Electromagnetic Particle-in-cell Code Research Articles

Integrating a ponderomotive guiding center algorithm into a quasi-static particle-in-cell code based on azimuthal mode decomposition

High fidelity modeling of plasma based acceleration (PBA) requires the use of three dimensional, fully nonlinear, and kinetic descriptions based on the particle-in-cell (PIC) method. In PBA an intense particle beam or laser (driver) propagates through a tenuous plasma whereby it excites a plasma wave wake. Three-dimensional PIC algorithms based on the quasi-static approximation (QSA) have been successfully applied to efficiently model the interaction between relativistic charged particle beams and plasma. In a QSA PIC algorithm, the plasma response to a charged particle beam or laser driver is calculated based on forces from the driver and self-consistent forces from the QSA form of Maxwell's equations. These fields are then used to advance the charged particle beam or laser forward by a large time step. Since the time step is not limited by the regular Courant-Friedrichs-Lewy (CFL) condition that constrains a standard 3D fully electromagnetic PIC code, a 3D QSA PIC code can achieve orders of magnitude speedup in performance. Recently, a new hybrid QSA PIC algorithm that combines another speedup technique known as an azimuthal Fourier decomposition has been proposed and implemented. This hybrid algorithm decomposes the electromagnetic fields, charge and current density into azimuthal harmonics and only the Fourier coefficients need to be updated, which can reduce the algorithmic complexity of a 3D code to that of a 2D code. Modeling the laser-plasma interaction in a full 3D electromagnetic PIC algorithm is very computationally expensive due the enormous disparity of physical scales to be resolved. In the QSA the laser is modeled using the ponderomotive guiding center (PGC) approach. We describe how to implement a PGC algorithm compatible for the QSA PIC algorithms based on the azimuthal mode expansion. This algorithm permits time steps orders of magnitude larger than the cell size and it can be asynchronously parallelized. Details on how this is implemented into the QSA PIC code that utilizes an azimuthal mode expansion, QPAD, are also described. Benchmarks and comparisons between a fully 3D explicit PIC code (OSIRIS), as well as a few examples related to laser wakefield acceleration, are presented.

Research on effect of emission uniformity on X-band relativistic backward oscillator using conformal PIC code

Explosive emission cathodes (EECs) are adopted in relativistic backward wave oscillators (RBWOs) to generate intense relativistic electron beam. The emission uniformity of the EEC can render saturation of the power generation unstable and the output mode impure. However, the direct measurement of the plasma parameters on the cathode surface is quite difficult and there are very few related numerical study reports about this issue. In this paper, a self-developed three-dimensional conformal fully electromagnetic particle in cell code is used to study the effect of emission uniformity on the X-band RBWO; the electron explosive emission model and the field emission model are both implemented in the same cathode surface, and the local field enhancement factor is also considered in the field emission model. The RBWO with a random nonuniform EEC is thoroughly studied using this code; the simulation results reveal that when the area ratio of cathode surface for electron explosive emission is 80%, the output power is unstable and the output mode is impure. When the annular EEC does not emit electron in the angle range of 30°, the RBWO can also operate normally.

Simulation of multipactor on the rectangular grooved dielectric surface

Multipactor discharge on the rectangular grooved dielectric surface is simulated self-consistently by using a two-and-a-half dimensional (2.5 D) electrostatic particle-in-cell (PIC) code. Compared with the electromagnetic PIC code, the former can give much more accurate solution for the space charge field caused by the multipactor electrons and the deposited surface charge. According to the rectangular groove width and height, the multipactor can be divided into four models, the spatial distributions of the multipactor electrons and the space charge fields are presented for these models. It shows that the rectangular groove in different models gives very different suppression effect on the multipactor, effective and efficient suppression on the multipactor can only be reached with a proper groove size.

