Numerical "Particle-in-Cell" Methods

Grigoryev, Yu. N.; Вшивков, В. А.; Федорук, М. П.

doi:10.1515/9783110916706

Cited by 96 publications

(67 citation statements)

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“…[28]. The units of measure are: the electron mass m e for masses, the light velocity c for velocities, the elementary charge e for charges, the unperturbed plasma density n 0 for densities, the inverse electron plasma frequency ω…”

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confidence: 99%

Note on quantitatively correct simulations of the kinetic beam-plasma instability

et al. 2015

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A large number of model particles is shown necessary for quantitatively correct simulations of the kinetic beam-plasma instability with the clouds-in-cells method. The required number of particles scales inversely with the expected growth rate, as in the kinetic regime only a narrow interval of beam velocities is resonant with the wave.PACS numbers: 52.65. Rr, 52.35.Qz Beam-plasma interaction plays an important role in various physical phenomena such as transport of relativistic electrons in the fast ignition scheme of inertial fusion, gamma-bursts, solar type II and III radio bursts, and collisionless shock waves in the space plasma (see review [1] and references therein). Also, beam-plasma collective interaction determines the efficiency of turbulent plasma heating [2,3] and electromagnetic emission [4][5][6][7] in fusion-oriented mirror traps.One of the most popular and effective tools for theoretical studies of the beam-plasma interaction is numerical simulations by the Particle-In-Cell (PIC) method. At present there is a great number of one-, two-, and three-dimensional PIC codes developed. These codes are used to reproduce fine details of the complex chain of intermediary processes that lead to plasma heating or electromagnetic radiation. The beam densities of interest n b are usually much smaller than the plasma density n p . For the fast ignition problem, the electron beams are relatively dense (n b /n p ∼ 0.1) [8][9][10]. Weakly relativistic beams with n b /n p ∼ 10 −4 ÷ 10 −3 are interesting for mirror traps [11][12][13]. Non-relativistic beams of very low density, n b /n p ∼ 10 −8 ÷ 10 −5 are of interest for radiation generation in solar radio bursts [14], though simulated with higher beam densities because of code limitations [14][15][16][17]. The numerical study usually begins from the linear stage of the beam-plasma instability, so the quantitatively correct simulation of this stage at low beam densities is important for the whole process.There are many realizations of the PIC method that differ in the algorithm of charge and current evaluation from positions of model particles. This algorithm is usually referred to as the shape function. One of the simplest shape functions is the triangular one also called CloudsIn-Cells (CIC) or linear interpolation [18]. This shape function is still widely used [14,[19][20][21][22][23][24][25] in spite of availability of more accurate algorithms [26,27].In this paper we show that an uncommonly large number of model particles is necessary for quantitatively correct simulations of the kinetic beam-plasma two-stream instability with the CIC method. The smaller the growth rate the more particles are needed. If the number of particles is insufficient, then the results are only qualitatively correct, that is the beam-plasma system behaves realistically, but the growth rate is underestimated. To prove this statement, we simulate various regimes of the twostream instability with a rather typical three-dimensional CIC code and compare the simulated growth rates with a...

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Note on quantitatively correct simulations of the kinetic beam-plasma instability

et al. 2015

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“…The PIC algorithm represents the distribution function of plasma species as a set of computational particles (also known as superparticles or markers), whose position in the phase space is evolved according to Newton's laws. The forces acting on the particles are obtained by solving the Maxwell equations, having assigned to a numerical grid the charge and the current carried by the particles [2][3][4][5][6].…”

Section: The Particle-in-cell Methodsmentioning

confidence: 99%

“…Originally developed to simulate fluid flows in two dimensions [1], the Particle-in-Cell (PIC) algorithm [2][3][4][5][6] is now a valuable tool to solve the Vlasov-Maxwell system of equations. The PIC algorithm approximates the distribution function with a set of computational particles that are evolved in time according to Newton's laws, and computes selfconsistently the electric and magnetic fields acting on the particles by solving the Maxwell's equations.…”

Section: Introductionmentioning

confidence: 99%

A methodology for the rigorous verification of Particle-in-Cell simulations

2017

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A methodology to perform a rigorous verification of Particle-in-Cell (PIC) simulations is presented, both for assessing the correct implementation of the model equations (code verification), and evaluating the numerical uncertainty affecting the simulation results (solution verification).The proposed code verification methodology is a generalization of the procedure developed for plasma simulation codes based on finite difference schemes that was described by Riva et al.

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“…Initially suggested in the 1950s for hydrodynamics simulations and popularized in the 1960s for plasma research, it is well described in the literature [9,10]. The method aims to model dynamics of a large number of charged particles in external electromagnetic fields taking into account particle-particle interaction.…”

Section: Implementation Detailsmentioning

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Ef: Software for Nonrelativistic Beam Simulation by Particle-in-Cell Algorithm

Boytsov

Bulychev

2018

EPJ Web Conf.

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Abstract. Understanding of particle dynamics is crucial in construction of electron guns, ion sources and other types of nonrelativistic beam devices. Apart from external guiding and focusing systems, a prominent role in evolution of such low-energy beams is played by particle-particle interaction. Numerical simulations taking into account these effects are typically accomplished by a well-known particle-in-cell method. In practice, for convenient work a simulation program should not only implement this method, but also support parallelization, provide integration with CAD systems and allow access to details of the simulation algorithm. To address the formulated requirements, development of a new open source code -Ef -has been started. It's current features and main functionality are presented. Comparison with several analytical models demonstrates good agreement between the numerical results and the theory. Further development plans are discussed.

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Numerical "Particle-in-Cell" Methods

Cited by 96 publications

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Note on quantitatively correct simulations of the kinetic beam-plasma instability

Note on quantitatively correct simulations of the kinetic beam-plasma instability

A methodology for the rigorous verification of Particle-in-Cell simulations

Ef: Software for Nonrelativistic Beam Simulation by Particle-in-Cell Algorithm

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