Decadimento b e bb: codici e tools di calcolo

Transcription

1 Decadimento b e bb: codici e tools di calcolo Il sito nucleonica.net: Decay engine Dosimetry and shielding++ Beta dose rate Gamma spectrum generator++ Wespa++ (peak analysis) Virtual Cloud Chamber Databases: Nucleosynthesis simulator NACRE EXFOR EXPACS Codici di calcolo analitici: Talys Neutrino Oscillation Simulator Codici MC: Metodo MC Generatori decadimento Fluka Geant4

2 Nucleonica.net: decay engine

3 Nucleonica.net: decay engine

4 Nucleonica.net: dosimetry and shielding++

5 Nucleonica.net: dosimetry and shielding++

6 Nucleonica.net: dosimetry and shielding++

7 Nucleonica.net: beta dose rate

8 Nucleonica.net: beta dose rate

9 Nucleonica.net: gamma spectrum generator++

10 Nucleonica.net: gamma spectrum generator++

11 Nucleonica.net: WESPA++ (Web Spectrum Analyzer)

12 Nucleonica.net: WESPA++ (Web Spectrum Analyzer)

13 Nucleonica.net: Virtual Cloud Chamber

14 Nucleonica.net: Virtual Cloud Chamber electron-positron pairs are created through the interaction of 10 MeV gamma photons incident on lead. 3 MeV positrons (red) from the radioactive source are blocked by a lead shield (green).

15 Nucleosynthesis simulator

16 Nucleosynthesis simulator

17 NACRE-II

18 NACRE-II

19 EXFOR

20 EXPACS

21 TALYS

22 NOS: Neutrino oscillation Simulator

23 NOS: Neutrino oscillation Simulator

24 Il metodo montecarlo (MC)

25 Il metodo montecarlo (MC)

26 Il metodo montecarlo (MC)

27 Il metodo montecarlo (MC)

28 Particle transport Particle transport is a typical physical process described by probabilities (cross sections = interaction probabilities per unit distance) Therefore it lends itself naturally to be simulated by Monte Carlo Many applications, especially in high energy physics and medicine, are based on simulations where the history of each particle (trajectory, interactions) is reproduced in detail However in other types of application, typically shielding design, the user is interested only in the expectation values of some quantities (fluence and dose) at some space point or region, which are calculated as solutions of a mathematical equation This equation (the Boltzmann equation), describes the statistical distribution of particles in phase space and therefore does indeed represent a physical stochastic process But in order to estimate the desired expectation values it is not necessary that the Monte Carlo process be identical to it

29 Particle transport Monte Carlo Assumptions made by most MC codes: Static, homogeneous, isotropic, amorphous media and geometry Problems: e.g. moving targets, atmosphere must be represented by discrete layers of uniform density, radioactive decay may take place in a geometry different from that in which the radionuclides were produced Markovian process: the fate of a particle depends only on its actual present properties, not on previous events or histories Particles do not interact with each other Problem: e.g. the Chudakov effect (charges cancelling in e + e pairs) Particles interact with individual electrons / atoms / nuclei / molecules Problem: invalid at low energies Material properties are not affected by particle reactions Problem: e.g. burnup

30 Particle transport Application of Monte Carlo to particle transport and interaction: Each particle is followed on its path through matter At each step the occurrence and outcome of interactions are decided by random selection from the appropriate probability distributions All the secondaries issued from the same primary are stored in a stack or bank and are transported before a new history is started The accuracy and reliability of a Monte Carlo depend on the models or data on which the probability distribution functions are based Statistical accuracy of results depends on the number of histories" Statistical convergence can be accelerated by biasing" techniques.

