arXiv subjects

Gian Luca Delzanno

Publications and source records attributed to Gian Luca Delzanno.

30 records · Page 2Linked to original sources

arXiv2020

The multi-dimensional Hermite-discontinuous Galerkin method for the Vlasov-Maxwell equations

We discuss the development, analysis, implementation, and numerical assessment of a spectral method for the numerical simulation of the three-dimensional Vlasov-Maxwell equations. The method is based on a spectral expansion of the velocity space with the asymmetrically weighted Hermite functions. The resulting system of time-dependent nonlinear equations is discretized by the discontinuous Galerkin (DG) method in space and by the method of lines for the time integration using explicit Runge-Kutta integrators. The resulting code, called Spectral Plasma Solver (SPS-DG), is successfully applied to standard plasma physics benchmarks to demonstrate its accuracy, robustness, and parallel scalability.

physics.comp-ph↗

arXiv2020

Electron-only reconnection in kinetic Alfvén turbulence

We study numerically small-scale reconnection events in kinetic, low-frequency, quasi-2D turbulence (termed kinetic-Alfvén turbulence). Using 2D particle-in-cell simulations, we demonstrate that such turbulence generates reconnection structures where the electron dynamics do not couple to the ions, similarly to the electron-only reconnection events recently detected in the Earth's magnetosheath by Phan et al. (2018). Electron-only reconnection is thus an inherent property of kinetic-Alfvén turbulence, where the electron current sheets have limited anisotropy and, as a result, their sizes are smaller than the ion inertial scale. The reconnection rate of such electron-only events is found to be close to $0.1$.

physics.plasm-ph↗

arXiv2019

Decomposition of Plasma Kinetic Entropy into Position and Velocity Space and the Use of Kinetic Entropy in Particle-in-Cell Simulations

We describe a systematic development of kinetic entropy as a diagnostic in fully kinetic particle-in-cell (PIC) simulations and use it to interpret plasma physics processes in heliospheric, planetary, and astrophysical systems. First, we calculate kinetic entropy in two forms -- the ``combinatorial'' form related to the logarithm of the number of microstates per macrostate and the ``continuous'' form related to $f \ln f$, where $f$ is the particle distribution function. We discuss the advantages and disadvantages of each and discuss subtleties about implementing them in PIC codes. Using collisionless PIC simulations that are two-dimensional in position space and three-dimensional in velocity space, we verify the implementation of the kinetic entropy diagnostics and discuss how to optimize numerical parameters to ensure accurate results. We show the total kinetic entropy is conserved to three percent in an optimized simulation of anti-parallel magnetic reconnection. Kinetic entropy can be decomposed into a sum of a position space entropy and a velocity space entropy, and we use this to investigate the nature of kinetic entropy transport during collisionless reconnection. We find the velocity space entropy of both electrons and ions increases in time due to plasma heating during magnetic reconnection, while the position space entropy decreases due to plasma compression. This project uses collisionless simulations, so it cannot address physical dissipation mechanisms; nonetheless, the infrastructure developed here should be useful for studies of collisional or weakly collisional heliospheric, planetary, and astrophysical systems. Beyond reconnection, the diagnostic is expected to be applicable to plasma turbulence and collisionless shocks.

physics.plasm-ph↗

arXiv2018

Inertial Kinetic-Alfvén Turbulence

Recent observational and analytical studies suggested that a new regime of kinetic turbulence may exist in plasma environments with low electron beta (Chen and Boldyrev, 2017). Such a regime, termed inertial kinetic-Alfvén turbulence, is relevant for the solar corona, Earth's magnetosheath, and other astrophysical systems where the electron and ion plasma beta parameters satisfy the condition $β_e\ll β_i\lesssim 1$. In this paper we present kinetic numerical simulations that confirm existence of the iKAW regime. Specifically, the simulations demonstrate a transition at scales below electron inertial length $d_e$ when $β_e\ll β_i\lesssim 1$. Spectral slopes and other statistical properties of turbulence at sub-$d_e$ scales are consistent with the phenomenological theory of inertial kinetic-Alfvén turbulence proposed by Chen and Boldyrev (2017) and with the recent observations in the Earth's magnetosheath.

