BEAMBEAM: Beam-beam Interaction

label: BEAMBEAM, SIGX=real,SIGY=real,
                 XMA=real,YMA=real,CHARGE=real
                 BBSHAPE=int,WIDTH=real,BBDIR=int;

• SIGX: The horizontal extent of the opposite beam (default: 1 m). Meaning depends on parameter BBSHAPE.
• SIGY: The vertical extent of the opposite beam (default: 1 m). Meaning depends on parameter BBSHAPE.
• XMA: The horizontal displacement of the opposite beam with respect to the ideal orbit (default: 0 m).
• YMA: The vertical displacement of the opposite beam with respect to the ideal orbit (default: 0 m).
• CHARGE: The charge of particles in the opposite beam in elementary charges. It is set by default CHARGE=1. So, if you want to describe collisions between beams containing the same particles having a charge different from 1, you have to set CHARGE explicitly in BEAM and in BEAMBEAM.
• BBSHAPE: The parameter to choose the radial density shape of the opposite beam (default: 1)
  • BBSHAPE=1: Gaussian shape (default), SIGX/SIGY: standard deviation in vertical/horizontal direction.
  • BBSHAPE=2: trapezoidal shape, SIGX/SIGY: half width of density profile, i.e. distance from the centre to half edge region with linear decrease of density in horizontal/vertical direction. Still only circular opposite beam possible, i.e. in the calculations SIGX'=SIGY'=(SIGX+SIGY)/2 is used, if SIGX and SIGY have different values
    
  • BBSHAPE=3: hollow-parabolic shape, SIGX/SIGY: distance from the centre to the maximum of the parabolic density profile in vertical/horizontal direction. Still only circular opposite beam possible, i.e. in the calculations SIGX'=SIGY'=(SIGX+SIGY)/2 is used, if SIGX and SIGY have different values
    
  The restriction to circular opposite beams in the cases BBSHAPE=2,3 appears to be sufficient, because such beam profiles are more important for the description of the interaction between the particle beam and an electron beam of an electron cooler, which are usually circular.
• WIDTH: The relative extent of the edge region, absolute value is given by WIDTH*SIGX and WIDTH*SIGY vertical and horizontal direction, respectively. For
  • BBSHAPE=1, WIDTH is meaningless and will be ignored.
  • BBSHAPE=2, WIDTH denotes the full width of the edge region in units of SIGX (or SIGX' and SIGY', respectively, if SIGX and SIGY are not equal), i.e. if WIDTH=0.01 and SIGX=5 mm, the edge region has a full width of 0.05 mm. It must be WIDTH < 2.0.
  • BBSHAPE=3, WIDTH denotes the full width at half maximum of the parabolic density profile in units of SIGX (or SIGX' and SIGY', respectively, if SIGX SIGY are not equal. It must be WIDTH < SQRT(2.0).
• BBDIR: The parameter to choose the direction of motion of the opposite beam relative to the beam considered. It determines the sign of the Lorenz force between the both beams (default: -1):
  • BBDIR=-1: Beams move in the opposite direction as in a collider. Therefore, the Lorenz force enhances the beam-beam interaction.
  • BBDIR=0: Opposite beam does not move, Lorenz force is neglected
  • BBDIR=1: Beams move in the same direction as in an electron cooler. So, the Lorenz force reduces the beam-beam interaction.
  Note:
  • The particles in the beam considered may have a momentum deviation given by DELTAP defined in the TRACK command.
  • The opposite beam is assumed to have the velocity according to the unperturbed energy o the particles in the beam considered. So, only the direction of motion can be chosen.
  • In the case of motion in the opposite direction (BBDIR=-1), the time of interaction between the beams is given by tau = length/(2*beta*c_light), where length is the length of a bunch in the opposite beam. In the case of motion in the same direction (BBDIR=1) as in an electron cooler, this time is given by tau = length/(beta*c_light), where length is the length of the cooler. So, the factor 1/2 is inserted only for BBDIR=-1 to calculate correct results.

A beam-beam element requires the particle energy (ENERGY) and the particle charge (CHARGE) as well as the number of particles per bunch (NPART) to be set by a BEAM command before any calculations are performed.

Examples of a four-dimensional beam-beam element definition:

Collider regime example:

beam,   particle=positron,npart=1.e12,energy=50.0;
bb:     beambeam,sigx=1.e-3,sigy=5.e-4,charge=1.;

Electron cooler example:

gamma0=1.032;                           ! relativistic factors
beta0=sqrt(1.0-1.0/gamm0/gamma0);

i_e=0.2;                                ! electron current
re_cool=0.01;                           ! electron beam radius
l_cool=5.0;                             ! cooling length
nelect=i_e*l_cool/beta0/clight/qelect;  ! electron number in e-cooler

beam,particle=antiproton,gamma=gamma0,npart=nelect; 
bb_ecool:beambeam,sigx=re_cool,sigy=re_cool,bbshape=2,width=0.01,charge=-1,bbdir=1;

For the definition of the LHC head-on and parasitic beam-beam elements see beam-beam element examples.