Self-consistent Problem Research Articles

Cloud-based design of high average power traveling wave linacs

The design of industrial high average power traveling wave linacs must accurately consider some specific effects. For example, acceleration of high current beam reduces power flow in the accelerating waveguide. Space charge may influence the stability of longitudinal or transverse beam dynamics. Accurate treatment of beam loading is central to the design of high-power TW accelerators, and it is especially difficult to model in the meter-scale region where the electrons are nonrelativistic. Currently, there are two types of available codes: tracking codes (e.g. PARMELA or ASTRA) that cannot solve self-consistent problems, and particle-in-cell codes (e.g. Magic 3D or CST Particle Studio) that can model the physics correctly but are very time-consuming and resource-demanding. Hellweg is a special tool for quick and accurate electron dynamics simulation in traveling wave accelerating structures. The underlying theory of this software is based on the differential equations of motion. The effects considered in this code include beam loading, space charge forces, and external magnetic fields. We present the current capabilities of the code, provide benchmarking results, and discuss future plans. We also describe the browser-based GUI for executing Hellweg in the cloud.

Mixing of Gaussian pulses by nonlinear periodic semiconductor structures

The nonlinear scattering of two non-collinear Gaussian pulses with different central frequencies and lengths, incident on the periodic stacks of semiconductor layers, is analyzed in the self-consistent problem formulation, taking into account the dynamics of carriers. It is demonstrated that the waveform evolution in passive weakly nonlinear semiconductor periodic structure is strongly affected by the parameters of incident pulses. The obtained solutions have revealed the effect of stack spectral characteristics on the properties of the emitted waveforms of combinatorial frequencies. Significant increase of the amplitude of scattered waveform is observed as central frequencies of pump pulses are close to the plasma frequencies of semiconductor layers. It is remarkable that collision frequencies of the carriers in semiconductor materials strongly influence the mixing of incident pulses in the stacks. The enhanced amplitudes of the generated waveforms have been demonstrated numerically for the semiconductors with high collision frequencies.

Source-function synthesis in the self-consistent problem of radiation

A new approach to a rigorous theory of aperture antennas is proposed, which is based on solution of the self-consistent problem of radiation. It is ascertained that this formulation of the problem leads to a system of homogeneous Fredholm integral equations of the second kind—i.e., a problem for eigenfunctions and eigenvalues that provides a basis for solving the problem of field generation in the open space. The passage to Fredholm integral equations of the first kind allows one to solve the task of synthesis of the source function for a given radiation field.

Contraction of the positive column of a glow discharge in inert gases with account of resonance radiation transport

A previously proposed method for accurate description of resonance radiation transport in solving self-consistent problems is applied to a model of the contraction of the positive column of a glow discharge in argon. The exact solution to the problem and the solution obtained within the framework of the traditional approximation of local effective transition probability according to Biberman are compared. The influence of radiation transport on various plasma parameters is demonstrated

Features of wave generation by a source moving along a one-dimensional flexible guide lying on an elastic-inertial foundation

A self-consistent dynamic problem is posed for a system including a one-dimensional flexible guide (a string), elastic-inertial foundation (an array of oscillators), and moving oscillating load. The effect of the foundation parameters on the dispersion characteristics (frequency, phase velocity, and group velocity as functions of the wavenumber) of transverse waves propagating along the string has been analyzed. It has been shown that taking into account the foundation inertia leads to the presence of two critical (cutoff) frequencies. Regularities of wave generation by a source moving along the string have been analyzed.

Analysis of random point images with the use of symbolic computation codes and generalized Catalan numbers

Original codes and combinatorial-geometrical computational schemes are presented, which are developed and applied for finding exact analytical formulas that describe the probability of errorless readout of random point images recorded by a scanning aperture with a limited number of threshold levels. Combinatorial problems encountered in the course of the study and associated with the new generalization of Catalan numbers are formulated and solved. An attempt is made to find the explicit analytical form of these numbers, which is, on the one hand, a necessary stage of solving the basic research problem and, on the other hand, an independent self-consistent problem.

How theory and simulation can drive fuel cell electrocatalysis

Over the last decade, theory and modeling have become essential tools to navigate the parameter space that governs activity and stability of electrocatalyst systems for polymer electrolyte fuel cells. This perspective covers essential phenomena from atomic scale to nanoscale and discusses the impact of the key parameters at play. It is centered around the development of first-principles electrochemical methods as a foremost goal in the field. The general modeling framework entails at its core a self-consistency problem that must be solved to relate the metal phase potential to descriptors of catalyst activity and stability. Density functional theory has captured a central role in this rapidly evolving field. The article puts more than usual emphasis on aspects of the multifaceted challenges in fuel cell electrocatalysis that at present lie beyond the capabilities of density functional theory; they include metal charging and solvent effects. Following the general discussion of the theoretical-computational framework, an approach for “deciphering” the oxygen reduction reaction is demonstrated; it reconciles reaction pathways and free energy profiles obtained from density functional theory simulations with kinetic modeling of surface reactions and effective kinetic parameters. Another section dwells on the importance of metal charging phenomena that are especially important for the catalytic function of nanoporous media. The penultimate section exposes the ambivalent role of Pt oxide formation in modulating catalytic properties for the oxygen reduction reaction as well as for catalyst corrosion.

