HU9900720 Neutron Sources G.S. Bauer Paul Scherrer Institut CH-5232 Mlligen PSI email: [email protected] 1 Introduction As neutron scattering experiments have grown more and more demanding with respect to resolution and quality, it became more and more necessary to include the neutron source #; itself in the design of an experimental setup. In this sense the generic representation of a neutron scattering arrangement fciypfi nrFiffrAj includes the primary neutron source and the associated spectrum shifter (or moderator). PS ss PO' PO" SD DP PS = primary source SE = Sample envrironment SS = spectrum shifter S = Sample PO = (selective) phase space operator SD = Signal detector DP = Data processing Figure 1: Generic representation of a neutron scattering setup. In fact, the design of a modern neutron source will start from a set of users' requirements and will proceed "inwards" through a selection of the moderators (spectrum shifters) to the primary source best suited to meet these often conflicting needs. This paper aims at explaining the options source designers have to match the neutron source performance to the users' demands. 2 Thermal neutron fission and spallation as primary sources of neutrons Although a number of reactions are known which release neutrons from nuclei, only ther- mal neutron fission and proton induced spallation play a real role a s primary sources for neutron scattering facilities. 2.1 Fission In the past fission of the uranium isotope 235 by slow neutron capture has been the most frequently used reaction in neutron sources. The reaction can be made self-sustaining because it is exothermal and releases more neutrons per fission process than are needed to initiate the process. If a slow neutron is captured by a fissionable nucleus, the resulting 12 deformation can cause the nucleus to break up into two fragments (Fig. 2). Very often a neutron is released directly during this process but mostly the neutrons "evaporate" off the surface of the fragments. This is a very important feature because a small fraction of these evaporation neutrons are released with a time delay of the order of seconds and thus enable a critical arrangement to be run in a controlled fashion. The fraction of delayed neutrons in 235U is 8 = 0.6% and the average decay constant of the parent nuclei is A = 0.0785 s — 1 Fission chain reaction via moderated neutrons Spallation evaporation • proton highly excited O neutron nucleus Figure 2: Schematic representation of fission and spallation The spectral distribution of the fission neutrons can be well described by a Maxwellian distribution ^(!) (2.1) with a characteristic energy ET = 1-29 MeV. This characteristic energy is | of the mean energy E of the neutron which leads to a mean energy of fission neutrons of about 2 MeY. A calculated spectrum of fission neutrons is shown in Fig. 3. 2.2 Spallation The term "spallation" is applied to a sequence of events that take place, if target nuclei are bombarded with particles of a de-Broglie wavelength A = yJh2/2mE which is shorter than the linear dimensions of the nucleus. In this case collisions can take place with individual nuclides inside the nucleus and large amounts of energy are transferred to the nuclides which, in turn, can hit other nuclides in the same nucleus. The net effect of this intra-nuclear cascade is twofold: 1: Energetic particles may leave the nucleus and carry the cascade on to the other nuclei (inter-nuclear cascade) or escape from the target. 2. Energy is more or less evenly distributed over the nucleus leaving it in a highly excited state 13 The excited nucleus left behind will start evaporating neutrons - and to a lesser extent protons and other light nuclei - from, its surface. The spectrum of these evaporation neutrons is quite similar to the one resulting from fission, but as a consequence of the neutron escape during the intranuclear cascade, the overall spectrum extends to energies up to that of the incident particles (see curve in Fig. 3). The release of spallation neutrons takes place within less than 10~15 sec after the nucleus was hit. This means, that the time distribution of spallation neutrons is exlusively determined by the time distribution of the driving particle pulse. 1 ' ' ' ""'1 '""! 1 1 1 \ 1 iff p ~3 - • * o \ • r 0 • 0 - r- • 0 • 0 o : • 0 ; . ° o Fission o = • • 0 0 • Spallation 800 MeVp+ • ** • II I ? 0 (W Target) 1 T 0 0 \ n , ii ,,,,,1 ,1,1 ' 1 1,,,..! , , ,,it,,| i , ,,,ml 1 I i < lim 1 1(P 10"' 10'' 10" 1 10 100 1000 Energy (MeV) Figure 3: Logarithmic representation of calculated neutron spectra from fission and spallation [1] It should be noted that, while there are only a few thermally fissionable isotopes, spallation can occur in every nucleus, although the neutron yield increases with the nuclear mass. Finally, whereas about 200 MeV of energy are deposited in a reactor core per useful neutron generated, this value is down to somewhere near 25 MeV in a spallation target (lead). 