p1 Summary DETERMINATION OF BASIC STATIC REACTOR PARAMETERS IN THE GRAPHITE PILE AT THE VENUS FACILITY P. Baeten (pbaeten@sccen.be) The purpose of this laboratory session is the determination of the basic static reactor parameters: the diffusion length, the diffusion coefficient and the Fermi-age of a graphite moderator. The obtained results will be discussed in view of the applied methods. Meanwhile the students will be familiarized with the main principles of slow neutron detection and determine the type of applied detector and comment on its suitability for the experiment. 1 Introduction To solve the homogenized diffusion equation, an accurate determination of the different reactor parameters which are involved is needed. The nowledge of the basic reactor parameters also provides a good insight into the basic properties of the considered core, since they determine the orders of magnitude of the phenomena in reactor physics. Moreover, the experimental determination of these parameters can be used to validate the computer codes in very specific conditions. In this respect the determination of the basic static reactor parameters by experimental techniques has more than solely an academic purpose. In this exercise, a graphite pile will be used to demonstrate some experimental techniques for the determination of basic static reactor parameters (figure 1). The graphite pile at the VENUS facility consists of an arrangement of graphite blocs with a specific density of 1,6 g/cm 3. This graphite has the same quality as the one used for the BR1 reactor and is very pure graphite. Table 1: Axial positions in the graphite pile Layer Position z (cm) 5 i 14.68 5 s 4.96 6 i 35.3 6 s 45.51 7 i 55.79 7 s 66.07 8 i 76.34 8 s 86.6 9 i 96.9 9 s 107.18 10 i 117.45 10 s 17.73 11 i 138.01 11 s 148.9 1 i 158.57 1 s 168.84 13 s 189.40 14 s 09.96
p Figure 1: Schematic lay-out of the graphite pile at the VENUS facility
p3 The pile has a square basis of 6,4 x 6,4 cm and a height of 39,3 cm and consists of 16 layers which alternate with respect to their orientation. Some graphite blocs can be removed from the pile to allow for the positioning of the source. Some rulers are used to position the activation foils or detectors in the pile. The measurement positions are in horizontal channels passing through the vertical axis and separated from each other by about 10 cm (table 1). The Ra-Be source is situated in layer 4 and the centre of the source is located on the vertical axis. The present flux at the reference position can be calculated from the flux at that position in 1983 taing into account the decay of Radium with a halve-life of 160 year and the build-up of polonium with a rate of 0.4% per year. Therefore the present flux at position 6i.0 is estimated to be: Slow neutron detection ϕ(6i.0, t = 003) = ϕ(6i.0, t = 1983) e = 1.06x10 4 = 1.140 x 10 nv x 0.9914 x 1.0831 4 nv 0.693 0 160 (1.004) Since in this experiment "neutrons" will have to be detected, we will in this paragraph briefly summarize the main principles of slow neutron detection..1 Principles of slow neutron detection Detection of slow neutrons is achieved by causing a nuclear reaction in the detector between the neutron and a target material. This reaction results in heavy charged particles having a certain energy. These particles will deposit their energy in the detector gas through collisions with the gas molecules, creating extra ions and free electrons. The electrons are accelerated by the electric field of the applied voltage and will cause even more ionizations. This is called gas multiplication. The output of the detector is a pulse with amplitude proportional to the number of ionizations. So this amplitude is not defined by the neutron energy but by the energy of the charged particles created by the nuclear reaction. The efficiency and usefulness of a detector is defined by following factors: - Cross section of the target material for the reaction: must be large to obtain a high efficiency. - Q-value : the energy liberated by the reaction. A high Q provides an easy discrimination of the gamma-ray induced ionizations.. Detector types for slow neutron detection a) BF 3 detector The detector is filled with boron trifluoride gas which serves both as target for the neutrons as well as multiplication gas. 0
p4 The 10 B(n,α) reaction: 10 5 1 B+ 0 n 7 3 7 3 Q=,79 or,310mev 4 Li+ α,79mev 4 Li * + α,310mev ( ground _ state : 6% ) ( exited _ state: 94% ) The individual energy of both products can be defined as follows: Total energy after the reaction: E Li + E α = Q =,31MeV Conservation of energy and of momentum causes: m Li.v Li = m α.v α. m E m E Li. Li =. α. α Solving these equations results in: E Li = 0,84Mev and E α = 1,47Mev The exited state of the Li will cause the emission of a 0,48MeV gamma ray that will not contribute to the detector response. If the detector is large then all the energy will be deposited in the proportional gas. The detector output amplitude spectrum will show a pea at both possible reaction energies as shown in figure. Figure : Large BF 3 detector spectrum If however the detector is small, some particles can strie the detector wall before all energy is deposited in the gas. Since both reaction particles move in opposite direction, it is possible that for reactions close to the detector wall one of them stries the wall and only the other particle deposits its energy into the gas. The spectrum will show an energy distribution as shown in figure 3. The lowest possible energy detected is the energy of the Li nucleus, 0,84Mev. A second step is present at the energy level of the α particle (1,47Mev) and the pea will be at the sum level of,31mev.
