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| @}G ,hh1=1=O ig5{.2 tw]π)VCHEʟ2QY)x9rŉk8J5CONTENTSMENU ITEMSFileOpen FileSave FileSave As...Print WindowExport to MathematicaQuitParametersTrap Type...Paul TrapPenning TrapNo trapParticle...Numerical%=i KCIAL!r+IX8q0Ku
aJҀ!sObP?d m\"SpeedInteraction TypeSystem ReservoirReduced Units...Two-Ion Equilibrium Sep...InitializationPositionVelocityZero ForcesParticle DataSelect Particle Data to CollectInspect Particle GraphClear Particle Data*O~ U2vyl\u'J+OpDc㣟tL"sl:(Ԁ9BVState DataSelect State Data to CollectInspect State GraphClear State DataBoundariesNo BoundariesHard WallsPeriodic BoundariesReplace Escaped ParticlesIgnore Escaped ParticlesBUTTONSRun ButtonStop ButtonClear ButtonBiH ` -}Ramp ButtonsSLIDERSMOUSE CLICKS ON GRAPH OBJECTS5~=1=File, &UFileOptions under the file menu item are Open, Save, Save As..., Print Window, Export to Mathematica, and Quit.Each of these sub-menu items has its own help screen: =M1MOpen Filep7 >Open FileLoad a saved configuration. Files created by TrapApp.EXE generally have the extension .TRP.: M. 1M. ASave File;iF ZSave FileSave 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* particles positions and all pertinent derivitives of particles positions (up to fifth-order when Gear algorithm is used). A- (W* damping parameters* specifications for interaction with reservoir* last initialization method for position and velocity* data to collect* boundary conditions8iy1yL
Save AsAL
7 <9Save As...Save a configuration (same format as with Save option) under the specified file name.The user is encouraged to use the extension .TRP.=y
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PPrint WindowL
P2 2+Print WindowNot yet implemented. This option, if functional, would print (to a printer or to a .PS file) the main window of the simulation.F
1YExport to MathematicaP2 2Export to MathematicaExports the position coordinates of the ions for inspection of the configuration`s geometry in a mathematical package such as Mathematica, which has a nice routine for three-dimensional rotation.51Y@Quito>Y@1 2|Y@QuitGracefully exits TrapApp.EXE. (Have a nice day.);
@1@WBParametersYY@WBj ParametersThis menu item allows the user to set the parameters which control the content and execution of the simulation.Options available under the Parameters menu item are Trap Type..., Particle..., Numerical, Speed, Damping, Interaction Type, System Reservoir, Reduced Units, and Two-Ion Equilibrium Separation...: @B1 B\CTrap TypeWB\C, &?Trap TypeAllows the user to select the type of trap (i.e., Paul trap, Penning trap, or no trap) and to modify parameters relevant to the trap selection.: BC1
CDPaul Traph\CDL f9Paul TrapSelect a Paul trap simulation and set the Paul Trap parameters: * dimensions (mm) of the electromagnetic trap; * magnitude (Volts) of the static potential, U0;* magnitude of the, oscillating potential V0;* frequency (Hz) of the oscillating potential.=C;E1};E{FPenning Trap@D{FD VPenning TrapSelect a Penning trap simulation and set the Penning Trap parameters: * dimensions (mm) of the electromagnetic trap; * magnitude (Volts) of the static potential, U0;* magnitude of the axially-aligned magnetic field, Bz;8;EF14FGNo Trap{FG> J}No TrapSet the side length of the box associated with the No Trap option. This box is relevant when boundary conditions are implemented (i.e., hard walls, periodic boundaries).9FG1
GHParticleGHD V'Particle...Set parameters describing simulated particles:* number of particles* mass per particle (amu)* charge (e) per particle: GH1 HNNumericalx%HqKS tKNumericalSet the parameters which control numerical methods of the simulation: * finite difference method : velocity-Verlet and fifth-order Gear predictor-corrector algorithm are available. Gear algorithm is recommended for superior stability and speed.* choose method for scaling the time step, dt:** Einstein frequency scaling option sets dt to a fraction of the Einstein period, where the Einstein frequency is calculated as the root-mean-squared average acceleration divided by the root mean squared average velocity.>HM, &%** micromotion option sets dt to a fraction of the period associated with the fast motion defined by the trap or by the interaction type, in the case of Lennard-Jones simulations. For Paul trap simulations, the fast frequency is that of the oscillating potential; for Penning trap simulations, the fast motion is the cyclotron orbit; for Lennard-Jones simulations, the time step is set to 0.005 reduced time units, and the reduced units are set according to the energy and distance parameters which define the potential.qKN, &** user-specified option ensures that the time step remains unchanged, even when the simulation parameters are changed. The Einstein- and micromotion-scaled time steps are re-calculated each time the simulation parameters change.6MN1NOSpeedzNO+ &SpeedSpecify the number of milliseconds between calls to the timer which prompts the propagation of the simulation.AN1a,Interaction TypeOO O,R rInteraction TypeParticles may interact through the following mechanisms:* Coulomb replusion: |F(r)|=1/(4p(e0)r2) where e0 is the permittivity of free space.* Lennard-Jones interaction: F(r)=24E[(s/r)^7-2(s/r)^13], where E is the depth of the potential well and s is the separation at which potential energy is a minima..* User-Defined: simulates a user-defined parsed force.* No Interaction particles do not interact with each other.Am1nmSystem Reservoir-,2 2System-ReservoirSpecify parameters relating to simulation of Monte Carlo collisions with background gas:* turn collisions on/off (The absolute absence of collisions corresponds to a simulation of point particles in a perfect vacuum.)* set the temperature of the reservoir gas. Each time a collision occurs, the participating particles velocity is reassigned according to Maxwell-Boltzmann statistics at the temperature of the background gas.* set the mean time per particle between collisions.Amۄ1ۄReduced Units.... *QReduced Units...Because the simulation involves inconveniently small physical values in terms of SI units, quantities are expressed in reduced units which scale values to easier-to-deal-with magnitudes. The Reduced Units menu item displays conversion factors from fundamental reduced units to physical quantities. All other conversion factors are easily derivable in terms of this basis set of conversion factors.Kۄ1LTwo-Ion Equilibrium Sep...PL> J%Two-Ion Equilibrium Sep...Displays the equilibrium separation, as predicted by an approximation which assumes small values of the Mathieu parameters (a, q), of two ions in a Paul trap. (This option is not valid for simulations which do not involve Paul traps.)?1EInitializationL, &InitializationThe user may assign initial conditions according to algorithms for velocity and position assignment. (Alternately, the user may take as initial conditions the final configuration of a saved file).9ʉ1ʉzPositiongzI `PositionThe three methods available for position initialization are:* random distribution within a cube centered at the origin. (The size of the cube is specified by the user).* gaussian distribution whose variance is set by the user.* a face-centered-cubic lattice (fcc) centered at the origin. The lattice parameter (spacing between consecutive vertices in the lattice) may be explicitly set by the user or it may be calculated by TrapApp to approximate a charge density for which potential energy of the charge distribution is of the same order of magnitude as a user-specified temperature.9ʉ1"Velocityo+z"D VWVelocityThe three methods available for velocity initialization are:* Maxwell-Boltzmann Speed Distribution at a desired temperature.* random velocity assigment scaled such that total kinetic energy corresponds to desired temperature.* zero velocities to remove all kinetic energy.<^1^ƎZero Forcesh="Ǝ+ &zZero ForcesSets higher-order Gear derivitives to zero.>
^1tFParticle DataHƎP n Particle DataThis menu item allows the user to make changes regarding:* which particle-related (i.e., pertaining to the tagged (black) particle) data are collectedƎ* which particle-related data are displayed on the particle (upper-right) analysis graph.Note that the tasks of selecting which data to collect and which data to display are separate. This separation of tasks allows the user to collect a large amount of data without cluttering the screen and/or slowing the simulation by unnecessarily graphing parameters which need not be continuously monitored.zF$ A related command is the double mouse-click or right-mouse-button-down on the particle (upper right) analysis graph. P17Select Particle Data to Collect$Fd
Select Particle Data to Collect* The axial, x-, and/or radial positions may be monitored continuously or strobed at user-specified intervals.* TrapApp can collect a Poincare plot of the tagged (black) ions radial position when radial momentum equals zeroThe Strobe precision parameter sets the width of the window during which strobed data are collected. Data will be collected at: (N/f - delT) < time < (N/f + delT)}S7* $where N is an integer, f is the strobe frequency, and delT=strobe precision/fG~1~Inspect Particle Graphn27< FeInspect Particle GraphThis option spawns a pop-up menu on the particle analysis graph. The options available on this pop-up menu, which is also accessable by double-clicking or pressing right mouse button on particle graph, allow user to:* specify the Graph Type* Inspect Scale of the graphD~0160"Clear Particle Data", &Clear Particle DataClears all data storage objects associated with particle data options. The option is especially useful when the simulation gets slow after long periods of collecting data.;
0]16]XState Data`"P n! State DataThis menu item allows the user to make changes regarding:* which state-related data are collected* which particle-related data are displayed on the particle (lower-right) analysis graph.Note that the tasks of selecting which data to collect and which data to display are separate. This separation of tasks allows the user to collect a large amount of data without cluttering the screen and/or slowing the simulation by unnecessarily graphing parameters which need not be continuously monitored.w]X$ A related command is the double mouse-click or right-mouse-button-down on the state (lower right) analysis graph. M1JSelect State Data to Collect-X] Select State Data to Collect* Instantaneous, Running Average, and Strobed data may be collected for the items below:** Total Energy (potential(trap) + potential(particle interaction) + kinetic)** Potential Energy--- the check box beside this selection allows the user to toggle between monitoring the total potential energy (potential (trap) + potential (interaction)) or only the potential energy associated with particle interactions.*ph U** Kinetic Energy** x-, y-, z-, Kinetic Components** Mean Separation = average separation between pairs of particles; this parameters is labelled D on the state graph.** rms Distance from Origin** Interaction Coupling--- coupling is defined as the ratio of interaction potential energy to average kinetic energy. The instantaneous coupling option uses instantaneous potential energy and running average kinetic energy, pXwhile the running average coupling option uses running averages of potential and kinetic energies.@ N* Distribution data may be collected continuosly or at time intervals whose width and frequency are defined by the strobe precision and strobe frequency, respectively. The range of distribution fucntions runs from 0 to the user-specified parameter maximum distance. The resolution of distribution functions is determined by partitioning the range into the number of intervals specified by number of bins. The following distributions are available:pS tq** 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 z-axis** Axial Displacement from Center of Trap--- a distribution of the ions` axial distances from the z=0 plane** Pair Distribution--- a distribution of the distances between all possible pairs of particles.+ $* 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, Cv, used in TrapApp is derived from the expression:-SQR()=(2/(3N))2[1-(3kN/(2Cv)]from which we obtain:J' Cv=k/[1-(/SQR()-(2\(3N))]where k is Boltzmanns constant, N is the number of particles, and KE is kinetic energy. D1Inspect State Graphd(J< FQInspect State DataThis option spawns a pop-up menu on the state analysis graph. The options available on this pop-up menu, which is also accessable by double-clicking or pressing right mouse button on state graph, allow user to:* specify the Graph Type* Inspect Scale of the graphA3 103 "
Clear State Data"
, &Clear State DataClears all data storage objects associated with particle data options. The option is especially useful when the simulation gets slow after long periods of collecting data.;
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^2 2BoundariesAllows the user to implement various types of boundary conditions. The fastest boundary condition to implement is No Boundaries, since it requires no thinking on the part of the computer.>
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6 :No BoundariesWhen No Boundaries is selected, no limit is explicitly imposed on spatial coordinates of the ions.This option is the fastest to implement, since it requires no additional computation.This boundary type is usually appropriate for simulations of trapped ions, since the trajectories of the ions are spatially confined due to the forces induced by the trap.;
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{8 >uHard WallsWhen the Hard Walls boundary is chosen, a particle undergoes an elastic collision whenever it hits a trap wall or , in the case of a No Trap simulation, a box wall. D
