τ\gg 1$, relevant because $T_{\text{i}}$ is measured to be a few times larger than $T_{\text{e}}$ near divertor targets of fusion devices, ions reach the Debye sheath entrance (and subsequently the wall) at a shallow angle whose size is given by $\sqrtα$ or $1/\sqrtτ$, depending on which is largest.

physics.plasm-ph↗

arXiv2018

Solution to a collisionless shallow-angle magnetic presheath with kinetic ions

Using a kinetic model for the ions and adiabatic electrons, we solve a steady state, electron-repelling magnetic presheath in which a uniform magnetic field makes a small angle $α\ll 1$ (in radians) with the wall. The presheath characteristic thickness is the typical ion gyroradius $ρ_{\text{i}}$. The Debye length $λ_{\text{D}}$ and the collisional mean free path of an ion $λ_{\text{mfp}}$ satisfy the ordering $λ_{\text{D}} \ll ρ_{\text{i}} \ll αλ_{\text{mfp}}$, so a quasineutral and collisionless model is used. We assume that the electrostatic potential is a function only of distance from the wall, and it varies over the scale $ρ_{\text{i}}$. Using the expansion in $α\ll 1$, we derive an analytical expression for the ion density that only depends on the ion distribution function at the entrance of the magnetic presheath and the electrostatic potential profile. Importantly, we have added the crucial contribution of the orbits in the region near the wall. By imposing the quasineutrality equation, we derive a condition that the ion distribution function must satisfy at the magnetic presheath entrance --- the kinetic equivalent of the Chodura condition. Using an ion distribution function at the entrance of the magnetic presheath that satisfies the kinetic Chodura condition, we find numerical solutions for the self-consistent electrostatic potential, ion density and flow across the magnetic presheath for several values of $α$. Our numerical results also include the distribution of ion velocities at the Debye sheath entrance. We find that at small values of $α$ there are substantially fewer ions travelling with a large normal component of the velocity into the wall.

physics.plasm-ph↗

arXiv2018

Stability of scrape-off layer plasma: a modified Rayleigh-Benard problem

We present a linear stability analysis of a two-dimensional fluid model used to study the plasma dynamics in the scrape-off layer of tokamaks. The model equations are based on the Braginskii fluid equations under the assumptions of drift ordering and an electrostatic plasma. The model also employs the common slab geometry approximation, whereby the magnetic field is assumed constant and straight, with the effects of curvature reintroduced as effective gravitational terms. We demonstrate that the governing plasma equations for the scrape-off layer can be viewed as describing a thermal convection problem with additional effects. The new features include a non-uniform basic state gradient, linear damping terms, and additional advective terms. We characterise the conditions at the onset of instability, and perform an extensive parameter scan to describe how the stability threshold varies as a function of plasma parameters.

physics.plasm-ph↗

arXiv2018

Influence of plasma background on 3D scrape-off layer filaments

This paper presents the effect of self-consistent plasma backgrounds including plasma-neutral interactions, on the dynamics of filament propagation. The principle focus is on the influence of the neutrals on the filament through both direct interactions and through their influence on the plasma background. Both direct and indirect interactions influence the motion of filaments. A monotonic increase of filament peak velocity with upstream electron temperature is observed, while a decrease with increasing electron density is observed. If ordered by the target temperature, the density dependence disappears and the filament velocity is only a function of the target temperature. Smaller filaments keep a density dependence, as a result of the density dependence of the plasma viscosity. The critical size $δ^*$, where filaments are fastest, is shifted to larger sizes for higher densities, due to the plasma viscosity. If the density dependence of the plasma viscosity is removed, $δ^*$ has no temperature dependence, but rather a density dependence.

