Neutron field characterization using TFBCs and comparison to Monte Carlo simulations

NEUTRON FIELD CHARACTERIZATION USING TFBCS AND COMPARISON TO MONTE CARLO

SIMULATIONS

June 10, 2015

Benjamin Eriksson Degree Project C in Physics

Department for Physics and Astronomy Uppsala University

Supervisor: Andrea Mattera

Subject Reader: Cecilia Gustavsson

Contents

1 Introduction 5

1.1 Ethical aspects . . . . 6

2 Theoretical background 6 2.1 The IGISOL technique . . . . 7

2.2 Thin Film Breakdown Counters . . . . 8

2.2.1 TFBC efficiency . . . . 9

2.3 Time-of-Flight mode . . . 11

2.3.1 The wrap around effect . . . 12

2.4 Simulated data . . . 12

2.5 Treatment of uncertainties . . . 13

3 Experimental setup and treatment of simulated data 15 3.1 Experimental setup . . . 15

3.2 Treatment of experimental data . . . 17

3.3 Treatment of simulated data . . . 18

3.3.1 Conversion from energy to ToF . . . 19

3.3.2 Conversion from differential neutron flux to number of detected events 20 3.3.3 Determining the cross sections corresponding to the incident neutron energies . . . 21

3.3.4 Uncertainty analysis of simulated data . . . 21

3.3.5 Rebinning of simulated data . . . 23

4 Results 24

5 Discussion 28

6 Recommendation 31

7 Conclusions 32

Benjamin Eriksson Uppsala University

Abstract

Between March 30

and April 2

in 2015, a series of experiments were conducted at the Jyväskylä cyclotron facility in Finland. Protons accelerated to 30 MeV impinged on a proton-neutron converter consisting of a water-cooled beryllium target in an aluminium casing. The resulting neutron field will be used for the study of exotic nuclei created through neutron-induced fission. Knowledge of the neutron field is a prerequisite to determine for example how many fission events are to be expected. Measurements of the neutron field were performed in three different positions: at 3.1 cm, 37.1 cm and 64.9 cm distance from the neutron source. This report presents some of the results from these measurements.

The neutron field was characterized using Thin-Film Breakdown Counters which indi- rectly detect neutrons through the detection of fission fragments from a target material.

Information on the energy of the neutrons was determined using the Time-of-Flight (ToF) technique. The ToF-spectra collected in each position were compared to those obtained from Monte Carlo simulations of the experimental setup performed in FLUKA. The goal was to find which simulations were compatible with the experimental ToF distributions and to compare results obtained with two different target materials:

U and

U.

The simulation that was most compatible with the experiment was the ToF-spectrum taken at 37.1 cm from the proton-neutron converter, none of the simulations however agreed with the experiments within the provided uncertainties. The simulations under- estimated the number of detected events. In addition to that, there is an uncertainty with which the ToF-system can determine the flight time due to the intrinsic time resolution of the TFBCs as well as the time spread in the proton bunch from the cyclotron, which is not included in the simulations. This is particularly noticeable in the spectra obtained at 3.1 cm, where the width of the experimental peak is dominated by the time resolution.

The ToF spectra taken with the

U target were affected by noise in the signal used to

extract the ToF. These problems were eliminated for the other runs. This made it difficult

to compare the two targets, however the

U target should result in ToF-spectra with

lower background as a result of the low cross section for neutron-induced fission at

energies below 1 MeV.

Abstract

Mellan 30 mars och 2 april 2015, utfördes en serie experiment vid cyklotronanläggningen vid Jyväskylä universitet i Finland. Protoner accelererades till 30 MeV och leddes till en proton-neutron-konverterare som bestod av en vattenkyld berylliumskiva i en alumini- umbehållare. Det resulterande neutronfältet kommer att användas till studier av exotiska kärnor som skapats genom neutroninducerad fission. En god kunskap om neutronfältet är en grundförutsättning för att bland annat kunna bestämma mängden av klyvningar som förväntas. Mätningar av neutronfältet utfördes därför i tre olika positioner: 3.1 cm, 37.1 cm, och 64.9 cm från neutronkällan. Denna rapport presenterar resultaten från dessa mätningar.

Neutronfältet karaktäriserades med hjälp av "Thin-Film Breakdown Counters" som in- direkt detekterar neutroner genom detektion av fissionsprodukter producerade genom klyvning av ett klyvbart material. Neutronernas flygtid bestämdes med hjälp av en "Time- of-Flight"-teknik (ToF) för att skapa ToF-spektra i varje position. Den experimentella uppsättningen simulerades med hjälp av Monte Carlo koden FLUKA och jämfördes med experimentella ToF-spektra. Målet var att bestämma vilken simulering som bäst stämde överens med experimentet samt att jämföra ToF-spektra tagna med två olika klyvbara material:

U och

U.

Den simulering som bäst stämde överens med experimentet var ToF-spektret taget 37.1 cm från neutronkällan, inga simuleringar överensstämde dock med experimentet inom ramen för osäkerheterna. Simuleringen vid 3.1 cm överensstämde sämst med experimentet på grund av detektorns låga tidsupplösning samt protonbuntarnas tid- sutbredning från cyklotronen. ToF-spektret som togs med

U försämrades på grund av störningar i signalerna. Dessa kunde dock elimineras för de senare körningarna.

Störningarna gjorde det svårt att jämföra de två olika materialen, dock kunde slutsatsen

dras att bakgrunden för

U borde vara lägre än för

U på grund av det låga tvärsnittet

för neutroninducerad fission för

U vid energier lägre än 1 MeV.

Benjamin Eriksson Uppsala University

1 I NTRODUCTION

Between March 30 ^th and April 2 ^nd , 2015, a series of experiments were conducted at the Jyväskylä cyclotron facility in Finland, specifically at the IGISOL (Ion Guide Isotope Separator On-Line) beam line. The main experiment at IGISOL was the study of exotic nuclei created through neutron-induced fission. By bombarding different fissionable targets with neutrons the goal was to produce very neutron-rich nuclides in order to study the physics of nuclei far from the valley of stability. A substantial knowledge of the neutron field close to the target being bombarded is required. This, along with the target thickness, target material and distance from the source, is an important parameter to estimate, amongst other things, the fission rate. The BRIGIT-2 (Breakdown counters at IGIsol Target) campaign conducted measurements using Thin Film Breakdown Counters (TFBCs) in order to characterize the neutron field at three positions around the IGISOL target. The IGISOL technique will be treated in section 2.1.

