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Luis O. Silva

Publications and source records attributed to Luis O. Silva.

At least 73 records · Page 4Linked to original sources
arXiv2015

On a linear interpolation problem for n-dimensional vector polynomials

This work provides a complete characterization of the solutions of a linear interpolation problem for vector polynomials. The interpolation problem consists in finding n scalar polynomials such that an equation involving a linear combination of them is satisfied for each one of the N interpolation nodes. The results of this work generalize previous results on the so-called rational interpolation and have applications to direct and inverse spectral analysis of band matrices.

math.CA↗
arXiv2015

Shock formation in electron-ion plasmas: mechanism and timing

We analyse the full shock formation process in electron-ion plasmas in theory and simulations. It is accepted that electromagnetic shocks in initially unmagnetised relativistic plasmas are triggered by the filamentation instability. However, the transition from the first unstable phase to the quasi-steady shock is still missing. We derive a theoretical model for the shock formation time, taking into account the filament merging in the non-linear phase of the filamentation instability. This process is much slower than in electron-positron pair shocks, so that the shock formation is longer by a factor proportional to sqrt(m_i/m_e) ln(m_i/m_e).

astro-ph.HE↗
arXiv2015

Singular Schroedinger operators as self-adjoint extensions of n-entire operators

We investigate the connections between Weyl-Titchmarsh-Kodaira theory for one-dimensional Schrödinger operators and the theory of $n$-entire operators. As our main result we find a necessary and sufficient condition for a one-dimensional Schrödinger operator to be $n$-entire in terms of square integrability of derivatives (w.r.t. the spectral parameter) of the Weyl solution. We also show that this is equivalent to the Weyl function being in a generalized Herglotz-Nevanlinna class. As an application we show that perturbed Bessel operators are $n$-entire, improving the previously known conditions on the perturbation.

math.SP↗
arXiv2015

Mitigation of numerical Cerenkov radiation and instability using a hybrid finite difference-FFT Maxwell solver and a local charge conserving current deposit

A hybrid Maxwell solver for fully relativistic and electromagnetic (EM) particle-in-cell (PIC) codes is described. In this solver, the EM fields are solved in $k$ space by performing an FFT in one direction, while using finite difference operators in the other direction(s). This solver eliminates the numerical Cerenkov radiation for particles moving in the preferred direction. Moreover, the numerical Cerenkov instability (NCI) induced by the relativistically drifting plasma and beam can be eliminated using this hybrid solver by applying strategies that are similar to those recently developed for pure FFT solvers. A current correction is applied for the charge conserving current deposit to correctly account for the EM calculation in hybrid Yee-FFT solver. A theoretical analysis of the dispersion properties in vacuum and in a drifting plasma for the hybrid solver is presented, and compared with PIC simulations with good agreement obtained. This hybrid solver is applied to both 2D and 3D Cartesian and quasi-3D (in which the fields and current are decomposed into azimuthal harmonics) geometries. Illustrative results for laser wakefield accelerator simulation in a Lorentz boosted frame using the hybrid solver in the 2D Cartesian geometry are presented, and compared against results from 2D UPIC-EMMA simulation which uses a pure spectral Maxwell solver, and from OSIRIS 2D lab frame simulation using the standard Yee solver. Very good agreement is obtained which demonstrates the feasibility of using the hybrid solver for high fidelity simulation of relativistically drifting plasma with no evidence of the numerical Cerenkov instability.

physics.comp-ph↗
arXiv2015

Elimination of the numerical Cerenkov instability for spectral EM-PIC codes

When using an electromagnetic particle-in-cell (EM-PIC) code to simulate a relativistically drifting plasma, a violent numerical instability known as the numerical Cerenkov instability (NCI) occurs. The NCI is due to the unphysical coupling of electromagnetic waves on a grid to wave-particle resonances, including aliased resonances, i.e., $ω+ 2πμ/Δt=(k_1+ 2πν_1/Δx_1)v_0$, where $μ$ and $ν_1$ refer to the time and space aliases and the plasma is drifting relativistically at velocity $v_0$ in the $\hat{1}$-direction. Recent studies have shown that an EM-PIC code which uses a spectral field solver and a low pass filter can eliminate the fastest growing modes of the NCI. Based on these studies a new spectral PIC code for studying laser wakefield acceleration (LWFA) in the Lorentz boosted frame was developed. However, we show that for parameters of relevance for LWFA simulations in the boosted frame, a relativistically drifting plasma is susceptible to a host of additional unstable modes with lower growth rates, and that these modes appear when the fastest growing unstable modes are filtered out. We show that these modes are most easily identified as the coupling between modes which are purely transverse (EM) and purely longitudinal (Langmuir) in the rest frame of the plasma for specific time and space aliases. We rewrite the dispersion relation of the drifting plasma for a general field solver and obtain analytic expressions for the location and growth rate for each unstable mode, i.e, for each time and space aliased resonances. We show for the spectral solver that when the fastest growing mode is eliminated a new mode at the fundamental resonance ($μ=ν_1=0$) can be seen. (Please check the whole abstract in the paper).