physics.plasm-ph↗

arXiv2017

Gyrokinetic treatment of a grazing angle magnetic field

We develop a gyrokinetic treatment for ions in the magnetic presheath, close to the plasma-wall boundary. We focus on magnetic presheaths with a small magnetic field to wall angle, $α\ll 1$ (in radians). Characteristic lengths perpendicular to the wall in such a magnetic presheath scale with the typical ion Larmor orbit size, $ρ_{\text{i}}$. The smallest scale length associated with variations parallel to the wall is taken to be across the magnetic field, and ordered $l = ρ_{\text{i}} / δ$, where $ δ\ll 1$ is assumed. The scale lengths along the magnetic field line are assumed so long that variations associated with this direction are neglected. These orderings are consistent with what we expect close to the divertor target of a tokamak. We allow for a strong component of the electric field $\vec{E}$ in the direction normal to the electron repelling wall, with strong variation in the same direction. The large change of the electric field over an ion Larmor radius distorts the orbit so that it is not circular. We solve for the lowest order orbits by identifying coordinates, which consist of constants of integration, an adiabatic invariant and a gyrophase, associated with periodic ion motion in the system with $α= δ= 0$. By using these new coordinates as variables in the limit $α\sim δ\ll 1$, we obtain a generalized ion gyrokinetic equation. We find another quantity that is conserved to first order and use this to simplify the gyrokinetic equation, solving it in the case of a collisionless magnetic presheath. Assuming a Boltzmann response for the electrons, a form of the quasineutrality equation that exploits the change of variables is derived. The gyrokinetic and quasineutrality equations give the ion distribution function and electrostatic potential in the magnetic presheath if the entrance boundary condition is specified.

physics.plasm-ph↗

arXiv2015

Investigation of the Effect of Resistivity on Scrape Off Layer Filaments using Three Dimensional Simulations

The propagation of filaments in the Scrape Off Layer (SOL) of tokamaks largely determine the plasma profiles in the region. In a conduction limited SOL, parallel temperature gradients are expected, such that the resistance to parallel currents is greater at the target than further upstream. Since the perpendicular motion of an isolated filament is largely determined by balance of currents that flow through it, this may be expected to affect filament transport. 3D simulations have thus been used to study the influence of enhanced parallel resistivity on the dynamics of filaments. Filaments with the smallest perpendicular length scales, which were inertially limited at low resistivity (meaning that polarization rather than parallel currents determine their radial velocities), were unaffected by resistivity. For larger filaments, faster velocities were produced at higher resistivities, due to two mechanisms. Firstly parallel currents were reduced and polarization currents were enhanced, meaning that the inertial regime extended to larger filaments, and secondly a potential difference formed along the parallel direction so that higher potentials were produced in the region of the filament for the same amount of current to flow into the sheath. These results indicate that broader SOL profiles could be produced at higher resistivities.

physics.plasm-ph↗

arXiv2014

3D Simulations of Plasma Filaments in the Scrape Off Layer: A Comparison with Models of Reduced Dimensionality

This paper presents simulations of isolated 3D filaments in a slab geometry obtained using a 3D reduced fluid code. First, systematic scans were performed to investigate how the dynamics of a filament are affected by its amplitude, perpendicular size and parallel extent. The perpendicular size of the filament was found to have a strong influence on its motions, as it determined the relative importance of parallel currents to polarisation and viscous currents, whilst drift-wave instabilities were observed if the initial amplitude of the blob was increased sufficiently. Next, the 3D simulations were compared to 2D simulations using different parallel closures; namely, the sheath dissipation closure, which neglects parallel gradients, and the vorticity advection closure, which neglects the influence of parallel currents. The vorticity advection closure was found to not replicate the 3D perpendicular dynamics and overestimated the initial radial acceleration of all the filaments studied. In contrast, a more satisfactory comparison with the sheath dissipation closure was obtained, even in the presence of significant parallel gradients, where the closure is no longer valid. Specifically it captured the contrasting dynamics of filaments with different perpen- dicular sizes that were observed in the 3D simulations which the vorticity advection closure failed to replicate. However, neither closure successfully replicated the Boltzmann spinning effects and associated poloidal drift of the blob that was observed in the 3D simulations. Although the sheath dissipation closure was concluded to be more successful in replicating the 3D dynamics, it is emphasised that the vorticity closure may still be relevant for situations where the parallel current is inhibited from closing through the sheath due to effects such as increased resistivity near the targets.

physics.plasm-ph↗