This report shows some of the results from the measurements of the BRIGIT-2 campaign and compares them to Monte Carlo simulations of the experimental setup at the IGISOL target. The TFBCs used during the experiment are a small type of detector that can be used to indirectly detect neutrons through the detection of fragments from neutron-induced fission.

The detectors were used in Time-of-Flight (ToF) mode, where the energy of the neutron is determined by measuring its flight time between creation and detection. With knowledge of the distance traveled, the velocity of the neutron (and in turn its kinetic energy) can be found. The experimental data resulted in ToF spectra, showing histograms with the number of events for each ToF bin. The Monte Carlo simulations of the experimental setup on the other hand, give the differential neutron flux as a function of the neutron energy. In order to be able to compare the experimental and simulated data, the simulated data must be converted into a ToF spectrum and corrected for the parameters that influence the TFBCs such as the cross sections of the target materials and detector efficiency. See section 2.2 for greater detail.

The goal of this project is to produce neutron ToF-spectra from the different experimental

measurements and compare them with Monte Carlo simulations of the same experimental

setup. Once the Monte Carlo neutron energy spectra have been adjusted with respect to the

cross sections of the different fissile target materials, the experimental and simulated ToF

spectra can be compared. The simulated data will be discussed in section 2.4 and 3.3.

Two important problems to be solved may consequently be formulated as:

• What simulated neutron energy spectra are compatible with the ToF distribution mea- sured with the TFBCs, once the fission cross sections of the targets are taken into account?

• Can we see some difference between the results that were obtained looking at data acquired with natural uranium and ²³⁸ U?

1.1 Ethical aspects

Ethical aspect are always a relevant topic of discussion for any project or scientific field, ex- perimental physics being no exception. Ethics within research implies a big responsibility on the individuals conducting the research. The researchers often have an in-depth knowledge of their field which others lack, making it easier for them to alter or fabricate information without the general public noticing. Whether this is done to scare the general public or to aid a cause, in the few cases where it occurs, it is almost always done with the purpose of self gain. In the context of this project, data fabrication is probably the most relevant form of scientific misconduct as it is a study of both experimental and simulated data, which technically is not hard to alter to one’s liking. A way of preventing data fabrication and similar scientific misconduct is by working in research groups where you share your data and tools for acquiring the data.

Another aspect which may be connected to ethics, however loosely, is the collaboration of scientific research between different countries. The experiment in Jyväskylä was funded by the European Commission through the CHANDA project[18], which encourages European countries to cooperate on scientific projects by funding research groups that wish to perform an experiment in a different European country in which research groups from two or more countries are involved. This inspires researchers to look for projects outside their borders and helps create projects that otherwise would not be possible.

2 T HEORETICAL BACKGROUND

In this chapter some of the theory concerning this experiment will be discussed. The IGISOL

technique will be briefly treated (section 2.1) and background information related to TFBCs

Benjamin Eriksson Uppsala University

are discussed (section 2.2). Information about the ToF technique can be found in section 2.3 and some details about the simulated data will be given in section 2.4. Finally, the treatment of uncertainties will be discussed (section 2.5).

2.1 The IGISOL technique

The IGISOL group is located at the Jyväskylä cyclotron facility and makes use of high-energy protons to create exotic fission products in particle-induced fission reactions. More than 40 new fission products have been discovered and studied using the IGISOL technique.[4]

The idea with the ion guide technique is to create ion beams of short lived radionuclides by irradiating a fissionable target with protons or neutrons. The fission products are slowed down by a gas flow of helium and transported by the same gas flow to a high vacuum chamber where they are accelerated and separated by mass. The masses of the ions are determined using a Penning trap. The IGISOL technique can deliver ion beams of radionuclides with half lives as short as 0.1 ms.[5] For details on the IGISOL technique and mass separation using the Jyväskylä Penning trap see, amongst others, [5, 6].

In 2009 plans to design and build a proton-neutron converter in collaboration with Uppsala University were expressed.[7] This will allow for studies of neutron-induced fission yields.

Furthermore the yields of isotopes far from the valley of stability from neutron-induced fission have been calculated to be higher than the proton-induced fission yields.[8] Neutrons can be produced in a proton-neutron converter, exploiting the high-intensity 30 MeV proton beams that can be delivered by the cyclotron installed at IGISOL. In 2012 an experiment to measure the neutron field from a prototype of the proton-neutron converter was performed at the The Svedberg Laboratory in Uppsala. Tests were done on different geometries, the main prototype consisting of a 5 mm thick beryllium plate with a 10 mm layer of cooling water behind it and a 3 mm aluminium back plate.[9] Other geometries included a full-stop target (6 mm thick beryllium plate) in which the protons would not reach the cooling water.

The final design of the proton-to-neutron converter was presented in 2014 and consisted of a

5 mm thick beryllium plate, 15 mm cooling water and a 3 mm thick aluminium back plate

(figure 1).[10]

(a) (b)

Figure 1: (a) The proton-neutron converter mounted in the IGISOL chamber. The proton beam enters from the left and impinges on the neutron converter mounted on the end of the beam line. (b) Blueprint of the neutron converter consisting of 5 mm thick beryllium target (orange) and 15 mm cooling water (blue) placed in aluminium target holder (white hatched). Green represents the vacuum at the end of the beam line. The proton beam is represented by the red arrow. (Design by D. Gorelov)

2.2 Thin Film Breakdown Counters

Thin Film Breakdown Counters (TFBCs) are a small kind of detector that consists of thin circular layers of aluminium-coated silicon interleaved by a SiO ₂ dielectric, all submitted to a voltage (see figure 3). TFBCs are sensitive to electric breakdowns: when a heavy charged particle impinges on the TFBC, such a breakdown occurs resulting in a discharge between the silicon and aluminium layer which creates an electric pulse which can be recorded. TFBCs are often used together with a fissionable target material mounted flat onto the sensitive surface (figure 2). Neutrons may induce fission in the target material, resulting in one of the fission products hitting the TFBC creating a pulse. TFBCs have thus been used in many cases to characterize neutron fields, see amongst others [1, 2, 3].