physics.plasm-ph↗
arXiv2014

Particle Merging Algorithm for PIC Codes

Particle-in-cell merging algorithms aim to resample dynamically the six-dimensional phase space occupied by particles without distorting substantially the physical description of the system. Whereas various approaches have been proposed in previous works, none of them seemed to be able to conserve fully charge, momentum, energy and their associated distributions. We describe here an alternative algorithm based on the coalescence of N massive or massless particles, considered to be close enough in phase space, into two new macro-particles. The local conservation of charge, momentum and energy are ensured by the resolution of a system of scalar equations. Various simulation comparisons have been carried out with and without the merging algorithm, from classical plasma physics problems to extreme scenarios where quantum electrodynamics is taken into account, showing in addition to the conservation of local quantities, the good reproducibility of the particle distributions. In case where the number of particles ought to increase exponentially in the simulation box, the dynamical merging permits a considerable speedup, and significant memory savings that otherwise would make the simulations impossible to perform.

physics.plasm-ph↗
arXiv2014

Spectral analysis for semi-infinite mass-spring systems

We study how the spectrum of a Jacobi operator changes when this operator is modified by a certain finite rank perturbation. The operator corresponds to an infinite mass-spring system and the perturbation is obtained by modifying one interior mass and one spring of this system. In particular, there are detailed results of what happens in the spectral gaps and which eigenvalues do not move under the modifications considered. These results were obtained by a new tecnique of comparative spectral analysis and they generalize and include previous results for finite and infinite Jacobi matrices.

math-ph↗
arXiv2014

On dB spaces with nondensely defined multiplication operator and the existence of zero-free functions

In this work we consider de Branges spaces where the multiplication operator by the independent variable is not densely defined. First, we study the canonical selfadjoint extensions of the multiplication operator as a family of rank-one perturbations from the viewpoint of the theory of de Branges spaces. Then, on the basis of the obtained results, we provide new necessary and sufficient conditions for a real, zero-free function to lie in a de Branges space.

math-ph↗
arXiv2014

Collisionless Weibel shocks: full formation mechanism and timing

Collisionless shocks in plasmas play an important role in space physics (Earth's bow shock) and astrophysics (supernova remnants, relativistic jets, gamma-ray bursts, high energy cosmic rays). While the formation of a fluid shock through the steepening of a large amplitude sound wave has been understood for long, there is currently no detailed picture of the mechanism responsible for the formation of a collisionless shock. We unravel the physical mechanism at work and show that an electromagnetic Weibel shock always forms when two relativistic collisionless, initially unmagnetized, plasma shells encounter. The predicted shock formation time is in good agreement with 2D and 3D particle-in-cell simulations of counterstreaming pair plasmas. By predicting the shock formation time, experimental setups aiming at producing such shocks can be optimised to favourable conditions.

physics.plasm-ph↗
arXiv2013

Modeling of Laser wakefield acceleration in Lorentz boosted frame using EM-PIC code with spectral solver

Simulating laser wakefield acceleration (LWFA) in a Lorentz boosted frame in which the plasma drifts towards the laser with $v_b$ can speedup the simulation by factors of $γ^2_b=(1-v^2_b/c^2)^{-1}$. In these simulations the relativistic drifting plasma inevitably induces a high frequency numerical instability that contaminates the interested physics. Various approaches have been proposed to mitigate this instability. One approach is to solve Maxwell equations in Fourier space (a spectral solver) as this has been shown to suppress the fastest growing modes of this instability in simple test problems using a simple low pass, ring (in two dimensions), or shell (in three dimensions) filter in Fourier space. We describe the development of a fully parallelized, multi-dimensional, particle-in-cell code that uses a spectral solver to solve Maxwell's equations and that includes the ability to launch a laser using a moving antenna. This new EM-PIC code is called UPIC-EMMA and it is based on the components of the UCLA PIC framework (UPIC). We show that by using UPIC-EMMA, LWFA simulations in the boosted frames with arbitrary $γ_b$ can be conducted without the presence of the numerical instability. We also compare the results of a few LWFA cases for several values of $γ_b$, including lab frame simulations using OSIRIS, a EM-PIC code with a finite difference time domain (FDTD) Maxwell solver. These comparisons include cases in both linear, and nonlinear regimes. We also investigate some issues associated with numerical dispersion in lab and boosted frame simulations and between FDTD and spectral solvers.

