Electromagnetic Particle Code Research Articles

Electromagnetic Particle Code Simulations to Analyze Formation Mechanisms of Laser Induced Periodic Nano-structures

Electromagnetic Particle Code Simulations to Analyze Formation Mechanisms of Laser Induced Periodic Nano-structures

A 0.14 THz coaxial surface wave oscillator

To increase the output power of the surface wave oscillator (SWO) at the terahertz band, this paper presents a new type of coaxial-structured SWO, and its dispersive curve of TM01 mode is calculated numerically. The working properties of this new device are numerically simulated by using the self-developed fully electromagnetic particle code UNIPIC. Numerical results show that the working frequency of the coaxial-structured SWO is identical to that of the cylindrical-structured SWO, and the output power from this new coaxial-structured SWO is 67.8% more than that from the cylindrical-structured SWO, and the output mode of the terahertz wave is the transverse electromagnetic mode.

Particle-in-cell simulations on spontaneous thermal magnetic field fluctuations

In this paper an electromagnetic particle code is used to investigate the spontaneous thermal emission. Specifically we perform particle-in-cell simulations employing a non-relativistic isotropic Maxwellian particle distribution to show that thermal fluctuations are related to the origin of spontaneous magnetic field fluctuation. These thermal fluctuations can become seed for further amplification mechanisms and thus be considered at the origin of the cosmological magnetic field, at microgauss levels. Our numerical results are in accordance with theoretical results presented in the literature.

Effects of Electromagnetic Fluctuations along Shock Front on Electron Motions in an Oblique Shock Wave

The evolution of a large number of electrons in a shock wave propagating obliquely to an external magnetic field is analyzed by means of a two-dimensional electromagnetic particle code. Furthermore, the motions of the same number of test electrons in the electromagnetic fields averaged along the shock front are calculated, that is, in the equation of motion for the test electrons, two-dimensional electromagnetic fluctuations with finite wave numbers along the shock front are excluded. A comparison of the two groups of electrons shows that the two-dimensional electromagnetic fluctuations, which grow up to large amplitudes because of whistler wave instabilities excited by electrons trapped in the main pulse region of the shock wave, can cause the detrapping of energetic electrons from the main pulse and their subsequent acceleration to much higher energies. It is also found that two-dimensional fluctuations can contribute to the reflection of electrons near the end of the main pulse.

A Multi-Scale Electromagnetic Particle Code with Adaptive Mesh Refinement and Its Parallelization

Abstract Space plasma phenomena occur in multi-scale processes from the electron scale to the magnetohydrodynamic scale. In order to investigate such multi-scale phenomena including plasma kinetic effects, we started to develop a new electromagnetic Particle-In-Cell (PIC) code with Adaptive Mesh Refinement (AMR) technique. AMR can realize high-resolution calculation saving computer resources by generating and removing hierarchical cells dynamically. In the parallelization, we adopt domain decomposition method and for good locality preserving and dynamical load balancing, we will use the Morton ordered curve. In the PIC method, particle calculation occupies most of the total calculation time. In our AMR-PIC code, time step intervals are also refined. To realize the load balancing between processes in the domain decomposition scheme, it is the most essential to consider the number of particle calculation loops for each cell among all hierarchical levels as a work weight for each processor. Therefore, we calculate the work weights based on the cost of particle calculation and hierarchical levels of each cell. Then we decompose the domain according to the Morton curve and the work weight, so that each processor has approximately the same amount of work. By performing a simple one-dimensional simulation, we confirmed that the dynamic load balancing is achieved and the computation time is reduced by introducing the dynamic domain decomposition scheme.

Multidimensional effects on relativistic electrons in an oblique shock wave

Multidimensional effects on electron motion in a magnetosonic shock wave propagating obliquely to an external magnetic field are studied by means of a two-dimensional (two space coordinates and three velocities) relativistic, electromagnetic particle code. The simulations demonstrate that after trapping and energization in the main pulse of the shock wave, electrons can be detrapped from it keeping their ultrarelativistic energies. This detrapping is caused by magnetic fluctuations propagating along the wave front. Furthermore, some of the detrapped electrons can be accelerated to much higher energies by the shock wave because they can enter and exit the shock wave as a result of their gyromotions.

