DOI 10.1140/epjp/i2013-13077-1

Regular Article

Eur. Phys. J. Plus (2013) 128: 77 THE EUROPEANPHYSICAL JOURNAL PLUS

Concrete shielding of neutron radiations of plasma focus anddose examination by FLUKA

M.J. Nematia, R. Amrollahi, and M. Habibi

Nuclear Engineering and Physics Department, Amirkabir University of Technology, Tehran, Iran

Received: 30 January 2013 / Revised: 26 May 2013Published online: 22 July 2013 – c© Societa Italiana di Fisica / Springer-Verlag 2013

Abstract. Plasma Focus (PF) is among those devices which are used in plasma investigations, but thisdevice produces some dangerous radiations after each shot, which generate a hazardous area for the op-erators of this device; therefore, it is better for the operators to stay away as much as possible from thearea, where plasma focus has been placed. In this paper FLUKA Monte Carlo simulation has been used tocalculate radiations produced by a 4 kJ Amirkabir plasma focus device through different concrete shieldingconcepts with various thicknesses (square, labyrinth and cave concepts). The neutron yield of Amirkabirplasma focus at varying deuterium pressure (3–9 torr) and two charging voltages (11.5 and 13.5 kV) is(2.25±0.2)×108 neutrons/shot and (2.88±0.29)×108 neutrons/shot of 2.45 MeV, respectively. The mostinfluential shield for the plasma focus device among these geometries is the labyrinth concept on four sidesand the top with 20 cm concrete.

1 Introduction

FLUKA is a general purpose tool for calculations of particle transport and interactions with matter, covering anextended range of applications spanning from proton and electron accelerator shielding to target design, calorimetry,activation, dosimetry, detector design, Accelerator Driven Systems, cosmic rays, neutrino physics, and radiotherapy [1].

The Plasma Focus (PF) is a coaxial discharge device that can generate short-lived (10–100 ns) but high-temperature(0.1–2.0 keV) and high-density (1018–1020 particles/cm3) plasma which gives fast neutron pulses (when using deuteriumgas), soft as well as hard X-rays and highly energetic ion and relativistic electron beams [2]. The PF first was discoveredindependently by Mather (in the USA) and Filippov (in the former Soviet Union) [3]. The Mather and Filippovconfigurations are different in the electrode dimensions and the aspect ratio (diameter/length) of the inner electrode.The aspect ratio is lower and higher than one for the Mather- and the Filippov-type PFs, respectively [4].

A capacitor bank, a fast spark gap switch, coaxial electrodes, and a vacuum chamber are the fundamental elementsof a PF device [5]. Over the years, many plasma focus devices with store bank energy ranging from 1 kJ to 1MJhave been built [6]. Recently, some experiments have been carried out on the small PF devices in the range of tensto hundreds of joules of capacitor energy [7]. When using deuterium gas, plasma focus devices produce fusion D–Dreactions generating fast neutron pulses with energies around 2.45MeV. The neutron bursts usually last for abouttens to hundreds of nanoseconds. Lee [8] proposed the scaling law which relates the stored energy to the physical sizesof the PF. He reported that by changing in the range of bank energy from 1 kJ to 1MJ neutron emission spans theinterval from 107 to 1012 neutrons per pulse [9]. Neutron scaling law of Yn = 3.2×1011×I4.5

pinch; Yn = 1.8×1010×I3.8peak;

Ipeak (0.3 to 5.7), Ipinch (0.2 to 2.4) in MA from numerical experiments was presented by S. Lee [10], where Yn is theneutron yield.

Although the neutron production mechanism of PFs has not been clearly determined yet, the thermonuclear fusionand beam target models are two widely accepted mechanisms to be in charge of neutron production [11].

Antanasijevic et al. and Castillo et al. [12,13] have shown that, when the working gas is pure deuterium, theneutron angular distribution has a Gaussian function. Experimental results of A. Rossel and Choi proposed that,when a doping gas is added, there is a significant increase in the neutron anisotropy [14]. According to Zakaullah

a e-mail: arash nemati@aut.ac.ir

Page 2 of 9 Eur. Phys. J. Plus (2013) 128: 77

Fig. 1. Conceptual drawing of the plasma focus: (1) electrical breakdown along the insulator surface, (2) accelerating currentlayer due to the Lorentz force, and (3) dense plasma column formation.

