This Readme.md contains a brief description of the code purpose, installation instructions and usage.

For a more comprehensive description, refer to the bibliography section, where you can find :

[1] a conceptual review,

[2] use and detailed python code explanations,

[3] the implemention with C++ and CUDA libraries,

[4] effects of radiation in dipoles and quadrupoles (Oide effect),

[5] the fort.18 file details, in Appendix B,

[6] the MAD-X project,

[7] and the initial MAPCLASS code.

The transport of a particle beam through out an accelerator requires the calculation of the beam properties, e.g. beamsize in the transverse planes, correlation, etc. Typically, it is done by tracking several hundreds to thousands of particles, with an statistical post-analysis. Such process could be computationally intensive and too slow for very long or complicated transfer lines. On top of that, during the lattice design and iterative optimization one would like to explore several possibilities, and it would be advantageous to reduce the time of calculation.

MAPCLASS was written to perform a fast calculation of the outgoing beam size, given a transport lattice and a beamsize at the input. Therefore, it avoids the time consuming single particle tracking. It has been extended in MapClass2 to calculate twiss functions inside elements, correlations in the phase space and many others.

The main input to MapClass2 is the lattice, either from

• a fort.18 file generated in MAD-X PTC, or, alternatively
• a twiss file from MAD-X

Naturally, in order to give fast results we must make a simplification. MAPCLASS assumes the beam at the entry point is gaussian in the horizontal phase space (x, px), vertical phase space (y, py) and longitudinal position (t). The beam energy spread distribution could be chosen to be gaussian or uniform. Also, the lattice twiss parameters alfx and alfy must be zero at the entry point.

Two options are available: C++ libraries (recommended),and CUDA libraries (parallelization)

1. From a bash terminal, move to desired location, and then execute the following lines:

git clone https://github.com/pylhc/MapClass2.git
cd MapClass2
git submodule init
git submodule update

2. The Python variables need to be modified. Here are two ways to do it :

• Include the path inside the python script where you call MapClass2, e.g.

### my python script loading MapClass2_C++
import sys, ctypes
sys.path.append('/home/o/MapClass2/')
sys.path.append('/home/o/MapClass2/C++MapConstruction/')
ctypes.cdll.LoadLibrary("/home/o/MapClass2/libs/boost_1_53_0/libboost_python.so.1.53.0")

• by adding to the paths to your ~/.bashrc file, e.g.

### Mapclass2_C++
export PYTHONPATH="/home/o/MapClass2:$PYTHONPATH"
export PYTHONPATH="$PYTHONPATH:/home/o/MapClass2/C++MapConstruction"
export LD_LIBRARY_PATH="$LD_LIBRARY_PATH:/home/o/MapClass2/libs/boost_1_53_0"

git pull #To update
git reset --hard #To recover in an accidental file remove or modification

• Python 2.6 or higher is required (not tested with Python 3)
  • numpy library must be installed or added to the 'libs' folder (tested 1.13.3)
• gcc 4.4.3 or higher.
  • If working on the cern afs and your gcc is lower than 4.4.3, then do

          source /afs/cern.ch/sw/lcg/external/gcc/4.4/x86_64-slc5/setup.sh

• (OPTIONAL) CUDA libraries

From any Python terminal environment or script, it is possible to load the modules mapclass and metaclass2.

import mapclass
import metaclass2

now, a twiss or fort.18 file (from MAD-X 5.X.X) is required to perform beamsize calculations.

• fort.18 files from MAD-X PTC

  Check the PTC module docs in MAD-X as it is very powerful. Here is a common MAD-X coding example to generate fort.18 file.

      !!! MAD-X PTC Code to produce fort.18
        ptc_create_universe;
        ptc_create_layout,model=2,method=6,nst=10;
        ptc_normal,icase=5,no=8,deltap=0.00;
        ptc_end; 
      !!! End MAD-X Code

• twiss files from MAD-X Twiss command should be generated with at least the following columns:

NAME, KEYWORD, S, L, BETX, BETY, ALFX, ALFY, MUX, MUY, DX, DPX, DY, DPY, ANGLE, K1L, K2L, K3L, K4L

WARNING: Some MAPCLASS2 functions assume elements referenced to its exit side.

Some examples of use can be found in ./doc/FFSexample

• How to load a twiss file?

  In a python script or shell:

    import metaclass2
    tw = metaclass2.twiss2("twissfilename")

• How to check what was loaded?

  len(tw.elems) tells you how many elements were loaded, while tw.elems[0] is the first loaded element.

  tw.elems[0].KEYWORD is the keyword used in MAD-X for the element zero. MapClass2 uses the same twiss file column names except for TNAME which is TableNAME (TNAME does not exist in MAD-X).

  tw.elems[0].BETX is the betax twiss value at the EXIT of the element.