physics.comp-ph↗
arXiv2013

A class of $n$-entire Schrödinger operators

We study singular Schrödinger operators on a finite interval as selfadjoint extensions of a symmetric operator. We give sufficient conditions for the symmetric operator to be in the $n$-entire class, which was defined in our previous work, for some $n$. As a consequence of this classification, we obtain a detailed spectral characterization for a wide class of radial Schrödinger operators. The results given here make use of de Branges Hilbert space techniques.

math-ph↗
arXiv2013

Full-scale ab initio 3D PIC simulations of an all-optical radiation reaction configuration at $10^{21}\mathrm{W/cm^2}$

Using full-scale 3D particle-in-cell simulations we show that the radiation reaction dominated regime can be reached in an all optical configuration through the collision of a $\sim$1 GeV laser wakefield accelerated (LWFA) electron bunch with a counter propagating laser pulse. In this configuration radiation reaction significantly reduces the energy of the particle bunch, thus providing clear experimental signatures for the process with currently available lasers. We also show that the transition between classical and quantum radiation reaction could be investigated in the same configuration with laser intensities of $10^{24}\mathrm{W/cm^2}$.

physics.plasm-ph↗
arXiv2013

The class of n-entire operators

We introduce a classification of simple, regular, closed symmetric operators with deficiency indices (1,1) according to a geometric criterion that extends the classical notions of entire operators and entire operators in the generalized sense due to M. G. Krein. We show that these classes of operators have several distinctive properties, some of them related to the spectra of their canonical selfadjoint extensions. In particular, we provide necessary and sufficient conditions on the spectra of two canonical selfadjoint extensions of an operator for it to belong to one of our classes. Our discussion is based on some recent results in the theory of de Branges spaces.

math-ph↗
arXiv2013

Inverse problems for Jacobi operators III: Mass-spring perturbations of semi-infinite systems

Consider an infinite linear mass-spring system and a modification of it obtained by changing the first mass and spring of the system. We give results on the interplay of the spectra of such systems and on the reconstruction of the system from its spectrum and the one of the modified system. Furthermore, we provide necessary and sufficient conditions for two sequences to be the spectra of the mass-spring system and the perturbed one.

math-ph↗
arXiv2012

Numerical instability due to relativistic plasma drift in EM-PIC simulations

The numerical instability observed in the Electromagnetic-Particle-in-cell (EM-PIC) simulations with a plasma drifting with relativistic velocities is studied using both theory and computer simulations. We derive the numerical dispersion relation for a cold plasma drifting with a relativistic velocity and find an instability attributed to the coupling between the beam modes of the drifting plasma and the electromagnetic modes in the system. The characteristic pattern of the instability in Fourier space for various simulation setups and Maxwell Equation solvers are explored by solving the corresponding numerical dispersion relations. Furthermore, based upon these characteristic patterns we derive an asymptotic expression for the instability growth rate. The asymptotic expression greatly speeds up the calculation of instability growth rate and makes the parameter scan for minimal growth rate feasible even for full three dimensions. The results are compared against simulation results and good agreement is found. These results can be used as a guide to develop possible approaches to mitigate the instability. We examine the use of a spectral solver and show that such a solver when combined with a low pass filter with a cutoff value of $|\vec{k}|$ essentially eliminates the instability while not modifying modes of physical interest. The use of spectral solver also provides minimal errors to electromagnetic modes in the lowest Brillouin zones.

physics.plasm-ph↗
arXiv2012

The spectra of selfadjoint extensions of entire operators with deficiency indices (1,1)

We give necessary and sufficient conditions for real sequences to be the spectra of selfadjoint extensions of an entire operator whose domain may be non-dense. For this spectral characterization we use de Branges space techniques and a generalization of Krein's functional model for simple, regular, closed, symmetric operators with deficiency indices (1,1). This is an extension of our previous work in which similar results were obtained for densely defined operators.

math-ph↗
arXiv2010

Spectral measures of Jacobi operators with random potentials

Let $H_ω$ be a self-adjoint Jacobi operator with a potential sequence $\{ω(n)\}_n$ of independently distributed random variables with continuous probability distributions and let $μ_ϕ^ω$ be the corresponding spectral measure generated by $H_ω$ and the vector $ϕ$. We consider sets $A(ω)$ which depend on $ω$ in a particular way and prove that $μ_ϕ^ω(A(ω))=0$ for almost every $ω$. This is applied to show equivalence relations between spectral measures for random Jacobi matrices and to study the interplay of the eigenvalues of these matrices and their submatrices.

math-ph↗