p5 Figure 3: Small BF 3 detector spectrum b) The 3 He detector Following reaction taes place: 1 3 1 He+ n H + p 0, 764Mev 3 0 1 1 Energies of the particles can again be calculated. E p = 0,573Mev and E 3H = 0,191Mev Figure 4 shows the output amplitude spectrum of the detector. As in the BF 3 detector, the wall effects cause a similar spectrum shape. c) Fission chambers Figure 4: 3 He detector spectrum In these detectors the slow neutrons cause a reaction with the fissile deposit, in many cases U-35, in the detector. Figure 5.a shows the typical energy spectrum caused by a fission. A thicer deposit increases the efficiency but distorts the spectrum as shown in figure 5.b, this is due to the fact that the fission fragments lose their energy within this deposit.
p6 Possible reaction: 35 3 1 9 0 38 54 0 1 93 140 U + n Sr + Xe + n 00MeV Figure 5: Fission chamber spectrum for a thin deposit (5.a) and a thic deposit (5.b) The Q of fission detectors is very high, theoretically about 00 Mev. This energy however is not linearly reflected in the output pulse and will be lower but still considerably higher than for other reactions. This means that the suppression of bacground noise and gamma-rays will be very good. 3.3 Comparison between the different detector types Figure 6 shows indicative values for cross section (efficiency) and Q (capability for gamma-ray discrimination) of the different detector types. cross section (barn) 10000 9000 8000 7000 6000 5000 4000 3000 000 1000 0 s (barn) Q (MeV) He3 BF3 Fission Detector Figure 6: Thermal cross-section and Q-value for the different detector types 100 90 80 70 60 50 40 30 0 10 0 Q-value (Mev
p7 3 Theoretical bacground of the Sigma Pile experiment The general Boltzman equation which describes the neutron transport can be reduced to equation (1) when some approximations are made such as: Diffusion approximation Homogenised reactor and homogenised cross-sections Steady state equation One (thermal) energy group Unreflected bare reactor In that case, the associated critical homogeneous one-energy group diffusion equation is given by: 1 D ϕ Σ aϕ + νσ f ϕ = 0 (1) Rewriting this equation and maing use of the conventional expression for the 1 material bucling B m = equation (1) results in: L th D ϕ + ϕ = 0 () Bm To solve this equation, the flux function has to be found which obeys the mathematical operators in expression () and the boundary conditions thereby defining the geometrical bucling B g in equation (3): D ϕ + ϕ = 0 (3) Bg From the identity of the geometrical and material bucling, the expression for the effective multiplication factor is inferred. = (4) 1+ L B th g Expression (4) underlines the importance of the determination of the diffusion length, since it is the basic material parameter describing the leaage from the core. In the following paragraph, we will show how this parameter can be measured. 4 Measurement of the diffusion length We will use the graphite pile to measure the diffusion length of a graphite moderated reactor such as the BR1. Since the graphite pile does not contain any fissile material and only a well-localised neutron source as depicted in figure 1 is present, the sourcedriven homogeneous one-energy group diffusion equation is given by: D ϕ Σa ϕ = S (5)
p8 To solve expression (5), an expansion of the source and the flux in eigenmodes of equation (6) is generally adopted. 1 D ϕ ϕ = 0 (6) L th When a point source in the center of an X-Y plane at z = 0 is considered in a rectangular pile, the flux will be given by the following expression by applying a complete separation of variables: ϕ n π mπ γ n, mz = ϕn, m cos x cos y e (7) n m a b As a consequence of the separation of variables, the following equation has to be satisfied: 1 nπ mπ γ n, m = + + (8) a b L th After some distance from the source, the higher eigenmodes have disappeared and the flux can be well characterized by the fundamental mode given by: ϕ π a π b γ1,1z = ϕ1,1 cos x cos y e (9) Measurement of the flux profile in X, Y and Z direction allow to derive the geometrical bucling parameters a and b and the decay constant? 