beam_beam_MAD-X_2012.txt

# This file describes van der Meer scan in ATLAS simulated using MAD-X in
# 2012. It is intended to compare this new and the old simulations. The latter
# was used in LHC in 2012-2018 luminosity calibrations.
#----------------------------------------------------------------------
#
# Beam momentum in GeV
p = 3500.
# Charge of particles in beam1 and beam2 in units of the proton charge
Z1 = 1
Z2 = 1
# Value of the beta-function in the interaction point (beta-star), in meters
beta = 1.5
# The tune values (the number of betatron transverse oscillation periods in one
# LHC orbit), from Hostettler PhD, p.25, Table 4.1
# before_2017:
Qx = 64.31
Qy = 59.32

# Number of particles in 1st and 2nd bunch
N1 = 8.5e10
N2 = 8.5e10

# The traced points of the 1st bunch are selected in the following way. The
# first bunch Gaussian is sampled in two-dimensional X-Y grid covering
# +/-N.sigma * sig1.x times +/-N.sigma * sig1.y rectangle with
# int(sqrt(N.points)) points along each side. Then, all points with
# sqrt((X/sig1.x)^2 + (Y/sig1.y)^2) distance greater than N.sigma are
# removed. For every position of the 2nd bunch the points with the
# corresponding distance from its center, sqrt(((X-x2)/sig2.x)^2 +
# (Y-y2)/sig2.y)^2), greater than N.sigma are also removed. Positions of all
# remaining points are traced N.turns in the accelerator.
N.sigma = 5
N.points = 10000

# Beam-beam interaction is switched on not immediately but after
# N.no.beam.beam.turns in accelerator. This allows to calculate numerically
# the undisturbed overlap integral, compare it with the exact analytic formula
# and estimate the bias of the numerical integration. The final correction is
# then calculated as the ratio of the numerical integration with and without
# the beam-beam interaction. The bias is cancelled in the ratio at least
# partially and this potentially allows to improve the precision.
N.no.beam.beam.turns = 1000

# Beam-beam interaction can be switched on not abruptly but "adiabatically",
# linearly from zero to its value during N.transitional.turns
#
# N.transitional.turns can be omitted, then it is assigned to 1000 by default
N.transitional.turns = 1000

# After beam-beam is fully switched on, one should wait for the
# stabilization. Normally, it is reached after <2000 turns (less if beam-beam
# is switched on adiabatically).
#
# If N.stabilization.turns is omitted, it is set by default to 2000
N.stabilization.turns = 2000

# After N.no.beam.beam.turns + N.transitional.turns + N.stabilization.turns
# turns, the positions of the selected points (the intersections of their
# orbits with the X-Y plane at the Interaction Point) are calculated in the
# accelerator during N.turns.with.beam.beam. This is the period when the
# luminosity correction is determined.
N.turns.with.beam.beam = 5000

# 1st and 2nd bunch Gaussian sigmas in X and Y in um
sig1.x = 40.
sig1.y = 40.
sig2.x = 40.
sig2.y = 40.

# The sequence of the relative X,Y positions of the 2nd bunch center
# w.r.t. the 1st one in um as two white-space separated lists (corresponding
# to the van der Meer scan steps)
x2 = 0.  10.  20.  30.  40.  50.  60.  70. 80. 90. 100. 110. 120. 130. 140. 150. 160. 170. 180. 190. 200.
y2 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.

# What should be the output of the computation (a white-space separated list
# of keywords below, the files will be named like
# "beam_beam_output_<keyword>.txt.gz" except the shortest
# "beam_beam_output_summary.txt" which will not be gzip'ed):
#
#   "summary"   the main results on the overlap rho1 * rho2 integrals and the
#               corresponding beam-beam correction. This file will always be
#               printed, regardless of the settings.
#
#   "rx.ry.weights"   for every point: its maximal x and y (ie. the circle radii
#                     rx, ry in x,x' and y,y' phase spaces, x',y' denote the
#                     derivatives w.r.t. z multiplied by beta) and "weights" at 
#                     which the point should be taken in the averages (the
#                     cenetral points have more weight).
#                     Format: step x2 y2 point rx ry weight
#
#   "integrals" overlap integrals per turn (not averaged), rho1,2 bunch
#               densities are either modified by the beam-beam electromagnetic
#               interaction or not, depending on whether the accelerator turn
#               is greater than "N.no.beam.beam.turns" or not, respectively.
#               Format: step x2 y2 turn integral
#
#   "centers"   averaged over points x- and y-positions per turn
#               Format: step x2 y2 turn average_x average_y
#
#   "points"    the traced points of the 1st bunch after accelerator turn "i",
#               this file might be very long.
#               Format: step x/y turn point coordinate derivative_w.r.t._z*(-beta)
#
output = rx.ry.weights integrals centers points

# By default all output files and also the copy of the configuration file will
# be stored in the subdirectory with the name obtained by dropping .txt from
# the end of the configuration file name, like
# beam_beam_1.txt -> beam_beam_1/. One can overwrite this rule by giving an
# explicit name (relative to the current directory or absolute) below.
# A fresh output subdirectory will be created. If it already exists, the program
# will terminate without overwriting anything.
# output.directory = beam_beam_lhcb_example

# Storage of the traced point positions after all accelerator turns might
# require too much disk space. Instead, one can "select.one.turn.out.of" N turns.
# Eg. if this parameter is 100, only the positions of the points after
# 0, 100, 200, ... turns will be stored.
select.one.turn.out.of = 1000

