Macroparticle Method Research Articles

Numerical simulation of cold emission in coaxial diode with magnetic isolation

Due to the emergence and active development of new areas of application of powerful and super-powerful microwave vacuum devices, interest in studying the behavior of ensembles of charged particles moving in the interaction space has increased. An example is an electron beam formed in a coaxial diode with magnetic isolation. Numerical simulation of emission in such a diode is traditionally carried out using particle-in-cell methods. They are based on the simultaneous calculation of the equations of motion of particles and the Maxwell’s equations for the electromagnetic field. In the present work, a new computational approach called the point macroparticle method is proposed. In it, the motion of particles is described by the equations of relativistic mechanics, and explicit expressions are written out for fields in a quasi-static approximation. Calculations of the formation of a relativistic electron beam in a coaxial diode with magnetic isolation are performed and a comparison is made with the known theoretical relations for the electron velocity in the beam and for the beam current. Excellent agreement of calculation results with theoretical formulas is obtained.

Гибридная модель стационарного плазменного двигателя

A mathematical model is proposed for studying the processes in a stationary plasma thruster (SPT) taking into account the ionization of the working substance - Xenon, based on the hybrid equations of electromagnetic hydrodynamics (EMHD) of the plasma. The 1D2V case of plane symmetry is considered in detail, for which a numerical algorithm for investigating solutions of hybrid EMHD equations is constructed, based on the method of macroparticles. The solution of a number of fundamental issues is given: the calculation of average values, interpolation, construction of the initial distribution of macroparticles, the choice of boundary conditions for the electric field, etc. The results of calculations with and without taking into account the induction fields in the SPT are presented.

Side extraction: A novel method of filtering ions or macro-particles for vacuum arc ion sources.

A novel ion-extraction method named side extraction, i.e., extracting ions from the direction perpendicular to that of plasma expansion, is proposed in this paper, which can be used to filter ions or macro-particles for vacuum arc ion sources. Particle-in-cell simulations were performed to study filtering effects of side extraction on ions with different mass, different charges, and different initial kinetic energies. The results indicate that side extraction can separate ions by their charge states or initial kinetic energies and the extracting efficiency for different ion species is identical. Influences of extraction voltages, extraction interval, and the aspect ratio of the extraction aperture on ion filtering effects were also studied, which suggests that lower extraction voltages and longer extraction interval are beneficial for ion filtering and a high-aspect-ratio aperture contributes to the increase in the ratio of lighter ions in extracted beams. A theoretical analysis on the deflected distance of beams in the y direction was made and shows good agreement with the simulation results.

CFD development for macro particle simulations

Numerous industrial operations involve fluid-particle systems, in which both phases display very complex behaviour. Some examples include fluidisation technology in catalytic reactors, pneumatic transportation of grain or powder materials, carbon nanotube alignment in the nano-devices and circuit integration and so on. In this paper, a macro particle method is developed to model the fluid-particle flows. The macro particle is formed by a collection of micro-sized particles so that the number of macro particles to be tracked is much less than the number of smaller particles. Unlike the calculations of instantaneous point variables of fluid phase with moving discrete boundaries of the smaller particles with direct numerical simulation, the boundary of each macro particle is just dealt with the blocked-off approach. On the other hand, the flow fields based on the present method is solved by original Navier–Stokes, rather than the modified ones based on the locally averaged theorem. The flow fields are solved on the length scale of computational cells, while the resolutions of solid particles are the size of macro particle, which is determined as needed in specific applications. The macro particle method is validated by several selected cases, which demonstrate that the macro particle method could accurately resolve fluid-particle systems in an efficient, robust and flexible fashion.

Using the compute unified device architecture programming environment in simulation of ion-beam injection line with account for space charge effect

A simulation of the beam injection line in a synchrotron is performed within the Veksler and Baldin Laboratory of High Energy Physics, Joint Institute for Nuclear Research (VBLHEP JINR), project “The Development and Implementation of Units of a Synchrotron for Hadron Therapy.” The parameters of the injection line are chosen for the transport of beams with intensities of 25–100 mA through the injection channel of the synchrotron with account for the space-charge effect. The simulation was performed using the method of macroparticles (the PIC method). The approach of massively parallel computations on graphics processors using Compute Unified Device Architecture (CUDA) technology was applied for the acceleration of computations. The 66-fold speedup of computations was obtained using the Tesla C1060 computing module instead of a single-core CPU with 2.4 GHz.

