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Table of Contents

• 1. Tracking
  • 1.1. Track Mode
  • 1.2. Track Particles
  • 1.3. STATISTICAL-ERRORS

1. Tracking

Table 1. Commands accepted in Tracking Mode

Command	Purpose
TRACK	Enter tracking mode
LINE	Label of LINE or SEQUENCE
BEAM	Label of BEAM
T0	Initial time [s]
DT	Array of time step sizes for tracking [s]
MAXSTEPS	Array of maximal number of time steps
ZSTART	z-location [m], from where to run simulation
ZSTOP	Array of z-location [m], after which the simulation switches to the next set of DT, MAXSTEPS and ZSTOP
STEPSPERTURN	Number of time steps per revolution period
TIMEINTEGRATOR	Defines the time integrator used in OPAL-cycl
NNB	Number of neighbouring bunches in OPAL-cycl
name=expression	Parameter relation
RUN	Run particles for specified number of turns or steps
ENDTRACK	Leave tracking mode

1.1. Track Mode

Before starting to track, a beam line and a beam must be selected. The time step (DT) and the maximal steps to track (MAXSTEPS) or ZSTOP should be set. This command causes OPAL to enter "tracking mode", in which it accepts only the track commands see Table 1. In order to perform several tracks, specify arrays of parameter in DT, MAXSTEPS and ZSTOP. This can be used to change the time step manually.

The attributes of the command are:

LINE

The label of a preceding LINE (no default).

BEAM

The named BEAM command defines the particle mass, charge and reference momentum (default: UNNAMED_BEAM).

T0

The initial time [s] of the simulation, its default value is 0.

DT

Array of time step sizes for tracking, default length of the array is 1 and its only value is 1 ps.

MAXSTEPS

Array of maximal number of time steps, default length of the array is 1 and its only value is 10.

ZSTART

Initial position of the reference particle along the reference trajectory, default position is 0.0 m.

ZSTOP

Array of z-locations [m], default length of the array is 1 and its only value is 1E6 [m]. The simulation switches to the next set, i+1, of DT, MAXSTEPS and ZSTOP if either it has been tracking with the current set for more than \mathrm{MAXSTEPS}_i steps or the mean position has reached a z-position larger than \mathrm{ZSTOP}_i. If set i is the last set of the array then the simulation stops.

TIMEINTEGRATOR

Define the time integrator. Currently only available in OPAL-cycl. The valid options are RK-4, LF-2 and MTS:

• RK-4 the fourth-order Runge-Kutta integrator. This is the default integrator for OPAL-cycl.

• LF-2 the second-order Boris-Buneman (leapfrog-like) integrator. Currently, LF-2 is only available for multi-particles with/without space charge. For single particle tracking and tune calculations, use the RK-4 for the time being.

• MTS the multiple-time-stepping integrator. Considering that the space charge fields change much slower than the external fields in cyclotrons, the space charge can be calculated less frequently than the external field interpolation, so as to reduce time to solution. The outer step (determined by STEPSPERTURN) is used to integrate space charge effects. A constant number of sub-steps per outer step is used to query external fields and to move the particles. The number of sub-steps can be set with the option MTSSUBSTEPS and its default value is 1. When using this integrator, the input file has to be rewritten in the units of the outer step. For example, extracts of the input file suited for LF-2 or RK-4 read

  Option, PSDUMPFREQ=100;
  Option, REPARTFREQ=20;
  Option, SPTDUMPFREQ=50;
  Option, VERSION=10600;
  REAL turns=5;
  REAL nstep=3000;
  TRACK, LINE=l1, BEAM=beam1, MAXSTEPS=nstep*turns, STEPSPERTURN=nstep,
  TIMEINTEGRATOR="LF-2";
      RUN, METHOD = "CYCLOTRON-T", BEAM=beam1, FIELDSOLVER=Fs1, DISTRIBUTION=Dist1;
  ENDTRACK;

  and should be transformed to

  Option, MTSSUBSTEPS=10;
  Option, PSDUMPFREQ=10;
  Option, REPARTFREQ=2;
  Option, SPTDUMPFREQ=5;
  Option, VERSION=10600;
  REAL turns=5;
  REAL nstep=300;
  TRACK, LINE=l1, BEAM=beam1, MAXSTEPS=nstep*turns, STEPSPERTURN=nstep,
  TIMEINTEGRATOR="MTS";
      RUN, METHOD = "CYCLOTRON-T", BEAM=beam1, FIELDSOLVER=Fs1, DISTRIBUTION=Dist1;
  ENDTRACK;

  In general all step quantities should be divided by MTSSUBSTEPS.