TFBCs have the advantage of being small and have been referred to as "...promising, due to timing properties, compact design, insensitivity to background particles and gamma- radiation, and long term stability under heavy radiation conditions."[2] This stability under heavy radiation conditions implies a high applicability concerning, for example, reactor experiments and accelerator experiments.[3]

Since the TFBCs detect neutrons through the fission of a target material, the number of

detected pulses does not only depend on the number of incident neutrons, but also on the

probability of these neutrons to induce fission. The number of incident fission fragments

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Figure 2: Thin-Film Breakdown Counter used during the BRIGIT-2 campaign with a

U target mounted flat on top of it. The yellow circular disk is the

U target, behind it is the silicon detector with an aluminium coating.

from a fissionable target material onto the detector is given by

N incident FF = S TFBC ρ N

m

σ

Φ

(1)

where S _TFBC is the detector surface area perpendicular to the incident neutron beam, ρ is the thickness of the target material given in g/cm ² , N

is the Avogadro constant, m

is the atomic mass of the target material in g/mole, σ

is the neutron induced fission cross section of the target material at the energy of the incident neutron beam given in cm ² and Φ

is the neutron fluence in cm ⁻² which can be related to the neutron flux through

Φ

= j

t (2)

where j

is the neutron flux in cm ⁻² s ⁻¹ and t is the time given in seconds.

2.2.1 TFBC efficiency

The efficiency, ², of the TFBC expresses what fraction of fission fragments is detected and can be given as a percentage

² = N detected FF

N incident FF

(3)

Rearranging equation 3 and applying equation 1 we find

N detected FF = ² N incident FF = ² S TFBC ρ N

m

σ

Φ

(4)

where we define

² = ² S ˜ TFBC (5)

as the reduced efficiency, given in cm ² . Combining equations 4 and 5 gives us the equation for the number of detected fission fragments

N detected FF = ˜² ρ N

m

σ

Φ

(6)

The reduced efficiency is measured in a calibration run using a ²⁵² Cf source. ²⁵² Cf decays through alpha decay and spontaneous fission, with a rate of r

/r

≈ 31.[12] The TFBC is however not sensitive to light ions such as α particles.[2] Using equation 4 with the incident fission fragments related to ²⁵² Cf we find

N detected FF = ² N incident FF = ² S TFBC a

= ˜² a

(7) where a

is the number of spontaneous fissions per cm ² produced by the ²⁵² Cf source. This makes it possible to determine the reduced efficiency[2]

² = ˜ N detected FF

a

(8)

where N detected FF is counted during calibration and a

is a given characteristic of the cal- ifornium deposit. The advantage of measuring the reduced efficiency is that the detector area is not taken into consideration. As can be seen in figure 3, the detector is not completely circular, which makes it difficult to calculate an exact area. The detector used to gather data for this project has a reduced efficiency ˜ ² ^∗ = 0.164 ± 0.006 cm ² . Further corrections to the reduced efficiency must be done since the fission fragment properties from spontaneous fissions are different to the fission fragments from particle induced fissions. How these cor- rections are performed is beyond the time scope of this project, the corrections are however given as κ

_U = 0.994 ± 0.050 and κ

U = 0.958 ± 0.048.[11] The corrected efficiency for each target material is given by

² = ˜² ˜ ^∗ · κ (9)

Benjamin Eriksson Uppsala University

Figure 3: TFBC without a fissionable target mounted on top of the silicon plate. The sensitive part of the detector is in the centre, the aluminium coating on the silicon can be seen. Due to manufacturing reasons the sensitive part of the detector is not completely circular making it difficult to determine an exact area. (Picture by M. Lantz)

which gives ˜ ²

U = 0.157 ± 0.010 cm ² (6.3 %) and ˜ ²

_U = 0.163 ± 0.010 cm ² (6.3 %). See section 3.3.4 for details on how the uncertainty in the corrected efficiency was determined.

2.3 Time-of-Flight mode

When studying neutron fields it is not only of interest to find the neutron flux but also the energy distributions of the neutrons. This may be done by using the TFBCs in Time- of-Flight mode (ToF-mode). In this technique, the energy of the neutron is deduced by measuring its flight time (t _tof ) between the time of creation and detection in the TFBC.

Assuming a straight path and a given length between the point of creation and detection, together with the measured t _tof , the energy can be determined while taking relativistic effects into consideration. The velocity of the neutron in the lab frame is

v

= L

t _tof (10)

where L is the distance between the point of creation of the neutron and the TFBC. In order to determine the kinetic energy of the neutron the rest mass is subtracted from the relativistic formula for energy

E

= m

γc ² − m

c ² (11)

where m

is the rest mass of the neutron, c is the speed of light and

γ = 1

p 1 − (v

/c) ² (12)

2.3.1 The wrap around effect

One of the limitations of the Time-of-Flight technique is the so called wrap around effect (also referred to as time frame overlap), which may be explained as the effect of mistaking slow neutrons for fast neutrons.[10] To understand this effect one must have knowledge of the mechanism behind the acceleration of protons in a cyclotron.

Cyclotrons accelerate charged particles in spiral paths outwards from the centre. The particles are held in the spiral paths with a static magnetic field and accelerated using a rapidly oscillating electric field with a frequency defined as the radio frequency (RF). The cyclotron accelerates the charged particles in bunches rather than a continuous stream and the time at which the bunches are extracted from the cyclotron can be correlated to the RF signal.

Each neutron arriving at the TFBC originates from one of the proton bunches, which in turn implies that the time of creation of the neutron in the neutron converter can be correlated to the RF signal. The ToF of a neutron can then be determined as the time difference between one RF signal pulse and the pulse detected in the TFBC. The wrap around effect occurs when a neutron is so slow that its ToF is longer than an RF period (the RF at Jyväskylä was 78.12 ns), so that it is misidentified to originate from the subsequent proton bunch. This makes the slow neutron appear to be a fast neutron. This effect is however not expected to affect measurements taken with a ²³⁸ U target, since the cross section for neutron-induced fission quickly drops at energies lower than ≈1 MeV. The effect may however be visible for the natural uranium target due to the contribution to the total cross section from ²³⁵ U at low energies.

Other effects due to the data acquisition program will be discussed in 3.2.

