...Fortran
Project conducted as part of the 1994 Research Experiences for Undergraduates (REU) Program Using High-Performance Computing conducted by the Northeast Parallel Architectures Center (NPAC) at Syracuse University. The National Science Foundation provides primary funding for the 1994 NPAC REU Program, through NSF Grant CDA-9200577. Additional funding is provided by the Vice President for Research and Computing, the College of Engineering and Computer Science, the College of the Arts and Sciences, the Graduate School, and NPAC, Syracuse University.
...Fischer
Research Apprentice, 1994 NPAC REU Program; email: sfischer@npac.syr.edu; Physics Major, Davidson College; email: sfisher@phyhost.davidson.edu
...Hawick
Research Scientist, NPAC; email: hawick@npac.syr.edu
...Coddington
Research Scientist, NPAC; email: paulc@npac.syr.edu
...difference
An electric potential difference between two points is the amount of work per unit charge which must be done to move the charge through the electric field that exists between the two points.
...gradient
The gradient is a vector which indicates the rate of change of a function in the , , and directions.
...radial
The radial component is the distance from the origin in the x, y plane: .
...chaotically
Chaotic motion is characterized by sensitive dependence on initial conditions, which renders it unpredictable in the long run; unlike periodic motion, chaotic motion never repeats itself.
...region
This ``certain region'' corresponds to region A of the Mathieu stability regime, where . For more detail, see section 5.2 or refer to [3].
...field
Fields of up to 5 Tesla, which is approximately 50000 times stronger than the earth's magnetic field, have been used [4].
...interactions
The justification for expressing the motion as the sum of cyclotron and Coulomb behaviors is that, in the strong -field limit, the two motions are decoupled [6].
...machine
Implementation of a ``tree-based force calculation" can reduce computational time to on a sequential machine; this method involves an adjustable error term which controls the tradeoff between speed and accuracy [8][2].
...magnitudes
Allen and Tildesley [1] and Haile [9] provide excellent explanations of reduced units.
...incorrect
Methods for assessing accuracy will be discussed in section 5.
...step
Recall that time is expressed in reduced units where s.
...nonlinear
The Coulomb interaction provides a nonlinear coupling term.
...ion
When more that one ion is considered, there is an additional term corresponding to Coulomb interaction.
...analysis
Fourier analysis allows for representation of a time-dependent signal in the frequency domain; the time-dependent signal is decomposed into a sum of frequencies.
...temperature
At this stage of the simulation, there is not sufficient damping to keep the ions cold, and plots of kinetic energy reflect higher temperatures than would be found in a laboratory. However, ions in the unstable regions of the Mathieu stability plot escape promptly, suggesting that even cold ions would escape.
...intrinsic
A reductional intrinsic function is a ``built-in'' Fortran function for efficient array manipulation.
...operations
...such as those involving FORALL constructs with reductional intrinsic functions or INDEPENDENT DO loops.

sfischer@
Thu Aug 11 20:43:34 EDT 1994