Foreword
Collimation and beam cleaning studies are carried out with the well established SixTrack [1] code, extended for tracking large numbers of halo particles, and to take into account halo interaction with arbitrarily placed collimators.
Particles are transported through the lattice element by element and their phase space coordinates are transformed according to the type of element. When a particle hits a collimator jaw, it is randomly scattered through matter.
The effect of collimator scattering is modeled using COLLTRACK/K2 [2, 3] routines.
The main characteristics of the SixTrack used for collimations studies are:
·
Proton scattering in various collimator materials, including:
□
Multiple Coulomb scattering,
□
Ionization of the collimator material,
□
Elastic protonproton (pp) scattering, and inelastic diffractive
pp scattering
(single diffractive scattering),
□
Inelastic protonnucleon
scattering,
□
Elastic and inelastic protonnucleus scattering,
□
Rutherford scattering.
·
Various
types of
halo and
possibility of including
diffusion.
·
Tracking of large particle ensembles (~10^{6}
protons)
over hundreds of turns.
·
Multiple imperfections on the beam and the
collimator properties (setting errors, tilts, orbit, beta beat, …)
Input parameters are divided in 3 files:
·
fort.2 (generated by
MADX), defining the lattice of the machine without magnetic field errors.
·
Collimator database
file, containing the details of collimators geometry, material, settings
(opening)
·
fort.3
(modified from the one used for SixTrack without collimation), including tracking
parameters
(number of particles and turns), type of beam, type of halo.
MADX is used to generate the LHC lattice, the optics and eventual orbit and
focusing errors. 
[1]
F. Schmidt: ”SixTrack,
User’s Reference Manual”, CERN SL/9456 (AP), 1994 (Update July 2008).
[2] T. Trenkler, J.B. Jeanneret:
“K2, A software package evaluating collimation systems in circular colliders
(manual)”, CERN SL/94–105 (AP), 1994.
[3]
G. RobertDemolaize, R. Assmann, S. Redaelli, F. Schmidt, CERN, Geneva,
Switzerland: A new version of SixtTrack with collimation and aperture
interface (PAC 2005).
[4] R. Assmann, J.B.
Jeanneret, D. Kaltchev: “Status of Robustness Studies for the LHC
Collimation”, APAC 2001.
BeamLossPattern
·
Implementation of the LHC aperture model with analysis of loss locations for
all tracked protons.


SixTrack for collimation studies tracks particles populating an halo (with typically σ ≥ 6)
throughout the LHC lattice (as defined by the MADX output file fc.2)
The halo is represented in the phase diagram Y (offset from beam orbit axes),Y' (angle w.r.t. beam orbit axes) in Figure 1.
One defines the Impact Parameter b (see Figure 2.) as the transverse offset between the jaw surface and the impact point.
b typically equals 1um at the first impact. 
Figure 1: Halo particles in the phase diagram.

Figure 2: Impact Parameter 

These changes implied to modify/add some input files:
 the generic SixTrack parameter file fort.3 now has a
new block for collimation parameters,
 a separate collimator database file is now mandatory if
collimation studies are to be done,
this database including the
name, length, orientation and material of every single collimator of the
ring (1 file per Collimation System Phase though).
Apart from these two, the other required SixTrack
files are produced via MADX and its conversion module. 
INPUT PARAMETERS 
MADX input:
fort.2
fort.34 (optional)
fort.3 
MADX can produce readytouse
input files for
SixTrack : it must be run with LHC lattice and optics
files V6.500 (or more recent layouts), 'thin lens' approximation,
and the addition of collimators.
Try for example to run it with " madx <
GenerateSixTrInput.madx ".For "perfect" machines, the files
produced are fc.2
and fc.34 (optional) which must be renamed (for
SixTrack) fort.2, and fort.34.
The file fort.3 is built expressly and found
in the examples annexed (see also below).
Below are some sample package of input files for preliminary
studies of a perfect LHC machine (perfect means that you only
require fort.2, fort.3, fort.34 being optional) and for the full
collimation system:
injection optics & energy
collisions at top energy with squeezed optics at IP1 & IP5
via the sixtrack command,

