Integration of the Vlasov equation along characteristics in one and two dimensions

Methods of integration of the Vlasov equation along characteristics in one and two dimensions are discussed, in connection with the problem of the formation of a charge separation at a plasma edge. Application of these methods to the problem in which the Vlasov equation is integrated in a cylindrical geometry to calculate the electric field at a plasma edge, is presented.     

Numerical simulations of the ionospheric striation model in a non-uniform magnetic field

The striation model describes the evolution of plasma clouds along and across the geomagnetic field B in the earth ionosphere. The plasma clouds drift across the ionosphere in the presence of an ambient electric field and a neutral wind. In this article we introduce new techniques to extend the simulation tools to the earth magnetic field geometry. The model moreover allows a three-dimensional representation of the plasma density evolution. The derivation of this model is recalled in the context of a non-uniform magnetic field and involves a new set of local coordinates. A numerical scheme is proposed to solve the resulting system of nonlinear partial differential equations. Numerical simulations are realized and the striation of the initial plasma cloud into a cluster of smaller clouds is obtained. The present work allows the observation of the structures along the magnetic field lines.     

Second-order, exact charge conservation for electromagnetic particle-in-cell simulation in complex geometry

A second-order, exact charge-conserving algorithm for accumulating charge and current on the spatial grid for electromagnetic particle-in-cell (EM-PIC) simulation in bounded geometry is presented. The algorithm supports standard EM-PIC exterior boundary conditions and complex internal conductors on non-uniform grids. Boundary surfaces are handled by smoothly transitioning from second to first-order weighting within half a cell of the boundary. When a particle is exactly on the boundary surface (either about to be killed, or just created), the weighting is fully first-order. This means that particle creation and particle/surface interaction models developed for first-order weighting do not need to be modified. An additional feature is the use of an energy-conserving interpolation scheme from the electric field on the grid to the particles. Results show that high-density, cold plasmas with ωpeΔt∼1, and Δx/λD?1, can be modeled with reasonable accuracy and good energy conservation. This opens up a significant new capability for explicit simulation of high-density plasmas in high-power devices.     

Three-dimensional anisotropic pressure free boundary equilibria

Free boundary three-dimensional anisotropic pressure magnetohydrodynamic equilibria with nested magnetic flux surfaces are computed through the minimisation of the plasma energy functional . The plasma-vacuum interface is varied to guarantee the continuity of the total pressure [p_⊥+B²/(2μ₀)] across it and the vacuum magnetic field must satisfy the Neumann boundary condition that its component normal to this interface surface vanishes. The vacuum magnetic field corresponds to that driven by the plasma current and external coils plus the gradient of a potential function whose solution is obtained using a Green's function method. The energetic particle contributions to the pressure are evaluated analytically from the moments of the variant of a bi-Maxwellian distribution function that satisfies the constraint B⋅∇Fh=0. Applications to demonstrate the versatility and reliability of the numerical method employed have concentrated on high-β off-axis energetic particle deposition with large parallel and perpendicular pressure anisotropies in a 2-field period quasiaxisymmetric stellarator reactor system. For large perpendicular pressure anisotropy, the hot particle component of the p_⊥ distribution localises in the regions where the energetic particles are deposited. For large parallel pressure anisotropy, the pressures are more uniform around the flux surfaces.     

Transport control in fusion plasmas by changing electric and magnetic field spatial profiles

For magnetically confined plasmas in tokamaks, we have numerically investigated how Lagrangian chaos at the plasma edge affects the plasma confinement. Initially, we have considered the chaotic motion of particles in an equilibrium electric field with a monotonic radial profile perturbed by drift waves. We have showed that an effective transport barrier may be created at the plasma edge by modifying the electric field radial profile. In the second place, we have obtained escape patterns and magnetic footprints of chaotic magnetic field lines in the region near a tokamak wall with resonant modes due to the action of an ergodic magnetic limiter. For monotonic plasma current density profiles we have obtained distributions of field line connections to the wall and line escape channels with the same spatial pattern as the magnetic footprints on the tokamak walls.     

Implementation of the CIP algorithm to magnetohydrodynamic simulations

An implementation of the Constrained Interpolation Profile (CIP) algorithm to magnetohydrodynamic (MHD) simulations is presented. First we transform the original momentum and magnetic induction equations to unfamiliar forms by introducing Elsässer variables [W.M. Elsässer, The hydromagnetic equations, Phys. Rev. (1950)]. In this formulation, while the compressional and pressure gradient terms remain as non-advective terms, the advective and magnetic stress terms are expressed in the form of an advection equation, which enables us to use the CIP algorithm. We have examined some 1D test problems using the code based on this formula. Linear Alfvén wave propagation tests reveal that the developed code is capable of solving any Alfvén wave propagation with only small numerical diffusion and phase errors up to k?h=2.5 (where ?h is the grid spacing). A shock tube test shows good agreement with a previous result with less numerical oscillation at the shock front and the contact discontinuity which are captured within a few grid points. Extension of the 1D code to the multi-dimensional case is straightforward. We have calculated the 3D nonlinear evolution of the Kelvin-Helmholtz instability (KHI) and compared the result with our previous study. We find that our new MHD code is capable of following the 3D turbulence excited by the KHI while retaining the solenoidal property of the magnetic field.     