Fig. 2. Inner electrode (anode), outer electrode (cathode) and insulator arrangement of the device.

the deuterium filling pressure has an important effect on the magnitude of the anisotropic factor in the way that theanisotropic factor has a tendency to increase with pressure [15]. In fig. 1 a conceptual drawing of the plasma focus isillustrated.

In this study the plasma focus has been considered as a neutron source which will present a radiological hazard topersonnel. Therefore, a total elimination of the dose to the personnel who is operating the device cannot be achievedwithout placing the device in a very remote location. Additionally, the device must be accessible for both experimentaluse and maintenance, so we must provide enough shielding to reduce the radiation dose to the personnel to a safelevel while still retaining functionality of the device. Also, both shield thicknesses and materials are important for doseattenuation [16]. In this study the influence of each shielding will be rated by the number of times the plasma focuscan be fired before the personnel receive 20mSv at tally points that are considered out of the shields (fig. 5). Theyearly dose of 20mSv is a regulation limit in Iran, which should account for additional radiation sources located inthe laboratory of the Amirkabir University. The plasma focus has been placed in an area of about 900m2, in order todecrease the secondary radiations that have been scattered in the laboratory. In other word, the laboratory extendsover a wide area, so that the radiations which can pass through the shield do not have much influence on personnel.

In this paper, the experimental results about neutrons which have been radiated by the Amirkabir Plasma Focus(APF) device will be regarded, then, by using all the results as input, FLUKA Monte Carlo analysis of the dose aroundthe APF will be done. This paper aims at verifying the shielding of the concrete square, labyrinth and cave geometriesin declining the dose to the personnel near the device by using FLUKA code.

2 Experimental result

The simulation is performed on the Amirkabir plasma focus device (APF) that is powered by a 40μf capacitor,operating at 16 kV [17]. The inner electrode with a diameter of 20mm and 148mm in length is a hollow coppercylinder. The outer electrode is composed of six copper rods which form the shape of a squirrel cage with an innerdiameter of 44mm. Anode and cathode are separated by a Pyrex tube 45mm in length. The vacuum system consistsof a rotary and diffusion pump which evacuates the chamber up to 10−5 torr before filling it which, deuterium gas. Inorder to reduce the impurity effects, the chamber is evacuated up to 10−3 torr after every 5 shots and is refilled withfresh deuterium gas. In APF the total discharge current is measured by a Rogowski coil. A picture of the arrangementof electrodes and insulator sleeve is shown in fig. 2.

Eur. Phys. J. Plus (2013) 128: 77 Page 3 of 9

Fig. 3. Schematic (left) and experimental (right) arrangement for measuring the neutron anisotropy of the APF device with anarray of seven Geiger-Muller counters at a distance of 90 cm and at angles 0◦, ±30◦, ±60◦, and ±90◦ regarding to the z-axis.

Fig. 4. Dependence of the neutron yield on the deuterium pressure for two operating voltages (11.5, 13.5 kV).

In the APF laboratory, Geiger-Muller (model LND 72514) activation counters biased at 650V have been used forthe time-integrated measurements of the neutron yield and its angular distribution. Fast neutrons are thermalizedby a polyethylene moderator cylinder with a diameter of 6 cm, a length of 16 cm and an axial hole of 2 cm diameter.As shown in fig. 3, the measurement of the neutron anisotropy was made possible by placing an array of seven silveractivation counters at a distance of 90 cm and at the angles of 0◦, ±30◦, ±60◦, and ±90◦ in relation to the innerelectrode tip (the z-axis) [18].

Experiments were carried out with pure deuterium with pressures varying from 3 to 9 torr at 11.5 kV and 13.5 kVcharging voltage. Results reported here are the conclusions of almost 600 discharges. The neutron yield per shotwas measured with the activated silver counter which has been calibrated in situ using a Am-Be neutron source(housed on the anode tip). The neutron yield at varying deuterium pressure (3–9 torr) and two charging voltages(11.5 and 13.5 kV) was studied and the results are shown in fig. 4. According to fig. 4, the neutron yield increasesinitially as a function of deuterium pressure to an optimum pressure and thereafter decreases on further raising thepressure. It can be concluded that at the low working pressures the neutron production values are greater for lowoperating voltages and as the pressure increases the neutron yield becomes dominant by higher voltages. As can beseen, the average neutron yield of (2.25 ± 0.2) × 108 neutrons/shot at 11.5 kV in Ipinch = 0.2MA, Ipeak = 0.31MA,and (2.88 ± 0.29) × 108 neutrons/shot at 13.5 kV in Ipinch = 0.21MA, Ipeak = 0.34MA have been achieved.