Collimator database

The collimator database
is stored in files named
CollDB_V6.500_[type]_st.[beam].data,
with
[type] being either inj for injection case or
lowb for collision case, and [beam] being b1
or b2. These files contain
mechanical and optical data related to the collimators planned for
LHC. (Note that at present only Phase I collimators have a length
different from zero)
A sample block of either one of these input files follows:
TCP.D6L7.B1
< collimator name in capital letters tcp.d6l7.b1
< collimator name in minimal letters 5.7
< collimator nominal opening (in sigma units)
C
< collimator material (C = graphite, CU = copper, W=tungsten)
0.2000000000000000
< collimator length [m] 1.5710000000000000
< collimator angle [rad] 0.0000000000000000
< collimator offset [m]
90.4467000000000070
< design Beta x [m]
156.4360000000000070
< design Beta y [m]
#
< line jump to next block
The introduction of the optic parameter β allows studies of error
scenarios (orbit distortion, betabeating) and/or to see the effect
of misaligned collimators.
This structure is then repeated within the file for each of the
collimators to be included in the study.

Source code of SixTrack

The "repository" for
MADX and SixTrack is in /afs/cern.ch/eng/sl/lhccollimation/code/
The SixTrack version in the repository was last updated in 2006
The latest version of the SixTrack code (compiled by Thomas Weiler) for Collimation Studies can be found at :
SixTrack(TW)
[note].
Source code: SixTrack source code can be found in the
SixTrack code webpage
(restricted access).
An example of input files:
fort.2,
fort.3,
CollDB_V6.500_lowb_st.b1.data
with corresponding output files: amplitude.dat, betafunctions.dat,
efficiency.dat, FirstImpacts.dat, FlukaImpacts.dat.
[note]
It should be noted that to date (Feb. '09) latest
modifications to SixTrack code have not been implemented into the
CVS version. 