Green's function approach to the non-equilibrium superconductivity near the critical line

In spite of the absent friction of super-currents, normal currents affect the superconducting condensate. The BCS approach with Bogoliubov-Valutin quasiparticles is not suited for description of the normal current near the critical line. We review an alternative theory of the non-equilibrium superconductivity dealing exclusively with normal-state quasiparticles. It is based on the Thouless T-matrix criterion, which is extended to non-equilibrium. The problem of selfconsistency of the T-matrix in the superconducting state is examined and solved with the help of the multiple-scattering theory.

Suppression of space charge induced beam halo in nonlinear focusing channel

An intense non-uniform particle beam exhibits strong emittance growth and halo formation in focusing channels due to nonlinear space charge forces of the beam. This phenomenon limits beam brightness and results in particle losses. The problem is connected with irreversible distortion of phase space volume of the beam in conventional focusing structures due to filamentation in phase space. Emittance growth is accompanied by halo formation in real space, which results in inevitable particle losses. A new approach for solving a self-consistent problem for a matched non-uniform beam in two-dimensional geometry is discussed. The resulting solution is applied to the problem of beam transport, while avoiding emittance growth and halo formation by the use of nonlinear focusing field. Conservation of a beam distribution function is demonstrated analytically and by particle-in-cell simulation for a beam with a realistic beam distribution.

Effect of Material Damage on Parameters of a Torsional Wave Propagated in a Deformed Rotor

The proposed approach allows formulation formulating a self-consistent problem that includes an equation, describing rotor dynamics, and an equation, describing the damage to the material of the rotor. It is shown that the damage to the material causes frequency-dependent attenuation and phase speed dispersion of elastic torsion waves, which allows for the acoustic assessment of the damage. The applied field of deformations, in turn, leads to damage accumulation. The resulting kinetic equation shows that the increase in damage has exponential character. System parameters have been assessed, which makes it possible to consider the accumulation of damage linearly in time.

TRIQS/CTHYB: A continuous-time quantum Monte Carlo hybridisation expansion solver for quantum impurity problems

We present TRIQS/CTHYB, a state-of-the art open-source implementation of the continuous-time hybridisation expansion quantum impurity solver of the TRIQS package. This code is mainly designed to be used with the TRIQS library in order to solve the self-consistent quantum impurity problem in a multi-orbital dynamical mean field theory approach to strongly-correlated electrons, in particular in the context of realistic electronic structure calculations. It is implemented in C++ for efficiency and is provided with a high-level Python interface. The code ships with a new partitioning algorithm that divides the local Hilbert space without any user knowledge of the symmetries and quantum numbers of the Hamiltonian. Furthermore, we implement higher-order configuration moves and show that such moves are necessary to ensure ergodicity of the Monte Carlo in common Hamiltonians even without symmetry-breaking. Program summaryProgram title: TRIQS/CTHYBCatalogue identifier: AEYU_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEYU_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland.Licensing provisions: GNU General Public Licence (GPLv3)No. of lines in distributed program, including test data, etc.: 159,017No. of bytes in distributed program, including test data, etc.: 10,215,893Distribution format: tar.gzProgramming language: C++/Python.Computer: Any architecture with suitable compilers including PCs and clusters.Operating system: Unix, Linux, OSX.RAM: Highly problem-dependentClassification: 7.3, 4.4.External routines: TRIQS, cmake.Nature of problem: Accurate solvers for quantum impurity problems are needed in condensed matter theory.Solution method: We present an efficient C++/Python open-source implementation of a continuous-time hybridisation expansion solver.Running time: Tests take less than a minute. Otherwise it is highly problem dependent (from minutes to several days).

Three-dimensional analysis of ion optics with misalignments of apertures

A three-dimensional computer model of ion optics is developed to analyze the focusing properties and lifetime characteristics of ion engines. The simulation model includes the following main parts: solution of the self-consistent problem with calculation of the potential and space charge distribution; calculation of rarefied gas flows in the free-molecule approximation; modeling of charge-exchange collisions; calculation of surface erosion rate; prediction of the ion optics lifetime. In the present study, manufacturing tolerances on the mutual alignment of the apertures are investigated. The modeling results are compared with predictions of the linear optical theory. It is shown that operating values of the perveance at an offset of the holes may be estimated using a two-dimensional axisymmetric model. According to the simulation results the beamlet deflection angle weakly depends on the ion beam current and agrees well with linear optical theory. The observed displacement of the erosion pattern on the acceleration grid can be a measure of the apertures misalignment in the hot operational state of the ion optics. The reasons of the observed asymmetry of the erosion pattern on the periphery of the ion-optical system, which may arise even at a perfect alignment of the apertures, are investigated.

