@inbook {598,
title = {A data parallel pseudo-spectral semi-implicit magnetohydrodynamics code},
booktitle = {High-Performance Computing and Networking},
series = {Lecture Notes in Computer Science},
volume = {1225},
year = {1997},
pages = {190-199},
abstract = {The set of eight nonlinear partial differential equations of magnetohydrodynamics (MHD) is used for time dependent simulations of three-dimensional (3D) fluid flow in a magnetic field. A data parallel code is presented, which integrates the MHD equations in cylindrical geometry, combining a semi-implicit time integration with a pseudo-spectral treatment of the poloidal and longitudinal directions. The semi-implicit method is devised to lift the severe CFL-condition imposed by the fastest waves. In the radial direction, we use centered finite differences on a staggered mesh. Together with the semi-implicit method, this leads to tridiagonal systems to be solved for each 2D Fourier mode. The parallelism is required to fully resolve small-scale dynamics in MHD simulations at affordable CPU costs. It is obtained by performing the 2D FFTs in an embarrassingly parallel way, and by solving the tridiagonal systems using a pipelined elimination algorithm. We discuss the scalability of the full code for a CM-Fortran implementation.},
isbn = {0302-97433-540-62898-3},
author = {Keppens, R. and Poedts, S. and Meijer, P. M. and Goedbloed, J. P.},
editor = {Hertzberger, B. and Sloot, P.}
}
@article {516,
title = {Parallel magnetohydrodynamics on the Cray T3D},
journal = {Future Generation Computer Systems},
volume = {12},
number = {4},
year = {1996},
month = {Dec},
pages = {307-323},
abstract = {The equations of magnetohydrodynamics (MHD) are discussed in the framework of parallel computing. Both linear and nonlinear MHD models are addressed. Special attention is given to the parallellisation of the kernels of the existing sequential MHD codes. These kernels involve matrix-vector multiplications and dot products for the linear MHD calculations, and Fast Fourier Transforms and tri-diagonal systems solvers for the nonlinear MHD simulations. The parallel results, such as scaling with the number of processors and the performances, are given for a 256 node Gray T3D. Impressive results are obtained by combining the implicit shared memory shmem_get routine of Gray with single node BLAS routines.},
isbn = {0167-739X},
doi = {10.1016/0167-739x(95)00029-r},
author = {Meijer, P. M. and Poedts, S. and Goedbloed, J. P.}
}
@article {443,
title = {Frequency-Effects in Capacitively Coupled Radiofrequency Glow-Discharges - a Comparison between a 2-D Fluid Model and Experiments},
journal = {Ieee Transactions on Plasma Science},
volume = {23},
number = {4},
year = {1995},
month = {Aug},
pages = {644-649},
abstract = {The results of a 2-D fluid model for argon radiofrequency (RF) discharges in a closed cylindrical vacuum chamber are compared with experimental data from an amorphous silicon deposition reactor operated in argon. Good agreement is obtained for the relation between the DC autobias voltage and the dissipated power in the frequency range 40-100 MHz at pressures between 10 and 60 Pa. Scaling laws are presented for the dissipated power and for the ion fluxes toward the electrodes. These quantities are expressed in the DC bias voltage, the RF excitation frequency and the background pressure, Also the uniformity of the ion fluxes is studied. The model yields a linear relation between the applied RF voltage and the DC bias voltage. This relation depends only on the geometry of the discharge chamber and shows an offset.},
isbn = {0093-3813},
doi = {10.1109/27.467986},
author = {W. J. Goedheer and Meijer, P. M. and Bezemer, J. and Passchier, J. D. P. and van Sark, Wgjhm}
}
@article {409,
title = {Frequency-Effects in Capacitively Coupled Radiofrequency Glow-Discharges - a Comparison between Experiments and a 2-Dimensional Fluid Model},
journal = {Applied Physics Letters},
volume = {64},
number = {14},
year = {1994},
month = {Apr 4},
pages = {1780-1782},
abstract = {The results of a two-dimensional fluid model for argon rf discharges in a closed cylindrical vacuum chamber are compared with experimental data from an amorphous silicon deposition reactor. Good agreement is obtained for the relation between the dc autobias voltage and the dissipated power in the frequency range 50-100 MHz at pressures between 12 and 90 Pa. A scaling law is presented for the relation between the power, the dc bias voltage, the rf excitation frequency, and the background pressure. The model yields a linear relation between the applied rf voltage and the dc bias voltage. This relation depends only on the geometry of the discharge chamber and shows an offset.},