New block in the fort.3
file

In order to keep
SixTrack as close as possible to its original form (i.e. to
avoid the need of multiples input files), it has been decided to
include a new block in the parameter file for SixTrack
(fort.3).
Here is a sample of what this block looks like:
COLLIMATION
(1) .TRUE.
(2)
50 7000000 (3) 3 5 .958
.0015 0. 0. "nothing" 1. 129E4 75.5
(4) .TRUE. 15.
18. 18. 20. 6. 7. 7. 10.0 1 0.0
999.0 8.0 7.5 999.0 (5) 8.3 8.3 8.3
8.3 8.3 8.3 8.3 8.3 5. 15.
(6) 0 19789.0 20150.0 1
1
(7) 1.3899e6 9.345e5
5.05324e3 1.6595e2 2.15955e2 9.96261e3
1.0 (8) 1.3899e6
9.345e5 5.05324e3 1.6595e2 2.15955e2
9.96261e3 1.0
(9) 0.503E09 0.503E09 (10) .FALSE. .FALSE. 0 .TRUE.
TCP.C6L7.B1 .FALSE. .TRUE. .TRUE. .TRUE. (11) 0. 0. 0. 0. (12) 0 0 0
0 0 0 0 0
0 0 .FALSE. (13) .FALSE. 6.003 0.0015 (14)
0. 0. .FALSE. .FALSE. (15) 0 0.0025 0.0
0.0 0 (16)
"CollDB_V6.500_lowb_st.b1.data"
1 (17) .TRUE.
.FALSE. WAbsVertLowbcoll 101 1 1.
NEXT
Description of the parameters:
(1) DO_COLL : logical, switches on/off the
collimation studies
(2) NLOOP : number of packs
of 64 particles to be tracked (breaks internal limitation)
MYENOM : energy of the beam to be tracked
(3)
Defines
initial distribution to be tracked
DO_THISDIS: integer, selects the type of distribution of the particles to be tracked (see DO_THISDIS)
MYNEX : A_{x} normalized amplitude of particles (in sigma units) in the X direction.
MDEX : dA_{x} smear (in sigma units) of the beam halo around A_{x} (in X direction).
MYNEY : A_{y} normalized amplitude of particles (in sigma units) in the Y direction.
MDEY : dA_{y} smear (in sigma units) of the beam halo around A_{y} (in Y direction).
FILENAME_DIS: name of the distribution file to be read if DO_THISDIS is set to 4.
ENERROR: energy spread of the tracked beam (read only if DO_THISDIS = 3).
BUNCHLENGTH: bunch length of the tracked beam in millimeters (read only if DO_THISDIS = 3).
(4) DO_NSIG: logical, if TRUE use collimators settings from fort.3. If FALSE from CollDB_V6.500_[type]_st.[beam].data.
nsig_tcp3: opening of the primary collimator in IR3 (in sigma units)
nsig_tcsg3: opening of the secondary graphite collimator in IR3 (in sigma units)
nsig_tcsm3: opening of the secondary metallic collimator in IR3 (in sigma units)
nsig_tcla3: opening of the active absorbers in IR3 (in sigma units)
nsig_tcp7: opening of the primary collimators in IR7 (in sigma units)
nsig_tcsg7: opening of the secondary graphite collimator in IR7 (in sigma units)
nsig_tcsm7: opening of the secondary metallic collimator in IR7 (in sigma units)
nsig_tcla7: opening of the active absorbers collimator in IR7 (in sigma units)
nsig_tclp: opening of the physics debris collimator (in sigma units)
nsig_tcli: opening of the absorbers for injection protection (in sigma units)
NSIG_TCDQ: opening of the beam dump protection collimator (in sigma units) [note1]
NSIG_TCSTCDQ: opening of secondary collimator dedicated to beam dump (in sigma units)
NSIG_TDI: opening of the injection protection collimator (in sigma units)
(5)
nsig_tCTH1: opening of the horizontal tertiary collimator in IR1 (in sigma units)
nsig_tCTH2: opening of the horizontal tertiary collimator in IR2 (in sigma units)
nsig_tCTH5: opening of the horizontal tertiary collimator in IR5 (in sigma units)
nsig_tCTH8: opening of the horizontal tertiary collimator in IR8 (in sigma units)
nsig_tCTV1: opening of the vertical tertiary collimator in IR1 (in sigma units)
nsig_tCTV2: opening of the vertical tertiary collimator in IR2 (in sigma units)
nsig_tCTV5: opening of the vertical tertiary collimator in IR5 (in sigma units)
nsig_tCTV8: opening of the vertical tertiary collimator in IR8 (in sigma units)
nsig_tCXRP: opening of the Roman Pots (in sigma units) [note1]
nsig_tCRYO: opening of the collimators in the DS regions (in sigma units)
[note1]
Onesided collimators (only positive x).
(6) N_SLICES : surface model of the jaw  number of slices in which each jaw should be cut
SMIN_SLICES : surface model of the jaw  s position for the start of the slicing
SMAX_SLICES : surface model of the jaw  s position for the end of the slicing
RECENTER1 : surface model of the jaw  moving the 1st jaw to the new smallest opening
RECENTER2 : surface model of the jaw  moving the 2nd jaw to the new smallest opening
(7) FIT1_1 : surface model of the jaw  order 0 of the polynomial fit for the 1st jaw
FIT1_2 : surface model of the jaw  order 1 of the polynomial fit for the 1st jaw
FIT1_3 : surface model of the jaw  order 2 of the polynomial fit for the 1st jaw
FIT1_4 : surface model of the jaw  order 3 of the polynomial fit for the 1st jaw
FIT1_5 : surface model of the jaw  order 4 of the polynomial fit for the 1st jaw
FIT1_6 : surface model of the jaw  order 5 of the polynomial fit for the 1st jaw
SSF1 : surface model of the jaw  scaling factor of the polynomial fit for the 1st jaw
(8) FIT2_1 : surface model of the jaw  order 0 of the polynomial fit for the 2nd jaw
FIT2_2 : surface model of the jaw  order 1 of the polynomial fit for the 2nd jaw
FIT2_3 : surface model of the jaw  order 2 of the polynomial fit for the 2nd jaw
FIT2_4 : surface model of the jaw  order 3 of the polynomial fit for the 2nd jaw
FIT2_5 : surface model of the jaw  order 4 of the polynomial fit for the 2nd jaw
FIT2_6 : surface model of the jaw  order 5 of the polynomial fit for the 2nd jaw
SSF2 : surface model of the jaw  scaling factor of the polynomial fit for the 2nd jaw
(9) EMITX0 : geometric emittance in the horizontal plane
EMITY0 : geometric emittance in the vertical plane
(10) DO_SELECT :
logical, does dedicated study of selected collimator (see
NAME_SEL) DO_NOMINAL :
logical, switches on/off the use of design β values of
collimators RND_SEED :
seed studied; if set to 0, seed will be selected randomly for every
run DOWRITE_DIST :
logical, saves or not the initial distribution to be tracked
NAME_SEL : name as in the fort.2 file of the collimator one wants a
dedicated study
DO_ONESIDE :
logical, switches on/off the collimator being onesided. Only
positive jaw. If the negative jaw is to be used, it is necessary to
turn collimator by 180 degrees in the collimator database
file (CollDB_V6.500_[type]_st.[beam].data).
DOWRITE_IMPACT : logical, saves the impact parameters for
each collimator
DOWRITE_SECONDARY : logical, writes a 2ry halo file based on
normalized amplitude
DOWRITE_AMPLITUDE : logical, writes checking files for
amplitude, closed orbit...
(11) XBEAT : offset in X for the computation of collimator in case of betabeating
XBEATPHASE : phase offset in X for the computation of collimator in case of betabeating
YBEAT : offset in Y for the computation of collimator in case of betabeating
YBEATPHASE : phase offset in X for the computation of collimator in case of betabeating
(12) C_RMSTILT_PRIM : rms value of tilt to apply to primary collimators
C_RMSTILT_SEC : rms value of tilt to apply to secondary collimators
C_SYSTILT_PRIM : systematic value of tilt to apply to primary collimators
C_SYSTILT_SEC : systematic value of tilt to apply to secondary collimators
C_RMSOFFSET_PRIM : rms value of offset to apply to primary collimators
C_RMSOFFSET_SEC : rms value of offset to apply to secondary collimators
C_SYSOFFSET_PRIM : systematic value of offset to apply to primary collimators
C_SYSOFFSET_SEC : systematic value of offset to apply to secondary collimators
C_OFFSETTILT_SEED : random number seed to be used for the simulation
C_RMSERROR_GAP : rms error of collimator gap
DO_MINGAP : logical, if TRUE the particle distribution is generated at the collimator with the smallest gap (to be used with sheet/pencil beam)
(13) RADIAL : logical, switches on/off the radial distribution
NR : size of the beam to be tracked in number of radial sigma's
NDR : smear of the beam to be tracked in number of radial sigma's
(14) DRIFTSX : to apply an emittance drift in x direction
DRIFTSY : to apply an emittance drift in y direction
CUT_INPUT : logical, formerly used to select particles to be tracked (set .FALSE.)
SYSTILT_ANTISYM : logical, to deduce C_SYSTILT to C_RMSTILT instead of adding
(15) IPENCIL : resets original distribution to pencil beam distribution on selected collimator
PENCIL_OFFSET : size in sigma units of the desired impact parameter
PENCIL_RMSX : ü
PENCIL_RMSY : ý Parameters defining the beam distribution
PENCIL_DISTR : þ