One-dimensional electromagnetic relativistic PIC-hydrodynamic hybrid simulation code H-VLPL (hybrid virtual laser plasma lab)

In this paper we present a new one-dimensional full electromagnetic relativistic hybrid plasma model. The full kinetic particle-in-cell (PIC) and hydrodynamic model have been combined in the single hybrid plasma code H-VLPL (hybrid virtual laser plasma laboratory). The semi-implicit algorithm allows to simulate plasmas of arbitrary densities via automatic reduction of the highest plasma frequencies down to the numerically stable range. At the same time, the model keeps the correct spatial scales like the plasma skin depth. We discuss the numerically efficient implementation of this model. Further, we carefully test the hybrid model validity by applying it to a series of physical examples. The new mathematical method allows to overcome the typical time step restrictions of explicit PIC codes.     

dHybrid: A massively parallel code for hybrid simulations of space plasmas

A massively parallel simulation code, called dHybrid, has been developed to perform global scale studies of space plasma interactions. This code is based on an explicit hybrid model; the numerical stability and parallel scalability of the code are studied. A stabilization method for the explicit algorithm, for regions of near zero density, is proposed. Three-dimensional hybrid simulations of the interaction of the solar wind with unmagnetized artificial objects are presented, with a focus on the expansion of a plasma cloud into the solar wind, which creates a diamagnetic cavity and drives the Interplanetary Magnetic Field out of the expansion region. The dynamics of this system can provide insights into other similar scenarios, such as the interaction of the solar wind with unmagnetized planets.     

A transport simulation code for inertial confinement fusion relevant laser-plasma interaction

We present a code for the simulation of laser-plasma interaction processes relevant for applications in inertial confinement fusion. The code consists of a fully nonlinear hydrodynamics in two spatial dimensions using a Lagrangian, discontinuous Galerkin-type approach, a paraxial treatment of the laser field and a spectral treatment of the dominant non-local transport terms. The code is fully parallelized using MPI in order to be able to simulate macroscopic plasmas.One example of a fully nonlinear evolution of a laser beam in an underdense plasma is presented for the conditions previewed for the future MegaJoule laser project.     

Parallel TREE code for two-component ultracold plasma analysis

The TREE method has been widely used for long-range interaction N-body problems. We have developed a parallel TREE code for two-component classical plasmas with open boundary conditions and highly non-uniform charge distributions. The program efficiently handles millions of particles evolved over long relaxation times requiring millions of time steps. Appropriate domain decomposition and dynamic data management were employed, and large-scale parallel processing was achieved using an intermediate level of granularity of domain decomposition and ghost TREE communication. Even though the computational load is not fully distributed in fine grains, high parallel efficiency was achieved for ultracold plasma systems of charged particles. As an application, we performed simulations of an ultracold neutral plasma with a half million particles and a half million time steps. For the long temporal trajectories of relaxation between heavy ions and light electrons, large configurations of ultracold plasmas can now be investigated, which was not possible in past studies.     

Constructing plasma response models from full toroidal magnetohydrodynamic computations

We explore accurate and efficient algorithms for constructing plasma response models, based on the computed data using a full toroidal MHD stability code MARS-F. These response models are used to study feedback stabilization of resistive wall modes for fusion plasmas. Three approaches are discussed and compared. A direct full-model computation offers the most accurate response, unfortunately without producing analytical expressions for the response model. The pole-residue expansion methods yield analytical and asymptotically rigorous response models. A low-order Padé approximation serves as a model reduction technique that simplifies the controller design, while keeping a reasonable accuracy for the response models. From the computational viewpoint, the most efficient approaches are the pole-residue expansion based on eigenfunction projection, and the low-order Padé approximation.     

移动机器人基于多传感器信息融合的室外场景理解

本文研究了移动机器人多传感器信息融合技术,提出一种融合激光测距与视觉信息的实时室外场景理解方法．基于三维激光测距数据构建了高程图描述场景地形特征,同时利用条件随机场模型从视觉信息中获取地貌特征,并以高程图中的栅格作为载体,应用投影变换和信息统计方法将激光信息与视觉信息进行有效融合．在此基础上,对融合后的环境模型分别在地形和地貌两个层面进行可通过性评估,从而实现自主移动机器人实时室外场景理解．实验结果和数据分析验证了所提方法的有效性和实用性．     

Simulations of biomedical atmospheric-pressure discharges

The comparison between fluid and particle-in-cell simulation results in different nonthermal helium plasma sources; including an overview of kinds, strengths and limitations of the numerical models is reported. The kinetic information indicates that the electron energy probability function (EEPF) evolves from a three-temperature distribution in RF atmospheric-pressure discharges into a Druyvesteyn type distribution as the driving frequency increases. In microwave helium microplasma, the power delivered to the electrons in the bulk increases, and as a result, the EEPF becomes closer to a Maxwellian distribution. Although the results obtained with fluid models that a Maxwellian energy distribution function are not capable of capturing nonlocal effects in high pressure discharge, the appropriate fluid models will be a good selection to investigate particular problems because of their short simulation time. In addition, since frequent ion-neutral collisions limit the energy acquired by the ions as they transit the sheath, the average ion energy near the electrodes is found to be significantly lowered at atmospheric pressure.     