31 Analog vs non-analog simulation

32 Analogue vs non-analogue What is analogue simulation? Sample using natural probability distribution, N(x) Predicts mean with correct fluctuations Can be inefficient for certain applications What is non-analogue/event biased simulation? Cheat - apply artificial biasing probability distribution, B(x) in place of natural one, N(x) B(x) enhances production of whatever it is that is interesting To get meaningful results, must apply a weight correction Predicts same analogue mean with smaller variance Increases efficiency of the Monte Carlo Doesn t predict correct fluctuations Should be used with care

33 Monte Carlo Flavors: microscopic Microscopic Analog Monte Carlo Uses theoretical models to describe physical processes whenever possible Samples from actual physical phase space distributions Predicts average quantities and all statistical moments of any order Preserves correlations (provided the physics is correct, of course!) Reproduces fluctuations (provided... see above) Is (almost) safe and (sometimes) can be used as a black box" (idem) But: Can be inefficient and converge slowly Can fail to predict contributions due to rare events

34 Monte Carlo Flavors: macroscopic Macroscopic Monte Carlo: Instead of simulating interactions, use parametrizations of the reaction product distributions, obtained from fits to data and extrapolations Fast, especially when reactions are complex Can be more accurate than microscopic MC if the theory contains uncertainties/approximations But: The single probability distribution functions are reproduced, but the correlations among interaction products are not Cannot be extended outside the data range

35 Monte Carlo Flavors: biased Biased Monte Carlo: samples from artificial distributions, and applies a weight to the particles to correct for the bias (similar to an integration by a change of variable) predicts average quantities, but not the higher moments (on the contrary, its goal is to minimize the second moment!) same mean with smaller variance faster convergence allows sometimes to obtain acceptable statistics where an analog Monte Carlo would take years of CPU time to converge But: cannot reproduce correlations and fluctuations only privileged observables converge faster (some regions of phase space are sampled more than others)

36 The Geometry The algorithms to build a geometry and to track particles inside it differ from code to code. In general: The geometry is built from basic solids and/or surfaces: EGS: original CG, or user-defined FLUKA (extended CG): solid bodies and surfaces GEANT: solid volumes MARS: 5 different geometries, including FLUKA and MCNP geometry MCNP(X): originally surfaces, now also macrobodies MORSE, SAM-CE (original Combinatorial Geometry, CG): solid bodies PENELOPE: surfaces PHITS: MCNP geometry TRIPOLI: solid bodies and surfaces The geometry must have a way to limit the tracking, in some codes by defining an external boundary Defined by input cards (MCNP, CG) or by user-written routines (GEANT) In some codes it can allow for repetition of structures In some codes it can allow for voxel representation (CT import)

37 Discrete events Atomic interactions: Physics Photons: Compton, photoelectric, pair, coherent, Charged particles: bremsstrahlung, ray emission, large angle Coulomb scattering (all above given thresholds) Nuclear interactions: Nuclear elastic scattering Nuclear non-elastic interactions Absorption Decays Boundary crossing Escape Geometry

38 Continuous processes Physics: Charged particles lose energy and change direction as a result of thousands of discrete collisions with atomic electrons. To simulate in detail each collision would require prohibitive CPU times, except at very low particle energies. Many discrete scatterings are then replaced by a straight continuous step, and the corresponding energy losses and changes of direction are condensed into a sum of losses (de/dx) and an overall scattering angle (condensed-history technique) Ionization energy losses: all losses lower than a preset threshold are continuously distributed along the step. Any loss larger than threshold is simulated as a discrete energy imparted to an electron ( ray, transported) energy loss fluctuations can be simulated for the losses below threshold Multiple Coulomb Scattering: a deflection angle, sampled from a theoretical distribution, is applied to each particle step. Some corrections are needed: Path Length Correction (PLC) lateral displacement Transport: neutral particle displacements, particle displacements in vacuum ( steps ) When magnetic/electric field are present, substeps are necessary to follow the curvature of the trajectory, de/dx and MCS