  WARNING!!!: it is always the EXIT, twiss file should be generated accordingly.

• How to get betas at any point?

  e.g. tw.getBeta(3,0.5) where 3 is the element number and 0.5 is position in the element in meters. tw.getBeta(3,0) refers the twiss beta at the ENTRY side.

  To get betas at the output you could use:

      tw.elems[3].BETX #(faster option)
      tw.getBeta(3,tw.elems[3].L)

• How to get the phase advance at any point?

  e.g. tw.getPhase(1,0) exactly the same as in getBeta()

• How do I load a map?

  Create a Map2 from either a fort.18 or a twiss file.

  import mapclass
  mf = mapclass.Map2(4,"fort.18")
  mt = mapclass.Map2(tw,4)

  where tw is a twiss object created with metaclass2 module and 4 is the map order.

  In the case of a fort.18 file, please, checka that The map order in Map2 is smaller or equal to the fort.18 map.

• How to calculate the beamsize

  Using a map m, from either a twiss or a fort.18 file (the calculation from a fort.18 is generally more precise)

    import math
    var=m.sndmmt('y',[sx,spx,sy,spy,dpp,t])
    mu =m.rstmmt('y',[sx,spx,sy,spy,dpp,t])
    beamsize = math.sqrt(var - mu**2)

  NOTE: sx, spx, sy, spy and t are one sigma of the gaussian distribution, while dpp: either one sigma of the gaussian distribution or total width of uniform centered energy spread distribution

  WARNING: m.sigma returns squared value already! m.sigma and m.offset are still valid for backwards compatibility

• How to calculate oide effect?

  tw.oide(emitn,gamma) where emitn is normalized emittance, gamma is the relativistic factor. Check the function declaration, it has other parameters, this is an example with minimum parameters

• How to calculate beam size contribution due to radiation in bending magnets?

  tw.sigmaBends2a(E=theenergy)

  NOTE: it returns the squared value.

• How do I get the horizontal polynomial expression?

  print mymap.x   ### prints all the monoms in x

  It can be used with x, px, y, py, d, s.

• How do I check an specific component on the map?

    print mymap.x[0,0,0,0,1] # 5 dim map, prints the hor. dependence on d
    print mymap.y[0,0,0,1,2] # 5 dim map, prints the  ver. dep. on py * d**2 

  if the map is 6 dimensional, then, it needs 6 indexes

•    Traceback (most recent call last):
     File ".../MapClass2/mapclass.py", line 227, in sigma
     sigmaprod = self.__sigma(ind, sig, gaussianDelta)
     File ".../MapClass2/mapclass.py", line 392, in __sigma
     qq = pow(i[5] / dv, ind[5])

  ANSWER: Only 5 elements in the passed sigmas list [sx,...], there must be six

• mw=mapclass.Map2("fort.18")
  Traceback (most recent call last):
  File ".../MapClass2/mapclass.py", line 219, in sigma
  for ind1, coeff1 in self[xory].iteritems():
  KeyError: 'x'

  ANSWER: Missing argument. A correct call example is mw=mapclass.Map2(1,"fort.18")

• print math.sqrt(mw.sigma(xory='x',sig=sigmaFFS))
  Traceback (most recent call last):
  TypeError: can't convert complex to float

  ANSWER: When using twiss objects in mapclass, retuned values are complex.

  Use real: print math.sqrt(mw.sigma(xory='x',sig=sigmaFFS.real)

• No implementation for element:  TWISS MARKER

  ANSWER: all is OK, this is an info message

[1] R. Tomas. Nonlinear optimization of beams lines. PRST - AB 9,081001 (2006).

[2] Martinez, David et al. MAPCLASS2: a code to aid the optimization of lattice design. CERN-ATS-Note-2012-087 TECH. Nov 01, 2012.

[3] Diana Andreea Popescu. Parallel Computing Methods for Particle Accelerator Design. Master Thesis. Ecole Polytechnique Federale de Lausanne, CERN. July, 2013.

[4] O.R. Blanco et al. CLIC 3TeV Beam Size Optimization with Radiation Effects. Proceedings of IPAC2013, Shanghai, China. TUPW0003.

[5] E. FOREST et al. Introduction to Polymorphic Tracking Code. Fibre Bundles, Polymorphic Taylor Types and "Exact Tracking". Geneva, Switzerland. July 24, 2002. CERN-SL-2002-044 (AP). KEK-Report 2002-3.

[6] MAD-X. http://mad.web.cern.ch/mad/

[7] R. Tomas. MAPCLASS: a code to optimize high order aberrations. CERN-AB-Note-2006-017. Jan 15, 2007.

Code was originally written by R. Tomas (CERN)

email: orblancog@gmail.com, rogelio.tomas@cern.ch