RADIATION FROM RELATIVISTIC SHOCKS WITH TURBULENT MAGNETIC FIELDS

Using our new 3D relativistic electromagnetic particle (REMP) code parallelized with MPI, we investigated long-term particle acceleration associated with a relativistic electron–positron jet propagating in an unmagnetized ambient electron–positron plasma. We have also performed simulations with electron-ion jets. The simulations were performed using a much longer simulation system than our previous simulations in order to investigate the full nonlinear stage of the Weibel instability for electron–positron jets and its particle acceleration mechanism. Cold jet electrons are thermalized and ambient electrons are accelerated in the resulting shocks for pair plasma case. Acceleration of ambient electrons leads to a maximum ambient electron density three times larger than the original value for pair plasmas. Behind the bow shock in the jet shock strong electromagnetic fields are generated. These fields may lead to time-dependent afterglow emission. We calculated radiation from electrons propagating in a uniform parallel magnetic field to verify the technique. We also used the new technique to calculate emission from electrons based on simulations with a small system with two different cases for Lorentz factors (15 and 100). We obtained spectra which are consistent with those generated from electrons propagating in turbulent magnetic fields with red noise. This turbulent magnetic field is similar to the magnetic field generated at an early nonlinear stage of the Weibel instability.

Detrapping Mechanism of Ultrarelativistic Electrons from an Oblique Shock Wave

Multi-dimensional effects on electron motion in a magnetosonic shock wave propagating obliquely to an external magnetic field are studied by means of a two-dimensional (two space coordinates and three velocities), relativistic, electromagnetic particle code. The simulations demonstrate that after trapping and energization in the main pulse of the shock wave, some electrons are detrapped from it while maintaining their ultrarelativistic energies. The detrapping is caused by magnetic fluctuations propagating along the wave front. Furthermore, some of the detrapped electrons are found to be accelerated by the shock wave to much higher energies because they can enter and exit the shock wave several times as a result of their gyromotions.

Repeated Acceleration of Thermal Ions by an Oblique Shock Wave and Associated Whistler Instabilities

A magnetosonic shock wave propagating obliquely to an external magnetic field can repeatedly accelerate thermal ions if θ0≈45°, where θ0 is the angle between the wave normal and the external magnetic field. The ion energy gains in this process are theoretically analyzed, and an expression for the maximum energy is derived. This theory is verified using a two-dimensional, electromagnetic particle code. Furthermore, whistler wave instabilities generated by the accelerated ions are studied. The simulation demonstrates that whistler waves are excited in both the upstream and downstream regions, but that the whistler waves in these two regions have different frequencies and wavenumbers. It is shown that the characteristics of these waves can be explained by linear theory.

A theoretical and simulation study of the contact discontinuities based on a Vlasov simulation code

[1] Contact discontinuity (CD) is the simplest solution that can be obtained from the magnetohydrodynamics (MHD) Rankine-Hugoniot jump conditions. Due to the limitations of the previous kinetic simulation models, the stability of the CD has become a controversial issue in the past 10 years. The stability of the CD is reexamined analytically and numerically. Our theoretical analysis shows that the electron temperature profile and the ion temperature profile must be out of phase across the CD if the CD structure is to be stable in the electron time scale and with zero electron heat flux on either side of the CD. Both a newly developed fourth-order implicit electrostatic Vlasov simulation code and an electromagnetic finite-size particle code are used to examine the stability and the electrostatic nature of the CD structure. Our theoretical prediction is verified by both simulations. Our results of Vlasov simulation also indicate that a simulation with initial electron temperature profile and ion temperature profile varying in phase across the CD will undergo very transient changes in the electron time scale but will relax into a quasi-steady CD structure within a few ion plasma oscillation periods if a real ion-electron mass ratio is used in the simulation and if the boundary conditions allow nonzero heat flux to be presented at the boundaries of the simulation box. The simulation results of this study indicate that the Vlasov simulation is a powerful tool to study nonlinear phenomena with nonperiodic boundary conditions and with nonzero heat flux at the boundaries of the simulation box.

On a magnetosphere disturbed by solar wind; observations of macroelectrons

Abstract. Three-dimensional electromagnetic full kinetic particle code (a version of TRISTAN) is used to study the interaction of a weakly-magnetized object with a solar wind of low density. The details of two magnetospheric processes – wave activity and energetic electrons appearing at the flanks of the magnetosphere – are presented. The results of the simulation are compared with known magnetospheric data.

RELATIVISTIC PARTICLE ACCELERATION IN DEVELOPING ALFVÉN TURBULENCE

A new particle acceleration process in a developing Alfv\'{e}n turbulence in the course of successive parametric instabilities of a relativistic pair plasma is investigated by utilyzing one-dimensional electromagnetic full particle code. Coherent wave-particle interactions result in efficient particle acceleration leading to a power-law like energy distribution function. In the simulation high energy particles having large relativistic masses are preferentially accelerated as the turbulence spectrum evolves in time. Main acceleration mechanism is simultaneous relativistic resonance between a particle and two different waves. An analytical expression of maximum attainable energy in such wave-particle interactions is derived.