3 Simulation setup

3.1 Source distribution

An accurate FLUKA simulation requires the input of a source term representing the emitted radiation [19]. Both theplasma created in the PF device and the possible fusion reactions emit large amounts of radiation [20]. According to

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Table 1. Composition of the concrete used in this study with density of 2300 kg/m3.

Composition of concrete

Atomic number Fraction by weight

1 0.010000

6 0.001000

8 0.529107

11 0.016000

12 0.002000

13 0.033872

14 0.337021

19 0.013000

20 0.044000

26 0.014000

the experimental result, the neutrons yield at varying deuterium pressure (3–9 torr) and two charging voltages (11.5and 13.5 kV) are (2.25± 0.2)× 108 neutrons/shot and (2.88± 0.29)× 108 neutrons/shot, respectively. However, thesenumbers are changeable if the structure of the PF has been changed. So by using a higher estimation on the numberof neutrons which will be emitted by the APF not only will the neutron yield of the APF be covered in the simulation,but also this simulation could be used for other PF devices, and, in this study, it may be assumed that 109 neutronsof 2.45MeV per shot will be radiated by the APF.

If we consider the neutron production just as a result of fusion reactions, one should expect an isotropic emissionof neutrons, whereas many experimental results proved that the emission of neutrons is higher at axial direction thanat the radial direction and cannot be considered as an isotropic emission [21]. However, in order to solve this conflict,the neutron emission region in the plasma focus device has been modeled by FLUKA as an isotropic neutron sourcethat, in the worst-case scenario, emits more neutrons in the lateral direction than the real source. In view of the factthat all the numbers that will be offered in this study are the result of a higher estimation for the source, the amountof dose that will be absorbed in reality by the personnel is a little lower than the number which is reported here. Inother words, the impact of the approximation chosen for the source is such that, if in the real construction of theshield some problem raise, the personnel could still work beyond the shield in a safe situation. In the following, theZ-axis is oriented in the vertical direction, and is parallel to the symmetry axis of the inner PF electrode. The X-axispoints towards the east direction and the Y -axis northwards. The isotropic neutron source is located on the anodetip practically in the same position where the pinch forms, until neutron saturation is reached (Z = 140 cm). Thisstructure of the source is illustrated in figs. 6, 7 beyond the concrete shield.

In addition, for simulations the Monte Carlo method is used, which is a physical system operating by trackingthe history of a single primary particle, and all generated secondary particles. The secondary particles generated byneutron interactions in concrete were transported in the simulations such as prompt gamma rays, recoil protons,secondary neutrons generated in (n,2n) reactions, reaction products from fast neutron interactions, and also secondaryelectrons from prompt gamma ray interactions. In fact, when particles of plasma focus radiation smash into atomswithin the shield, they trigger tiny nuclear reactions, which are all considered in the FLUKA for the calculation of thedose and radiation shielding analysing.

Furthermore, the ambient dose H∗(10), which is the required operational quantity when designing an installation,has been calculated during the FLUKA runs using the conversion coefficients from ICRP n. 74.

3.2 Shielding configurations

SimpleGeo, the 3D modeling software [22], has been used to create the simulation geometry. Radiation-shieldinganalysis involves the investigation of concrete square, labyrinth and cave shielding shapes of different thicknesses. Theadvantage of concrete materials is that they produce far less “secondary radiation” than heavier materials like lead.Moreover, neutron slowing down on the hydrogen contained in concrete contributes to reducing the neutron energy.The composition of concrete used in this study has density of 2300 kg/m3, and contains 1% by weight of hydrogenshown in table 1.

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Fig. 5. FLUKA geometry plotted on four sides and the top with 80 cm concrete shielding in the X-Y plane for the (a) squareshielding, (b) the labyrinth shielding, and (c) the cave shielding.