physics.plasm-ph↗

arXiv2017

Convergence of spectral discretizations of the Vlasov-Poisson system

We prove the convergence of a spectral discretization of the Vlasov-Poisson system. The velocity term of the Vlasov equation is discretized using either Hermite functions on the infinite domain or Legendre polynomials on a bounded domain. The spatial term of the Vlasov and Poisson equations is discretized using periodic Fourier expansions. Boundary conditions are treated in weak form through a penalty type term, that can be applied also in the Hermite case. As a matter of fact, stability properties of the approximated scheme descend from this added term. The convergence analysis is carried out in details for the 1D-1V case, but results can be generalized to multidimensional domains, obtained as Cartesian product, in both space and velocity. The error estimates show the spectral convergence, under suitable regularity assumptions on the exact solution.

math.NA↗

arXiv2016

Comparison of dust charging between Orbital-Motion-Limited theory and Particle-In-Cell simulations

The Orbital-Motion-Limited (OML) theory has been modified to predict the dust charge and the results were contrasted with the Whipple approximation [Tang and Delzanno, Phys. Plasmas 21, 123708 (2014)]. To further establish its regime of applicability, in this paper the OML predictions (for a non-electron-emitting, spherical dust grain at rest in a collisionless, unmagnetized plasma) are compared with Particle-In-Cell simulations that retain the absorption radius effect. It is found that for large dust grain radius $r_d$ relative to the plasma Debye length $λ_D$, the revised OML theory remains a very good approximation as, for the parameters considered ($r_d/λ_D\le10$, equal electron and ion temperatures), it yields the dust charge to within $20\%$ accuracy. This is a substantial improvement over the Whipple approximation. The dust collected currents and energy fluxes, which remain the same in the revised and standard OML theories, are accurate to within $15-30\%$.

physics.plasm-ph↗

arXiv2015

Orbital-motion-limited theory of dust charging and plasma response

The foundational theory for dusty plasmas is the dust charging theory that provides the dust potential and charge arising from the dust interaction with a plasma. The most widely used dust charging theory for negatively charged dust particles is the so-called orbital motion limited (OML) theory, which predicts the dust potential and heat collection accurately for a variety of applications, but was previously found to be incapable of evaluating the dust charge and plasma response in any situation. Here we report a revised OML formulation that is able to predict the plasma response and hence the dust charge. Numerical solutions of the new OML model show that the widely-used Whipple approximation of dust charge-potential relationship agrees with OML theory in the limit of small dust radius compared with plasma Debye length, but incurs large (order-unity) deviation from the OML prediction when the dust size becomes comparable with or larger than plasma Debye length. This latter case is expected for the important application of dust particles in a tokamak plasma.

physics.plasm-ph↗

arXiv2014

Charging and heat collection by a positively charged dust grain in a plasma

Dust particulates immersed in a quasineutral plasma can emit electrons in several important applications. Once electron emission becomes strong enough, the dust enters the positively charged regime where the conventional Orbital-Motion-Limited (OML) theory can break down due to potential well effects on trapped electrons. A minimal modification of the trapped-passing boundary approximation in the so-called OML$^+$ approach is shown to accurately predict the dust charge and heat collection flux for a wide range of dust size and temperature.