39 Thresholds and cut-off s Transport and production thresholds are needed because of: Limits of validity of the physics models CPU time Transport thresholds: they depend on the granularity of the geometry and/or of the scoring mesh and on the interest in a given region. To reproduce correctly electronic equilibrium, neighboring regions should have the same electron energy threshold (not the same range threshold!) Photon thresholds should be lower than electron thresholds (they travel more) Production thresholds: δ-ray threshold: sets the limit between discrete and continuous ionization energy losses e/ production threshold : similar to δ-ray for other electro-magnetic processes, including bremsstrahlung

40 Results from a MC calculation Estimators It is often said that Monte Carlo is a mathematical experiment. Each aspect of a real experiment has its Monte Carlo equivalent: Experimental technique Estimator Instrument Detector Measurement Score, or Tally Result of an experiment Monte Carlo result Just as a real measurement, a score is obtained by sampling from a statistical distribution As an experimental result consists in an average of the measurements, a statistical error and a systematic error, a MC result is an average of scores, a statistical error (and a systematic error, generally unknown) There are often several different techniques to measure the same physical quantity: in the same way the same quantity can be calculated with different kinds of estimators

41 Estimator types Various types of estimators, depending on the quantity to be estimated and on the topology (phase space region over which the quantity is integrated) Boundary Crossing. Quantity: the fluence or the current of particles Phase space: a physical boundary between two space regions. Result: mono or multi-differential fluence spectra, function of energy, angle, particle type, Track length. Quantity: the fluence of particles Phase space: a region of real space Result: fluence spectra as a function of particle energy, based on the path length of the particles within the region volume

42 Estimator types Pulse-height detector (e.g. simulation of a Ge spectrometer): Quantity: energy deposited Phase space: a region of real space Result: spectrum of deposited energy within the region volume Scalar integral estimator: Quantity: deposited energy, inelastic interactions (stars), activity... Phase space: a region of real space Result: amount of given quantity (or its density) within the volume Mesh: Quantity: fluence, energy deposition, stars Phase space: regular subdivision of a portion of real space in subvolumes, generally independent from the tracking geometry Result: a 2D or 3D spatial distribution of the estimated quantity

43 Statistical Errors The variance of the mean of an estimated quantity x (e.g., fluence), calculated in N batches, is: mean of squares square of means N 1 where: n i = number of histories in the i th batch n = Σn i = total number of histories in the N batches x i = average of x in the i th batch: In the limit N = n, n i =1, the formula applies to single history statistics n x n n x n N N i i i N i x n i j i ij i n x x 1

44 Statistical Errors Can be calculated for single histories, or for batches of several histories each (not necessarily the same identical number) Distribution of scoring contributions by single histories can be very asymmetric (many histories contribute little or zero) Scoring distribution from batches tends to Gaussian for N, provided 2. (Central Limit Theorem) The standard deviation of an estimator calculated from batches or from single histories is an estimate of the standard deviation of the actual distribution ( error of the mean ) How good is such an estimate depends on the type of estimator and on the particular problem (but it converges to the true value for N )

45 Statistical Errors Practical tips: Use always at least 5-10 batches of comparable size (it is not at all mandatory that they be of equal size) Never forget that the variance itself is a stochastic variable subject to fluctuations Be careful about the way convergence is achieved: often (particularly with biasing) apparently good statistics with few isolated spikes could point to a lack of sampling of the most relevant phase-space part Plot 2D and 3D distributions! In those cases the eye is the best tool in judging the quality of the result

46 Statistical errors, systematic errors, and... mistakes Statistical errors, due to sampling (in)efficiency Relative error Quality of Tally (from the MCNP Manual) 50 to 100% Garbage 20 to 50% Factor of a few 10 to 20% Questionable < 10% Generally reliable except for point detectors < 5% Generally reliable for point detectors Why does a 30% σ mean an uncertainty of a factor of a few? Because σ in fact corresponds to the sum (in quadrature) of two uncertainties: one due to the fraction of histories which give a zero contribution, and one which reflects the spread of the non-zero contributions The MCNP guideline is empirically based on experience, not on a mathematical proof. But it has been generally confirmed also working with other codes Small penetrations and cracks are very difficult to handle by MC, because the detector is too small and too few non-zero contributions can be sampled, even by biasing