3.2.1 Square

The first shield configuration that has been modeled is the simple square shield shown in fig. 5a. This configurationprovides excellent dose reduction since radiation must pass through the shielding material to reach the personnel orscatter from the ceiling. The obvious downside of this configuration will be the limited line of sight operation sinceexperiments must be placed inside the shield. Maintenance of the device is also difficult since the personnel must climbover the shielding material to reach the device. Additionally, the PF device must be lifted or the shielding materialremoved in order to allow movement of the device out of the shield. In this study the simple square shield concept ispresented as a benchmark for other shields. Also, utilization of different shielding thicknesses has been examined here.For the square shield, the tally points and dimensions are shown in fig. 5a with the shield location.

3.2.2 Labyrinth

While the square shield is effective at reducing the dose, the usability of the device is severely limited since the roofof the shield must be removed whenever access to the device is required, so increasing the functionality of the squareshield results in the “labyrinth” configuration. The labyrinth is presented in figure 5b. This configuration allows moreversatility as the device can be moved in and out of the shielding easily while the line of sight operation is still limited.An additional advantage of the labyrinth is that one side offers two layers of shielding protection. In addition, labyrinthshielding allows the personnel to access the device for upgrades, alterations or other modifications. Also, the materialswhich will be used in the construction the labyrinth shield decrease slightly than the square shield. However, radiationcan still leave the shield by scattering from the ceiling or undergoing scatter. For this shield the passage faces southand away from tally 2, and the width of the passage is 100 cm. The layout for the labyrinth tally points is identical tothe square shield as illustrated in fig. 5b.

3.2.3 Cave

Increasing the line of sight operation is possible with a “cave”-type design by removing one side of the square shield.This concept is shown in fig. 5c. The line of sight operation is dramatically improved as experiments can be easilyplaced without interference from the shield. However, the personnel in direct line of sight with the device will nothave the protection of any shielding. In other words, this shield is the most versatile design, but also the least effectivein radiation protection since one side of the shield is removed. Additionally, scatter of the unshielded radiation wallcould present a hazard to the personnel on the shielded side. In this configuration the open side faces south and thewidth of the passage is 400 cm.

Page 6 of 9 Eur. Phys. J. Plus (2013) 128: 77

1e-08

1e-07

1e-06

1e-05

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0.001

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Equ

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ose

(Sv)

Y(cm)

Distribution of Dose

Distribution of Dose

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Y(cm)

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m)

1e-09

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X(cm)

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1e-11

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Distribution of Dose

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Y(cm)

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1e-08

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X(cm)

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(cm

)

1e-08

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Equ

ival

ent D

ose

(Sv)

(a)

(d)

(g)

(b) (c)

(e) (f)

(h) (i)

Fig. 6. FLUKA equivalent dose plotted on the four sides and the top with 80 cm concrete shielding in: a) Y -plane for squareshielding; b) Y -Z plane for square shielding; c) X-Y plane for square shielding; d) Y -plane for labyrinth shielding; e) Y -Z planefor labyrinth shielding; f) X-Y plane for labyrinth shielding; g) Y -plane for cave shielding; h) Y -Z plane for cave shielding;i) X-Y plane for cave shielding.

4 Simulation result

For the square, labyrinth and cave structures, three tally points have been regarded, and they were illustrated in fig. 5.The simulation results will be analyzed in three steps so that, in the first step, the source has been completely enclosedon four sides and the top by 80 cm concrete. Distribution of the dose in the Y -direction, and the graphical view of theequivalent dose results in the X-Y , and Y -Z directions for this configuration have been simulated in fig. 6.

In this study the impact of each shielding will be rated by the number of times the device can be fired beforethe personnel receive 20mSv at tally points 2 and 3. The Amirkabir plasma focus device could be fired about 1000times in a year, so a thinner shielding would be suitable for this PF. In the next steps we continue by decreasing thethickness of the shield to 40 and 20 cm. In fig. 7 the distribution of the dose for a 20 cm concrete shielding thicknessare shown.

Eur. Phys. J. Plus (2013) 128: 77 Page 7 of 9

1e-06

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1e-06

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1e-06

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1e-06

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ival

ent D

ose

(Sv)

(a)

(d)

(g)

(b) (c)

(e) (f)

(h) (i)

Fig. 7. FLUKA equivalent dose plotted on the four sides and the top with 20 cm concrete shielding in: a) Y -plane for squareshielding; b) Y -Z plane for square shielding; c) X-Y plane for square shielding; d) Y -plane for labyrinth shielding; e) Y -Z planefor labyrinth shielding; f) X-Y plane for labyrinth shielding; g) Y -plane for cave shielding; h) Y -Z plane for cave shielding; i)X-Y plane for cave shielding.