1,1. After the determination of these parameters, the diffusion length can be obtained via equation (10). 1 L th π π = γ 1,1 (10) a b 5 Measurement of the diffusion coefficient Another parameter present in the diffusion equation (1) is the diffusion coefficient. In this paragraph, we will show how from the previous measurement of the flux profiles, the diffusion coefficient can be determined. From basic reactor theory for a bare unreflected rectangular reactor pile, we now that the bucling parameters a and b are related to the dimensions of the reactor pile by equation (11): a = b = 6.4 cm + d (11)
p9 In this equation, the parameter d is called the extrapolation length. Based on the assumption that the neutrons cannot return to the reactor pile once they have left the pile at the interface graphite-air, the flux decreases linear according to the flux gradient at the interface graphite-air and the extrapolation length obeys relation (1): 1 1 ϕ = 1 ϕ = d ϕb x x= x ϕ border b y y= y border (1) Based on basic reactor (diffusion) theory, expression (1) can be evaluated in terms of basic reactor constants and hence the diffusion coefficient will be given by: d = Σ tr = D (13) 3 6 Measurement of the Fermi age In paragraph, one of the most limiting assumptions was the fact that the neutrons were supposed to have all the same (thermal) energy, which is of course not the case in a thermal reactor. By applying this assumption, fast and epithermal neutron interactions are neglected and the thermalisation process which involves a certain distance is completely ignored. To be able to tae these effects into account, a two energy group model should be used. With this assumption, basic reactor theory points out that relation (4) transforms to equation (14): = ( + L B )( 1 + τ B ) 1 + ( L + τ ) B 1 + M B 1 th g th g th th g g = (14) The only difference between relation (4) and (14) is the introduction of a fast/epithermal leaage term. This fast/epithermal leaage term is entirely characterized by the so-called Fermi age t for thermal neutrons. This Fermi age can be determined from the Fermi age equation given by equation (15) where q means the slowing-down density: q( z, τ ) q( z, τ = ) z τ (15) When this equation is solved in the case of a planar X-Y source in an infinite moderating and non-absorbing medium, one obtains for the slowing-down density q the following expression: q 4τ 0 e q( z, τ ) = (16) πτ The measurement of the thermal Fermi age is however very difficult, since one cannot experimentally distinguish between neutrons that just arrive at the thermal neutron energy and those that have been diffusing with a thermal energy through the medium. z
p10 In fact by measuring the spatial distribution of thermal neutrons, one will rather measure the migration area instead of the thermal Fermi age. One can therefore only measure the Fermi age for certain energies, more particularly energies which correspond with resonance energies for certain absorbers with a very high integral resonance cross-section such as Indium. Indium 115 (95% abundance in natural Indium) has an absorption resonance of 30000 barns and is therefore very well suited to measure the Fermi age. Indium activation foils will therefore be used to measure the saturated activation of the Indium by the neutron flux. This saturated activity A is related to the flux by equation (17): A = V ϕ ( r, E) Σ ( E) de (17) resonance From basic reactor theory, we also now that the epithermal flux can be related to the slowing-down density by equation (18): q( r, τ ) ϕ( r, τ ) = (18) ξσ ( τ ) If we insert equation (18) into equation (17) and suppose that the slowing-down density is constant over the narrow resonance, we obtain equation (19): s a Vq( r, τ ) A = Σ Σ a, In ( u) du ξ s resonance (19) Equation (19) shows that the measured activity is proportional to the slowing-down density and hence can be used to determine the Fermi age for the Indium resonance energy at 1.46 ev by fitting equation (0) to the measured data. q( x, τ In x 4τ In q0 e ) = (0) πτ In