physics.plasm-ph↗

arXiv2014

Survivability of dust in tokamaks: dust transport in the divertor sheath

The survivability of dust being transported in the magnetized sheath near the divertor plate of a tokamak and its impact on the desired balance of erosion and redeposition for a steady-state reactor are investigated. Two different divertor scenarios are considered. The first is characterized by an energy flux perpendicular to the plate $q_0\simeq 1$ MW/m$^2$ typical of current short-pulse tokamaks. The second has $q_0\simeq 10$ MW/m$^2$ and is relevant to long-pulse machines like ITER or DEMO. It is shown that micrometer dust particles can survive rather easily near the plates of a divertor plasma with $q_0\simeq 1$ MW/m$^2$ because thermal radiation provides adequate cooling for the dust particle. On the other hand, the survivability of micrometer dust particles near the divertor plates is drastically reduced when $q_0\simeq 10$ MW/m$^2$. Micrometer dust particles redeposit their material non-locally, leading to a net poloidal mass migration across the divertor. Smaller particles (with radius $\sim 0.1$ $μ$m) cannot survive near the divertor and redeposit their material locally. Bigger particle (with radius $\sim 10$ $μ$m) can instead survive partially and move outside the divertor strike points, thus causing a net loss of divertor material to dust accumulation inside the chamber and some non-local redeposition. The implications of these results for ITER are discussed.

physics.plasm-ph↗

arXiv2013

On the velocity space discretization for the Vlasov-Poisson system: comparison between Hermite spectral and Particle-in-Cell methods. Part 1: semi-implicit scheme

We discuss a spectral method for the numerical solution of the Vlasov-Poisson system where the velocity space is decomposed by means of an Hermite basis. We describe a semi-implicit time discretization that extends the range of numerical stability relative to an explicit scheme. We also introduce and discuss the effects of an artificial collisional operator, which is necessary to take care of the velocity space filamentation problem, unavoidable in collisionless plasmas. The computational efficiency and the cost-effectiveness of this method are compared to a Particle-in-Cell (PIC) method in the case of a two-dimensional phase space. The following examples are discussed: Langmuir wave, Landau damping, ion-acoustic wave, two-stream instability, and plasma echo. The Hermite spectral method can achieve solutions that are several orders of magnitude more accurate (at a fraction of the cost) with respect to the PIC method.

physics.plasm-ph↗

arXiv2013

CPIC: a Curvilinear Particle-In-Cell code for plasma-material interaction studies

We describe a new electrostatic Particle-In-Cell (PIC) code in curvilinear geometry called Curvilinear PIC (CPIC). The code models the microscopic (kinetic) evolution of a plasma with the PIC method, coupled with an adaptive computational grid that can conform to arbitrarily shaped domains. CPIC is particularly suited for multiscale problems associated with the interaction of complex objects with plasmas. A map is introduced between the physical space and the logical space, where the grid is uniform and Cartesian. In CPIC, most operations are performed in logical space. CPIC was designed following criteria of versatility, robustness and performance. Its main features are the use of structured meshes, a scalable field solver based on the black box multigrid algorithm and a hybrid mover, where particles' position is in logical space while the velocity is in physical space. Test examples involving the interaction of a plasma with material boundaries are presented.

physics.plasm-ph↗

arXiv2013

Lower hybrid to whistler mode conversion on a density striation

When a wave packet composed of short wavelength lower hybrid modes traveling in an homogeneous plasma region encounters an inhomogeneity, it can resonantly excite long wavelength whistler waves via a linear mechanism known as mode conversion. An enhancement of lower hybrid/whistler activity has been often observed by sounding rockets and satellites in the presence of density depletions (striations) in the upper ionosphere. We address here the process of linear mode conversion of lower hybrid to whistler waves, mediated by a density striation, using a scalar-field formalism (in the limit of cold plasma linear theory) which we solve numerically. We show that the mode conversion can effectively transfer a large amount of energy from the short to the long wavelength modes. We also study how the efficiency scales by changing the properties (width and amplitude) of the density striation. We present a general criterion for the width of the striation that, if fulfilled, maximizes the conversion efficiency. Such a criterion could provide an interpretation of recent laboratory experiments carried out on the Large Plasma Device at UCLA.

physics.space-ph↗