Correction for source spectra for HFRadMon monitor

Energy spectra in user defined region using FLUKA

When energy spectra is investigated in some particular region in CMS cavern, these steps have to be followed:

1. Some existing region made out of AIR could be used. If none of regions is suitable, new AIR region has to be created (create body, assign region and material to this body, remove body from existing regions). To suppress the statistical uncertainty in some meaningful time scope, it is recommended to use regions with volume of at least 1 cubic meter, when one is interested in neutrons in cavern apart from central detector.
2. To gather energy spectra in some region in FLUKA, the USRTRACK card needs to be defined in input file. After selecting particle type(neutrons in this case) and energy range of interest, the volume of region, where one is interested in particle properties needs to be specified in card description.
3. If all above is done and FLAIR project doesn’t report any errors, simulation can start.

For this particular study five regions was constructed (see figures below). Four of them are inside HF region and last one is just outside HF. Information about regions are in table below.

Index of region	Description	Distance from IP	z [cm]	r [cm]	ϕ [°]	Volume [cm3]
A	Inside HF		[1376,1409]	[101,156]	[30,60]	122 117.63
B	Inside HF		[1376,1409]	[101,156]	[120,150]	122 117.63
C	Inside HF		[1376,1409]	[101,156]	[210,240]	122 117.63
D	Inside HF		[1376,1409]	[101,156]	[300,330]	122 117.63
Index of region	Description	Distance from IP	z [cm]	x [cm]	y [cm]	Volume [cm3]
E	Outside HF		[1170,1270]	[-250,-150]	[210,310]	1 000 000

NORMALISATION

To get correct results, the normalisation procedure has to be performed correctly. Firstly FLUKA normalises all output per one primary, so If one is interested in results from "N" particles, each value has to be multiplied by factor of N. We will furter benefit from scaling results for one microbarn. Using inelastic cross section of 80 mb gives that that there is 80 000 primary innelastic collisions per microbarn. Secondly another normalisation arises from normalising output per volume. If volume of region is not specified in USRTRACK card's description before the start of simulation it can be introduced later (WARNING! If region is projected using "LATTICE" card, then its actual volume is in fact twice bigger so another multiply of 1/2 has to be introduced).

Energy spectra results

Distribution of energy spectra in all five regions could be seen on plot below. Normally the neutron spectra are visualised in so-called "isolethargic" format, where is each content of bin multiplied by bin width.

Then if one is interested in number of neutrons in some explicit energy range then integral is performed over that range. We are interestred in neutrons measurable by HFRadMon monitors, so in other words in energy gap, where response function of HFRadMon is non zero. It was found that HFRadMon is capable to detect neutrons in between 0.258 eV and 445 MeV. Number of neutrons per one inverse μb^-1 with energy between 0.258 eV and 445 MeV is specified below.

Index of region	ϕsim [cm-2 μb-1]
A	6.7
B	7.0
C	6.9
D	6.7
E	0.38

Response function

Is defined by monitors's sensitivity to neutrons in certain energy range. HFRadMon was builded in way that it is most sensitive to neutrons with energy close to 1 MeV. These values were provided by Alexandre Ershov Alexandre.Erchov@cernNOSPAMPLEASE.ch.

Americium-Berilium source spectrum

From here: LINK

Tabulated here: LINK

Because tabulated values are in isoletargic format (^E.dΦ⁄_dE), so each bin content has to be divided by bin width to obtain plain distribution (^dΦ⁄_dE) !!!

Computation of calibration coefficient

Calibration coefficient describes the difference between spectrum expected at monitor location in CMS cavern and spectrum of neutrons from calibration source. Using this one can understand neutrons counted by HFRadMon monitor as neutrons in terms of Am-Be source

,

where (dΦ_Ambe^norm /dE) is distribution spectrum of Americium-Berilium source used for calibration of detector normalised to same number of neutrons as, (dΦ_sim /dE) distribution spectrum of neutrons from FLUKA normalised per μb^-1, R(E) is HFRadMon 's sensitivity function as function of energy (here its normalisation doesn't play any role, because it occurs in both denominator and numerator), M is energy range, where our monitor is able to count neutrons so in this case M = [2.58e-8 MeV, 445 MeV ]. To respect all bining, union of all domains is done first. Number of neutrons from FLUKA was normalised per μb^-1, so next step is to nomalise source spectrum on same number of neutrons on set M (superset of Am-Be domain). On plots below one can see the both distributions after scaling for neutrons in regions A and E.