# Seed for the random number generator. If not given, the current time will be
# used as a seed.
# seed = 12121212121

# For the debugging purposes one can redefine the kick formula by choosing
# the "kick.model" parameter below from the list:
#  precise, 
#  precise.minus.average,
#  average, 
#  precise.minus.one.third.of.average,
#  one.third.of.average,
#  precise.minus.at.center,
#  at.center,
#  quadrupole,
#  average.and.quadrupole
#
# By default it is set to "precise" (also when kick.model is left undefined),
# then the exact kick formula is used.
#
# "average" means constant X,Y-independent kick equal to the value averaged
# over the bunch. Ie. the value of this constant angular kick is chosen to be
# equal to the sum of the kicks of all bunch particles divided by their
# number. This constant average kick only depends on the bunch separation, but
# not on X,Y. Namely, it can be calculated as the action of the bunch with
# (Capital) sigma = sqrt(sigma1^2 + sigma2^2) on one particle placed at the
# distance equal to the separation between the bunches. Ie. bunch one should
# be substituted by one particle at its center, while sigma of bunch 2 should
# be changed to this Capital sigma. Such constant kick only shifts the first
# bunch center, but do not modify its shape, so the resulting luminosity
# change can be computed using analytic formula.
#
# Between 2012 and 2018 the beam-beam correction in vdM scans was approximated
# by modifying the Gaussian bunch shapes: their centers were shifted according
# to the average kick described above while their sigmas were modified
# according to MAD-X simulation ("dynamic-beta" effect). Setting kick.model to
# "average" below allows to check that the results coincide with the
# old simulation without dynamic-beta effect, ie. when only taking into
# account the shift of the bunch centers.
#
# kick.model = quadrupole models the dynamic-beta correction, ie. the
# modification of the Gaussian widths. Here, the beam-beam interaction is
# approximated by the quadrupoles placed at the center of the first bunch. The
# quadrupole fields are proportional to the x,y (w.r.t. bunch center), the
# proportionality coefficients are chosen to be equal to the x,y-derivatives
# of the precise kick again at the first bunch center. Of corse, the beam-beam
# kick is not linear, so this approximation is good only in the vicinity of
# the first bunch center, though it is applied here to the full bunch. The
# advantage of the quadrupole is that one can calculate the associated change
# of the Gaussian width analytically.
#
# It was found that MAD-X'2012 simulation of dynamic-beta effect is close to
# such idealized quadrupole model. The cross section calibration corrections
# coincide within 0.1% for the MAD-X'2012 simulated conditions (depending on
# the random seed in the new simulation I've got 0.03 and 0.06%, this is at
# the level of stat. errors). There are small visible deviations only at large
# beam separations. However, the luminosity drops there and this suppresses
# the contribution to the correction. The discrepancy at large beam
# separations might be due to the fact that MAD-X simulates also the
# non-linearities, namely, one turn transfer matrix of the accelerator might
# slightly depend on the distance from the orbit. This effect is absent in
# this simulation. As mentioned above, the effect on the luminosity is
# negligible (<0.1%) and this also estimates the importance of such
# non-linearities.
#
# kick.model = average.and.quadrupole simulates the sum of the constant
# average kick (equivalent to the bending magnet) and the quadrupole kick
# (dynamic-beta effect) and gives the results close to the overall corrections
# applied between 2012 and 2018. Note, the non-linearities were taken care of
# in MAD-X'2012 dynamic-beta effect but were also neglected in the past for
# the constant average kick.
#
# All these options have been implemented only to compare the present
# simulation with the previous results. To obtain the best precision one
# should always use
#
# kick.model = precise.
#
# In this case one does not linearize the kick force (like with
# average.and.quadrupole) but uses the exact formula. Depending on the vdM
# scan conditions this gives sizable difference with the old (linear)
# approximation used at LHC in 2012-2018. The non-linear effects mentioned
# above are neglected at the moment but they should be negligible according to
# the comparison with the old MAD-X simulation described above.
#
# To debug separately the influence of the dipole orbit shift, there are 3
# more options:
#   kick.model = precise.minus.average
#   kick.model = precise.minus.one.third.of.average
#   kick.model = precise.minus.at.center
#
# For the first, "precise.minus.average", the kick is equal to
# precise kick - average kick. Here, "average.kick" is the same as with
# kick.model = average. This "precise.minus.average" model is implemented to
# demonstrate that the "precise" results coincide with the combined correction
# from kick.model = precise.minus.average and kick.model = average. Ie. the
# "precise" correction can be decoupled into two: from the orbit change and
# from the relative change of the bunch shape but with the fixed orbit
# (ie. using the kick = precise - average).
#
# The kick in the model "precise.minus.one.third.of.average" is equal to
# precise kick - average kick / 3. The factor 3 here is chosen arbitrarily to
# demonstrate that even for an arbitrary dipole magnitude the "precise"
# correction still decouples into the corresponding dipole orbit change and
# the correction due to the remaining precise kick - dipole kick. In this case
# "precise" = "precise.minus.one.third.of.average" + "one.third.of.average".
# The kick in the model "one.third.of.average" is constant and equal to
# average kick / 3.
#
# Similarly,
# "precise" = "precise.minus.at.center" + "at.center", where
# "at.center" means the kick exerted by bunch 2 in the center of bunch 1.
#
kick.model = precise