PENCIL_RMSX
[m] 
PENCIL_RMSY
[m] 
PENCIL_DISTR 
Pencil beam 
0 
0 
0 
Rectangular beam 
¹0 
¹0 
0 
Gaussian beam both in X and Y 
¹0 
¹0 
1 
Rectangular in X, Gaussian in Y 
¹0 
¹0 
2 
PENCIL_DISTR=0:
PENCIL_OFFSET = 0
Pencil beam distribution
PENCIL_RMSX = 0
PENCIL_RMSY = 0
PENCIL_DISTR=0:
PENCIL_OFFSET = center of rectangle
rectangular
distribution
PENCIL_RMSX = spread of impact parameter
(uniform)
PENCIL_RMSY = spread parallel to jaw surface
(uniform)PENCIL_DISTR=1:
PENCIL_OFFSET = mean of Gaussian distribution
Gaussian
distribution
PENCIL_RMSX = spread of impact parameter
(Gaussian)
PENCIL_RMSY = spread parallel to jaw surface
(Gaussian)
PENCIL_DISTR=2:
PENCIL_OFFSET = mean of Gaussian distribution
half Gaussian
distribution
PENCIL_RMSX = spread of impact parameter
(uniform)
PENCIL_RMSY = spread parallel to jaw surface
(Gaussian)
NOTE:
The distribution with PENCIL_DISTR=2 is used when wanting to
simulate the loss of a magnet.
(16) COLL_DB : name of the collimator
database; must be quoted
IBEAM : "name" of the beam tracked (1 or 2) => TO BE UPGRADED
(17) DOWRITETRACKS : logical, writes secondary/tertiary
halo files CERN :
logical, switches on/off to cut halo files in separate
pieces, one per 64 particles
CASTORDIR : name of the run; MUST BE EXACTLY 16 characters
JOBNUMBER : 5 digit number, name of the complement to the name of
the run (gives seed)
SIGSECUT2 : cut in square sigma's x/y for saving particles (e.g. 64
for a cut at 8 σ_{x}/σ_{y})
SIGSECUT3 : cut in square sigma's radial for saving particles (e.g.
90.25 for a cut at 9.5 σ_{r})
One should know that a large value for NLOOP combined with
DOWRITE_TRACKS set to .TRUE. may create really huge output files,
depending on the optics you run with. For example, in our current
simulations, a run with NLOOP = 50 (i.e. simulations over 3200
particles) for the LHC collision optics will produce a tracks2.dat file of 2.8 Go (!!), for just
1/1000th of the statistics we need.
Remark: the flag DO_THISDIS provides the user with
5 different options:
 DO_THISDIS = 1 : distribution in
the plane for which the parameters are specified ONLY:
flat distribution in the selected plane
between Ax
± δAx
(horizontal) or
Ay
± δAy
(vertical). The amplitude in the
other plane is zero.
 DO_THISDIS = 2 : distribution in
the plane for which the parameters are specified +
a Gaussian distribution cut at 3
s in the other plane.
 DO_THISDIS = 3 : distribution in
the plane for which the parameters are specified +
a Gaussian distribution cut at 3
s in the other plane +
energy spread given by ENERROR (nominally 3.06E04 at
450GeV and 1.129E04 at 7TeV) and a longitudinal component given by BUNCHLENGTH
(nominally 11.24cm at 450GeV and 7.55cm at 7TeV).
 DO_THISIDS = 4 : reads an external file that
contains the beam distribution to be tracked.
 DO_THISIDS = 5 : radial
transverse distribution of radius A_{r}.
This corresponds to a flat distribution both in the horizontal and
vertical planes between Ax
± δAx
and Ay
± δAy,
with A_{x}
= A_{y} = A_{r}/Ö2

