Nondestructive assay of plutonium and minor actinide in spent fuel using nuclear resonance fluorescence with laser Compton scattering γ-rays

Nuclear Instruments and Methods in Physics Research A 621 (2010) 695–700

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Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima

Nondestructive assay of plutonium and minor actinide in spent fuel using nuclear resonance fluorescence with laser Compton scattering grays Takehito Hayakawa a,, Nobuhiro Kikuzawa b,c, Ryoichi Hajima c, Toshiyuki Shizuma a, Nobuyuki Nishimori c, Mamoru Fujiwara a,d, Michio Seya e a

Advance Photon Research Center, Japan Atomic Energy Agency, Kizugawa, Kyoto 619-0215, Japan J-PARC Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan c Advance Photon Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan d Research Center for Nuclear Physics, Osaka University, Ibaraki, Osaka 567-0047, Japan e Nuclear Nonproliferation Science and Technology Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan b

a r t i c l e in fo

abstract

Article history: Received 28 December 2009 Received in revised form 23 February 2010 Accepted 11 June 2010 Available online 17 June 2010

We propose a new nondestructive assay method for 235U, 239Pu, and minor actinides in spent nuclear fuel assembly in a water pool. Nuclear fuel materials are detected using nuclear resonance fluorescence (NRF) with laser Compton scattering (LCS) grays. The NRF assay can provide a finger print of each isotope since the NRF gray energy is characteristic of a specific nuclide. We design a high-flux LCS gray source, in which grays are generated by collision of laser photons provided from Yb-doped fiber laser and electrons from energy recovery linac. This system has following advantages; this can detect isotopes of most elements behind heavy materials such as uranium of a thickness of several centimeters, and analyze the fuel assembly in a water pool. A simulation calculation shows that we can detect 1% fraction 239Pu in all the fuel rods with statistical error lower than 2% using the high flux LCS gray source and the measurement time of 4000 s. & 2010 Elsevier B.V. All rights reserved.

Keywords: Spent fuel Safeguards of nuclear materials Nondestructive assay

1. Introduction Nondestructive assay (NDA) of plutonium in spent nuclear fuel is a key technology for safeguards of nuclear materials. One of safeguards issues is the shipper receiver difference (SRD), which is the difference between the quantity of a fissionable nuclide such as 239Pu have to be shipped to the reprocessing plant and the quantity that is measured after the reprocessing. The SRD is sometimes not zero, suggesting a possibility that a part of a nuclide of interest might lost in the reprocessing. This is, however, considered to originate from a fact that the quantity before the reprocessing is only calculated with a nuclear fuel burn-up simulation code. We should develop therefore a nondestructive assay for 239Pu and other fissionable isotopes in the spent nuclear fuel. In the next generation safeguards initiative (NGSI) program of United States department of energy (DOE), NDA of Pu in the spent nuclear fuel is the top priority in technology development. For the NDA of Pu in the spent fuel, K X-ray resonance fluorescence [1], or differential die-away analysis with neutrons [2,3] have been studied. However, the NDA of 239Pu in the nuclear fuel assembly has not been well established yet. The first reason

 Corresponding author. Fax: +81 774 71 3316.

E-mail address: [email protected] (T. Hayakawa). 0168-9002/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2010.06.096

stems from the fact that high-Z element uranium in the nuclear fuel absorbs detection probes such as low-energy X-rays. Second we should not only detect elements but also analyze each isotope of interest. However, the nondestructive detection of such an isotope in heavy materials is generally difficult. Third the spent nuclear fuel is heated up due to the presence of the residual radioactivities. Thus, the spent fuel is often kept in a cooling water pool; the water absorbs or scatters neutrons and low energy X-rays. Gamma-rays have been used as a probe to detect an isotope of interest with nuclear resonance fluorescence (NRF) for industrial applications [4]. Although Bremsstrahlung grays have been widely used for NRF, Pruet et al. have proposed a novel nondestructive detection of 235U hidden in a cargo transporter by using NRF in conjunction with laser Compton scattering (LCS) gray beam [5]. The LCS gray source can produce energy-tunable, monochromatic grays by the scattering of short-duration laser pulses from relativistic electrons. In the present paper we propose a nondestructive assay method for each isotope of uranium, plutonium, and minor actinides in spent nuclear fuel located in a water pool using NRF with grays generated by a high-flux LCS source based on an energy recovery linac (ERL). This method has excellent advantages. Each isotope of elements located deeply in the nuclear fuel is detected by measuring the NRF grays since high energy

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grays of several MeV are used as the probe. In addition, the spent fuel can be analyzed with keeping in a water pool. This is important, in particular, in viewpoint of the nuclear material safeguards since anyone cannot easily access fissionable nuclides through water and walls of the pool. In the present paper, we discuss this new detection method, a design of the photon source, the detection system, and a simulation result of a 239Pu detection in a fuel assembly.