Folding

After correctly normalising the both distributions, they are folded with with sensitivity function and integral over set M is performed. By dividing those two numbers the calibration coefficient is obtained.

Index of region	kcalibration
A	0.665
B	0.667
C	0.667
D	0.664
E	0.784

Identifing scored regions with physical detectors

Following tables are copied from HFRadmon Overview twiki, colorfull text was added.

Detector Code	Detector ID	z [cm]	y [cm]	z [cm]	Proposed scoring region
PFIT	6	-92	92	1390	D
PNIB	8	92	-92	1390	B
PNIT	9	92	92	1390	A
MFIB	11	-92	-92	-1390	C
MFIT	12	-92	92	-1390	D
MNIB	14	92	-92	-1390	B
MNIT	15	92	92	-1390	A
PFXT	4	-179	179	1220	E
MFXT	10	-179	179	-1220	E

• Column 1 - "RAW" calibration factors (Run 2014)
• Column 2 - Factors corrected for neutron background (updated after Run 2018)
• Column 3 - Factors corrected for neutron background and cylindrical shape of the detector (anisotropy)
• Column 4 - Factors corrected for neutron background and cylindrical shape of the detector and correction for difference of the source and UXC spectrum

Detector ID	1	2	3	4
6	1.33	1.59	1.87	1.24
8	1.31	1.56	1.84	1.23
9	1.51	1.80	2.12	1.41
11		1.66	1.96	1.31
12	1.37	1.64	1.93	1.28
14	1.36	1.62	1.91	1.27
15	0.87	1.04	1.22	0.81
4	1.32	1.55	1.83	1.44
10	1.31	1.56	1.84	1.44

Benchmarking Run 2 HFRadMon data against simulation FLUKA simulation

Set of physiscal data taken during Run2 (years 2017,2018) measured with HFRadMons were provided by Andrein Gribushin andrei.gribushin@cernNOSPAMPLEASE.ch.

Detector ID	Detector name	ϕdata [cm-2 μb-1 ] (13TeV, 2017)	ϕdata [cm-2 μb-1 ] (13TeV, 2018)
6	PFIT	3.65	3.25
8	PNIB	4.5	4.15
9	PNIT	3.62	3.22
11	MFIB	4.33	4.2
12	MFIT		3.17
14	MNIB	4.25	4.12
15	MNIT	3.41	3.12
4	PFXT	0.27	0.27
10	MFXT	0.25

To compare ϕ^data and ϕ^sim one have to recalculate measured data with calibration coefficient ϕ^final = k_{calibration .} ϕ^data, where ϕ^final can can be further compared to simulated number of neutrons ϕ^sim.

Detector ID+ region	Detector name	ϕfinal [cm-2 μb-1 ] (13TeV, 2017)	ϕfinal [cm-2 μb-1 ] (13TeV, 2018)
6D	PFIT	2.35	2.09
8B	PNIB	3.00	2.77
9A	PNIT	2.33	2.08
11C	MFIB	2.89	2.80
12D	MFIT		2.04
14B	MNIB	2.83	2.75
15A	MNIT	2.20	2.01
4E	PFXT	0.21	0.21
10E	MFXT	0.20

Finally data/simulation ratios could be compared, where ϕ^sim is fluence of neutrons in region specified in first column.

Detector ID+ region	Detector name	ϕsim /ϕfinal(13TeV, 2017)	ϕsim /ϕfinal(13TeV, 2018)
6D	PFIT	2.86	3.23
8B	PNIB	2.33	2.50
9A	PNIT	2.86	3.23
11C	MFIB	2.38	2.44
12D	MFIT		3.33
14B	MNIB	2.50	2.56
15A	MNIT	3.03	3.33
4E	PFXT	1.76	1.79
10E	MFXT	1.92

From there it could be seen that from simulation we expect more neutrons then is actually measured by detectros. In outer region of HF it is approximately by factor of two and in inter regions it is roughly by factor of three.