3 Moderation of neutrons 3.1 The slowing-down process The energy spectrum of neutrons released in the primary neutron sources (reactor fuel or spallation target) is in the MeV range whereas meV or at most eV neutrons are required for scattering experiments. Therefore a shift of several orders of magnitude is necessary, which is accomplished by collisions with the atoms of a ':moderator"-substance. The goal in the layout of a moderator is to create the highest possible flux of moderated neutrons either in the shortest possible time (pulsed neutron sources) or in the largest possible volume (steady state neutron sources). It is therefore important to consider the number of collisions that occur per unit time and the energy transferred in each collision. An important quantity to characterize a moderator is its mean logarithmic energy decrement per collision, f, which is for all practical purposes given by —- for A > 2 = inEo — A + 2/3 (3.1) 1 for A = 1 14 with EQ and E\ being the neutron energies before and after the collison and A the atomic number of the moderator atom. So, hydrogen is the most effective moderator in terms of energy transfer per collision. This allows to calculate immediately the average number of collisions x, to shift the spectrum from one mean energy value to another. For EQ = 2 MeV and Ej = 25 meV. one has for example: 18.2 n 7 (3.2) x = 7 • * TF = 7 ">(8 • 10 ) = Table 1 gives values of A, £ and x for several commonly used moderator atomic species and, for comparison, for Uranium. Element Parameter H D Be C O U 1 2 9 12 16 238 1.000 0.725 0.209 0.158 0.120 0.00838 x (2 MeV -» 25 meV) 18 25 86 114. 150 2172 Table 1: Slowing-down parameters of various elements [2] In a mixture of nuclei, f is given by N (3.3) with Es being the macroscopic scattering cross section. The important quantities to characterize the performance of a moderator for steady state neutron sources are called its "slowing-down power" £-Es and its "moderating ratio" £ • £S/Ea with Ea being the mean absorption cross section. Values for the moderator substances of practical importance are given in Table 2. Moderator Densitv Slowing-Down Moderating Power Ratio 3 1 (g/cm ) £ • Ss (cm" ) (£ • Ss/Ea) H2O 1.00 1.35 71 D2O (pure) 1.10 0.176 5670 D2O (99.8 mole %) 1.10 0.178 2540 Graphite 1.60 0.060 192 Beryllium 1.85 0.158 143 Table 2: Slowing-down power and moderating ratio of common moderator substances [2] 15 3.2 Time characteristics For neutron sources with a pronounced time structure of the neutron flux ("pulsed sources") the time characteristics of the slowing-down process and the life time of neu- trons in equilibrium with the moderator are important. During the slowing-down process, the time interval during which a neutron "lives" at a certain velocity is the mean time between collisons t{ — —, or ti • Vi = A = const (3-4) with A being the mean'free path between collisons (A = ^ in the absence of absorption). Similarly, the product of neutron velocity and the average slowing down time ts (i.e. the time required to shift the spectrum to the energy E = m-v2/2) and the standard deviation of the slowing-down time Ats (i.e. the "width" of the time distribution of the neutrons reaching the energy E or velocity v) are also found to be constant for any given moderator [3]. 7 ts • v = (1 4- 2/7) (3.5) 7 (3.6) (£ for .4=1 (3.7) This is an important feature of intrinsically pulsed sources relative to chopped beams, because it means that the time-of-flight resolution is constant down to energies where thermal equilibrium is reached in the moderator of pulsed sources. Values of the relevant quantities for the most commonly used moderator materials are given in Table 3, where £1/2 is the full width at half maximum of the slowing-down time distribution. This shows, that for neutrons of 2.2 • 105 cm/sec (thermal energy), it takes about 10 fxs to slow down from the primary fast spectrum in H2O. The FWHM of the time, during which neutrons reach thermal energies ("transient" regime) is about 11 /is. There is no way to achieve shorter thermal neutron pulses with an H2O-moderator! v Material Density 7 v • ta v • At, v • h/2 (cm"1) (cm) (cm) (cm) H2O 1 1.5 0.92 0.99 2.17 1.25 2.4 CH4 0.94 1.8 0.9 0.98 1.84 1.05 2.0 D2O 1.1 0.35 0.51 0.56 14.3 6.71 14.2 Be 1.7 0.75 0.21 0.15 13.6 3.61 7.9 C 1.8 0.43 0.16 0.11 30.7 7.0 16.0 Fe 7.9 0.75 0.035 0.024 77.1 8.4 19.2 Table 3: Neutron slowing-down properties of some materials [2], [5] with slowing-down times calculated according to [3] Methane can be seen to be about 20% better, but in practice is difficult to use except on very low power sources due to its susceptibility to radiation damage.