2.4 Simulated data

Simulations of the experimental setup were performed using the particle physics Monte

Carlo simulation package FLUKA[15, 16]. The simulation included the most important parts

of the geometry of the experiment such as the proton-neutron converter with its different

components, the IGISOL vacuum chamber, the air around the chamber and the detectors at

different positions inside and outside the chamber. To simulate the neutron field, FLUKA

stores the neutron energy at the detector position in histograms. The data is given as four

Benjamin Eriksson Uppsala University

Figure 4: Geometry of the simulation (with some parts removed for clarity). The box represents the IGISOL chamber, the top and one of the sides have been removed in this figure. Inside the box the proton-neutron converter can be seen. The three detector positions are represented by the different coloured squares. The black square is 3.1 cm from the centre of the beryllium target in the neutron converter (close position), the red square is 37.1 cm from the centre of the beryllium target (far position) and the blue square is outside the IGISOL chamber at a distance 64.9 cm from the centre of the beryllium target (outside position). The red arrow shows how the proton beam enters the target assembly. (Design by M. Lantz) (Visualised using SimpleGeo[19])

columns, two describe the energy bin edges E min and E max (in GeV), one column describes the differential neutron flux,

, in the specified bin (in neutrons/cm ² /GeV/proton) and the last column gives the statistical uncertainty in the differential neutron flux as a percentage.

The point of table 1 is to show that E _min and E _max represent bin edges. This becomes apparent because the first value of E _max is equal to the second value of E _min , the second value of E _max is equal to the third value of E _min and so on. One of the difficulties with the bins that FLUKA automatically creates is that they are all of different size. The bins are smaller for lower energies and larger for higher energies. This makes it necessary to bin the experimental data in bins of the same size as the simulated data in order to make it possible to compare the two.

How the bins were treated will be discussed in sections 3.2 and 3.3.5.

2.5 Treatment of uncertainties

The main uncertainties in the majority of the simulated runs are statistical, however, for some

of the runs the systematic uncertainties tend to dominate (see section 3.3.4). The simulated

Table 1: Excerpt of one of the simulated data files. E

and E

are given in GeV, the differential neu- tron flux is given in neutrons/cm

/GeV/proton and the statistical uncertainty is given as a percentage of the differential neutron flux. The first value of E

is equal to the second value of E

etc., this is because E

and E

represent the bin edges for the corresponding value of the differential neutron flux.

E _min (GeV) E _max (GeV) Differential neutron flux (

) Statistical uncertainty (%)

.. . .. . .. . .. .

1.92E-02 1.96E-02 2.52E-03 2.27

1.96E-02 2.00E-02 2.38E-03 2.56

2.00E-02 2.095E-02 2.12E-03 1.76

.. . .. . .. . .. .

data returns statistical uncertainties in the differential neutron flux as a percentage uncer- tainty of the flux in each energy bin as shown in table 1. The uncertainty in the experimental data is assumed to obey Poisson statistics giving an uncertainty, ∆N counts , in the number of counts

∆N counts = p

N _counts (13)

where N _counts is the number of events detected by the TFBC.

Lastly, there is an uncertainty in the efficiency of the TFBC as stated in 2.2.1. This uncertainty can be considered a systematic uncertainty even though its origin is mainly statistical. It stems from an uncertainty in the number of spontaneous fissions per cm ² produced by the

252 Cf source, a

, seen in equation 8. Using formulas which include multiple parameters with their own uncertainty implies a propagation of uncertainties. If a parameter, Z, is acquired as a function of one or several variables, Z (x, y, ...), the uncertainties ∆x, ∆y..., propagate to an uncertainty in Z according to

∆Z = s

µ ∂Z

∂x ∆x

¶ 2

+ µ ∂Z

∂y ∆y

¶ 2

+ ... (14)

where ∆Z is the uncertainty in the parameter Z. Such a propagation is for example valid for

equation 6, as there is an uncertainty in both the neutron fluence, Φ

, and in the reduced

efficiency, ˜ ².

Benjamin Eriksson Uppsala University

3 E XPERIMENTAL SETUP AND TREATMENT OF SIMUL ATED DATA

The experimental setup is discussed in this section (section 3.1) including information about each run and a scheme of the electronics setup used for the data acquisition. The treatment of the experimental data is discussed in section 3.2 and treatment of the simulated data is found in section 3.3.

3.1 Experimental setup

The experiment at Jyväskylä was performed with TFBCs in three main positions:

• The close postion: at a distance of 3.1 cm from the centre of the beryllium target in the neutron converter (the black square in figure 4).

• The far position: at a distance of 37.1 cm from the centre of the beryllium target in the neutron converter (the red square in figure 4).

• The outside position: located outside the IGISOL chamber 13.5 cm from the long side and 7 cm from the short side (see the blue square in figure 4), resulting in a distance of 64.9 cm from the edge of the neutron converter.

Other positions were also studied, this report will however only present results from these positions. Seven different experimental runs were made in these three positions. Information about each run can be found in table 2. The nominal beam current was 1 µA for the first five runs and 5 nA for the other runs. The beam currents for run 1 and 2 were however not recorded, therefore the values were chosen to be the same as for run 3 and an uncertainty was added to the number of detected events in run 1 and 2. The uncertainty was determined by calculating the standard deviation of the beam current in run 3, 4 and 5.

In figure 5 the electronics scheme of the experiment is shown. The main steps of the signal processing are explained below.

• The TFBC is subject to a voltage of +75 V from the power supply (PS N1470 in figure 5).

When a breakdown occurs in the TFBC, a negative delta function shaped pulse is sent to the shaper box which broadens the signal, making it treatable by the discriminator.

• The discriminator sends identical pulses whenever the input pulse exceeds a threshold

voltage. This was set to -150 mV for runs 1-5 & 7, and -500 mV for run 6.

Table 2: Characteristics of the different experimental runs. The average beam current for each run is shown as well as the fissionable target material used, the position of the TFBC (defined earlier in this section), the duration of each run and the number of recorded events for the specified experimental run.

Run Beam current [ µA] Target Position Run time [s] Number of events

1 0.89 ²³⁸ U Far 1121.4 951

2 0.89 ²³⁸ U Far 2610 1941

3 0.89 ^nat U Far 158.8 1000

4 0.89 ^nat U Far 335 1980

5 0.85 ^nat U Outside 1224.2 996

6 0.0052 ^nat U Close 187.3 999

7 0.0054 ^nat U Close 276.1 1000

• The discriminated pulse was sent to a scaler (Ortec 778,875 in figure 5) which recorded the number of detected pulses. The same scaler was also used to record the number of pulses from a digital current integrator.

• The digital current integrator measures pulse currents such as those from a proton accelerator. It produces a pulse when it has accumulated a specified amount of charge.