2. Measurement using nuclear resonance fluorescence The NRF measurement provides a unique finger print of each isotope. If the energy of the incident gray is identical with the M1, E1, or E2 transition energy from the ground state of the nucleus of interest, the incident gray is effectively absorbed in the nucleus and subsequently the nucleus de-excite by gray emission. The energies of the states excited by NRF is inherent in the atomic number and mass of the nucleus of interest as shown in Fig. 1. Note that this method is applicable to detect both stable and unstable isotopes for most elements. A NRF scattering cross-section over an excited level is given by   ds p‘c 2 G0 Gi Wðy, fÞ ¼g dO G Eg 4p g¼

2J1 þ1 2J0 þ 1

ð1Þ

where Eg is the gray energy, g is the spin factor, J0 and J1 are spin of the ground state and the excited state, respectively, G, G0 , and G1 are the total width, the ground-state decay width, and the partial decay width, respectively, and WðyÞ is the normalized angular distribution. By measuring the energies of the NRF grays, we can analyze nuclear species. The number of NRF events is proportional to the number of relevant nucleus. The weight of the nuclear material is evaluated from the peak counts of the NRF gray taking into the account detection efficiency and the gray absorption. The NRF detection technique using Bremsstrahlung grays have been studied for industrial applications [4]. Bertozzi et al. measured the NRF cross-sections in 235U and 239Pu using the Bremsstrahlung grays [6], which are important nuclear data for the NRF method. However, the Bremsstrahlung grays generally produce large background at the low-energy side. Energy [keV]

2464 2423 2143

Tunable

2003 1862 1815 1733

2040

Absorption

Emission

938 861 770

11/2 -

1123 1053 977 933

1084

Flux of gamma-rays

0+ 244

0

Cm

0

243

Am

5/2 + 237

0

Np

1/2 + 239

Pu

0

The NRF detection method in conjunction with LCS gray have been studied [5,7]. The LCS grays are generated by Compton scattering of relativistic electrons by laser photons. The LCS grays have excellent features: energy tunable, quasi-monochromatic, and beam-like distribution. In addition, gray pulses produced in this manner have an exceptional photon density [8]. The LCS gray sources in the energy range from sub-MeV to a few MeV have been developed in the world [9–12]. It should be noted that the LCS gray sources at the Duke Free Electron Laser Laboratory at Duke University [9], the National Institute of Advanced Industrial Science and Technology [13], and the New SUBARU [14] in SPring-8 have been used for the nuclear physics [15,16] and the nuclear astrophysics [17]. Fig. 2 shows a schematic view of the laser Compton scattering. The energy of the LCS gray depends on the angle between the direction of the electrons and the generated grays. The energy of the scattered grays, Eg , is presented by Eg ¼

EL ð1bcosy1 Þ EL ð1cosy2 Þ Ee

ð2Þ

1bcosy þ

where EL is the laser photon energy, Ee is the electron energy, pffiffiffiffiffiffiffiffiffiffiffiffiffiffi b ¼ 1g2 is the electron velocity in units of light speed c, and yi are scattering angles as shown in Fig. 2. If we consider backscattered photons from the head-on collision of photons and relativistic electrons: g b 1, b C1, y1 C y2 C p, and y 5 1, we obtain the following equation: Eg ¼

4g2 EL 2

1þ ðgyÞ þ 4gEL =ðmc2 Þ

:

ð3Þ

The energy of the scattering gray decreases with increasing the scattering angle y. The maximum energy of the LCS grays is determined by the energies of the electrons and the laser photons in the case of the scattering angle y ¼ 03 . In contrast, the lower limit of the energy width of the LCS gray is determined by a collimator limiting the scattering angle. Therefore, by using the collimator to limit the gray divergence, we can generate a gray beam with any energy spread. We have proposed an assay method of isotope hidden in heavy shields by using NRF with a LCS gray source [18]. We demonstrated to detect isotope of interest concealed at the inside of a heavy shield with an available LCS gray source at AIST [19]. A lead block was hidden by iron plates with a thinness of 15 mm. The position of the lead block was detected by measuring a 5512keV gray of 208Pb with the LCS grays. If the energy width is larger than the difference between energies of excited states of two different isotopes, we can detect these two isotopes at the same time with the energy-tunable gray beam. In fact, we measured two isotopes of 12C and 14N in a chemical compound,

Scattered Photon

920

Absorption

5/2 -

3. Nondestructive assay method using NRF with laser Compton scattering grays

θ2

Emission

7/2 -

0

235

U

Electron

θ

θ1 Incident Photon

Fig. 1. Schematic view of the nondestructive assay system based on nuclear resonance fluorescence with laser Compton scattering gray source. If the incident gray energy is identical with the excitation energy of the nucleus of interest, the incident gray is effectively absorbed in the nucleus and subsequently the nucleus de-excites by gray emission.

Fig. 2. A schematic view of laser Compton scattering. A high-energy photon (gray) is generated via the Compton scattering of an incident photon with a relativistic electron. The energy of the scattering gray changes as a function of the scattering angle (see also the text).

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melamine (C3H6N6), through a 15-mm thick iron plate and a 4-mm thick lead plate at AIST [20]. This method to detect several isotopes has an advantage that we can measure the isotope abundance ratio with high accuracy. Our proposed nondestructive assay method is demonstrated to be a powerful tool to detect isotopes of interest shielded deeply by materials.

4. Concept design of photon source and detection system

density profile equal to the rms size of electron beam at the collision point: w=2 ¼ se ¼ 70 mm. The rms size of the laser power density profile at the mirrors of the laser super cavity becomes w (at mirror)¼ 2.3 mm, which is small enough to keep the high-Q configuration with mirrors of a practical diameter d  10 cm. The laser super cavity is assumed to have an amplification factor of 3000. The total flux of laser Compton gray is obtained by using the following equation: Ftotal ¼

4.1. Photon source For the nondestructive detection of materials in an industrial scale, we have designed a high-flux gray facility utilizing a 350-MeV energy-recovery linac (ERL) equipped with a superconducting accelerator [21]. The ERL accelerator is a novel type of accelerator to generate a high-quality electron beam with a highintensity average-current. An electron beam from an injector is accelerated by time-varying radio-frequency (RF) field stored in a superconducting linear accelerator and subsequently is transported to a recirculation loop. After the recirculation, the electron beam is injected again to the superconducting accelerator with the deceleration RF phase. The re-circulated electrons are decelerated and feed back the energy to the superconducting RF cavity. This recycled RF energy is again used to accelerate subsequent electrons. The ERL is thus composed of an injector, a superconducting linac, an energy recovery loop. Recently, Litvinenko et al. also proposed the ERL based gray source [22]. Fig. 3 shows a schematic view of the LCS gray source designed on the basis of the ERL accelerator. A 3-loop design is employed for cost reduction and compactness. The electron beam is accelerated three times to gain energy needed for gray generation and then decelerated three times for energy recovery. In this way, the length of the superconducting linac and its cost are roughly three times reduced. A superconducting linac designed to accommodate high beam current in the accelerator [23] will be used in the present design. The high-flux gray beams with energies of Eg ¼ 0:529 MeV are generated from the Compton scattering with a ytterbiumdoped fiber laser with a frequency of 80 MHz and a power of 100 W, which is similar to a system shown in the previous study [24]. For the most efficient interaction of laser photons and electrons, we set the root-mean-square (rms) size of laser power

