The TREE method has been widely used for long-range interaction {\it 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.
Deep Dive into Parallel TREE code for two-component ultracold plasma analysis.
The TREE method has been widely used for long-range interaction {\it 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 ultr
For N-body problems in gravitational and electrostatic phenomena, significant computing resources are required due to the long range interactions. Despite advances in computing speed, it is still difficult to obtain sustainable results of realistically large configurations for many physical applications.
An ultracold plasma (UCP) is extensively studied in plasma physics, and is a typical example of long-range interactions for an open boundary. Experimentally, it is generated by photoionization of laser-cooled heavy atoms, and the system has a low temperature (T = µK to mK) compared to a conventional hot plasma (T = 10 3 to 10 7 K) [1]. By the initial disorder of particles, ions are heated, and active momentum transfer occurs between electrons and ions. We shall study the behavior of charged particles and the physical properties of ultracold neutral plasmas.
Studying electron-ion coupling relaxation, it was found that several millions of time steps are required for ultracold plasma evolution. This is a huge computing load, and the required time frame restricts the size of problems that can be considered. We first implemented a molecular dynamics (MD) method with all pair-wise calculations of long-range interactions. However, such an approach, while accurate, scales with the square of the number (N) of charged particles. Thus, it allowed only simulations of 10 3 to 10 4 particles over sufficiently long time [2,3,4]. In experiments, common sizes of ultracold plasmas are reported as more than 10 6 particles [1,5,6], and larger computing capacity is therefore imperative for realistic simulations.
Consequently, an approximate method for evaluating the electrostatic forces is necessary in order to accelerate computing speed and increase the simulation capacity. One of the candidates is the TREE method [7], which has been widely used in astrophysical problems due to its N log N scaling of the computing cost. The basic idea is that particle interactions are calculated explicitly at close range while effective, averaged properties are considered for far-field interactions. Gravitational problems have a potential of 1/r, where r is the distance between two points, and are similar to a Coulomb system. Therefore we will be able to apply all the methods, which have been developed for astrophysics, to electron and ion interactions.
In addition to the serial TREE method, a parallel version has been constructed in order to distribute the computing load and thereby accelerate computation. A specific shape of particle ensembles is considered from experimental data [5,6]: charged particles are distributed non-uniformly, but the overall shape is roughly symmetric. Particles are located inside of a certain spherical volume, and this confirms simple and balanced domain decompositions for parallel computing of ultracold neutral plasmas. With the help of dynamic memory management and effective TREE communication, a highly efficient parallel code has been built. Finally, we demonstrate that the program works well for ultracold plasma analysis. The following describes how the TREE method is implemented for a two-component plasma (TCP) simulation, and how it is parallelized. Basic applications are also presented.
For a fully ionized plasma, we describe the interactions as Coulomb forces between well-defined charged particles. However, because the electron mass is small compared to the ion, electrons will move faster than ions. This results in much smaller numerical time steps and longer relaxation times when simulating electrons compared to that of an ionic one-component plasma (OCP).
Since the dominating potential is Coulombic, each charged particle will interact with all the other charged particles and the interaction between particles cannot be truncated at a characteristic distance. Using a TREE method, this extensive calculation can be achieved efficiently, and the computing load can be balanced. The force on each charged particle is calculated from the interaction with the TREE. Velocity and position of particles are updated using velocity Verlet [8] time integration once the force field has been evaluated.
The Coulomb pair potential between two point-charges, separated by the distance r, is given by
where q i and q j are the fractional charges of particles i and j. e is the unit charge, and ǫ 0 is the vacuum permittivity. For the same kind of particles (electron-electron and ion-ion), the forces are repulsive whereas attractive forces are present for electron-ion interactions. Consequently, the bare Coulomb potential will result in an attractive singularity for the electron-ion pair at close distance (r ≈ 0). However, quantum diffraction between electrons and ions in physical systems prevents such point wise collisions, thus requiring a modification to the bare Coulomb potential. Several modified Coulomb interactions have been proposed [9,10,11]; we implemented the Kelbg potential:
where λ ei is the thermal de Broglie
…(Full text truncated)…
This content is AI-processed based on ArXiv data.