When used together with a timer, the beam current can be determined by multiplying the number of pulses by the specified value/pulse and dividing by the time. For this reason a pulse generator (PB-4 in figure 5) generating pulses at a frequency of 100 Hz was coupled with the scaler to be used as a timer.

• The discriminated TFBC signal was attenuated through two 6 dB attenuators before being sent to the data acquisition card (ADQ 412 in figure 5).

• The RF signal from the cyclotron was sent through a 30 kHz high-pass filter in order to eliminate low frequency disturbances, the signal was then amplified (Amplifier 776 in figure 5), and sent to the data acquisition card.

• The pulses recorded by the data acquisition card were saved on a PC, ready to be

treated.

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Figure 5: Electronics scheme of the experimental setup.

3.2 Treatment of experimental data

The ToF was extracted as the difference of the time at which the signals (of both the TFBC

and the RF) exceeded a threshold set at 20 % of the height of the pulses. In the cases where

the subsequent RF signal was missing, the ToF was mischaracterized by a multiple of 78.12

ns (see figure 6). This was however only the case for runs 1 and 2, and was a result of a

poor RF signal which was fixed for the other runs by using a high-pass filter to eliminate the low-frequency noise (see figure 5).

Time [ns]

0 50 100 150 200 250 300 350 400 450 500

-2500 -2000 -1500 -1000 -500 0 500 1000

(a)

Time [ns]

0 50 100 150 200 250 300 350 400 450 500

-2500 -2000 -1500 -1000 -500 0 500 1000

(b)

Figure 6: Discriminated RF signal (red pulses) plotted with single TFBC signal (black pulse). The dashed red and black lines are the thresholds determined by subtracting the maximal value from the minimal value of the pulse in question, and taking 20 % of that. The two rings show which points are used to find the ToF. The frequency of the RF signal is 78.12 ns. (a) Ideal RF signal with periodic pulses every 78.12 ns. (b) One RF pulse is missing next to the TFBC pulse. This leads to the ToF being determined incorrectly by one period of the RF signal (78.12 ns). If two pulses are missing, the ToF is determined with an error of 2 × 78.12 ns etc. Some TFBC pulses were in windows completely lacking an RF signal, these created odd peaks (as seen in figure 7) and were therefore removed.

The information extracted from the RF and TFBC pulses is given as a single column of ToF events which can be plotted in a histogram. However, due to the noisy RF signal, some of the ToF values must be shifted by a multiple of 78.12 ns. This effect can be seen in figure 7 After the small peaks were moved, and the TFBC signals lacking RF signal were removed, the whole plot was shifted arbitrarily in time in order to make it comparable to the simulated data. Finally, the experimental data was plotted in a histogram using the same bin widths as used for the simulated data (see section 3.3.5). Any ToF bin with a smaller/higher value than the minimal/maximal simulated bins was set to a size of 1 ns.

3.3 Treatment of simulated data

Simulations were done with detectors in the same three positions as in the experiment. The

simulated data was given as described in 2.4. The conversions and manipulations of the

simulated data that were made in order to be able to compare it to the experimental data will

be explained in this section.

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Time of flight [ns]

-400 -350 -300 -250 -200 -150 -100 -50 0

Number of events

0 20 40 60 80 100 120

Figure 7: Untreated ToF plot of run 2 with 1 ns bins. As a result of the imperfect RF signal, a certain number of events have been incorrectly characterised giving rise to the regularly spaced, smaller peaks.

These peaks are moved by multiples of the RF signal frequency. The rightmost peaks are a result of TFBC windows completely lacking RF pulses (as explained in figure 6).

3.3.1 Conversion from energy to ToF

The energy bins created by FLUKA were given in units of GeV and spanned between 10 µeV to 40 MeV with varying bin widths. All values below 0.1 MeV were removed because of three reasons:

1. High energies dominate the intensity of the incident neutron field. A low intensity of neutron flux implies few or no detected events in the TFBC.

2. The neutron-induced fission cross section for ²³⁸ U drops quickly below 1 MeV

3. The cross section for ^nat U is dominated at very low energies by the contribution from

235 U. However, high energy neutrons are mostly thermalized through elastic scattering, so it is valid to assume that the low energy neutrons in the fission chamber have scattered off some elements of the geometry before reaching the TFBC. This means that we can no longer assume a straight travel path from the point of creation to the point of detection, so the ToF cannot be correctly calculated from the energy of the neutron at the TFBC position.

The experiment used the ToF-technique and gave the flight time of the neutron in ns rather

than the energy of the neutron. The simulated energy bins were thus converted to ToF bins

in a unit of time in order to be able to compare them. This was achieved by combining equations 10-12 and solving for t _tof . From equation 11 and 12 we find

v

= c s

1 −

µ m

E

+ m

¶ 2

(15)

Inserting this in equation 10 and solving for t _tof we find

t _tof = L c

v u u t

1 1 −

³

+m

´ 2 (16)

which is the ToF for the neutron of energy E

and mass m

detected after flying a straight path with length L from the proton-neutron converter. L was defined as the distance from the middle of the Be-target to the closest edge of the TFBC.

3.3.2 Conversion from differential neutron flux to number of detected events

As earlier stated, FLUKA gives

in units of neutrons/cm ² /GeV/proton. In order to find the number of detected events we need to use equation 6, Φ

is however the neutron fluence with the unit cm ² . The differential neutron flux,

, must be converted to the neutron fluence, Φ

, and this is done by first multiplying

by the bin width. The bin widths, d E , were found by subtracting E _min from E _max

d E = E max − E min (17)

FLUKA gives the differential neutron flux produced by one proton impinging on the Be-target.