Demonstration of robust quantum gate tomography via randomized benchmarking

Typical quantum gate tomography protocols struggle with a self-consistency problem: the gate operation cannot be reconstructed without knowledge of the initial state and final measurement, but such knowledge cannot be obtained without well-characterized gates. A recently proposed technique, known as randomized benchmarking tomography (RBT), sidesteps this self-consistency problem by designing experiments to be insensitive to preparation and measurement imperfections. We implement this proposal in a superconducting qubit system, using a number of experimental improvements including implementing each of the elements of the Clifford group in single ‘atomic’ pulses and custom control hardware to enable large overhead protocols. We show a robust reconstruction of several single-qubit quantum gates, including a unitary outside the Clifford group. We demonstrate that RBT yields physical gate reconstructions that are consistent with fidelities obtained by RB.

Self-consistent problems of geophysics: A review

In the first part of the paper, the general information about self-consistent problems of geophysics is presented. It is shown that these problems most adequately describe the processes in the real geological medium. Examples of such problems are given. This section of the paper provides a number of new results which have not been published previously. These results are shown in italics in the text. The two subsequent sections address the analysis of the most elaborated self-consistent problems of geophysics: induced polarization and seismoelectrics.

Research on High Voltage Power for 10kV Linked SVG

10kV linked SVG module power supply from their own h-bridge power, supply is unstable. To solve this problem, this paper proposes a new way to take power, using a combination of full-bridge push-pull circuit with isolation transformer to solve the logical drive power between the power module and the SVG device self-consistent problem. The paper detailed analysis of the working principle and characteristics of this new way to take power, and verified on prototype, present the experimental results.

Numerical investigation of fast-wave propagation and radio-frequency sheath interaction with a shaped tokamak wall

Interactions between propagating fast waves and radio-frequency (RF) sheaths in the ion cyclotron range of frequencies are numerically investigated based on a cold fluid plasma model coupled with a sheath boundary condition. In this two-dimensional study, the capability of the finite element code rfSOL, which was developed in previous numerical work, is extended to analyze self-consistent RF sheath-plasma interaction problems in a tokamak with a non-circular cross-section. It is found that a large sheath voltage is generated near the edges of the limiter-shaped deformation as a result of the conversion from fast to slow waves on the sheaths. The sheath voltage associated with this conversion is particularly significant in the localized region where the contact angle between the magnetic field line and the conducting wall varies rapidly along the curved sheath surface, which is consistent with the results in previous one-dimensional theoretical work. The dependences of the RF sheaths on various parameters in plasma such as the toroidal wavenumber, edge plasma density, and the degree of the RF wave absorption in the core region are also examined in detail.

Theory of frequency synchronization in a ring laser

The self-consistent problem of the frequency synchronization of counter-propagating waves in a ring laser is rigorously solved. An intrinsic nonlinear mechanism of the phase coupling between the waves is considered for the first time. This ineradicable coupling is provided by modulation of the population difference of the energy levels of the active medium atoms in the electromagnetic field of two counter-propagating waves. The theoretical limit for the range of phase locking between the counter-propagating waves is established. The general equation of phase synchronization is obtained from the solution of a self-consistent problem. The frequency-dependent boundaries of the synchronization band calculated in the framework of this approach show good agreement with experimental results published in the literature.

Quantum causality in closed timelike curves

Although general relativity allows the existence of closed timelike curves (CTCs), self-consistency problems arise (the ‘grandfather paradox’ among others). It is known that quantum mechanical consideration of the matter formally removes all the paradoxes, but the questions about causal structure remain. On the other hand, the idea of postselected CTCs (P-CTC) in quantum teleportation has know been put forward and experimentally implemented. We consider these problems with the aid of quantum causal analysis, where causality is defined without invoking the time relation. It implements the Cramer principle of weak causality, which admits time reversal in entangled states. We analyze Deutsch CTCs (D-CTC) with different kinds of interactions between the chronology-violating and chronology-respecting particles, with refined inferences about mixedness, quantum/classical correlations, entanglement and thermodynamics in the D-CTC. The main result is that time reversal causality can really exist, however, the final quantum state does not place retrospective constraints on the initial state, instead the final state can influence the state inside the D-CTC. This is effectively the implementation of Novikov self-consistency principle. The P-CTC has radically different properties; in particular, if the initial state was pure, the final state is always pure too. Self-consistency is controlled by the initial state-dependent traversability of the P-CTC.

Analytical Technique in the Boundary Element Method for 3D Self-Consistent Problems of Electron Optics

Analytical Technique in the Boundary Element Method for 3D Self-Consistent Problems of Electron Optics

Gravi-weak unification and multiple-point principle

The problem of self-consistency of the unification of gravity and weak SU(2) interaction in a model that is invariant under the Spin(4, 4) group is studied. For this purpose, consequences of the multicritical-point principle, which admits the existence of two degenerate vacua in the Standard Model, are considered. Also, the existence of a visible and an invisible sector in our Universe is assumed.