  In our first experiments on PSI injector II cyclotron, simulations with reduced space charge solving frequency by a factor of 10 lie still very close to the original solution. How large MTSSUBSTEPS can be chosen of course depends on the importance of space charge effects.

STEPSPERTURN

Number of time steps per revolution period. Only available for OPAL-cycl, default value is 720.

In OPAL-cycl, instead of setting time step, the time steps per-turn should be set. The command format is:

TRACK, LINE=name, BEAM=name, MAXSTEPS=value,  STEPSPERTURN=value;

Particles are tracked in parallel i.e. the coordinates of all particles are transformed at each beam element as it is reached.

OPAL leaves track mode when it sees the command

  ENDTRACK;

1.2. Track Particles

This command starts or continues the actual tracking:

RUN, METHOD=string, FIELDSOLVER=label, DISTRIBUTION=label-vector, BEAM=label,
FILE=string, TURNS=integer, MBMODE=string, PARAMB=float,
BOUNDARYGEOMETRY=string, MULTIPACTING=logical, OBJECTIVES=string-vector;

The RUN command initialises tracking and uses the most recent particle bunch for initial conditions. The particle positions may be the result of previous tracking.

Its attributes are:

METHOD

The name (a string, see String Attributes) of the tracking method to be used. For the time being the following methods are known:

• PARALLEL-T This method puts OPAL in OPAL-t mode see Chapter OPAL-t.

• CYCLOTRON-T This method puts OPAL in OPAL-cycl mode see Chapter OPAL-cycl.

• STATISTICAL-ERRORS This is a method to let OPAL run multiple times in parallel while adding imperfections to alignment and other physical quantities.

FIELDSOLVER

The field solver to be used see Chapter Field Solver.

DISTRIBUTION

The particle distribution to be used see Chapter Distribution.

BEAM

The particle beam see Chapter Beam Command to be used is specified.

FILE

The name of the file to be written (default=“track”).

TURNS

The number of turns (integer) to be tracked (default: 1, namely single bunch).

In OPAL-cycl, this parameter represents the number of bunches those will be injected into the cyclotron. In restart mode, the code firstly read an attribute NumBunch from .h5 file which records how many bunches have already been injected. If NumBunch < TURNS, the last TURNS - NumBunch bunches will be injected in sequence by reading the initial distribution from .h5 file.

MBMODE

This defines which mode of multi-bunch runs. There are two options for it, namely, AUTO and FORCE. See Multi-bunch Mode for their explanations in detail.

For restarting run with TURNS larger than one, if the existing bunches of the read-in step is large than one, the mode is forcedly set to FORCE. Otherwise, it is forcedly set to AUTO.

This argument is available for OPAL-cycl.

PARAMB

This is a control parameter to define when to start to transfer from single bunch to multi-bunches for AUTO mode (default: 5.0).

This argument is only available for AUTO mode multi-bunch run in OPAL-cycl.

OBJECTIVES

An array of column names from the .stat file used in STATISTICAL-ERRORS to compute mean value and standard deviation across all runs.

Example:

run, file="table", turns=5, mbmode="AUTO", paramb=10.0,
     method="CYCLOTRON-T", beam=beam1, fieldsolver=Fs1,
     distribution=Dist1;

This command tracks 5 bunches in cyclotron and writes the results on file table.

1.3. STATISTICAL-ERRORS

This method can be used to quantify the effects of imperfections to alignment or other physical quantities such as e.g. the phase or the amplitude. It doesn’t propagate the particles directly. Instead it scans through the input file and replaces all occurrences of and with randomly generated values of appropriate distribution. Then one of the other methods, e.g. PARALLEL-T is called. These two steps are then repeated many times.

To use this method one has to specify the METHOD using the following form:

STATISTICAL-ERRORS(<trackmethod>, <ncores>, <nruns>),

where <trackmethod> is the method that should track the particles, <ncores> is the number of cores used for a run and <nruns> is the number of individual runs that should be performed. It should be noted that the total number of cores available has to be greater or equal to ncores + 1. One core is needed to manage the distribution of tasks and to collect the results. The other cores are used to perform the simulations. If in total N \times \mathrm{ncores} + 1 cores are available then N individual runs are processed in parallel each using ncores.

For each run of the method STATISTICAL-ERRORS a unique base name is generated of the form foo. Each individual run is then performed in a directory foo_run_ddddd. The files that are produced by the <trackmethod> are kept. This can lead to a large amount of data especially when snapshots of the phase space are stored frequently. The user should make sure that the file system can handle the amount of data or set the option PSDUMPFREQ to a big number.

In the end the method STATISTICAL-ERRORS computes the mean and the standard deviation for each variable in the array OBJECTIVES along the machine and stores this information in to the .stat file.