A nonuniform nested grid method for simulations of RF induced ionospheric turbulence

We present a numerical scheme to simulate radio-frequency (RF) induced ionospheric turbulence, in which an electromagnetic wave is injected into the overhead ionospheric plasma. At the turning point of the ordinary mode, the electromagnetic wave undergoes linear mode-conversion to electrostatic Langmuir and upper hybrid waves that can have a much shorter wavelength than the electromagnetic wave. In order to resolve both the electromagnetic and electrostatic waves, avoiding severe restrictions on the time step due to the Courant-Friedrich-Lewy (CFL) condition, the equation of motion for the plasma particles is solved on a denser grid than that for the Maxwell equations near the mode-conversion region. An interpolation scheme is employed to calculate the electromagnetic field in the equation of motion of the plasma particles, and an averaging scheme is used to calculate the current density acting as a source in the Maxwell equation. Special care has to be taken to reduce numerical recurrence effects when the wavelength of the electrostatic wave is of the same order or shorter than the coarse grid spacing of the electromagnetic wave.     

Linear comparison of gyrokinetic codes with trapped electrons

Three codes that solve the gyrokinetic equation in toroidal geometry are compared in the linear limit for the growth rates and real frequencies of the ion temperature gradient (ITG) mode and the trapped electron mode (TEM). The three codes are the gyrokinetic toroidal code (GTC) and GT3D, both of which are radially-global particle-in-cell initial-value codes, and FULL, which is a radially-local continuum eigenvalue code. With the same standard input parameters on a reference magnetic surface, the three codes give good agreement for the linear eigenfrequencies, both without (i.e. with adiabatic electron response) and with trapped electrons, as the perpendicular wavenumber and the ion temperature gradient input parameters are varied.     

基于色彩空间分块匹配的三维动画融合技术

为了提高影视动画制作的三维图像成像质量,需要进行动画图像的动态信息融合处理,提出一种基于二维色彩空间分块匹配的三维动画图像的动态信息融合处理技术,采用虚拟视景重构技术进行三维动画图像采集和特征投影处理,对三维动画图像进行二值拟合和边缘轮廓检测,采用RGB分解技术进行三维动画图像的颜色分量提取,采用颜色模板空间投影算法进行三维动画图像的分块融合处理,提高三维动画图像的边缘像素点的特征配对性能,结合三维动画图像的色彩空间分块融合结果进行像素特征优化配置,计算匹配窗口相关系数,实现三维动画图像的动态信息融合处理。仿真结果表明,采用该方法进行三维动画图像的动态信息融合处理,能提高图像输出峰值信噪比,提高动态成像质量。     

Effects of external magnetic field on propagation of electromagnetic wave in uniform magnetized plasma slabs

A simple method is proposed to describe the propagation of electromagnetic waves in magnetized uniform plasma slabs. Using this method, the reflection, absorption and transmission coefficients of such plasmas for right-hand circularly waves are studied and the effects of the continuously changing external magnetic field on the power of the electromagnetic waves propagated in magnetized plasma slabs with fixed parameters are presented. Our method enables more detailed numerical analyses which are useful in practical applications pertaining to the control of the reflection or absorption coefficients of electromagnetic wave through a uniform magnetized plasma slab by adjusting the external magnetic field.     

A parallel algorithm for global magnetic reconnection studies

A new algorithm is presented for the computation of two-dimensional magnetic reconnection in plasmas. Both resistive magnetohydrodynamic (MHD) and two-fluid models are considered. It has been implemented on several parallel platforms and shows good scalability up to 32 CPUs for reasonable problem sizes. A fixed, non-uniform rectangular mesh is used to resolve the different spatial scales in the reconnection problem. The resistive MHD version uses an implicit/explicit hybrid method, while the two-fluid version uses an alternating-direction implicit (ADI) method with high-order artificial dissipation. The technique has proven useful for comparing several different theories of collisional and collisionless reconnection.     

A load-balancing algorithm for a parallel electromagnetic particle-in-cell code

Particle-in-cell simulations often suffer from load-imbalance on parallel machines due to the competing requirements of the field-solve and particle-push computations. We propose a new algorithm that balances the two computations independently. The grid for the field-solve computation is statically partitioned. The particles within a processor's sub-domain(s) are dynamically balanced by migrating spatially-compact groups of particles from heavily loaded processors to lightly loaded ones as needed. The algorithm has been implemented in the quicksilver electromagnetic particle-in-cell code. We provide details of the implementation and present performance results for quicksilver running models with up to a billion grid cells and particles on thousands of processors of a large distributed-memory parallel machine.