External circuit integration with electromagnetic particle in cell modeling of plasma focus devices

The pinch performance of a plasma focus (PF) device is sensitive to the physical conditions of the breakdown phase. It is therefore essential to model and study the initial phase in order to optimize device performance. An external circuit is self consistently coupled to the electromagnetic particle in cell code to model the breakdown and initial lift phase of the United Nations University/International Centre for Theoretical Physics (UNU-ICTP) plasma focus device. Gas breakdown during the breakdown phase is simulated successfully, following a drop in the applied voltage across the device and a concurrent substantial rise in the circuit current. As a result, the plasma becomes magnetized, with the growing value of the magnetic field over time leading to the gradual lift off of the well formed current sheath into the axial acceleration phase. This lifting off, with simultaneous outward sheath motion along the anode and vertical cathode, and the strong magnetic fields in the current sheath region, was demonstrated in this work, and hence validates our method of coupling the external circuit to PF devices. Our method produces voltage waveforms that are qualitatively similar to the observed experimental voltage profiles of the UNU-ICTP device. Values of the mean electron energy before and after voltage breakdown turned out to be different, with the values after breakdown being much lower. In both cases, the electron energy density function turned out to be non-Maxwellian.

Wave-particle-interaction in kinetic plasmas

Resonant scattering of energetic protons off magnetic irregularities is the main process in cosmic ray diffusion. The typical theoretical description uses Alfvén waves in the low frequency limit. We demonstrate that the usage of Particle-in-Cell (PiC) simulations for particle scattering is feasible. The simulation of plasma waves is performed with the relativistic electromagnetic PiC code ACRONYM and the tracks of test particles are evaluated in order to study particle diffusion. Results for the low frequency limit are equivalent to those obtained with an MHD description, but only for high frequencies results can be obtained with reasonable effort. PiC codes have the potential to be a useful tool to study particle diffusion in kinetic turbulence.

Current sheath formation in the plasma focus

The shaping and formation of the current sheath takes place in the breakdown phase of a plasma focus device. Achieving a clear understanding of the current sheath formation process is important because the plasma focus device performance depends on the quality of this sheath. In this paper, we created and successfully run an electromagnetic particle in cell code to simulate the breakdown phase. Magnetic effects are self-consistently incorporated in this formalism, allowing us to carry the simulation all the way to the point prior to breakdown.

Particle-in-cell Simulations of Raman Forward Scattering Instability in Low-density Plasmas: A Computational Study

Electromagnetic-wave propagation through equilibrium plasmas can lead to medium instabilities whose formation and growth conditions are of importance to study. Raman forward scattering (RFS) instability in low-density plasmas is investigated through particle-in-cell (PIC) simulation, which is employed due to plasmas’ high complexity, costly experiment process, and nonlinear behavior in physical terms. A 2D electromagnetic PIC code is used to model RFS instability. Doing so, a plasma medium containing ions and electrons is PIC simulated and ions are assumed to form a constant background because of high inertia. The results indicate that as a plane electromagnetic wave enters the plasma medium, large-amplitude longitudinal waves, whose growth rate is well consistent with the theoretical results, begin to grow, suggesting the appearance of RFS instability.

Energy loss and longitudinal wakefield of relativistic short proton bunches in electron clouds

The aim of our study is the numerical computation of the wakefield and energy loss per unit length for relativistic, short ($l10\text{ }\text{ }\mathrm{ns}$) proton bunches interacting with an electron cloud inside the beam pipe. We present analytical expressions for the energy loss in the impulse kick approximation. For the simulation of the wakefields a 2D self-consistent, electrostatic particle-in-cell (PIC) code is employed. Results for the energy loss and for the wakefields are presented for the parameter scope of the CERN LHC and SPS. For selected parameters the results are compared to a three-dimensional (3D) electromagnetic PIC code.

Global and Kinetic MHD Simulation by the Gpic-MHD Code

In order to implement large-scale and high-beta tokamak simulation, a new algorithm of the electromagnetic gyrokinetic PIC (particle-in-cell) code was proposed and installed on the Gpic-MHD code [Gyrokinetic PIC code for magnetohydrodynamic (MHD) simulation]. In the new algorithm, the vorticity equation and the generalized Ohm's law along the magnetic field are derived from the basic equations of the gyrokinetic Vlasov, Poisson, and Ampere system and are used to describe the spatio-temporal evolution of the field quantities of the electrostatic potential φ and the longitudinal component of the vector potential Az. The basic algorithm is equivalent to solving the reduced-MHD-type equations with kinetic corrections, in which MHD physics related to Alfven modes are well described. The estimation of perturbed electron pressure from particle dynamics is dominant, while the effects of other moments are negligible. Another advantage of the algorithm is that the longitudinal induced electric field, ETz = −∂Az/∂t, is explicitly estimated by the generalized Ohm's law and used in the equations of motion. Furthermore, the particle velocities along the magnetic field are used (vz-formulation) instead of generalized momentums (pz-formulation), hence there is no problem of ‘cancellation', which would otherwise appear when Az is estimated from the Ampere's law in the pz-formulation. The successful simulation of the collisionless internal kink mode by the new Gpic-MHD with realistic values of the large-scale and high-beta tokamaks revealed the usefulness of the new algorithm.