The proton current, I

, delivered by the Jyväskylä cyclotron is shown in table 2, knowing this quantity together with the proton charge, q

= 1.602 · 10 ⁻¹⁹ C, we can rescale to units of protons/s. Let us call this quantity p.

p = I

q

(18)

The SI unit of charge is 1C = 1 A·s, which shows that p in fact has the unit s ⁻¹ . We can now convert

to the neutron flux, j

, by multiplying it by p and d E

j

= d φ

d E · p · dE (19)

By multiplying equation 19 by the duration (in seconds) of the corresponding experimental

run being simulated (see equation 2) it is possible to determine the neutron fluence, Φ

. Φ

Benjamin Eriksson Uppsala University

can now be used in equation 6 to find the number of detected fission fragments

N detected FF = ˜² ρ N

m

σ

dφ

d E p d E t (20)

3.3.3 Determining the cross sections corresponding to the incident neutron energies The neutron-induced fission cross section, σ

, must be taken into consideration in order to determine the fission rate in the TFBC target material as seen in equation 6. Cross sections for neutron-induced fission are dependent on the incident neutron energy. The objective was in other words to find the cross sections for the corresponding energy bin. This was done by using tabulated values of cross sections from the nuclear database provided by the Nuclear Energy Agency (NEA) ¹ . Values of the cross sections for neutron-induced fission of ²³⁵ U and

238 U for neutron energies between 100 keV and 40 MeV were taken from the JENDL/HE-2007 library.[13][14] The JENDL/HE-2007 library includes around 350 values of the cross sections for ²³⁸ U and around 500 values for ²³⁵ U within the given energy span. FLUKA provided around 170 values within the same span and the tabulated energy points did not correspond directly to the simulated energy bins. In order to choose the correct tabulated cross sections for each energy bin, the centre of each bin was calculated by ¹ ₂ (E _min +E max ), and the tabulated cross section as close to this value was selected. The chosen points correlated well with the tabulated values since there were roughly twice as many tabulated points as simulated points.

A comparison between the tabulated values and the chosen values for the simulation can be seen in figure 8.

The cross sections for ²³⁵ U were used to determine the cross sections for ^nat U. Natural uranium consists of ≈99.3% ²³⁸ U and ≈0.7% ²³⁵ U.[17] The cross sections, σ nat , for ^nat U were determined according to

σ nat = 0.993 · σ

+ 0.007 · σ

(21) where σ 235 and σ 238 are the cross sections for ²³⁵ U and ²³⁸ U respectively. σ nat and σ 238 can now be used in equation 6.

3.3.4 Uncertainty analysis of simulated data

Two parameters in the equation for the number of detected events (equation 20) were used to estimate the uncertainty on the final value. There is an uncertainty in the differential neutron flux, ∆

, and there is an uncertainty in the reduced detector efficiency, ∆˜². ∆

is determined by using the statistical uncertainty provided by FLUKA. The absolute uncertainty

1

NEA is an agency within the Organization for Economic Co-operation and Development (OECD)

Neutron energy [MeV]

0 5 10 15 20 25 30 35 40

Neutron induced fission cross section [cm

]

×10

0 0.5 1 1.5 2 2.5

235U 238U

Figure 8: Comparison between the tabulated cross sections (red line for

U, black line for

U) taken from the JENDL/HE-2007 library for neutron-induced fission cross sections and cross sections chosen for each simulated energy bin (red points for

U, black points for

U). The incident neutron energy spans between 0.1 MeV and 40 MeV. The chosen cross sections for each simulated bin corresponds well with the tabulated cross sections.

in the detector efficiency is determined by using the provided uncertainty in the calibration of the detector and the uncertainty in the correction of the detector efficiency. Applying the formula for uncertainty propagation (equation 14) to the equation for the corrected detector efficiency (equation 9) gives us the uncertainty in the corrected detector efficiency according to

∆˜² = s

µ ∂˜²

∂˜² ^∗ ∆˜² ^∗

¶ 2

+ µ ∂˜²

∂κ ∆κ

¶ 2

= q

( κ ∆˜² ^∗ ) ² + (˜² ^∗ ∆κ) ² (22) where (as earlier stated) ˜ ² is the corrected reduced efficiency of the detector, ˜² ^∗ is the uncor- rected reduced efficiency and κ is the correction factor. The uncertainty in the number of detected events is given by applying equation 14 to equation 20

∆N detected FF = v u u u t

à ∂N detected FF

∂

∆ dφ d E

! 2

+

µ ∂N detected FF

∂˜² ∆˜²

¶ 2

(23)

Expanding equation 23 gives us

∆N detected FF = s

µ

² ρ ˜ N

m

σ

p d E t ∆ d φ d E

¶ 2

+ µ

ρ N

m

σ

d φ

d E p d E t ∆˜²

¶ 2

(24)

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The first term in equation 24 dominates the total uncertainty in the number of detected pulses for the far and outside position, being a factor 2 and 6 higher respectively. This suggests that the main uncertainties are statistical since ∆

is the statistical uncertainty in the differential neutron flux. The second term however dominates the total uncertainty for the close position, being 5 times higher than the statistical uncertainty, suggesting that the main uncertainty in this case is systematic, since ∆˜² is a systematic uncertainty in the TFBC. Further uncertainties due to rebinning of the simulated data will be covered in section 3.3.5.

3.3.5 Rebinning of simulated data

As stated in section 3.3.1, the energy bin widths were given by FLUKA in different sizes. This leads to the ToF bins being of different sizes. The bin width for the experiment was chosen to be 1 ns. In order to make the simulations and experiment comparable, the bin widths should be similar. The objective was to rebin the converted ToF bins from the simulations, to sizes as close to 1 ns as possible. This was achieved by taking the first ToF bin, adding 1 ns to it and finding the bin edge closest to this value, the same procedure was then repeated on the chosen bin until the last bin was reached. The number of events in the rebinned histogram were obtained by summing the number of events in the old bins corresponding to the new bin. The uncertainty in the number of counts in each of the new bins N detected FF ^∗ was obtained using the propagation of uncertainty of the sum. If

N detected FF ^∗ = N detected FF ^(m) + N detected FF ^(m+1) + . . . + N detected FF ^(n-1) + N detected FF ⁽ⁿ⁾ (25) where m, m+1, ... , n-1, n are the bins of the initial histogram that are grouped to form bin N detected FF ^∗ , the uncertainty becomes

∆N detected FF ^∗ = v u u t

à ∂N detected FF ^∗

∂N detected FF ^(m)

∆N detected FF ^(m)

! 2

+ . . . +

à ∂N detected FF ^∗

∂N detected FF ⁽ⁿ⁾

∆N detected FF ⁽ⁿ⁾

! 2

(26)

which gives us

∆N detected FF ^∗ = r

³ ∆N detected FF ^(m)

´ 2

+ . . . +

³ ∆N detected FF ⁽ⁿ⁾

´ 2

(27)

After performing the conversions and data treatments explained in these sections, the simu-

lated and experimental data were comparable.