697

fNe NL sc A

ð4Þ

where f is the collision frequency, Ne is the number of electrons in an electron bunch, NL is the number of photon in a laser pulse, sc is the cross-section of Compton scattering, A is the effective sectional area of beams at the collision point, and is given by A ¼ pw2 =2 for the beam with a Gaussian profile. In the case of grays produced by the collision between laser photons with a wave length of 1064 nm (a photon energy of 1.165 eV) and electron energy of 350 MeV, the maximum energy is Eg ¼ 2:2 MeV, and the scattering cross-section can be approximated by Thomson scattering cross-section: sc ¼ ð8p=3Þre2 , where re is the classical electron radius. With the above assumptions, the flux of the laser Compton gray source amounts to 1.0  1013 photons/s, and a peak spectral density reaches at 7.0  109 photons/s/keV. This intensity is a factor of 105  108 higher than those obtained at present facilities in the world. 4.2. Detection system For detection of NRF grays, a multigray detector array is used, which has been widely used for the study of the nuclear physics. This type of detector system typically consists of 20–120 high energy resolution gray detectors (for example, see Refs. [25,26]) such as high-purity germanium (HPGe) detectors. Fig. 4 shows a schematic view of the detector system and a spent fuel assembly in a water pool. The width of the water pool is 50 cm and the thickness of the water between a fuel rod and a front of a detector is about 25–30 cm. This is determined by the size of the nuclear fuel assembly. The grays emitted from the spent fuel are measured with HPGe detectors. The resolution of the HPGe detectors is typically smaller than 0.2% (full width at half

Spent Fuel Pool Water Compton scattering

Concrete Wall

Dump

Laser 3rd 350 MeV Gamma rays

Water Concrete Wall

2nd 235 MeV 1st 120 MeV Measurement Room Concrete Wall

Linac Injector

Measurement Room

Beam dump

Fig. 3. Schematic view of the energy recovery linac (ERL). An electron beam from an injector is accelerated by a superconducting linac. After the three time recirculation, the electron beam is re-injected to the linac with a deceleration phase, and the electron energy are fed back to the RF cavity of the superconducting linac. The Compton scattering grays are generated by the collision of the electrons and laser photons.

Linac/Laser Area 3m

Spent Fuel Assembly LCS Gamma-rays

Fig. 4. Schematic view of the assay system of the spent fuel assembly near the water pool. The fuel assembly is moved to the detection position, and NRF grays emitted from the assembly are detected by 24 HPGe detectors located at the outside of the pool.

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maximum (FWHM)). The water around the spent fuel is useful for cooling and for the absorption of neutrons emitted from spontaneous fission of actinides. In addition the assay by keeping it in the water pool contributes to nuclear material safeguards; anyone cannot derive easily fissionable nuclides from the spent fuel in the water pool. Note that the energy range of the incident LCS gray beam is 1.9–2.3 MeV which is high enough to penetrate materials through shield water with a thickness of several 10 cm. Table 1 shows the gray energies emitted from the isotopes relevant to the present research work. The difference between energies of two any grays are larger than 0.2% and thus we can identify the relevant isotopes in the spent fuel. The detector system consists of 24 HPGe detectors (see Fig. 5). Sets of three detectors are located at about 721, 851, 951, and 1081 with respect to the incident beam axis (see Fig. 6). Here we consider the inspection of a BWR nuclear fuel. The BWR nuclear fuel assembly consists of 8  8 nuclear fuel rods. For a gray irradiation, the LCS gray beam passes through the eight nuclear fuel rods, and NRF events occur at these eight rods (see Fig. 6). Eight sets of HPGe detectors are located in a plane, and each detector set measures only grays emitted from a single rod. In this way, we can detect grays from all the eight rods at the same time, and the isotope distribution will be obtained as a function of the rod position. The distance between the front of the detector and the center of the fuel assembly is about 48 cm. A lead collimator with a thickness of 10 cm is located in front of each detector to limit their solid angles. The diameter of the inner hole of the collimators is 7 cm. We assume the wall of the water pool is made of lead with a thickness of 5 cm instead of each absorber for the 24 HPGe detectors (see Fig. 6). The absorbers are used to reduce the counting rate of the detectors. The grays with energies lower than 1 MeV are effectively absorbed by these thick absorbers. The nuclear fuel is vertically moved with a speed of 1 cm per 1 second to measure all the pellets. After a sequential measurement as a function of the vertical position of the fuel rods, the fuel

Fig. 5. Schematic view of the gray detection system. The detector system consists of 24 HPGe detectors. Two sets of 12 HPGe detectors are located at both the sides of the water pool.

Scattered Gamma-ray

Fuel Assenbly

Gamma-ray beam

Water

Table 1 Excitation energy and resonance width for important nuclides in spent nuclear fuel. Nuclide

Excitation energy (keV)

Cross-section (eV b)

235

1733.60 1769.16 1815.31 1827.54 1862.31 2003.32 2006.19

29.8 4.4 9.7 6.7 9.6 9.7 4.7

73.9 71.0 71.7 71.2 71.7 71.7 71.6

[6] [6] [6] [6] [6] [6] [6]

1782 1793 1846 2176 2209 2245 2295 2410 2468

21.9 5.1 23.0 57.7 53.4 26.3 7.1 21.8 25.3

72.5 71.0 72.6 73.4a 73.3a 71.8a 70.7a 71.4a 71.9a

[31] [31] [31] [29] [29] [29] [29] [29] [29]

72 72 72 72 72 72 72 73 73

[6] [6] [6] [6] [6] [6] [6] [6] [6]

238

239

a

U

U

Pu

2040.25 2046.89 2135.56 2143.56 2150.98 2289.02 2423.48 2431.66 2454.37

Calculated from experimental G0 =G.

8 5 4 13 5 8 10 9 9

Absorber Collimator

Ref.

Detector 20 cm Fig. 6. Result of simulation calculation. The solid lines are traces of grays. The incident grays are scattered by Compton scattering and NRF. The LCS grays reach at the fuel dots located at the opposite side.

assembly is horizontally moved for only a distance between two fuel rods. This measurements are repeated until the satisfactory data are accumulated for further computer analysis. In this manner, all the pellets in a fuel assembly can be measured for a period of 3000–4000 s.

5. Simulation of plutonium detection 5.1. Numerical modeling The question to be addressed here is whether this system can detect NRF grays from plutonium in all the nuclear fuel rods. To answer this question, we perform a Monte Carlo simulation for the nondestructive assay system. Interactions of the generated

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grays with an object to be measured are studied by using the

5.2. Results and discussion Fig. 6 shows the result of the simulation for the NRF process in the nuclear fuel assembly. The trace of each gray is displayed. One can find that grays can pass through all the rods with the maximum thickness of 8 cm. Moreover, we present the distribution

7000 +60 6000

X Position [mm]

+40 5000 +20 4000 0 3000 -20 2000 -40 1000

-60

0 -60

-40

-20

0

+20

+40

+60

Y Position [mm] Fig. 7. Distribution of NRF events in the fuel assembly consisting of 8  8 fuel rods. The 2143-keV LCS gray bean is introduced from the front of the fuel assembly (left side). This gray beam pass away to the opposite (right side) through the eight fuel rods. The position Y corresponds to the depth along the LCS gray beam. A part of the grays are scattered or absorbed by materials but other grays reach at the end of the assembly. The NRF events occur at all the eight rods on the axis of the incident gray beam.

10 4

10 3

2143 keV

Counts per Channel

code GEANT4, which is a package of toolkits for the simulation of the passage of particles through matter [27]. Although the toolkit for the GEANT4 is widely used in various science fields, the library to calculate the NRF process is not supported in the original GEANT4 package. We have, therefore, modified the code GEANT4 to calculate the NRF process in cascade interactions of photons and atomic nuclei. In the simulation, we assume that the diameter of each nuclear fuel pellet is 10 mm and the distance between two pellets is 8 mm. The nuclear fuel consists of UO2 (90%) + PuO2 (10%). The isotopic ratios of the plutonium are 52% (48%) for 239Pu (240Pu), and the uranium is assumed to be a mono isotope of 238U. This fuel assembly is located at the center of a water pool of a size of 50 cm  50 cm (see Fig. 4). The wall of this water pool is a lead shield with a thickness of 5 cm to absorb low energy grays. In a front of each HPGe detector, a collimator with the length of 10 cm is located. We introduce a 2143-keV gray beam with an energy width of 100 eV. The photon excitation reaction cross-section for the 2143-keV excited state in 239Pu is 13 barn eV, which is taken from the work by Bertozzi et al. [6]. In the present numerical simulation, a track of each photon is traced by taking into account atomic processes and nuclear reactions. When a NRF event occurs, we record its position (see Fig. 7). Most photons are finally scattered to the outside of the gray detectors. On the other hand, a part of photons reaches to the detectors after the atomic scattering or NRF, and we collect such events to make an expected gray spectrum as shown in Fig. 8. In the present simulation we calculate the tracks of 5  109 photons. This number is equal to the number of photons obtained from the designed high flux LCS grays for measurement time of 5s.

699

10 2

101

100 0

1000

2000

3000

Energy [keV] Fig. 8. Calculated energy spectrum of the NRF grays. The 2143-keV gray is clearly observed with a low signal-to-noise ratio.

of NRF events in the fuel assembly in Fig. 7. The LCS grays are introduced from the left side and pass toward the right side. The Y position means the depth on the axis of the LCS gray beam. In the present calculation, the incident grays are scattered by NRF as well as atomic processes and the number of photons with the NRF energy decreases with increasing the distance from the surface. However, we can see that the NRF events occur not only at the superficial position (left side) but also at the deep position (right side), although the event number of the deepest rod is smaller than that of the superficial rod by an order of magnitude. On other words, the gray with an energy of 2143 keV reaches at the deepest part in the fuel assembly from the surface part. In the present simulation, the NRF gray and background grays are measured with 24 HPGe detectors. Fig. 8 shows the sum of the energy spectra of the 24 HPGe detectors. The gray peak at 2143 keV is clearly observed, which corresponds to the excitation energy of 239Pu (see Table 1). An advantage of the use of NRF with high energy resolution HPGe detectors is to obtain the high signal-to-noise (S/N) ratio for the gray peak as shown in Fig. 8. This is because the background is dominantly originated from the Compton scattering of the incident photons at the fuel assembly and the energies of the Compton scattered grays are lower than the peak energy. The natural decay of radioisotopes at the inside of the spent fuel makes also the background. In the scheme of the nuclear cycle, the spent nuclear fuels will be shipped to the reprocessing plant after cooling time of several 10 years and thus the radioactivities decrease. What we are concerned here is whether the counting rate of individual detectors is small enough to detect grays and whether the S/N ratio is low enough to distinguish a NRF gray of a key nucleus. By using a lead absorber with a thickness of 5–10 cm, the grays are measured with a counting rate lower than 100 kcps. The S/N ratio around 2 MeV is more important for detection of 239 Pu. Lee et al. measured grays spectrum of a spent PWR fuel after cooling time of 8 years [28]. In this grays spectrum, gray yield decreases with increasing the gray energy. The yield at Eg ¼ 2:5 MeV is lower than that around zero keV by 4–5 orders of magnitudes. In energy region of Eg 42 MeV only a 2185.7-keV gray of 144Ce is observed and the continuous background is negligibly small since it originates dominantly from the Compton scattering of the 2185.7-keV gray. The NRF energies of 239Pu are quite different from 2185.7-keV (see Table 1). It is, therefore, expected that the background does not affect seriously to the assay of the nuclear materials.

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Here we estimate statistical uncertainty of the 239Pu detection. The peak count at 2143 keV in Fig. 8 is 36 photons for measurement time of 5 s. This suggests that we can detect the 239 Pu NRF grays at a rate of about 7 counts/s. For measurement duration of 4000 s, we can obtain a total count of 2.8  104. Note that, in the present calculation, we have assumed a spent fuel, of which PuO2 is highly concentrated compared with the typical expected concentration (1%). If the peak count is smaller than the present result by a factor of 10, the peak can be still observed because of the high S/N ratio (see Fig. 8). In this case we can obtain the total count of 2.8  103 for the 239Pu NRF peak. This result suggests that we can detect 239Pu whose fraction of 1% in the spent fuel with statistical error of about 2%. With grays whose flux is 10 times larger that of our designed gray source, we can measure the 1% fraction 239Pu with the statistical error of 0.6% with keeping the assay speed. As an alternative method to decrease the statistical error, we can introduce multi-LCS gray generation system for an ERL facility. If three laser systems are used at different positions on the electron beam line, three LCS gray beams are generated and we can assay three fuel assembly at one time. With the three LCS gray systems and a high flux gray beam which is three times higher than that assumed above, we can measure the fuel assembly with the nine times higher speed.

6. Nuclear data An advantage of our proposed system is to assay not only 239Pu but also isotopes of minor actinide, for example 237Np, 241,243Am, and 244,245,247Cm. A key nuclear data for the NRF assay is an excitation energy and a resonance width of an exited state in nucleus of interest. The resonance width (or mean lifetime) of an excited state has been usually measured using in-beam gray technique with nuclear reactions to populate nucleus of interest, or direct photon excitation experiments. These nuclear data for actinide have not been, however, studied well. The excitation energies of excited states which may excited directly from the ground state by photon-induced reactions for minor actinide are known but their resonance widths have not been measured. Recently, Bertozzi et al. studied the excited states on 235U and 239 Pu using NRF with Bremsstrahlung grays and reported the strong dipole resonances above 2 MeV [6]. The nuclear data for 232 Th [29], 235U [6], 236U [30], 238U [29], 239Pu [6] show that there exist strong magnetic dipole (M 1) resonances around an excitation energy of 2 MeV, which can be understood by scissors mode of nuclear collective motion in viewpoint of the nuclear physics [30]. This suggests that there are probably M 1 resonances around 2 MeV in most actinide isotopes. The study of these M 1 resonances are important for the NRF assay of minor actinide.

7. Summary We have proposed a novel nondestructive assay method for U, 239Pu, and minor actinide in the spent nuclear fuel assembly in a water pool. These isotopes are detected using nuclear resonance fluorescence in conjunction with energy-tunable quasi-monochromatic grays provided from an extremely highflux LCS gray source installed in the energy recovery linac (ERL) facility. This system has an advantage to detect isotopes such as 239 Pu in the fuel assembly in a water pool. The simulation calculation result shows that it is possible for us to detect 1% fraction 239Pu in all the fuel rods in the assembly using the high flux LCS gray source with statistical uncertainty lower than 2%. 235

Acknowledgments This work has been supported in part by Grants-in-Aid for Scientific Research in Japan (Grant nos. 20612014 and 21340068).

