The menu bar, located at the top of the main window, provides the user with a variety of options.

**File****Open**--- load a saved configuration. Files created by`TrapApp`generally have the extension`.TRP`.**Save**--- save a configuration to the*most recently referred-to*file name.*Caution*: be careful not to accidentally over-write files. Use the`Save As...`option if you need to edit the file name. The saved file includes up to four lines of user comments; specifications of the trap; mass, charge, and interaction type of the particles; time step; time; number of steps per data collection; particle positions and all pertinent derivatives of particle positions (up to fifth-order when the Gear algorithm is used); damping parameters; specifications for interaction with the reservoir; last initialization method for position and velocity; data to collect; boundary conditions.**Save As**--- save a configuration (as above) under the specified file name (the user is encouraged to use the extension`.TRP`).**PrintWindow****Export to Mathematica**--- export the position coordinates for inspection of the configuration's geometry in a mathematical package such as*Mathematica*, which has a nice routine for three-dimensional rotation.**Quit**

**Parameters****Trap Type...**--- allows the user to select trap type and to modify parameters relevant to the trap selection.**Paul**trap parameters: the dimensions (m) of the trap, , ; magnitude (Volts) of the static potential, ; amplitude (Volts) of the oscillating potential, ; frequency (Hz) of the oscillating potential.**Penning**trap parameters: the dimensions (m) of the trap, , ; magnitude (Volts) of the static potential, ; amplitude (Tesla) of the axial magnetic field, .**No Trap**parameters: user specifies side length of the box in reduced units (m for all simulations except those involving Lennard-Jones interaction.). This ``side length'' is pertinent for simulations with boundary conditions, e.g., periodic boundaries or hard walls.

**Particle...**--- allows user to specify number of particles, mass per particle, and charge per particle.**Numerical**- specify finite difference algorithm: fifth-order Gear predictor-corrector or velocity-Verlet (Sec. )
- choose method for scaling the time
step (Sec. ):
- scale by Einstein frequency
- choose
**dt**as a fraction of the micromotion (for Paul trap simulation); cyclotron motion (for Penning trap simulation); or as standard Lennard-Jones time step, in reduced units, where energy unit and length unit are defined by the depth and radial separation of the potential minima and mass unit corresponds to the mass of a particle - user-specified
**dt**which remains constant when simulation conditions are changed

- explicitly change
**dt** - set the number of time
steps,
`steps per data point`, between data collections.

**Speed**--- specify the number of milliseconds between calls to the timer which prompts ``propagation'' of simulation.**Damping**--- select viscous drag damping or select rescaling of velocities for equilibration at constant temperature (Sec. ). Note that viscous drag can be selected to act*only*on the axial component of velocity, rather than on all velocity components.**Interaction Type**--- particles may interact via**Coulomb**repulsion,**Lennard-Jones**interaction, a**User-Defined**parsed force, or there may be**No Interaction**.**System-Reservoir**--- specify parameters relating to collision with background gas: turn collisions on/off; set the temperature of the reservoir gas; set the mean time per particle between collisions (Sec. ).**Reduced Units...**--- displays conversion factors from reduced units to physical quantities (Sec. ).**Two-Ion Equilibrium Sep...**--- displays the equilibrium separation, as predicted by the theory of Sec. , of two ions in a Paul trap; valid only when the current simulation involves a Paul trap.

**Initial****Position**--- initial positions may be assigned to describe a random distribution within an origin-centered cube, a Gaussian distribution with user-specified variance, or a face-centered cubic lattice (Sec. ).**Velocity**--- velocities may be assigned according to the Maxwell-Boltzmann Speed Distribution at a given temperature, randomly assigned and scaled to a given temperature, or zeroed for zero kinetic energy (Sec. ).**Zero Forces**--- this option zeroes higher-order derivatives of Gear algorithm.

**Particle Data****Select Data to Collect**--- the axial,**x**-, and/or radial positions may be monitored ``continuously'' or strobed at user-specified intervals. The**Strobe precision**parameter sets width of the strobing ``time window'' as a fraction of the strobe period. The final particle data option is to collect a Poincare plot of the tagged ion's radial position when radial momentum is zero.**Inspect Graph**--- this option spawns a pop-up menu on the ``particle graph'' (upper right graph). The options available on this pop-up menu, which is also accessible by clicking the right mouse button on the particle graph, are discussed in Sec. .**Clear Data**--- clears all data storage objects associated with particle data options.

**State Data****Select Data to Collect****Instantaneous**,**Running Average**, and**Strobe**d data vectors may be collected for the items below. The running average option calculates the average value of a parameter over the interval defined by , where is the present time and is the**Time interval for running average**.**Total Energy****Potential Energy**--- the check box beside this selection allows the user to toggle between monitoring the*total*potential energy, i.e., potential energy associated with the trap and that associated with particle interactions, and the*interaction*potential energy only.**Kinetic Energy****x**,**y**,**z**, Kinetic Components**Mean Separation**--- average separation between pairs of particles.**rms Distance from Origin****Interaction Coupling**--- coupling, , is defined as the ratio of interaction potential energy to average kinetic energy. The ``instantaneous'' option uses instantaneous potential energy and average kinetic energy, while the ``running average'' option uses running averages of both interaction potential and kinetic energy.

- Distribution data may be
collected continuously or at time intervals whose width and frequency are defined by the strobe precision and strobe frequency, respectively. The
resolution of distribution functions is determined by partitioning the
length from
**0**to**maximum distance**into the number of intervals defined by**number of bins**. The following distributions are available:**Total Displacement from Center of Trap**--- a distribution of the ions'*total*distances from the origin.**Radial Displacement from Center of Trap**--- a distribution of the ions'*radial*distances from the origin.**Axial Displacement from Center of Trap**--- a distribution of the ions'*axial*distances from the origin.

**Heat Capacity**--- although this parameter is usually applied to a macroscopic system, statistical application of its formal definition to a microscopic collection of particles can yield insight into phase transitions since heat capacity often undergoes large fluctuations when the state of a system changes abruptly. The mathematical form of heat capacity, , used in`TrapApp`is derived from the expression:from which we obtain:

**Inspect Graph**--- this option spawns a pop-up menu on the ``state graph'' (lower right graph). The options available on this pop-up menu, which is also accessable by clicking the right mouse button on the state graph, are discussed in Sec. .**Clear State Data**--- clears all data storage objects associated with state data options.

**Bounds****No Boundaries**--- no limit is imposed on spatial coordinates.**Hard Walls**--- when a particle ``hits'' a trap wall (or a box wall, in the case of**No Trap**), it undergoes an elastic collision.**Periodic**--- valid only when**No Trap**is selected, this option imposes periodic boundaries on spatial coordinates and on interaction forces (particles interact with ``nearest neighbors,'' i.e., those particles within a distance , where**L**is half the side length of the box).[19,1] While this option fails for the long-range Coulomb force, it is a viable option for the short-range Lennard-Jones interaction.**Replace Escaped Particles**--- when a particle escapes the boundaries, a new particle is created and its velocity and position are initialized according to the most recently selected initialization methods.**Ignore Escaped Particles**--- particles which escape the boundaries of the electromagnetic trap (or the ``box'', in the case of**No Trap**), are deleted.

**Help**

Fri May 12 10:36:01 EDT 1995