Numerical Simulation of the Time Evolution of Small-Scale Irregularities in the F-Layer Ionospheric Plasma

Dynamics of magnetic field-aligned small-scale irregularities in the electron concentration, existing in the F-layer ionospheric plasma, is investigated with the help of a mathematical model. The plasma is assumed to be a rarefied compound consisting of electrons and positive ions and being in a strong, external magnetic field. In the applied model, kinetic processes in the plasma are simulated by using the Vlasov-Poisson system of equations. The system of equations is numerically solved applying a macroparticle method. The time evolution of a plasma irregularity, having initial cross-section dimension commensurable with a Debye length, is simulated during the period sufficient for the irregularity to decay completely. The results of simulation indicate that the small-scale irregularity, created initially in the F-region ionosphere, decays accomplishing periodic damped vibrations, with the process being collisionless.

Current Sheet in a non-Maxwellian collisionless plasma: Self-consistent theory, simulation, and comparison with spacecraft observations

A self-consistent theory is constructed of anisotropic current equilibria maintained in a non-Maxwellian plasma consisting of cold electrons and two hot ion components of different temperatures. The ion plasma components are described in the quasi-adiabatic approximation, and the plasma electrons, in the MHD approximation. Approximate steady solutions to the set of Vlasov-Maxwell equations are obtained and investigated parametrically. It is shown that the solutions can describe various current sheet profiles: from thin current structures with a maximum current density in the neutral sheet to comparatively “thick” current sheets with two to three maxima of the current density. It is also shown that the electron plasma component predominates at the current sheet center and can maintain a narrow central peak in the current density. The ion plasma component predominates at the edge of the current sheet, thereby determining the characteristic sheet thickness. The results of numerical simulations of a two-temperature plasma by the macroparticle method are compared with the experimental data from the Cluster spacecraft. Good agreement between the theoretical, numerical, and experimental results leads to the conclusion that the theory developed here provides a fairly adequate description of collisionless current sheets in space plasmas.

Free electron laser with bunched relativistic electron beam and electrostatic longitudinal wiggler

The system of the nonlinear nonstationary equations describing spatial-temporal dynamics of the amplitudes of an undulator radiation and a space charge wave of a relativistic electron beam in the resonator is obtained. The electrostatic longitudinal wiggler is considered. A bunch of the electron beam injects to the resonator, at the ends of which two mirrors are placed. After the interaction of electrons of bunch with radiation in the presence of wiggler and after amplifying electromagnetic pulse, a part of radiation is reflected back by semitransparent mirror. Then, it reaches to the initial of the system where the other mirror is placed. Synchronously, when the pulse is reflecting, the other electron bunch enters to the resonator and interacts with the pulse. This operation has simulated until saturation of growth of the electromagnetic pulse. The dynamics of the problem is simulated by the method of macro particles. The dynamics of pulse amplification, motion of the electrons, and spectra of output radiation in each stage are simulated.

On the theory of self-modulation instability in an FEL amplifier due to stimulated scattering of counterpropagating waves

We present the results of numerical simulation of the self-modulation processes in an amplifier based on the effect of stimulated scattering of two counterpropagating transverse electromagnetic waves by a relativistic electron beam (FEL amplifier). Two models of the studied system are considered. One model allows for the effects of overbunching of electrons and is based on the modified method of macroparticles. The other is a simplified wave model obtained in the approximation that the amplitude of a combination wave is small if the nonlinearity of the electron-beam processes is negligibly small. The mechanisms of self-modulation are studied. The scenarios of transition to chaos, observed with increase in the input-signal intensity and system length, are examined.

Vlasov treatment of coherent synchrotron radiation from arbitrary planar orbits

We study the influence of coherent synchrotron radiation (CSR) on particle bunches traveling on arbitrary planar orbits between parallel conducting plates which represent the vacuum chamber. Our goal is to follow the time evolution of the phase space distribution by solving the Vlasov–Maxwell equations in the time domain. This should provide simulations with lower numerical noise than the macro-particle method, and allow one to study such issues as emittance degradation and microbunching due to CSR in bunch compressors. The fields excited by the bunch are computed in the laboratory frame from a new formula that leads to much simpler computations than usual methods. The nonlinear Vlasov equation, formulated in the interaction picture, is integrated in the beam frame by approximating the Perron–Frobenius operator. For application to a chicane bunch compressor we take steps to deal with energy chirp.

Unsteady processes during stimulated emission from a relativistic electron beam in a quasi-longitudinal electrostatic pump field

The problem of stimulated emission from a relativistic electron beam in an external electrostatic pump field is studied. A set of nonlinear time-dependent equations for the spatiotemporal dynamics of the undulator radiation amplitude and the amplitude of the beam space charge field is derived. The beam electrons are described by a modified version of the macroparticle method. The regimes of the single-particle and collective Cherenkov effects during convective and absolute instabilities are considered. The nonlinear dynamics of radiation pulses emitted during the instabilities of the beam in its interaction with the forward and backward electromagnetic waves is investigated.