Detrapping of Energetic Electrons from Curved Shock Front

The effect of the curvature of a shock front on electron trapping is investigated by means of a two-dimensional, fully kinetic, relativistic, electromagnetic particle code. Electron trapping and acceleration are observed even in a cylindrical shock wave in an external magnetic field B 0 . Furthermore, unlike that in the case of planar shock waves in a uniform B 0 , a significant fraction of trapped electrons can escape from the wave maintaining their ultrarelativistic energies. Such detrapping is due to the curvature of the shock front, i.e., the angle between the wave normal and B 0 varies along the trajectory of a trapped particle. The detrapping in a planar shock wave in a nonuniform magnetic field is also shown with one-dimensional simulations.

Scalability analysis of parallel Particle-In-Cell codes on computational grids

We have performed benchmarks of two three-dimensional parallel Particle-In-Cell (PIC) codes that are similar but have quite different communication patterns on different computational Grids. An electrostatic code with only electrons based on the three-dimensional skeleton PIC code employs the FFT Poisson solver that uses collective communication patterns. Another is the TRISTAN (TRI-dimensional STATNford) code parallelized with MPI, an electromagnetic full particle code, which uses a field solver that only requires point-to-point neighbor communication patterns. We present the mpptest benchmarks on cluster-based computational Grids, where both the basic point-to-point communication patterns and the basic collective communication patterns used in these PIC codes are tested. The results of these benchmarks clearly allow us to quantify and understand the scalability of both communication patterns on the Grids. The present results show that the parallelized TRISTAN code (without all-to-all collective communication) is more scalable than the parallelized skeleton PIC code (with all-to-all collective communication), in cluster-based computational Grid systems where communication performances is poor.

Simulation studies of positron acceleration by a shock wave

Using a relativistie electromagnetic particle code, we investigate positron acceleration in a shock wave propagating obliquely to an external magnetic field B 0 in an electron-positron-ion plasma. After an encounter with a shock wave, some positrons are reflected and then accelerated along the magnetic field. They stay in the shock transition region and have velocities nearly parallel to B 0 . Owing to the deformation of the wave profile, the acceleration can become stagnant. However. if the shock speed v sh is close to ccosθ. where c is the speed of light and θ is the angle between the wave normal and B 0 . the acceleration can start again. In this second stage acceleration, three types of motion are found. The first type is the same as that in the first stage. In the second type, particles gain energy from the electric field perpendicular to the magnetic field in association with large-radius gyromotion. The third type of motion resembles the curtate cycloid in the wave frame. We give theoretical estimates for the energy increase in these processes.

Acceleration Mechanics in Relativistic Shocks by the Weibel Instability

Plasma instabilities (e.g., Buneman, Weibel, and other two-stream instabilities) created in collisionless shocks may be responsible for particle (electron, positron, and ion) acceleration. Using a three-dimensional relativistic electromagnetic particle code, we have investigated long-term particle acceleration associated with relativistic electron-ion or electron-positron jet fronts propagating into an unmagnetized ambient electron-ion or electron-positron plasma. These simulations have been performed with a longer simulation system than our previous simulations in order to investigate the nonlinear stage of the Weibel instability and its particle acceleration mechanism. The current channels generated by the Weibel instability are surrounded by toroidal magnetic fields and radial electric fields. This radial electric field is quasi stationary and accelerates particles that are then deflected by the magnetic field. Whether particles are accelerated or decelerated along the jet propagation direction depends on the velocity of particles and the sign of × in the moving frame of each particle. For the electron-ion case the large-scale current channels generated by the ion Weibel instability lead to more acceleration near the jet head. Consequently, the accelerated jet electrons in the electron-ion jet have a significant hump above a thermal distribution. However, in the electron-positron case, accelerated jet electrons have a smoother, nearly thermal distribution. In the electron-positron case, initial acceleration occurs as current channels form and then continues at a much lesser rate as the current channels and corresponding toroidal magnetic fields generated by the Weibel instability dissipate.

Electromagnetic full particle code with adaptive mesh refinement technique: Application to the current sheet evolution

We have developed a new two and a half dimensional electromagnetic particle code with adaptive mesh refinement (AMR) technique in an effort to give a self-consistent description of the dynamic change of the plasma sheet in association with magnetic reconnection, which includes multi-scale processes from the electron scale to the magnetohydrodynamic scale. The AMR technique subdivides and removes cells dynamically in accordance with a refinement criterion and it is quite effective to achieve high-resolution simulations of phenomena that locally include micro-scale processes. Since the number of particles per cell decreases in the subdivided cells and a numerical noise increases, we subdivide not only cells but also particles therein and control the number of particles per cell. Our code is checked against several well-known processes such as the Landau damping of the Langmuir waves and we show that the AMR technique and particle splitting algorithm are successfully applied to the conventional particle codes. We have also examined the nonlinear evolution of the Harris-type current sheet and realized basically the same properties as those in other full particle simulations. We show that the numbers of cells and particles are greatly reduced so that the time to complete the simulation is significantly shortened in our AMR code, which enables us to conduct large-scale simulations on the current sheet evolution.

Full particle simulation of the plasma sheet using adaptive mesh refinement technique

We have developed a new 2-1/2 dimensional electromagnetic particle code with adaptive mesh refinement (AMR) technique in an effort to give a self-consistent description of the dynamic change of the plasma sheet in association with magnetic reconnection, which includes multi-scale processes from the electron scale to the magnetohydrodynamic scale. The AMR technique dynamically subdivides the cells that satisfy a certain refinement criterion and it is quite effective to achieve high-resolution simulations such as those around the X-type neutral line. Our code is checked against several well known processes such as the Landau damping of the Langmuir waves and we show that the AMR technique is successfully applied to the conventional particle code. A preliminary result on the time evolution of the Harris-type current sheet using our code is also presented. The number of cells and particles are dramatically reduced by using the AMR.

Particle Acceleration and Magnetic Field Generation in Electron‐Positron Relativistic Shocks

Shock acceleration is a ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., Buneman, Weibel, and other two-stream instabilities) created in collisionless shocks are responsible for particle (electron, positron, and ion) acceleration. Using a three-dimensional relativistic electromagnetic particle (REMP) code, we have investigated particle acceleration associated with a relativistic electron-positron jet front propagating into an ambient electron-positron plasma with and without initial magnetic fields. We find small differences in the results for no ambient and modest ambient magnetic fields. New simulations show that the Weibel instability created in the collisionless shock front accelerates jet and ambient particles both perpendicular and parallel to the jet propagation direction. Furthermore, the nonlinear fluctuation amplitudes of densities, currents, and electric and magnetic fields in the electron-positron shock are larger than those found in the electron-ion shock studied in a previous paper at a comparable simulation time. This comes from the fact that both electrons and positrons contribute to generation of the Weibel instability. In addition, we have performed simulations with different electron skin depths. We find that growth times scale inversely with the plasma frequency, and the sizes of structures created by tine Weibel instability scale proportionally to the electron skin depth. This is the expected result and indicates that the simulations have sufficient grid resolution. While some Fermi acceleration may occur at the jet front, the majority of electron and positron acceleration takes place behind the jet front and cannot be characterized as Fermi acceleration. The simulation results show that the Weibel instability is responsible for generating and amplifying nonuniform, small-scale magnetic fields, which contribute to the electron s (positron s) transverse deflection behind the jet head. This small- scale magnetic field structure is appropriate to the generation of radiation from deflected electrons (positrons) as opposed to synchrotron radiation. The jitter radiation has different properties than synchrotron radiation calculated assuming a uniform magnetic field. The jitter radiation resulting from small-scale magnetic field structures may be important for understanding the complex time structure and spectral evolution observed in gamma-ray bursts or other astrophysical sources containing relativistic jets and relativistic collisionless shocks.

Particle acceleration, magnetic field generation, and emission in relativistic shocks

Shock acceleration is a ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., Buneman, Weibel and other two-stream instabilities) created in collisionless shocks are responsible for particle (electron, positron, and ion) acceleration. Using a 3D relativistic electromagnetic particle code, we have investigated particle acceleration associated with a relativistic jet front propagating into an ambient plasma. We find small differences in the results for no ambient and modest ambient magnetic fields. Simulations show that the Weibel instability created in the collisionless shock front accelerates jet and ambient particles both perpendicular and parallel to the jet propagation direction. The small scale magnetic field structure generated by the Weibel instability is appropriate to the generation of “jitter” radiation from defected electrons (positrons) as opposed to synchrotron radiation. The jitter radiation resulting from small scale magnetic field structures may be important for understanding the complex time structure and spectral evolution observed in γ-ray bursts or other astrophysical sources containing relativistic jets and relativistic collisionless shocks.