Dispelling the Myth of Super-Moderators

Outline• Introduction• Motivation• Basic Theory• Inelastic Scattering• (n, xn’) reactions• Elastic Scattering• ApplicationU N C L A S S I F I E DOperated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA

Introduction• Disturbing misuse of language• Creeping into official review comments from auditing agencies— May lead to inappropriate response and redirection of alreadytaxed and crucial resources• Case in point super-moderators• Why should we care when presumably the intent isknown• We are professionals and as such we have an obligation to betechnically accurate• Mentoring new staff is difficult enough without using inaccurateand incorrect terminologyU N C L A S S I F I E DOperated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA

Basic Theory of Moderation• Neutrons slow down via interactions with nuclei• Compound nucleus interactions— Inelastic scattering, (n,n’)— (n, xn’) reactions• Elastic scattering• Compound nucleus reactions• Colliding neutron is captured by the nucleus• Threshold reactions• For all but very energetic neutrons the inelastic spectrum is discrete• Regardless the inelastic spectrum does not include a thermal componentU N C L A S S I F I E DOperated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA

Reference FramesU N C L A S S I F I E DOperated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA

Elastic Scattering Energy LossE s 1 2 E s1 1cosIn which A 12 A 1Therefore for forward scattering, i.e., no scatter 0 E s E sNo Energy LossAnd for maximum scatter (head on) 180 E s E sMaximum Energy LossU N C L A S S I F I E DOperated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA

The Only Super Moderator A 1 A 12• For hydrogen A=1 and =0• 1 as A increases• A neutron can• Lose all of its energy in a single collision with hydrogen• Lose only a fraction of its energy in collisions with all other nucleiU N C L A S S I F I E DOperated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA

Hydrogen Is As Good As It GetsNucleusMassNumberMaximumPercentLossAverage #Collisions 2MeV to ThermalHydrogen 1 0 100.0 26Deuterium 2 0.111 88.89 31Beryllium 9 0.640 36.0 92Carbon 12 0.716 28.4 118Oxygen 16 0.779 22.14 155Iron 56 0.931 6.9 518239Pu 239 0.983 1.7 2130U N C L A S S I F I E DOperated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA

Sources of Confusion?• Be moderated systems can have a smaller minimumcritical mass water moderated systems• Moderation by Be and C can lead to lower limitingcritical densities• Poor Nomenclature has resulted from applyingcritical mass results as a “definition” of a physicalprocess• Moderation is a process governed by kinematics;• The definition is not linked to critical mass data;• If it were the definition would be variableU N C L A S S I F I E DOperated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA

Critical Mass Curve ComparisonWater Reflected Spherical Systems1.00E+02WaterCarbonBerylliumPure MetalDensity ReductionDominates239 Pu Critical Mass (kg)1.00E+011.00E+00Break Even Points1.00E-011.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02239 Pu ConcentrationU N C L A S S I F I E DOperated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA

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Break Even Point Values (M c =5.49 Kg)Material c (g/L)x/PuratioMass(kg)ModCoreVolume(L)SystemVolume(L)Hydrogen 1019 21.1 4.36 4.63 70Beryllium 122.4 399 82.4 44.8 217Carbon 17.4 2578 709 315 794U N C L A S S I F I E DOperated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA

Application• The fact that Be moderated systems has a marginallylower critical mass is of no practical importance• The amount of material required just to re-establishthe reactivity to undiluted system is very large• Processes that would encounter such situations are very rare— Experiments designed to test this very attribute— Exotic fuel manufacturing that does not exist as of nowU N C L A S S I F I E DOperated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA

5 kg Single Parameter Subcritical LimitUnit Size ComparisonU N C L A S S I F I E DOperated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA

Reflectors• There are conditions in which there are reflectingmaterials superior to water• Generalizations are just a imprudent in the case of reflectors as inthe case of moderators• There are the same multiple competing factors of scattering thateffects leakage, moderation, and absorptionU N C L A S S I F I E DOperated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA

Conclusion• The language used by professionals needs to becorrect, particularly in a safety discipline• Basic collision dynamics demonstrates there is nobetter moderator than hydrogen• Smaller critical masses for Be are not due to superiormoderation but less absorption and leakage• In all but esoteric applications it is not a practicalconcernU N C L A S S I F I E DOperated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA