VITESS Module Source

The module source initialises neutron rays originated at a short pulsed (SPSS), long pulsed (LPSS), or a continuous source (CWS). Their starting positions are randomly distributed over moderators, which are treated as a 2-dimensinonal surface of rectangular or circular shape. Their wavelength range, flight direction and starting time are restricted to ranges given by the user. They can also have a certain spin state. The values for all these parameters are determined for each neutron trajectory by random numbers.
Up to 10 moderators can be handled. They might be physically different moderators; but it is also possible to describe one physical moderator by a sum of several moderators in the simulation, e.g to describe its characteristics as a sum of 3 Maxwellians.
Neutrons are either directed to a certain rectangular target area or restricted in divergence ("direction defined by divergence"). It is possible to propagate the neutrons to the target window ("direction defined by window") or leave it on the moderator surface ("direction defined by virtual window"). Additionally, neutron rays can be restricted to those arriving in a certain time range at a certain distance from the moderatar in a certain time range. For special applications, neutrons can be selected in one run and only marked neutrons will be started in a subsequent run.
The coordinate system is oriented as illustrated in Figure 1, it is centered in the middle of the moderator surface. If the neutron is propagated to the window, the co-ordinate system is shifted parallel to the x-axis to the position of the propagation window (i.e. the x-coordinate of each neutron hitting the propagation window is zero). This is done in all modules until the neutrons arrive at the sample.
The source module is responsible for the normalization to get correct absolute intensities. (All other modules only treat the reduction of intensity by absorption, reflection etc. or bin the intensities into time, wavelength, ... channels.)
The intensity given in all modules - in neutrons per second - is the (long) time averaged intensity of neutrons arriving at the end of the component (independent of their position). For pulsed sources, the repetition frequency is already included assuming that the same neutron pulse arrives as many times per second as given as frequency in the sources module. So if 1 pulse is treated, the output is correct, but if e.g. 2 pulses are treated, the frequency has to be halved to get correct time averaged intensity values.

Source parameters:

Simulation parameters

Every neutorn trajectory represents a package of a certain number of neutrons passing per time, i.e. a certain neutron current. The sum over all trajectories gives the total neutron count rate. From one module to the following, the 'number of trajectories' decreases, e.g. if a window or the sample is not hit. The intensity further decreases by reflections or absorption inside a material. In these cases the number of trajectories is unchanged, but the count rate per trajectory is decreased. So absolute values of the count rate are given at any point of the instrument, if the moderator count rate can be determined.
The effect of gravity is considered in this module, if this option is chosen. The parameter 'minimal weight' is not considered.

Trajectories are distributed randomly on the moderator surface, lying within a time, wavelength and divergence range. The divergence range can either be determined by by the propagation window (see Figure 1) or by the divergence range. In the latter case, the direction is defined by the angles phi and theta, which define the angular deviation range with respect to the straight flight direction (parallel to the x-axis) as illustrated for special cases in Figure 2:
first sketch     : div-range illustrated for neutrons having no z-divergence;
second sketch: div-range for neutrons having no y-divergence

Propagation

Neutron trajectories are restricted to those hitting a rectangular target in a certain distance from the source, the so-called propagation windoew. Height and width of the aperture as well as its distance from the source must be given. Additionally an angle can be given defining the declination of the aperture center (= beam direction) from the normal of the moderator surface (in the horizontal plane). The default value is 0° meaning a beam direction vertical to the moderator surface. For angles not equal zero, the moderator surface is rotated around the (positive) z-axis (relative to the beam direction).
To omit this propagation, a zero distance and a aperture size exceeding the moderator size can be given. If the option "direction defined by virtual window" is chosen, the 'propagation window' is only used to define the flight direction, but the neutrons remain on the moderator surface.

Polarisation and special parameters

The polarization of the neutron beam is needed in some simulations. Therefore an "internal" polarizer is defined in the source module. Initial values of  the percentage and the direction of polarization have to be given. The spin vector belonging to each trajectory is represented in cartesian coordinates. The output represents an ansamble of "Up" and "Down" neutrons relative to the given direction of polarization. The average polarization will be that given by the input parameter "degree of polarization". For non-polarized beam (0%) the numbers of "Up" and "Down" trajectories are the same.

To enable ray-tracing, the 'ray-tracing file' has to be given here and the 'kind of ray-tracing' has to be chosen. The ray-tracing file contains the IDs of the trajectories to be traced. The 2 different modes of ray-tracing are explained in a special help file called 'Ray-tracing'.

Moderator parameters

Moderator parameters are taken from a file that contains information about the moderator system, consisting of up to 10 moderators. Data of 3 moderators can be given on the moderator window, for more moderators the file has to be extended by any text editor. So each source can be described by a file. The existing files are collected in <VITESS install. directory>/FILES/moderators. Please send us your files that we can distribute them.
The moderator characteristics can either be given by distribution files - intensity as a function of wavelength, of time, or of time and wavelength - or by parameters for analytical functions. Analytical functions are only used in the simulation, if the corresponing distribution file is not given, i.e. the Maxwellian distribution is calculated from the given temperature, only if no 'wavelength distribution file' is given, and the pulse shape is calculated from the given time constants, only if no 'time distribution file' is given. Table 1 gives a survey.
For ESS and SNS, the parameters defining wavelength and time characteristics of the pulse are fixed in the program. For the descriptions Butterfly-1 and Butterfly-2 of the ESS, this is also true for width, height and position. And they always show both moderators. However, the proton pulse length can still be varied and the intensity scaled linearly by varying the power.

Table 5: Use of Moderator Parameters.

source type	source name	temperature	distr. files	tau1, tau2	width, height	total flux	pulse rep. rate	pulse length of LPSS	flux distribution
ESS	ESS	from input 50 or 325 K	- -	fixed	from input  (12x12cm²)	calculated	from input  (50 Hz)	from input  (2 ms)	analytical funct.
SNS	SNS	from input 50 or 325 K	- -	fixed	from input  (12x12cm²)	calculated	from input  (50 Hz)	---	analytical funct.
continuous src.	-	from input	-	---	from input  (12x12cm²)	from input	---	---	Maxwell. distr.
continuous src.	-	-	wavelength	---	from input  (12x12cm²)	calculated	---	---	wavelength distr. file
pulsed src	-	from input	- -	from input (12 us; 60 us)	from input  (12x12cm²)	from input	from input  (50 Hz)	from input  (2 ms)	Maxwell. distr. function time distr. function
pulsed src	-	-	wavelength -	from input (12 us; 60 us)	from input  (12x12cm²)	calculated	from input  (50 Hz)	from input  (2 ms)	wavelength distr. file time distr. function
pulsed src	-	from input	- time	-	from input  (12x12cm²)	from input	from input  (50 Hz)	from input  (2 ms)	Maxwell. distr. function time distr. file
pulsed src	-	-	wavelength time	-	from input  (12x12cm²)	calculated	from input  (50 Hz)	from input  (2 ms)	wavelength distr. file time distr. file
pulsed src	-	-	wavelength-time	-	from input  (12x12cm²)	calculated	from input  (50 Hz)	from input  (2 ms)	wavelength-time distr. fct.

---: not existing
 -  : not used
( ) : numbers in brackets give the default values

Parameters for each moderator:

Moderator Characteristics by Analytical Functions

Wavelength dependence

For a moderator of effective temperature T, the Maxwellian distribution function can be used to describe the wavelength dependence of the neutron flux:

Therefore, the temperature has to be given.
A fraction of the neutrons is usually not moderated to the moderator temperature. Their wavelength depence is described by:

(as used for SNS and ESS). These functions are only used, if no 'wavelength distribution file' is given.

Time dependence

For a pulsed source, this wavelength dependence (or the 'wavelength distribution function' read from file) can be multiplied by a time dependent function F(t). For SPSS and LPSS we use:

In the VITESS code, the exact formulae are used, not the approximations. The parameters determining the pulse shapes must be given as an input. The first time constant describes the generation of the neutrons, the second time constant describes the decay of the pulse. Both determine the shape in the beginning of the pulse. The length of the long pulse is determined by the proton pulse length. The decay is identical with the correspondinge short pulse.  These functions are only used, if no 'time distribution file' is given.

Fort the undermoderated neutrons, the same functions are used, but with much shorter time constants.

ESS and SNS

The ESS "butterfly" moderator
The database version 2015_Butterfly selects the ESS moderator baseline as specified in the beginning of 2015. According to the specifications, there are two moderators: a 3 cm high moderator on top and a 6 cm high moderator on the bottom side of the target wheel. Both have a central thermal moderator and cold wings, as shown in the left-hand figure below. The only input parameter taken from the moderator description file is the height, which has to be either 3 cm or 6 cm. The declination angle sets the orientation of the beamport w.r.t. a reference direction chosen such that 0° is rectangular to the proton beam. The declination angle can be set between 0° and pm 55°. The origin of the coordinate system is the center of the thermal moderator. Note that, according to the current baseline, the monolith inserts point at the separation between the cold and thermal moderator (red crosses is figure below): this can be modelled by an additional frame module. In the same way, the viewpoint of the beamline can be adjusted to look at the cold moderator instead (or at another point on the thermal moderator than the center). The moderator is symmetric for pos. and neg. declination angles. Only the closer cold moderator can be viewed from a given declination angle. The only exception is a declination of 0°, from which both cold moderators are visible (cf brightness curves below).

The moderator description uses functions developed by T. Schoenfeldt, which are described in more detail in "Phenomenological Study of Expected Cold and Thermal Brightness Phase-Space at ESS" by T. Schoenfeld et. al (in preparation). The functions were fitted to the 3 cm top moderator and extended to the 6 cm bottom moderator based on previous fits to the pancake moderator of different heights. Hence the model of the 6 cm moderator has to be regarded with a slightly larger systematic uncertainty than the 3 cm moderator. The spatial dependence (horizontally) of the brightness of the 3 cm top moderator, which is one of the functions provided by T. Schoenfeldt, is shown in the right-hand side figure below for different viewpoints. The moderator width given in the VITESS log file is the one derived from these functions, without further projection of this width onto the viewpoint.

Engineering details which will reduce the performance were not part of the original model, but have been investigated since and found to decrease the brightness by 20-30%. Therefore, a factor of 0.75 is applied to the moderator brightness in VITESS. If the user desires a different factor, simulation results can simply be re-scaled.

Figure 4a: Butterfly moderator geometry (picture from K. Andersen, "New ESS moderator Baseline")

Figure 4b: Brightness factor as function of horizontal position for different declination angles.

Moderator Characteristics from File

Alternatively the moderator characteristics can be given in files. Instead of giving the temperature, a 'wavelength distribution function' can be read. Instead of giving the time constants, a 'time distribution function' can be read. Both can be substituted at the same time by a 'wavelength-time distribution function'.

Continuous sources

For reactor sources, the so-called 'wavelength distribution function' is needed. This file must contain a table of 2 columns. In the first column the wavelength in Angstroem is expected, in the second the flux in flux units (FU), i.e. n/(cm² s Ang str). The first column must have increasing values. The wavelength range that can be used must be covered by the range in this file.
From these data the 'total flux at the moderator' and the current into a solid angle W are calculated:

If the 'total flux at moderator' F_total is given, it is assumed that this is the real value and thus the data of the file are normalised to that value. If the 'neutron current' I_mod is given, the flux is normalized to that value. This is only sensible, if the calculated current is zero, i.e. if area A_mod, solid angle or wavelength range are zero.

Pulsed sources

For a pulsed source, the wavelength dependence of the intensity can be determined  by a given 'wavelength distribution function' as in the CW case. Additionally, the time dependence of the flux can be determined by a 'time distribution function'. It describes the time dependence of the pulse. In the first column the time [ms] has to be given, in the second the amplitude of the flux. The product of the amplitude given in the wavelength distribution and that given in the time distribution must have the unit n/(cm² s Å sr).
It is also possible to read a 2-dimensional file containing F(l,t). In the first row the wavelength values (in Å) are expected. All following have the time (in ms) in the first column followed by flux values (in FU) for all wavelengths - see examples 'FluxLmbdTime.dat' or files in 'IsisModData'. (Comment lines starting with '#' are allowed.)
In this approach of F(l,t) being the product of the wavelength and the time distribution function, one gets the following equations to determine the time averaged total flux andmthe time averaged current into a solid angle Ω:

Artificial sources

A simple rectangular or even instantaneous pulse can be generated by using the CWS module and restricting the time window (see neutron parameters) to the according range or to 0, respectively.

Normalizaton

For both ways to restrict the divergence (by window and by max. angles), the solid angle corresponding to the divergence window is calculated, in order to determine absolute flux values. For every trajectory, the count rate that it represents has to be calculated. If we have chosen an analytic function to describe the moderator (e.g. the Maxwellian distribution), we just use that value of M(λ), T(t) or F(λ,t) in the equation.

If the distribution files are used, M(λ) or T(t) are interpolated in logarithmic scale, e.g.