Bulletin of the American Physical Society
50th Annual Meeting of the Division of Plasma Physics
Volume 53, Number 14
Monday–Friday, November 17–21, 2008; Dallas, Texas
Session BO5: Nonlinear Waves, Simulation, and Modeling |
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Chair: William Daughton, Los Alamos National Laboratory Room: Reunion C |
Monday, November 17, 2008 9:45AM - 9:57AM |
BO5.00001: Wide phase space holes on the tail of an electron distribution Martin V. Goldman, David L. Newman In a recent Letter [1], a theoretical analysis showed weak electron phase space holes to be consistent with bipolar fields measured in space plasmas. The moving potential structure was found to be of the form $\mathrm{sech}^4(x/a)$, where ``$a$'' depends on the distribution of \textit{untrapped} electrons, which solely determines the hole spatial half-width as a function of hole speed. by contrast, the hole amplitude depends on the distribution of \textit{trapped} electrons and is therefore independent of the hole speed. Motivated by magnetic reconnection simulations and laboratory measurements that exhibit tails on the parallel electron distributions, this treatment has now been extended to include a broad tail on the untrapped Maxwellian electron distribution, which is self-consistent with a weak moving potential structure of the same $\mathrm{sech}^4$ form. Analytic solutions are found in which the holes are spatially wider and faster than for distributions without tails. The role of ions in these solutions is also studied. Vlasov simulation addressing the stability and and accessibility of these analytic phase-space solutions are discussed in a companion presentation (D.~L.~Newman, this meeting). \\[0pt] [1] Goldman, Newman, and Mangeney, \textit{PRL}, \textbf{99}, 145002 (2007). [Preview Abstract] |
Monday, November 17, 2008 9:57AM - 10:09AM |
BO5.00002: Vlasov evolution and stability of bipolar electrostatic field structures comoving with electrons in a broad nonthermal tail David L. Newman, Martin V. Goldman As shown by M.~V.~Goldman (this meeting), weak bipolar fields associated with shallow phase-space holes tend to be wider when comoving with electrons near the high-velocity edge of a broad nonthermal tail than theory [1] predicts for holes comoving with background thermal electrons. Here, we employ 1-D Vlasov-Poisson simulations to study routes by which such tail-resonant holes can form, and whether they are stable at all velocities for which there are analytical stationary solutions. We extend this numerical analysis beyond the weak-potential limit, including cases where the depletion of phase-space density on trapped electron orbits becomes vanishingly small. We also consider the self-consistent generation of both a broad tail and electron holes via saturation of the Buneman instability driven by electron-ion drift. \\[0pt] [1] M. V. Goldman, D. L. Newman, and A. Mangeney, ``Theory of Weak Bipolar fields and Electrons Holes with Applications to Space Plasmas,'' \textit{Phys.~Rev.~Lett}, \textbf{99}, 145002 (2007). [Preview Abstract] |
Monday, November 17, 2008 10:09AM - 10:21AM |
BO5.00003: Development of a 3D particle treecode for plasma simulations Benjamin Ong, Andrew Christlieb, Robert Krasny In this work we present a fully 3-D Boundary Integral Treecode (BIT). We apply the method to several classic problems such as sheath formation and 3D simulations of a Penning trap. In addition, we investigate the ability of the solver to naturally capture Coloumb scattering. A key point in the investigation is to understand the effect of different types of regularizations, and how to appropriately incorporate the regularization in the BIT framework. This work builds on substantial efforts in 1- and 2-D. [1] R. Krasny and K. Lindsay, {\em A particle method and adaptive treecode for vortex sheet motion in 3-D flow}, JCP, Vol. 172, No. 2, 879-907 [2] K. Matyash, R. Schneider, R. Sydora, and F. Taccogna, {\em Application of a Grid-Free Kinetic Model to the Collisionless Sheath}, Contrib. Plasma Phys, Vol. 48, No. 1-3, 116-120 (2008) [3] K. Cartwright and A. Christlieb, {\em Boundary Integral Corrected Particle in Cell}, SIAM Journal on Sci. Comput., submitted [4] A. Christlieb, R. Krasny, B. Ong and J. Qiu, {\em A Step Towards Addressing Temporal Multi-scale Problems in Plasma Physics}, in prep. [Preview Abstract] |