Results

Below are some inefficiency
curves obtained with the different optics input files provided
some lines above; these plots were obtained using only the
primary and secondary collimators of the IR7 LHC insertion region:
Click on the picture then "Save as.." to get a Powerpoint file
with enlarged curves.
The main purpose of the code is to produce loss maps along
the ring, in order to compare the level of local beam losses with
the magnetic quench limit. Below is an example of such loss maps
for the injection optics case (450 GeV beam energy): the top plot is
obtained if one only considers the IR7 insertion region collimators;
the bottom plot is obtained if one considers the full collimation
system, i.e. all collimators, all absorbers and all cleaning
elements (TCLP + TCDQ):
Click on the picture then
"Save as.." to get a Powerpoint file with enlarged curves.
It can be seen in
both figures (full ring and zoom downstream of IR7) that the
complete collimation system (bottom plots of each figure) has a
significantly better performance than the betatron cleaning system
with primary and secondary collimators alone: there is a notable
reduction of the loss spikes in the arc downstream of the IR7
insertion region, where the betatron cleaning is located. At the
same time, additional losses are observed in IR2, where the TDI
injection protection element is intercepting the secondary halo at
its nominal setting. 
Publications

A New Version of SIXTRACK with Collimation and Aperture Interface, G. RobertDemolaize, R.
Assmann, S. Redaelli, F. Schmidt, CERN, Geneva, Switzerland,
PAC05  

AM  GRD SR  CB,
Tue Sep 11 12:02:52 CEST 2012 
