Spectral analysis of forced turbulence in a non-neutral plasma

2017 ◽  
Vol 83 (3) ◽  
Author(s):  
S. Chen ◽  
G. Maero ◽  
M. Romé
Keyword(s):  
Initial Conditions ◽  
Initial Density ◽  
Final States ◽  
Self Similarity ◽  
Subsequent Formation ◽  
Electron Plasmas ◽  
Particle In Cell ◽  
Fluid Turbulence ◽  
Inviscid Incompressible Fluid ◽  
Forced Turbulence

The paper investigates the dynamics of magnetized non-neutral (electron) plasmas subjected to external electric field perturbations. A two-dimensional (2-D) particle-in-cell code is effectively exploited to model this system with a special attention to the role that non-axisymmetric, multipolar radio frequency (RF) drives applied to the cylindrical (circular) boundary play on the insurgence of azimuthal instabilities and the subsequent formation of coherent structures preventing the relaxation to a fully developed turbulent state, when the RF fields are chosen in the frequency range of the low-order fluid modes themselves. The isomorphism of such system with a 2-D inviscid incompressible fluid offers an insight into the details of forced 2-D fluid turbulence. The choice of different initial density (i.e. fluid vorticity) distributions allows for a selection of conditions where different levels of turbulence and intermittency are expected and a range of final states is achieved. Integral and spectral quantities of interest are computed along the flow using a multiresolution analysis based on a wavelet decomposition of both enstrophy and energy 2-D maps. The analysis of a variety of cases shows that the qualitative features of turbulent relaxation are similar in conditions of both free and forced evolution; at the same time, fine details of the flow beyond the self-similarity turbulence properties are highlighted in particular in the formation of structures and their timing, where the influence of the initial conditions and the effect of the external forcing can be distinguished.

Effect of initial conditions on electron–plasma turbulence: a multiresolution analysis

2015 ◽  
Vol 81 (5) ◽  
Author(s):  
S. Chen ◽  
G. Maero ◽  
M. Romé
Keyword(s):  
Multiresolution Analysis ◽  
Initial Conditions ◽  
Initial Density ◽  
Electron Plasma ◽  
Plasma Turbulence ◽  
Considerable Effect ◽  
Density Fluctuations ◽  
Final States ◽  
Particle In Cell ◽  
Similar Growth

The transverse dynamics of a pure electron plasma confined in a Penning–Malmberg trap is investigated, taking advantage of two-dimensional particle-in-cell numerical simulations. The evolution of the electron plasma turbulence is studied by means of a wavelet-based multiresolution analysis. In particular, a modified recursive denoising algorithm is developed to separate coherent and incoherent (not necessarily homogeneous) components of the flow. A set of simulations have been carried out changing systematically the radii of an initial annular density distribution of the electrons. The results of the multiresolution analysis indicate that the initial density configuration may have a considerable effect on the evolution of turbulence. Even very small initial density fluctuations can lead to quite different final states, especially in the presence of multiple active diocotron modes characterized by similar growth rates.

scholarly journals The Influence of Particle Concentration on the Formation of Settling-Driven Gravitational Instabilities at the Base of Volcanic Clouds

2021 ◽  
Vol 9 ◽  
Author(s):  
Allan Fries ◽  
Jonathan Lemus ◽  
Paul A. Jarvis ◽  
Amanda B. Clarke ◽  
Jeremy C. Phillips ◽  
...  
Keyword(s):  
Volcanic Ash ◽  
Particle Concentration ◽  
Initial Conditions ◽  
Initial Density ◽  
Fluid Phase ◽  
Dimensionless Number ◽  
Narrow Region ◽  
Gravitational Instabilities ◽  
Volcanic Clouds ◽  
Particle Imaging

Settling-driven gravitational instabilities observed at the base of volcanic ash clouds have the potential to play a substantial role in volcanic ash sedimentation. They originate from a narrow, gravitationally unstable region called a Particle Boundary Layer (PBL) that forms at the lower cloud-atmosphere interface and generates downward-moving ash fingers that enhance the ash sedimentation rate. We use scaled laboratory experiments in combination with particle imaging and Planar Laser Induced Fluorescence (PLIF) techniques to investigate the effect of particle concentration on PBL and finger formation. Results show that, as particles settle across an initial density interface and are incorporated within the dense underlying fluid, the PBL grows below the interface as a narrow region of small excess density. This detaches upon reaching a critical thickness, that scales with (ν2/g′)1/3, where ν is the kinematic viscosity and g′ is the reduced gravity of the PBL, leading to the formation of fingers. During this process, the fluid above and below the interface remains poorly mixed, with only small quantities of the upper fluid phase being injected through fingers. In addition, our measurements confirm previous findings over a wider set of initial conditions that show that both the number of fingers and their velocity increase with particle concentration. We also quantify how the vertical particle mass flux below the particle suspension evolves with time and with the particle concentration. Finally, we identify a dimensionless number that depends on the measurable cloud mass-loading and thickness, which can be used to assess the potential for settling-driven gravitational instabilities to form. Our results suggest that fingers from volcanic clouds characterised by high ash concentrations not only are more likely to develop, but they are also expected to form more quickly and propagate at higher velocities than fingers associated with ash-poor clouds.

