Last version:
, September 12th 2023 (last respin 2023.3.0) 13Sep2023

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USRBDX
defines a detector for a boundary crossing fluence or current estimator
See also USRBIN, USRCOLL, USRTRACK, USRYIELD
The full definition of the detector may require two successive cards
(the second card, identified by the character '&' in any column from
71 to 78, must be given unless the corresponding defaults are
acceptable to the user)
First card:
WHAT(1) = i1 + i2 * 10 + i3 * 100, where i1, i2 i3 have the following
meaning:
i1 = 1.0 : linear binning in energy and solid angle
= 1.0 : logarithmic binning in energy, linear in solid angle
= 2.0 : logarithmic binning in solid angle, linear in energy
= 2.0 : logarithmic binning in energy and solid angle
i2 = 0.0 : one way scoring
= +1.0 : twoway scoring
i3 = 0.0 : current scoring
= +1.0 : fluence scoring (inverse cosineweighted)
Default = 1.0 (oneway current, linear in energy and solid
angle)
WHAT(2) = (generalised) particle type to be scored
Default = 201.0 (all particles)
WHAT(3) = logical output unit
> 0.0 : formatted data are written on WHAT(3) unit
< 0.0 : unformatted data are written on WHAT(3) unit
Values of WHAT(1) < 21 should be avoided (with the
exception of +11).
Default = 11.0 (standard output unit)
WHAT(4) = first region defining the boundary
(in case of oneway scoring this is the upstream region)
Default = 1.0
WHAT(5) = second region defining the boundary
(in case of oneway scoring this is the downstream region)
Default = 2.0
WHAT(6) = area of the detector in cm**2
Default = 1.0
SDUM = any character string (not containing '&') identifying the
detector (max. 10 characters)
Continuation card:
WHAT(1) = maximum kinetic energy for scoring (GeV)
Default: Beam particle total energy as set by the BEAM
option (if no BEAM card is given, the energy corresponding
to 200 GeV/c momentum will be used)
WHAT(2) = minimum kinetic energy for scoring (GeV)
Note that the lowest energy limit of the last neutron group
is 1.E14 GeV (1.E5 eV) for the 260 data set.
Default = 0.0 if linear energy binning, 0.001 GeV otherwise
WHAT(3) = number of energy intervals for scoring
Default = 10.0
WHAT(4) = maximum solid angle for scoring in sr
Default = 2 pi for oneway estimators, 4 pi for twoway
WHAT(5) = If linear angular binning: minimum solid angle for
scoring (sr)
Default = 0.0
If logarithmic angular binning: solid angle of the first
bin (sr)
Default = 0.001
WHAT(6) = number of angular bins
Default = 1.0 for linear angular binning, 3.0 otherwise
SDUM = & in any position in column 71 to 78
Default (option USRBDX not given): no boundary crossing estimator detector
IMPORTANT!
Notes:
 1) IMPORTANT! The results of a USRBDX boundary crossing estimator are
always given as DOUBLE DIFFERENTIAL distributions of fluence (or
current) in energy and solid angle, in units of cm2 GeV1 sr1 per
incident primary, EVEN WHEN ONLY 1 INTERVAL (BIN) HAS BEEN
REQUESTED, which is often the case for angular distributions.
Thus, for example, when requesting a fluence or current energy
spectrum, with no angular distribution, to obtain INTEGRAL
BINNED results (fluence or current in cm2 PER ENERGY BIN per
primary) one must multiply the value of each energy bin by the
width of the bin (even for logarithmic binning), AND BY 2 pi
or 4 pi (depending on whether oneway or twoway scoring has
been requested).
Angular distributions must be intended as distributions in
cos(theta), where theta is the angle between the particle
trajectory and the normal to the boundary at the point of
crossing.
When logarithmic scoring is requested for angular distributions,
all intervals have all the same logarithmic width (equal ratio
between upper and lower limit of the interval), EXCEPT THE FIRST
ONE. The limits of the first angular interval are theta = 0 and
the value indicated by the user with WHAT(5) in the second
USRBDX card.
 2) Angular distributions must be intended as distributions in
cos(theta), where theta is the angle between the particle
trajectory and the normal to the boundary at the point of crossing.
When logarithmic scoring is requested for angular distributions, all
intervals have the same logarithmic width (equal ratio between upper
and lower limit of the interval), EXCEPT THE FIRST ONE. The limits
of the first angular interval are theta=0 and the value indicated by
the user with WHAT(5) in the second USRBDX card.
 3) If the generalised particle is 208.0 (ENERGY) or 211.0 (EMENRGY),
the quantity scored is differential energy fluence (if
cosineweighted) or differential energy current (energy crossing the
surface). In both cases the quantity will be expressed in GeV per
cm2 per energy unit per steradian per primary. That can sometimes
lead to confusion since GeV cm2 GeV1 sr1 = cm2 sr1, where
energy does not appear. Note that integrating over energy and solid
angle one gets GeV/cm2.
 4) The maximum number of boundary crossing detectors that the
user can define is 1100. This value can be changed by modifying
the parameter MXUSBX in member USRBDX of the flukaadd library
or directory and then recompiling and linking FLUKA.
 5) The logical output unit for the estimator results (WHAT(3) of
the first USRBDX card) can be any one of the following:

the standard output unit 11: estimator results will be
written on the same file as the standard FLUKA output

a preconnected unit (via a symbolic link on most UNIX systems,
ASSIGN under VMS, or equivalent commands on other systems)

a file opened with the FLUKA command OPEN

a file opened with a Fortran OPEN statement in a userwritten
initialisation routine such as USRINI, USRGLO or SOURCE (see (13))

a dynamically opened file, with a default name assigned by the
Fortran compiler (typically fort.xx or ftn.xx, with xx equal
to the chosen logical output unit number).
The results of several USRBDX detectors in a same FLUKA run can
be written on the same file, but of course only if they are all
in the same mode (all formatted, or all unformatted).
It is also possible in principle to write on the same file the
results of different kinds of estimators (USRTRACK, USRBIN, etc.)
but this is not recommended, especially in the case of an
unformatted file, because it would make very difficult any reading
and analysis.
 6) When scoring neutron fluence or current, and the requested
energy bin structure overlaps with that of the low energy
neutron groups, bin boundaries are forced to coincide with
group boundaries and no bin can be smaller than the
corresponding group.
Actually, the program uses the requested energy limits and
number of bins to estimate the desired bin width. The number
of bins above the upper limit of the first lowenergy neutron
group is recalculated according to such width.
Note that the lowest energy limit of the last neutron group
is 1.E14 GeV (1.E5 eV) for the 260 data set.
All group energy boundaries are listed in two Tables in (10).
 7) A program USXSUW is available with the normal FLUKA code distribution
in directory $FLUPRO/flutil. USXSUW reads USRBDX results in binary
form from several runs and allows to compute standard deviations. It
returns double differential and cumulative fluence, with the
corresponding percent errors, in a file, and in another file
formatted for easy plotting. It also returns a binary file that can
be read out in turn by USXSUW. The content of this file is
statistically equivalent to that of the sum of the files used to
obtain it, and it can replace them to be combined with further
output files if desired (the USXSUW program takes care of giving it
the appropriate weight).
Example:
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7....+....8
USRBDX 101.0 ANEUTRON 21.0 3.0 4.0 400.0 AntiNeu
USRBDX 5.0 0.0 200.0 0.0 0.0 0.0 &
* Calculate fluence spectrum from 0 to 5 GeV, in 200 linear energy intervals,
* of antineutrons passing from region 3 to region 4 (and not from 4 to 3).
* Write formatted results on unit 21. The area of the boundary is 400 cm2.
* A single angular interval is requested (from 0 to 2pi)