Monday, November 17, 2008 10:21AM - 10:33AM |
BO5.00004: Boundary Integral Treecode (BIT) as a sub-cell method in Particle-In-Cell (PIC) Andrew Christlieb, Keith Cartwright The Boundary Integral Treecode (BIT) is a method for computing long-range forces in $O(N \log N)$ without making use of an underlying mesh. The method use the point cluster form of fast summation. BIT has been shown to exhibit less numerical heating with higher accuracy than PIC and has been recently proposed as a sub-cell method in PIC as a way of extending efficient legacy PIC codes to dense plasma problems, where numerical heating is a challenge. The idea is that sub-cell BIT can extend PIC by circumventing the need to follow the traditional rule of thumb of $\Delta x< \lambda_D$, which controls numerical heating in traditional explicit PIC codes. This has been demonstrated in 1D periodic test problems. To use high order explicit time stepping, BIT and BIT corrected PIC use a regularized force kernel. In the work on BIT corrected PIC, the regularization was found to have a negative impact near boundaries. To overcome this issue, a systematic approach to localization of the kernel, based on Taylor expansions, and rigorous error bounds for the error near a boundary were developed. This paper discusses the extension of BIT and BIT corrected PIC to non- periodic domains through the use of adaptive regularization to control the error near boundaries. The 1D virtual cathode problem is investigated. [Preview Abstract] |
Monday, November 17, 2008 10:33AM - 10:45AM |
BO5.00005: Exact energy conservation in hybrid meshless model/code Sergei A. Galkin Energy conservation is an important issue for both PIC and hybrid models. In hybrid codes the ions are treated kinetically and the electrons are described as a massless charge-neutralizing fluid. Our recently developed Particle-In-Cloud-Of-Points (PICOP) approach [1], which uses an adaptive meshless technique to compute electromagnetic fields on a cloud of computational points, is applied to a hybrid model. An exact energy conservation numerical scheme, which describes the interaction between geometrical space, where the electromagnetic fields are computed, and particle/velocity space, is presented. Having being utilized in a new PICOP hybrid code, the algorithm had demonstrated accurate energy conservation in the numerical simulation of two counter streaming plasma beams instability. [1] S. A. Galkin, B. P. Cluggish, J. S. Kim, S. Yu. Medvedev ``Advansed PICOP Algorithm with Adaptive Meshless Field Solver'', Published in the IEEE PPPS/ICOP 2007 Conference proceedings, pp. 1445-1448, Albuquerque, New Mexico, June 17-22, 2007. [Preview Abstract] |
Monday, November 17, 2008 10:45AM - 10:57AM |
BO5.00006: Conservative high order semi-Lagrangian method for the Vlasov Equation Jing-Mei Qiu, Andrew Christlieb We propose to solve Vlasov equation by a high order grid-based Eulerian approach. We design a class of conservative semi-Lagarangian numerical schemes that evolve point values, instead of integrated mass, for solving Vlasov equation with Strang splitting. Specifically, the proposed scheme uses Strang splitting to treat advection terms in different directions seperately; uses high order WENO (stands for weighted essentially non-oscillatory) reconstruction in each direction; and uses a conservative semi-Lagrangian scheme to update the point values of numerical solution. While the third, fifth, seventh and ninth order reconstructions are presented, the resulting scheme can be extended to arbitrary high order. As it is well known that WENO reconstructions have the advantages of being able to achieve high order accuracy in smooth part of the solution, while being able to capture sharp interface without oscillations. In our proposed scheme, we take those advantages. Moreover, the CFL time step restriction of regular finite difference or finite volume WENO scheme is removed, allowing cheaper and more flexible numerical realization. The quality of proposed methods are demonstrated through numerical experiments on basic test problems and on classical plasma simulation, such as Landau damping and two stream instability. Our numerical results strongly suggest the usage of high order methods in space. [Preview Abstract] |