Statistical Theory of the SASE Fel Based on the Two-Particle Correlation Function Equation

2013 ◽  
Vol 8 (4) ◽  
pp. 25-34
Author(s):  
Oleg Shevchenko ◽  
Nikolay Vinokurov
Keyword(s):  
Correlation Function ◽  
Initial Conditions ◽  
Initial Density ◽  
Bbgky Hierarchy ◽  
Density Fluctuations ◽  
Distribution Functions ◽  
Time Coordinate ◽  
Particle Correlation ◽  
Sase Fel ◽  
Special Time

The startup from noise problem in SASE FELs is usually treated in linear approximation. In this case amplification of initial density fluctuations may be calculated, and averaging over initial conditions may be fulfilled explicitly. In general nonlinear case the direct averaging is not applicable. During last years we developed the approach based on the BBGKY hierarchy for the n-particle distribution functions. The interaction of particles in FEL is retarded. Nevertheless, using special time-coordinate transformation, it is possible to eliminate the interaction lag and then to write down the BBGKY equations. Similar to plasma physics, the equations may be truncated after the second one (for the two-particle correlation function). Using this approach we consider several particular cases which illustrate some peculiar features of the SASE FEL operation

scholarly journals The Kelvin–Helmholtz instability and smoothed particle hydrodynamics

2019 ◽  
Vol 488 (4) ◽  
pp. 5210-5224 ◽  
Author(s):  
Terrence S Tricco
Keyword(s):  
Smoothed Particle Hydrodynamics ◽  
Initial Conditions ◽  
Initial Density ◽  
Artificial Viscosity ◽  
Numerical Dissipation ◽  
Reference Solution ◽  
Helmholtz Instability ◽  
Non Linear ◽  
Particle Hydrodynamics ◽  
Smoothed Particle

ABSTRACT We perform simulations of the Kelvin–Helmholtz instability using smoothed particle hydrodynamics (SPH). The instability is studied both in the linear and strongly non-linear regimes. The smooth, well-posed initial conditions of Lecoanet et al. (2016) are used, along with an explicit Navier–Stokes viscosity and thermal conductivity to enforce the evolution in the non-linear regime. We demonstrate convergence to the reference solution using SPH. The evolution of the vortex structures and the degree of mixing, as measured by a passive scalar ‘colour’ field, match the reference solution. Tests with an initial density contrast produce the correct qualitative behaviour. The $\mathcal {L}_2$ error of the SPH calculations decreases as the resolution is increased. The primary source of error is numerical dissipation arising from artificial viscosity, and tests with reduced artificial viscosity have reduced $\mathcal {L}_2$ error. A high-order smoothing kernel is needed in order to resolve the initial velocity amplitude of the seeded mode and inhibit excitation of spurious modes. We find that standard SPH with an artificial viscosity has no difficulty in correctly modelling the Kelvin–Helmholtz instability and yields convergent solutions.

scholarly journals A medieval multiverse?: Mathematical modelling of the thirteenth century universe of Robert Grosseteste

2014 ◽  
Vol 470 (2167) ◽  
pp. 20140025 ◽  
Author(s):  
Richard G. Bower ◽  
Tom C. B. McLeish ◽  
Brian K. Tanner ◽  
Hannah E. Smithson ◽  
Cecilia Panti ◽  
...  
Keyword(s):  
Initial Conditions ◽  
Initial Density ◽  
Outer Region ◽  
Big Bang ◽  
Small Range ◽  
Density Profiles ◽  
Material Body ◽  
Fundamental Parameters ◽  
Entire Cosmos ◽  
Text Formation

In his treatise on light, written about 1225, Robert Grosseteste describes a cosmological model in which the universe is created in a big-bang-like explosion and subsequent condensation. He postulates that the fundamental coupling of light and matter gives rises to the material body of the entire cosmos. Expansion is arrested when matter reaches a minimum density and subsequent emission of light from the outer region leads to compression and rarefaction of the inner bodily mass so as to create nine celestial spheres, with an imperfect residual core. In this paper, we reformulate the Latin description in terms of a modern mathematical model, teasing out consequences implicit in the text, but which the author would not have had the tools to explore. The equations which describe the coupling of light and matter are solved numerically, subjected to initial conditions and critical criteria consistent with the text. Formation of a universe with a non-infinite number of perfected spheres is extremely sensitive to the initial conditions, the intensity of the light and the transparency of these spheres. In this ‘medieval multiverse’, only a small range of opacity and initial density profiles leads to a stable universe with nine perfected spheres. As in current cosmological thinking, the existence of Grosseteste’s universe relies on a very special combination of fundamental parameters.