Simulation and optimization of ion beam lines from ion sources

A program library based on the macro particle method for numerical simulation and optimization of multi-component ion beam transportation from ion sources to RFQ accelerators is presented. The latest version of library was applied for simulations of transverse dynamics of an argon ion beam in the beam line from the 18 GHz ECR Ion Source to the linear RFQ accelerator of the RIKEN Beam Factory.

Numerical simulation and optimization of multicomponent ion beam from RIKEN electron cyclotron resonance ion sources

A new version of a program library for numerical simulation of ion beam transportation is presented. The library is aimed at high current and low energy multicomponent beams from ion sources and based on the macroparticle method. It has been used to simulate and optimize the transport line between the 18 GHz ECR ion source and RFQ linac at RIKEN. It is shown that it is possible to improve the ion transportation efficiency to a factor of 2 or 3 using the solenoid instead of the present einzel lens as a first element of the line.

Electron kinetic effects in atmosphere breakdown by an intense electromagnetic pulse.

A physical model is proposed for description of electron kinetics driven by a powerful electromagnetic pulse in the Earth's atmosphere. The model is based on a numerical solution to the Boltzmann kinetic equation for two groups of electrons. Slow electrons (with energies below a few keV) are described in a two-term approximation assuming a weak anisotropy of the electron distribution function. Fast electrons (with energies above a few keV) are described by a modified macroparticle method, taking into account the electron acceleration in the electric field, energy losses in the continuous deceleration approximation, and the multiple pitch angle scattering. The model is applied to a problem of the electric discharge in a nitrogen, which is preionized by an external gamma-ray source. It is shown that the runaway electrons have an important effect on the energy distribution of free electrons, and on the avalanche ionization rate. This mechanism might explain the observation of multiple lightning discharges observed in the Ivy-Mike thermonuclear test in the early 1950's.

Study of transients in the formation of heavy-current nanosecond electron beams

Results are presented from experimental and numerical studies of the spatial and temporal microstructure of a relativistic heavy-current electron beam of nanosecond duration. The beam is formed in a magnetically insulated coaxial diode with an edge-emitting cathode. Microcurrent oscillations and azimuthal nonuniformity of the beam are seen, the scale of the latter depending on the maximum cyclotron radius of the electrons. Two- and three-dimensional numerical calculations performed by the macroparticle method show that space-charge oscillations near the cathode produce these phenomena even in the case of a uniform emission surface. It is shown that the increase in the full current of the beam that occurs during the pulse in a weak magnetic field is connected with the gradual propagation of emission to the cylindrical outside surface of the cathode. A study is made of the effect of the discreteness of the emission surface on the impedance and current of the vacuum diode. The linear increase seen in current during the pulse with a small number of emission centers is attributed to an increase in their size as a result of expansion of the cathode plasma.

Electrostatic deposition of inertially moving charged aerosol particles onto the earthed disk

Deposition of charged aerosol particles onto the earthed disk, placed within the flow of particles is analysed with inertia and electric field of the particles taken into account. Equations of motion for particles and Poisson's equation for the electric field potential are solved numerically for different values of dimensionless parameters determining the aerosol flow. Carrier gas is supposed to remain quiescent. The macroparticle method is used to obtain the one-dimensional steady distributions of particle concentration, velocity and electric field far from the obstacle. Two basic flows, corresponding to large and moderate values of Stokes' number St, are indicated and studied. The results of the calculations are compared with the analytical solution of the problem in the case St → ∞. Numerical solution of the two-dimensional problem for steady motion of disperse phase near the disk shows that deposition of particles onto the obstacle strongly depends on Stokes' number: at St ⪢ 1 there is a particle-free shadow behind the disk, and particle trajectories can intersect. At St ≲ 1 the particle velocity field is single-valued, and deposition onto the back side of the disk is possible. Capture coefficients, which represent the main characteristics of particle deposition, are calculated separately for each side of the disk. Typical distribution diagrams for particle concentration and electric fields are given.

UHF generation in sub-micron layers of GaAs

Mathematical modelling of n+-n-n+ GaAs structures using the macroparticle method and the Monte Carlo procedure for simulating scattering events indicates that at a lattice temperature of 4.2 K ballistic and quasiballistic electron transport can lead to electron plasma instabilities. If the main scattering mechanism is the emission of polar optical phonons, plasma instability leads to UHF current oscillations at frequencies near 460 GHz.

Numerical modelling of the propagation of compensated electron beams in a bounded system

The numerical modelling of the dynamics of electron beams whose space charge is compensated by the ion background charge is discussed. For the potential approximation, a problem-solving algorithm is based on the macroparticle method. Two methods of computation are compared for the non-potential case.

The convergence and accuracy of the method of macroparticles

THE ACCURACY of the method of macroparticls for the Child-Langmuir problem is investigated. It is shown that the difference the self-consistent electrostatic field obtained from the discrete model and the self-consistent electrostatic field of the kinetic model is O(N 1 2 ) .