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...
This paper describes the use of predictive simulation modeling for investigating the scalability of parallel algorithms. The study is carried out using a multiagent approach. The general principles of designing a model for the execution of a parallel algorithm on a given supercomputer architecture are described along with their application for researching this algorithm. The paper also presents the results of simulating the execution of this algorithm on more than a million cores.
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