ON THE DYNAMICAL EVOLUTION OF THE FRACTAL STRUCTURE OF INTERSTELLAR MEDIUM

Fractals ◽  
1993 ◽  
Vol 01 (04) ◽  
pp. 908-916 ◽  
Author(s):  
Z.Y. YUE ◽  
B. ZHANG ◽  
G. WINNEWISSER ◽  
J. STUTZKI
Keyword(s):  
Fractal Dimension ◽  
Interstellar Medium ◽  
Density Distribution ◽  
Fractal Structure ◽  
Initial Conditions ◽  
Initial Density ◽  
Dynamical Evolution ◽  
Fractal Dimensions ◽  
Compressible Turbulence ◽  
Initial States

Two-dimensional compressible turbulence in a self-gravitating, magnetic interstellar medium is calculated as an initial value problem. It is shown that even if the initial density distribution is homogeneous and the initial velocity distribution contains only a few Fourier components, the nonlinear interaction among the Fourier components will generate more and more Fourier components and lead to a turbulent and fractal structure in the interstellar medium. The calculations are carried out for three different initial states. In order to see the time evolution, detailed density distributions and fractal dimensions of the density contours are calculated at three moments of time for each of the initial states. The results show that the fractal dimension remains almost the same (~1.4–1.5), although the detailed density distribution has changed considerably. The insensibility of the fractal dimension of density contours to both the initial conditions and the evolution time is in good agreement with observations of molecular clouds in the interstellar medium.

scholarly journals Computationally efficient methods for modelling laser wakefield acceleration in the blowout regime

2012 ◽  
Vol 78 (4) ◽  
pp. 469-482 ◽  
Author(s):  
B. M. COWAN ◽  
S. Y. KALMYKOV ◽  
A. BECK ◽  
X. DAVOINE ◽  
K. BUNKERS ◽  
...  
Keyword(s):  
Initial Conditions ◽  
Cylindrical Symmetry ◽  
Small Time ◽  
Numerical Dispersion ◽  
Computationally Efficient ◽  
Plasma Bubble ◽  
Time Step ◽  
Simulation Code ◽  
Particle In Cell ◽  
Comput Phys

AbstractElectron self-injection and acceleration until dephasing in the blowout regime is studied for a set of initial conditions typical of recent experiments with 100-terawatt-class lasers. Two different approaches to computationally efficient, fully explicit, 3D particle-in-cell modelling are examined. First, the Cartesian code vorpal (Nieter, C. and Cary, J. R. 2004 VORPAL: a versatile plasma simulation code. J. Comput. Phys.196, 538) using a perfect-dispersion electromagnetic solver precisely describes the laser pulse and bubble dynamics, taking advantage of coarser resolution in the propagation direction, with a proportionally larger time step. Using third-order splines for macroparticles helps suppress the sampling noise while keeping the usage of computational resources modest. The second way to reduce the simulation load is using reduced-geometry codes. In our case, the quasi-cylindrical code calder-circ (Lifschitz, A. F. et al. 2009 Particle-in-cell modelling of laser-plasma interaction using Fourier decomposition. J. Comput. Phys.228(5), 1803–1814) uses decomposition of fields and currents into a set of poloidal modes, while the macroparticles move in the Cartesian 3D space. Cylindrical symmetry of the interaction allows using just two modes, reducing the computational load to roughly that of a planar Cartesian simulation while preserving the 3D nature of the interaction. This significant economy of resources allows using fine resolution in the direction of propagation and a small time step, making numerical dispersion vanishingly small, together with a large number of particles per cell, enabling good particle statistics. Quantitative agreement of two simulations indicates that these are free of numerical artefacts. Both approaches thus retrieve the physically correct evolution of the plasma bubble, recovering the intrinsic connection of electron self-injection to the nonlinear optical evolution of the driver.

scholarly journals Geostrophic adjustment in a closed basin with islands

2013 ◽  
Vol 738 ◽  
pp. 358-377 ◽  
Author(s):  
E. R. Johnson ◽  
R. H. J. Grimshaw
Keyword(s):  
Initial Conditions ◽  
Initial Density ◽  
Circular Domain ◽  
Kelvin Wave ◽  
Geostrophic Adjustment ◽  
Homogeneous Fluid ◽  
Initial State ◽  
Linearized Theory ◽  
Baroclinic Modes ◽  
Initial Density Distribution

AbstractWe consider the geostrophic adjustment of a density-stratified fluid in a basin of constant depth on an $f$-plane in the context of linearized theory. For a single vertical mode, the equations are equivalent to those for a linearized shallow-water theory for a homogeneous fluid. Associated with any initial state there is a unique steady geostrophically adjusted component of the flow compatible with the initial conditions. This steady component gives the time average of the flow and is analogous to the adjusted flow in an unbounded domain without islands. The remainder of the response consists of superinertial Poincaré and subinertial Kelvin wave modes and expressions for the energy partition between the modes in arbitrary basins again follow directly from the initial conditions. The solution for an arbitrary initial density distribution released from rest in a circular domain is found in closed form. When the Rossby radius is much smaller than the basin radius, appropriate for the baroclinic modes, the interior adjusted solution is close to that of the initial state, except for small-amplitude trapped Poincaré waves, while Kelvin waves propagate around the boundaries, carrying, without change of form, the deviation of the initial height field from its average.

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