4 R ESULTS

Results from the seven different runs will be presented in this section, each plot contains an

experimental run with the corresponding simulation. The experimental ToF-spectra have

been moved in time to make them comparable to the simulations. This may be done since the

RF does not have an absolute time-correlation with the time at which neutrons are created,

but is shifted by an unknown time δt. For more information about each run see table 2. A

discussion of the results will be presented in section 5.

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Run 1

Time of flight [ns]

-10 0 10 20 30 40 50 60

Number of events

0 20 40 60 80

Simulated data Experimental data

Run 2

Time of flight [ns]

-10 0 10 20 30 40 50 60

Number of events

0 50 100 150 200

Simulated data Experimental data

Figure 9: Experimental ToF spectrum (red histogram) with simulated data (black histogram) for run 1 and 2. A

U target was used, with the TFBC in the far position. The experimental data has been moved in time, in order to make it comparable to the simulated data.

Figure 9 shows the ToF spectra for run 1 and 2. The experimental data was taken with a ²³⁸ U

target at the far position. Run 1 was 1121.4 seconds long, run 2 was 2610 seconds long. The

beam current was not recorded and was in both cases assumed to be the same as for run 3

(0.89 µA). An uncertainty was added to the simulated data as a result of this assumption (see

section 3.1). The experimental data has been moved in time. The simulated data is narrower

than the experimental data in both cases and seems to underestimate the total number of

counts. The poor agreement of experimental ToF-spectra with the simulations may be a

result of the bad RF signal used for these runs. Some of the pulses were removed since they

completely lacked a corresponding RF pulse to determine the ToF from (see figure 6 and 7).

Run 3

Time of flight [ns]

-20 0 20 40

Number of events

0 20 40 60 80 100 120

Simulated data Experimental data

Run 4

Time of flight [ns]

-20 0 20 40 60

Number of events

0 50 100 150 200 250

Simulated data Experimental data

Figure 10: Experimental ToF spectra (red histogram) with simulated data (black histogram) for run 3 and 4. A

U target was used, with the TFBC in the far position. The experimental data has been moved in time in order to make it comparable to the simulated data. The simulated data underestimates the number of events and is narrower than the experimental data.

Figure 10 shows the ToF spectra for run 3 and 4. Run 3 and 4 are similar to run 1 and 2, the

detectors were both in the far postion, however a ^nat U target was used in run 3 and 4. Run

3 was 158.8 seconds long, run 4 was 335 seconds long. The beam current of both runs was

determined to be 0.89 µA using the digital current integrator. The simulated data is narrower

than the experimental data and underestimates the number of counts. The reason for this is

discussed in section 5

Benjamin Eriksson Uppsala University

Run 5

Time of flight [ns]

-10 0 10 20 30 40 50 60

Number of events

0 20 40 60 80

Simulated data Experimental data

Figure 11: Experimental ToF spectra (red histogram) with simulated data (black histogram) for run 5.

A

U target was used, with the TFBC in the outside position. The experimental data has been moved in time in order to make it comparable to the simulated data.

Figure 11 shows the ToF spectrum of run 5. A ^nat U target was used in the outside position. The

run was 1224.2 seconds long, with a beam current of 0.85 µA. The peak-to-background ratio

is lower compared to the previous runs. The simulation underestimates the total number of

counts.

Run 6

Time of flight [ns]

-10 -5 0 5 10

Number of events

0 50 100 150 200 250 300

Simulated data Experimental data

Run 7

Time of flight [ns]

-5 0 5 10 15 20

Number of events

0 100 200 300 400 500

Simulated data Experimental data

Figure 12: Experimental ToF spectrum (red histogram) with simulated data (black histogram) for run 6 and 7. The

U target was used, with the TFBC in the close position. The experimental data has been moved in time.

Figure 12 shows the ToF spectra of run 6 and 7 with the corresponding simulated data. The runs were done at the close position with a ^nat U target. Run 6 was 187.3 seconds long with a beam current of 5.2 nA, run 7 was 276.1 seconds long with a beam current of 5.4 nA.

5 D ISCUSSION

The first two experimental runs suffered from a poor RF signal. The RF signal was affected by low frequency noise which was removed in the subsequent runs by adding a high-pass filter between the RF-signal and the discriminator (see section 3.1). This resulted in TFBC pulses being characterized incorrectly by multiples of the RF signal (see figure 7). This may have introduced an uncertainty to the ToF spectra of run 1 and 2 (figure 9). If not for the poor RF signal, run 1 and 2 should be comparable to run 3, 4 (figure 10) in the sense that they are both measurements in the far position, where the number of counts for run 1 and 3 are similar, and the number of counts for 2 and 4 are similar. However, due to the difference in thickness of the ^nat U and ²³⁸ U target, run 1 is longer than run 3 and run 2 is longer than run 4. The only noteworthy difference between figure 9 and 10 is that the former shows a detector using a ²³⁸ U target and the latter a ^nat U target. Natural uranium contains 0.7 % ²³⁵ U and 99.3 %

238 U so the cross section for natural uranium is weighted towards ²³⁸ U according to equation

21. The fission cross section for ²³⁵ U however becomes large at low energies and pushes the

Benjamin Eriksson Uppsala University

Incident neutron energy [MeV]

10^-1 10⁰ 10¹ 10²

Cross section [cm

]

10^-29 10^-28 10^-27 10^-26 10^-25 10^-24 10^-23

235U natU 238U

Figure 13: Comparison between the neutron-induced fission cross section for

U (black line),

U (blue line) and

U (orange line) within the energy range 0.1-40 MeV. At energies below 1 MeV the contribution from

U becomes apparent in the natural uranium.

cross section up for natural uranium which can be seen in figure 13.

This might lead one to assume that we should see a contribution from the neutrons below 1 MeV in figure 10 (1 MeV corresponds to 24 ns for the simulated data in the figure). This is however not visible which leads us to conclude that the intensity of low energy neutrons must be low. If no such peak is seen in either the simulated or experimental data using the natural uranium, then there should not be a peak at low energies using ²³⁸ U, assuming the neutron field is the same in both runs.

Because of the poor ToF spectra in figure 9, it becomes difficult to compare them to run 3 and

4 in figure 10. Since we do not see any enhancement at low energies when using the natural

uranium target, it can be assumed that we would not be able to observe any great difference

between run 1,2 and 3,4 given a better measurement with ²³⁸ U. This claim may be supported

by comparing simulations of two runs with equal amounts of counts using the two different

targets.

