TY - CHAP
T1 - A data parallel pseudo-spectral semi-implicit magnetohydrodynamics code
T2 - High-Performance Computing and Networking
Y1 - 1997
A1 - Keppens, R.
A1 - Poedts, S.
A1 - Meijer, P. M.
A1 - Goedbloed, J. P.
ED - Hertzberger, B.
ED - Sloot, P.
AB - 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.
JF - High-Performance Computing and Networking
T3 - Lecture Notes in Computer Science
VL - 1225
SN - 0302-97433-540-62898-3
U5 - aae040c05d2543fd123eddd4e1a02f4e
ER -
TY - JOUR
T1 - Parallel magnetohydrodynamics on the Cray T3D
JF - Future Generation Computer Systems
Y1 - 1996
A1 - Meijer, P. M.
A1 - Poedts, S.
A1 - Goedbloed, J. P.
AB - 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.
VL - 12
SN - 0167-739X
U5 - 5449ea2dbdd4287f04c26f46c6700d36
ER -
TY - JOUR
T1 - Frequency-Effects in Capacitively Coupled Radiofrequency Glow-Discharges - a Comparison between a 2-D Fluid Model and Experiments
JF - Ieee Transactions on Plasma Science
Y1 - 1995
A1 - W. J. Goedheer
A1 - Meijer, P. M.
A1 - Bezemer, J.
A1 - Passchier, J. D. P.
A1 - van Sark, Wgjhm
AB - 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.
VL - 23
SN - 0093-3813
U5 - 89a98ecc332a29c3ec746647a0df4326
ER -
TY - JOUR
T1 - Frequency-Effects in Capacitively Coupled Radiofrequency Glow-Discharges - a Comparison between Experiments and a 2-Dimensional Fluid Model
JF - Applied Physics Letters
Y1 - 1994
A1 - Meijer, P. M.
A1 - Passchier, J. D. P.
A1 - W. J. Goedheer
A1 - Bezemer, J.
A1 - van Sark, Wgjhm
AB - 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.
VL - 64
SN - 0003-6951
U5 - dfa40e16998d474f2c47100d79ca0967
ER -
TY - JOUR
T1 - The Bohm Criterion for Radiofrequency Discharges - a Numerical Verification Based on Poisson Equation
JF - Physics of Fluids B-Plasma Physics
Y1 - 1993
A1 - Meijer, P. M.
A1 - W. J. Goedheer
AB - 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'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'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.
VL - 5
SN - 0899-8221
U5 - 0d0ca6e27bdde72a9b55f6382bfd5295
ER -
TY - JOUR
T1 - Numerical-Simulation of Rf Discharges for Plasma Processing
JF - Journal of Nuclear Materials
Y1 - 1993
A1 - W. J. Goedheer
A1 - Meijer, P. M.
AB - 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.
VL - 200
SN - 0022-3115
U5 - c3a5026c0053736823f40132656e3e3f
ER -
TY - JOUR
T1 - Calculation of the Ionization Rate and Electron-Transport Coefficients in an Argon Rf Discharge
JF - Physical Review A
Y1 - 1992
A1 - Meijer, P. M.
A1 - W. J. Goedheer
A1 - Passchier, J. D. P.
AB - 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.
VL - 45
SN - 1050-2947
U5 - 2efc5aa0cf54dfdbd9108e60a90d9435
ER -
TY - JOUR
T1 - The Bohm Criterion for Rf Discharges
JF - Physics of Fluids B-Plasma Physics
Y1 - 1991
A1 - Meijer, P. M.
A1 - W. J. Goedheer
AB - 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.
VL - 3
SN - 0899-8221
U5 - ab0bfa7ba3505173155329bddc739e3a
ER -