In table 2 the equivalent dose in tally 1, 2 and 3 for all types of shield with different thickness is illustrated. Thevertical position of the tally points is 150 cm, and the dimension of the tally points have been considered, accordingto the number of grids, which, in this study, are cubes with 7 cm in length.

5 Conclusions

A plasma focus creates a very dense focus point of plasma with temperatures high enough to induce fusion reactions.Disruption of the plasma column is responsible for the emission of fast neutrons, electrons, ions, and X-rays. This posesa radiological hazard to scientist and personnel operating the device. Ultimately, a decision on which the shieldingconfiguration is to be used will be based on the comparison of the installation costs compared to the number of timesthe device can be fired. The labyrinth shield with a 80 cm concrete thickness on the walls allows the greatest number

Page 8 of 9 Eur. Phys. J. Plus (2013) 128: 77

Table 2. Summary of the dose to tally points 1, 2 and 3, from all shield configurations.

Shield typeTally point Shot per +/-

(Sv) 20 mSv statistical errors

Tally1- 80 cm square concrete shielding 4.7 × 10−4 42 5%

Tally2- 80 cm square concrete shielding 8.3 × 10−8 240963 0.004%

Tally3- 80 cm square concrete shielding 8.3 × 10−8 240963 0.004%

Tally1- 80 cm labyrinth concrete shielding 4.5 × 10−4 44 4.7%

Tally2- 80 cm labyrinth concrete shielding 6 × 10−8 333333 0.003%

Tally3- 80 cm labyrinth concrete shielding 1 × 10−7 200000 0.003%

Tally1- 80 cm cave concrete shielding 4.3 × 10−4 47 4.8%

Tally2- 80 cm cave concrete shielding 9 × 10−8 222222 0.003%

Tally3- 80 cm cave concrete shielding 7.4 × 10−5 270 0.13%

Tally1- 40 cm square concrete shielding 3.5 × 10−4 57 0.03%

Tally2- 40 cm square concrete shielding 2.4 × 10−6 8333 0.003%

Tally3- 40 cm square concrete shielding 2.4 × 10−6 8333 0.003%

Tally1- 40 cm labyrinth concrete shielding 3.3 × 10−4 61 0.05%

Tally2- 40 cm labyrinth concrete shielding 2.1 × 10−6 9523 0.007%

Tally3- 40 cm labyrinth concrete shielding 3.5 × 10−6 5714 0.006%

Tally1- 40 cm cave concrete shielding 3.1 × 10−4 65 0.04%

Tally2- 40 cm cave concrete shielding 3.2 × 10−6 6250 0.006%

Tally3- 40 cm cave concrete shielding 6.8 × 10−5 294 0.06%

Tally1- 20 cm square concrete shielding 1.6 × 10−4 125 0.007%

Tally2- 20 cm square concrete shielding 1.65 × 10−5 1212 0.009%

Tally3- 20 cm square concrete shielding 1.65 × 10−5 1212 0.009%

Tally1- 20 cm labyrinth concrete shielding 1.5 × 10−4 133 0.04%

Tally2- 20 cm labyrinth concrete shielding 1.6 × 10−5 1250 0.007%

Tally3- 20 cm labyrinth concrete shielding 1.7 × 10−5 1176 0.006%

Tally1- 20 cm cave concrete shielding 1.4 × 10−4 143 0.08%

Tally2- 20 cm cave concrete shielding 1.8 × 10−5 1111 0.005%

Tally3- 20 cm cave concrete shielding 6.3 × 10−5 317 0.004%

of shots, almost 333333 per year, but it also would be the most expensive due to the material and installation costs.Furthermore, the Amirkabir plasma focus device could be fired about 1000 times in a year, so the best choice betweenconcrete shields for this plasma focus is the thinner one. It means that the shielding on the four sides and the topwith 10 cm concrete make a suitable protection from radiological hazard to the personnel. Also, the usability of theplasma focus device is limited by a squared shield, so the labyrinth concept with 20 cm concrete thickness is the mosteffective shield.

Eur. Phys. J. Plus (2013) 128: 77 Page 9 of 9

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