References [1] W.S. Charlton, D. Strohmeyer, A. Stafford, S. Saavedra, A.S. Hoover, C. Rudy, The use of self-induced XRF to quantify the Pu content in PWR spent nuclear fuel, in: Proceedings of 31st Annual Meeting of ESARDA, Vilnius, Lithuania, 26–28 May 2009. [2] K.A. Jordan, T. Gozani, Nucl. Instr. and Meth. A 579 (2007) 388. [3] H.O. Menlove, S.H. Menlove, S.J. Tobin, Nucl. Instr. and Meth. A 602 (2009) 588. [4] W. Bertozzi, R.J. Ledoux, Nucl. Instr. and Meth. B 241 (2005) 820. [5] J. Pruet, D.P. McNabb, C.A. Hagmann, F.V. Hartemann, C.P.J. Barty, J. Appl. Phys. 99 (2006) 123102. [6] W. Bertozzi, J.A. Caggiano, W.K. Hensley, M.S. Johnson, S.E. Korbly, R.J. Ledoux, D.P. McNabb, E.B. Norman, W.H. Park, G.A. Warren, Phys. Rev. C 78 (2008) 041601 (R). [7] C.A. Hagmann, J.M. Hall, M.S. Johnson, D.P. McNabb, J.H. Kelley, C. Huibregtse, E. Kwan, G. Rusev, A.P. Tonchev, J. Appl. Phys. 106 (2009) 084901. [8] F.V. Hartemann, W.J. Brown, D.J. Gibson, S.G. Anderson, A.M. Tremaine, P.T. Springer, A.J. Wootton, E.P. Hartouni, C.P. Barty, Phys. Rev. ST-AB 8 (2005) 100702. [9] V.N. Litvinenko, B. Burnham, M. Emamian, N. Hower, J.M.J. Madey, P. Morcombe, P.G. O’Shea, S.H. Park, R. Sachtschale, K.D. Straub, G. Swift, P. Wang, Y. Wu, Phys. Rev. Lett. 78 (1997) 4569. [10] H. Ohgaki, H. Toyokawa, K. Kudo, N. Takeda, T. Yamazaki, Nucl. Instr. and Meth. A 455 (2000) 54. [11] K. Aoki, et al., Nucl. Instr. and Meth. A 516 (2004) 228. [12] K. Kawase, M. Kando, T. Hayakawa, I. Daito, S. Kondo, T. Homma, T. Kameshima, H. Kotaki, L.-M. Chen, Y. Fukuda, A. Faenov, T. Shizuma, M. Fujiwara, S.V. Bulanov, T. Kimura, T. Tajima, Rev. Sci. Instr. 79 (2008) 053302. [13] H. Ohgaki, S. Sugiyama, T. Yamazaki, T. Mikado, M. Chiwaki, K. Yamada, R. Suzuki, T. Noguchi, T. Tomimasu, IEEE Trans. Nucl. Sci. NS-38 (1991) 386. [14] K. Aoki, K. Hosono, T. Hadame, H. Munenaga, K. Kinoshita, M. Toda, S. Amano, S. Miyamoto, T. Mochizuki, M. Aoki, D. Li, Nucl. Instr. and Meth. A 516 (2004) 228. [15] N. Pietralla, Z. Berant, V.N. Litvinenko, S. Hartman, F.F. Mikhailov, I.V. Pinayev, G. Swift, M.W. Ahmed, J.H. Kelley, S.O. Nelson, R. Prior, K. Sabourov, A.P. Tonchev, H.R. Weller, Phys. Rev. Lett. 88 (2002) 012502. [16] T. Shizuma, T. Hayakawa, H. Ohgaki, H. Toyokawa, T. Komatsubara, N. Kikuzawa, A. Tamii, H. Nakada, Phys. Rev. C 78 (2008) 061303 (R). [17] T. Hayakawa, S. Miyamoto, Y. Hayashi, K. Kawase, K. Horikawa, S. Chiba, K. Nakanishi, H. Hashimoto, T. Ohta, M. Kando, T. Mochizuki, T. Kajino, M. Fujiwara, Phys. Rev. C 74 (2006) 065802. [18] R. Hajima, T. Hayakawa, N. Kikuzawa, E. Minehara, J. Nucl. Sci. Technol. 45 (2008) 441. [19] N. Kikuzawa, R. Hajimam, N. Hishimori, E. Minehara, T. Hayakawa, T. Shizuma, H. Toyokawa, H. Ohgaki, Appl. Phys. Express 2 (2009) 036502. [20] T. Hayakawa, H. Ohgaki, T. Shizuma, R. Hajima, N. Kikuzawa, E. Minehara, T. Kii, H. Toyokawa, Rev. Sci. Instr. 80 (2009) 045110. [21] R. Hajima, N. Kikuzawa, T. Hayakawa, E. Minehara, in: Proceedings of the Eighth International Topical Meeting on Nuclear Applications and Utilization of Accelerators (AccApp-07), 2007, p. 182. [22] V.N. Litvinenko, I. Ben-Zvi, E. Pozdeyev, T. Roser, IEEE Trans. Plasm. Sci. 36 (2008) 1799. [23] K. Umemori, T. Furuya, S. Sakanaka, T. Suwada, T. Takahashi, H. Sakai, K. Shinoe, M. Sawamura, Design of L-band superconducting cavity for the energy recovery linacs, in: Proceedings of the Asian Particle Accelerator Conference 2007 (APAC 2007), 2007, p. 570. ¨ [24] T. Schreiber, C. Nielsen, B. Ortac, J. Limpert, A. Tunnermann, Opt. Lett. 30 (2005) 2754. [25] K. Furuno, H. Oshima, T. Komatsubara, K. Furutaka, T. Hayakawa, M. Kidera, Y. Hatsukawa, M. Matsuda, S. Mitarai, T. Shizuma, T. Saitoh, N. Hashimoto, H. Kusakari, M. Sugawara, T. Morikawa, Nucl. Instr. and Meth. A 421 (1999) 211. [26] M. Devlin, L.G. Sobotka, D.G. Sarantites, D.R. LaFosse, Nucl. Instr. and Meth. A 383 (1999) 506. [27] S. Agostinelli, GEANT4 Collaboration, Nucl. Instr. and Meth. A 506 (2003) 250. [28] Y.G. Lee, S.H. Eom, K.J. Park, K.P. Hong, S.G. Ro, J. Korean Nucl. Soc. 20 (2) (1992) 178. [29] R.D. Heil, H.H. Pitz, U.E.P. Berg, U. Kneissl, K.D. Hummel, G. Kilgus, D. Bohle, A. Richter, C. Wesselborg, P. von Brentano, Nucl. Phys. A 476 (1988) 39. [30] J. Margraf, A. Degener, H. Friedrichs, R.D. Heil, A. Jung, U. Kneissl, S. Lindenstruth, H.H. Pitz, H. Schacht, U. Seemann, R. Stock, C. Wesselborg, Phys. Rev. C 42 (1990) 771. [31] A. Zilges, P. von Brentano, R.-D. Herzberg, U. Kneissl, J. Margraf, H. Maser, N. Pietralla, H.H. Pitz, Phys. Rev. C 52 (1995) 468 (R).