CHIPIC: An Efficient Code for Electromagnetic PIC Modeling and Simulation

Computer-aided highly efficient electromagnetic particle-in-cell (PIC) (CHIPIC) code, developed at the University of Electronic Science and Technology of China, is a fully computer-aided code which combines modeling, calculations, and analysis with an integrated environment. CHIPIC is specifically designed for efficient modeling and simulation. CHIPIC includes a computer-aided design (CAD) system and a physical kernel. The CAD system is designed based on the common flowchart of PIC simulation to provide efficient modeling and analysis, and the physical kernel is developed to provide fast and accurate calculations. The physical kernel can run on a single processor or in parallel mode. When it runs in parallel mode, the message-pass interface and open specifications for multiprocessing are adopted. The validity of this electromagnetic PIC code is proved by simulating a magnetically insulated transmission-line-oscillator tube.

Space Charge Limited Currents Calculations in Coaxial Cylindrical Diodes Using Particle-in-Cell Simulations

Three dimensional particle-in-cell (PIC) simulations are conducted to measure the space charge limited (SCL) currents in coaxial cylindrical diodes. New cut-cell emission and absorption boundary algorithms implemented in the electromagnetic PIC code, VORPAL are utilized for this study. Comparisons of VORPAL SCL current results are made with i) theoretical SCL current results for the one dimensional planar diode, ii) analytical solutions of SCL current results for the one dimensional and two dimensional cylindrical diode cases, and iii) an experimental cylindrical diode operated as a virtual cathode oscillator. VORPAL SCL current results show agreement within a few percent with the analytical two dimensional cylindrical diode results for the non-relativistic operating voltages of 1-100 kV and within error bars with the experimental cylindrical diode results for the diode operating voltage of 340 kV.

MAGIC3D Simulations of a 500-W Ka-Band Coupled-Cavity Traveling-Wave Tube

The 3-D particle-in-cell (PIC) simulations of a Ka-band coupled-cavity traveling-wave tube (CCTWT) are shown. The computational analysis of the Ka-band coupled-cavity slow-wave structure was conducted through the use of an electromagnetic PIC code MAGIC3D. The choice of a double-slot staggered RF cavity circuit was made because of a wide frequency bandwidth, moderate interaction impedance, and excellent thermal dissipation properties. We investigated the large-signal and nonlinear beam dynamics of a Ka-band CCTWT using MAGIC3D. The center frequency of the Ka-band CCTWT can be tuned from 28.4 to 30 GHz by varying the cathode voltage. Hot-test simulations show that the 84-cavity Ka-band CCTWT produces 540 W of saturated output power at 29 GHz with an electronic efficiency of 8.1% and a gain of 28 dB when the beam voltage and current are set to 17 kV and 390 mA, respectively.

Three-dimensional deformable-grid electromagnetic particle-in-cell for parallel computers

We describe a new parallel, non-orthogonal-grid, three-dimensional electromagnetic particle-in-cell (EMPIC) code based on a finite-volume formulation. This code uses a logically Cartesian grid of deformable hexahedral cells, a discrete surface integral (DSI) algorithm to calculate the electromagnetic field, and a hybrid logical–physical space algorithm to push particles. We investigate the numerical instability of the DSI algorithm for non-orthogonal grids, analyse the accuracy for EMPIC simulations on non-orthogonal grids, and present performance benchmarks of this code on a parallel supercomputer. While the hybrid particle push algorithm has a second-order accuracy in space, the accuracy of the DSI field solve algorithm is between first and second order for non-orthogonal grids. The parallel implementation of this code, which is almost identical to that of a Cartesian-grid EMPIC code using domain decomposition, achieved a high parallel efficiency of over 96% for large-scale simulations.