isbn = {0003-6951},
doi = {10.1063/1.111806},
author = {Meijer, P. M. and Passchier, J. D. P. and W. J. Goedheer and Bezemer, J. and van Sark, Wgjhm}
}
@article {307,
title = {The Bohm Criterion for Radiofrequency Discharges - a Numerical Verification Based on Poisson Equation},
journal = {Physics of Fluids B-Plasma Physics},
volume = {5},
number = {5},
year = {1993},
month = {May},
pages = {1656-1660},
abstract = {Recently it was shown that, by using the analysis of electrostatic waves entering the plasma-sheath edge, the direct-current (dc) Bohm criterion also holds for discharges under radio-frequency (rf) conditions. In this paper, the influence of Bohm{\textquoteright}s criterion on the sheath characteristics for generator frequencies much higher than the ion plasma frequency has been examined by means of an analysis which is based directly on the numerical solution of the Poisson equation. The present calculations indicate that for high rf voltages the time-dependent potential profile does not always increase monotonically, even if Bohm{\textquoteright}s criterion is fulfilled. However, as this nonmonotonic behavior does not lead to a more stringent Bohm criterion, the statement that the original dc Bohm criterion also holds in the high-frequency regime is confirmed. The calculations show further that the time-dependent sheath potential is almost completely modulated in the major part of the sheath and that the modulation drops abruptly to zero close to the plasma-sheath edge.},
isbn = {0899-8221},
doi = {10.1063/1.860798},
author = {Meijer, P. M. and W. J. Goedheer}
}
@article {309,
title = {Numerical-Simulation of Rf Discharges for Plasma Processing},
journal = {Journal of Nuclear Materials},
volume = {200},
number = {3},
year = {1993},
month = {May},
pages = {282-290},
abstract = {In this paper, we present kinetic models for radio-frequency glow discharges. Discussed are models for bulk electrons and positive ions based on the solution of the Boltzmann equation in a one-dimensional geometry. The resulting spatiotemporal behaviour of the electrons is used to compute the plasma emission, which is compared with experimental data. The model for the ions is used to solve the coupled dynamics of the electric field and the ion density in the whole discharge as well as the ion velocity distribution at the electrodes. The results are compared with experimental data and with the results of a Monte Carlo code.},
isbn = {0022-3115},
doi = {10.1016/0022-3115(93)90296-b},
author = {W. J. Goedheer and Meijer, P. M.}
}
@article {288,
title = {Calculation of the Ionization Rate and Electron-Transport Coefficients in an Argon Rf Discharge},
journal = {Physical Review A},
volume = {45},
number = {2},
year = {1992},
month = {Jan 15},
pages = {1098-1102},
abstract = {The behavior of an rf discharge can be modeled by using a fluid approach. For this approach, the values of the mobility and diffusion coefficients as well as the ionization rate are necessary. These values are often obtained by extrapolating the data of dc Townsend discharges. To check whether this is justified we computed the coefficients for electrons in an rf discharge by using a kinetic model based on a two-term approximation of the electron energy distribution function. The calculated electron mobility and electron diffusion coefficients agree reasonably well with the extrapolated Townsend values. Significant deviations were found between the extrapolated Townsend ionization rate and the computed rf ionization rate as a function of the reduced electric field.},
isbn = {1050-2947},
doi = {10.1103/PhysRevA.45.1098},
author = {Meijer, P. M. and W. J. Goedheer and Passchier, J. D. P.}
}
@article {262,
title = {The Bohm Criterion for Rf Discharges},
journal = {Physics of Fluids B-Plasma Physics},
volume = {3},
number = {8},
year = {1991},
month = {Aug},
pages = {1804-1806},
abstract = {The well-known dc Bohm criterion is extended to rf discharges. Both low- (omega-rf << omega-pi) and high-(omega-pi << omega-rf) frequency regimes are considered. For low frequencies, the dc Bohm criterion holds. This criterion states that the initial energy of the ions entering the sheath must exceed a limit in order to obtain a stable sheath. For high frequencies, a modified limit is derived, which is somewhat lower than that of the dc Bohm criterion. The resulting ion current density in a high-frequency sheath is only a few percent lower than that for the dc case.},
isbn = {0899-8221},
doi = {10.1063/1.859649},
author = {Meijer, P. M. and W. J. Goedheer}
}