Monday, November 17, 2008 10:57AM - 11:09AM |
BO5.00007: Lagrangian Method for Warm Electrostatic Plasmas Robert Krasny, Andrew Christlieb, Benjamin Ong A numerical method is presented for warm electrostatic plasmas based on the Lagrangian formulation of the Vlasov-Poisson equations. The charge flow map is represented by quadrilateral panels in phase space. The particle-particle force is regularized and panels are adaptively subdivided to resolve filamentation. Simulations are presented for the dynamics of collisionless electron beams. [Preview Abstract] |
Monday, November 17, 2008 11:09AM - 11:21AM |
BO5.00008: Electromagnetic particle simulation with adaptive mesh refinement technique for analysis of multi-scale phenomena Masanori Nunami, Yoshihiro Kajimura, Hideyuki Usui, Iku Shinohara We have developed a new electromagnetic particle code with adaptive mesh refinement (AMR) technique for numerical analysis of plasma phenomena which include multi-scale processes, for example, magnetic or inertial confinement plasma and space plasma and so on. The AMR technique is effective to simulate the phenomena which include local micro-scale processes and global macro-scale processes with high-resolution by subdividing and removing cells dynamically according to refinement criteria monitoring the characteristic length, for instance, Debye length. In development of the code, we have applied the AMR technique to particle-in-cell (PIC) method by using fully threaded tree structure [1] and parallelized the code by using Morton ordering method. [1] A. M. Khokhlov, J. Comput. Phys. 143, 519(1998). [Preview Abstract] |
Monday, November 17, 2008 11:21AM - 11:33AM |
BO5.00009: Numerical modeling of steady state MHD turbulence Jean C. Perez, Stanislav Boldyrev An effective numerical setting for simulating universal regimes of steady state MHD turbulence is presented. We show by means of high resolution numerical simulations that this setting allows one to investigate the most important features of weak and strong MHD turbulence, such as anisotropy, energy spectra, critical balance, dynamic alignment and the role of cross helicity. The relevance of the results to Solar Wind and Interstellar Medium (ISM) turbulence is discussed. [Preview Abstract] |
Monday, November 17, 2008 11:33AM - 11:45AM |
BO5.00010: Hamiltonian formulation of reduced Vlasov-Maxwell equations Cristel Chandre, Alain J. Brizard We present a Hamiltonian formulation of the reduced Vlasov- Maxwell equations which is expressed in terms of the macroscopic fields ${\bf D}$ and ${\bf H}$. These macroscopic fields are themselves expressed in terms of the Lie-transform operator $\exp \pounds_{{\cal S}}$ generated by the functional ${\cal S}$, where $\pounds_{{\cal S}}{\cal F} \equiv [{\cal S},\;{\cal F}]$ is expressed in terms of the Poisson bracket $[\;,\;]$ for the exact Vlasov-Maxwell equations. Hence, the polarization vector ${\bf P} \equiv ({\bf D} - {\bf E})/4\pi$ and the magnetization vector ${\bf M} \equiv ({\bf B} - {\bf H})/ 4\pi$ are defined in terms of the expressions $4\pi\,{\bf P} \equiv [{\cal S},\;{\bf E}] + \cdots$ and $4\pi\,{\bf M} \equiv -\; [{\cal S},\;{\bf B}] + \cdots$, where lowest-order terms yield dipole contributions. [Preview Abstract] |
Monday, November 17, 2008 11:45AM - 11:57AM |
BO5.00011: ABSTRACT WITHDRAWN |
Monday, November 17, 2008 11:57AM - 12:09PM |
BO5.00012: ABSTRACT WITHDRAWN |
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