1w#+APeriodic Boundaries`{+AH ^1Periodic BoundariesPeriodic boundaries are valid only when No Trap is selected. (Hyperbolic traps are not conducive to periodic boundaries!)This option imposes periodic boundaries on spatial coordinates and on interaction forces. Partic+A{les interact with nearest neighbors, i.e., those particles within a distance of SQRT(3*L*L*L), where L is half of the side length of the box.While the periodic boundaries fail for the long-range Coulomb forces, it is a viable option for the short-range Lennard-Jones interaction.JuA1 $uAKCReplace Escaped Particles+AKCC T'Replace Escaped ParticlesWhen a particle escapes the boundaries imposed by the electromagnetic trap (Paul or Penning simulations) or the box (for a No Trap simulation), a new particle is created. The new particle`s velocity and position are initialized according to the most recently-selected initialization methods, i.e., the methods under the Initialization menu item which are checked.IuAC1<%CDIgnore Escaped ParticlesKCD= HmIgnore Escaped ParticlesParticles which escape the boundaries of the electromagnetic trap (Paul or Penning simulations) or the box (for a No Trap simulation) are deleted.;
CD1&DERun ButtonDE+ $ARun ButtonPropagate the simulation forward in time via the selected finite difference algorithm (fifth-order Gear predictor-corrector or velocity-Verlet).<DE17'EFStop ButtonEF3 4Stop ButtonPause the simulation.Its a good idea to Stop the simulation before changing parameters or performing any other mouse actions which require much effort on the part of the computer.=EG1?(GHClear ButtonFH9 @Clear ButtonClear all data, zero forces, clear graphs, and reset the time to 0.The Clear option does not reinitialize the configuration. It only provides the simulation with a clean slate.=G@H1z)@H}JRamp Buttons=H}JF ZRamp ButtonsThe Ramp Buttons allow the user to change, when applicable to the simulation:* the amplitude of the alternating voltage/magnetic field (V0/Bz)* the magnitude of the static electric potential (U0)* the temperature (in Kelvin) of the background gas which makes up the System Reservoir.The user specifies the intial and final values of the parameter and the time interval over which to change the parameter. The program linearly changes the selected parameter accordingly.8@HJ19*JMSLIDERSH}JLY SLIDERSThe sliders, located between the [Run]/[Stop]/[Clear] buttons and the ramping buttons, are for displaying and altering the magnitude of:* applied oscillating potential/magnetic field (V0/Bz)* the magnitude of the static electric potential (U0)* the temperature of the background gas which constitutes the system reservoir. Note: changing this temperature will only affect the simulation if the System Reservoir interaction of Monte Carlo collisions is turned on.JM% )Operate sliders by dragging the slider tab with the mouse or by clicking on the associated numeric field and entering the precise value desired.NLN1+N9MOUSE CLICKS ON GRAPH OBJECTSmMŀH ^ MOUSE CLICKS ON GRAPH OBJECTSThe analysis graphs (on the right side of the main window) and th particle view graph (upper left graph) are independent objects which recognize and respond to mouse clicks.Holding the left mouse button down in any of these graph objects displays a coordinate reader in the lower left corner of the respective graph. The coordinate reader is userful for reading numeric values from graphs.DouNŀMble-clicking or clicking the right mouse button prompts a pop-up menu in the upper left corner of the graph. The State Graph and the Particle Graph pop-up menus allow the user to:ENqg * choose the Graph Type** Time Series--- appropriate data may be graphed as a function of time. If the user attempts to graph an item for which data is not being collected, TrapApp graciously ignores the command.** Phase Space--- allows the user to graph an arbitrary data vector y vs. an arbitrary data vector x.** FFT--- performs a Fast Fourier Transform on the selected data vector.** option available only for the Particle Graph: Poincare: r when r-momentum=0--- Plots the radial position of the tagged ion when its radial momentum is zero.ŀk U** options available only for the State Graph: Pair Distribution, Total Displacement Distribution, Radial Displacement Distribution, Axial (z) Displacement Distribtution--- these distribution functions are explained under the State Data menu item.* Inspect Sacle--- user may set the scale and axes tics for the graph object. The graph object may also be cloned; a clonded graph object is an independent window with its own inspector for setting the scale. Alternately, the graph object may be copied to an archive, in which case its data is saved in a memory buffer for recall when the user selects Paste From Archive from the Inspect Scale option.eq9N jThe Trap View graph (upper left corner) has the following options:* Projection--- project particles positions onto the XY, XZ, or YZ plane.* Inspect Scale...--- customize the scale of the window or clone the graph.* Tag Particle--- tag a particle by clicking on it. The tagged particle is the one monitored by Particle Data selections.1j1W,j&9# 1j1-0Helv7JF~s$+p*VJ3V,+
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