TOF [ns]

0 5 10 15 20 25 30

Number of events

10 20 30 40 50 60 70

80

U 238U

Figure 14: Comparison between simulated ToF-spectra for the same number of counts for

U (red line) and

U (black line) target at the far position. The ToF-spectra have been scaled to be identical in the number of detected counts. There is no distinguishable difference between the two targets.

Figure 14 shows that the difference between the two targets for the simulated data is within the uncertainties provided, which suggests that there would be no visible difference in the experimental data even if the RF signal had been perfect. However, the simulation does not take the wrap around effect into account. There could be a difference between the two targets in the level of background from low energy neutrons.

In figure 10 and 11 a background can be seen on either side of the peaks. The TFBC used for

these runs showed very little background in the form of spontaneous fissions, approximately

one count every 100 seconds, giving an additional 1-2 counts for run 3 and 3-4 counts for run

4. The background could be a result of the wrap around effect, defined in section 2.3.1. The

reason we see no such background in the close position (figure 12), is that the minimal energy

for the wrap around effect to become apparent (around 0.001 MeV) is much lower than in the

far and outside position. For the far position the minimal energy is approximately 0.1 MeV,

in the outside position 0.3 MeV. This in turn implies that we have neutrons with energies

lower than 0.1 MeV. The reason the background-to-peak ratio is lower for the outside position

than the far position could also have to do with elastic scattering in the aluminium walls

of the IGISOL chamber. This would not change the energies of the neutrons substantially

(since they are much lighter than the aluminium cores), it could however scatter neutrons

into the TFBC, making it detect neutrons with non-linear paths. Another interesting detail is

Benjamin Eriksson Uppsala University

the lack of a consistent background in the raw experimental plot in figure 7. The poor ToF spectrum makes it difficult to draw any certain conclusions, however this might indicate that contribution from events in the wrap around effect disappears while using the ²³⁸ U target.

The cross section for neutron-induced fission quickly drops towards zero below 1 MeV for

238 U, one could say that there is an activation energy of a few MeV. This would mean that the low energy neutrons responsible for the wrap around effect would not be detected by the TFBC while using this target.

In figure 12 we see the comparison between the experimental and simulated ToF-spectra.

The simulated spectra are only a few ns wide, which is a result of the short distance between the point of creation and point of detection of the neutron. The first two bins are close to 1 ns wide each, which converted into energy corresponds to a span of approximately 30-0.6 MeV, which means almost all counts go into these bins. TFBCs however have a finite time resolution of around 1 ns. Another noteworthy effect which widens the experimental peak is the time spread of the proton bunches. Rather than accelerating protons in a continuous current, cyclotrons accelerate the protons in bunches. Each proton bunch corresponds to an RF-pulse, which is used to determine the ToF of the neutrons. However, the proton bunches have a certain width in time which results in the protons to impinge on the neutron converter with a time spread corresponding to the bunch width. This, in turn, results in an uncertainty in the ToF of the neutrons detected by the TFBC, which widens the peak. The time spread of the neutron bunches is probably what dominates the widening of the experimental peaks.

In conclusion, the simulations most compatible with the experiment were those correspond- ing to the far position inside the IGISOL chamber. The simulation of the close position corresponded the least to the experiment. The experimental peak was substantially wider than the simulated peak. The reasons for this are the time spread of the proton bunch and the finite time resolution of the TFBC. The run outside the IGISOL chamber showed a lower peak-to-background ratio compared to the other runs. This is most likely due to the effect of scattered neutrons. Since scattered neutrons make the assumption of straight flight paths between the source and detector fall, we lose the correspondence between energy and ToF.

6 R ECOMMENDATION

In order to determine the time resolution when using the ToF-technique at Jyväskylä, it would

be of interest to know the time spread of the proton bunch produced by the cyclotron. Using

this knowledge, a time spread could be added to the simulated data, as done in [10], in order to simulate the finite time resolution of the TFBCs. This would widen the simulations making them more comparable to the experimental data.

Another feature that could be added to the simulated data is a different method of achieving 1 ns large bins. This could be done by choosing bins exactly 1 ns wide even if it cuts the simulated data bins between two bin edges. A percentage of the differential neutron flux in the split bin corresponding to where the bin was cut can be added to the new bin.

It would be interesting to do more runs using the ²³⁸ U target in the far and outside position with a decent RF signal. The activation energy for neutron-induced fission of approximately 1 MeV could result in the wrap around effect being removed.

7 C ONCLUSIONS

Measurements of the neutron field in three positions inside and outside the IGISOL cham- ber at the Jyväskylä cyclotron facility were performed using TFBCs with the ToF-technique.

The experimental ToF-spectra were compared to simulations of the experimental setup in order to find if simulated spectra were compatible with the measurements. The ToF-spectra achieved using ²³⁸ U and ^nat U targets were compared and possible differences between using the different targets were discussed.

The comparison between ^nat U and ²³⁸ U was inconclusive, however the simulations suggested that there should be no differences between the ToF-spectra produced by the different tar- get materials. A difference between the two that could be of interest is whether the wrap around effect disappears using ²³⁸ U in the far and outside position. The minimum energy for the wrap around effect in the far position is 0.1 MeV and ²³⁸ U has an activation energy for neutron-induced fission of ∼1 MeV. This is also something that does not appear in the simulated data, since the simulation simulates the energy and absolute differential neutron flux of the neutron field. No background was visible in the close position suggesting that the minimal energy for the wrap around effect to become apparent was low enough. In the case of the close position it is in other words unnecessary to use both targets, as both would likely produce similar ToF-spectra.

The simulations did not agree with the experiment within the provided uncertainties, the

Benjamin Eriksson Uppsala University

simulations underestimated the number of counts as well as the width of the ToF-spectra. The runs using natural uranium at the far position (figure 10) agreed best with the simulated data, however using ²³⁸ U with a decent RF signal should produce (at least) as good ToF-spectra. In order for the simulation to better resemble the experiment, a time spread corresponding to the time resolution of the ToF-setup could be added to the simulated data. This would widen the simulated peaks, making it easier to compare them to the experimental data. Finally, it would be preferable to perform the simulations in ToF mode instead of converting from neutron energies to ToF. With information of both the ToF and the energy of the neutrons it would be possible to extract information about the background of scattered neutrons. In this case the simulation would not have to be truncated at 0.1 MeV, giving us interesting information about how the thermal-energy background neutrons appear in our ToF spectra.

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