47 Statistical errors, systematic errors, and... mistakes Systematic errors, due to code weaknesses Apart from the statistical error, which other factors affect the accuracy of MC results? physics: different codes are based on different physics models. Some models are better than others. Some models are better in a certain energy range. Model quality is best shown by benchmarks at the microscopic level (e.g. thin targets) artifacts: due to imperfect algorithms, e.g., energy deposited in the middle of a step, inaccurate path length correction for multiple scattering, missing correction for cross section and de/dx change over a step, etc. Algorithm quality is best shown by benchmarks at the macroscopic level (thick targets, complex geometries) data uncertainty: an error of 1% in the absorption cross section can lead to an error of a factor 2.8 in the effectiveness of a thick shielding wall (10 attenuation lengths). Results can never be better than allowed by available experimental data!

48 Statistical errors, systematic errors, and... mistakes Systematic errors, due to user ignorance Missing information: material composition not always well known. In particular concrete/soil composition (how much water content? Can be critical) beam losses: most of the time these can only be guessed. Close interaction with engineers and designers is needed presence of additional material, not well defined (cables, supports...) Is it worth to do a very detailed simulation when some parameters are unknown or badly known? Systematic errors, due to simplification Geometries that cannot be reproduced exactly (or would require too much effort) Air contains humidity and pollutants, has a density variable with pressure

49 Statistical errors, systematic errors, and... mistakes MC codes can contain bugs: Code mistakes ( bugs ) Physics bugs: I have seen pair production cross sections fitted by a polynomial... and oscillating instead of saturating at high energies, nonuniform azimuthal scattering distributions, energy non-conservation... Programming bugs (as in any other software, of course) User mistakes mis-typing the input: some codes are more or less good at checking, but the final responsibility is the user s error in user code: use the built-in features as much as possible wrong units wrong normalization: quite common unfair biasing: energy/space cuts cannot be avoided, but must be done with much care forgetting to check that gamma production is available in the neutron cross sections

50 Some of the most popular codes EGS5: EGSnrc: (e- e + γ) FLUKA : (multiparticle) Geant4: (multiparticle) MARS: (multiparticle) MCNP: (neutrons, e- e+ γ) MCNPX: (multiparticle) PENELOPE: (e- e+ γ) PHITS: (multiparticle) TRIPOLI: (neutrons, e- e+ γ) Specialized: CORSIKA: (cosmic rays) PEREGRINE: (radiotherapy)

51 General information for various all-particle transport codes General MCNPX GEANT4 FLUKA MARS PHITS Version p Lab. Affiliation LANL CERN ESA IN2P3 PPARC INFN LIP KEK SLAC TRIUMF CERN INFN FNAL JAEA RIST GSI Chalmers Univ. Language Fortran 90/C C++ Fortran 77 Fortran 95/C Fortran 77 Cost Free Free Free Free Free Release Format Source & binary Source & binary Source & binary Binary Source & binary Availability Conditions RSICC Beta test team Open web ne User s Agreement User Manual 470 pages 280 pages 387 pages 150 pages 176 pages Users ~2000 ~2000 ~1000 ~ Web Site mcnpx.lanl.gov cern.ch/geant4 www-ap.fnal. gov/mars Under const. Workshops ~7/year ~4/year ~1/year ~2/year ~1/year Input Format Free C++ main Fixed geometry Fixed or free Free Free Input Cards ~120 N/A ~85 0 to 100 ~100 Parallel Execution

52 Geometry Capabilities Geometry MCNPX GEANT4 FLUKA MARS PHITS Description MCNP-based Solids (CSG, Boolean, some BREP/STEP) Combinatorial Fixed shapes or MCNP-based MCNP-based MORSE-based Extensions Twisted Nested Repeated Voxel (universes) Lattice (rec, hex) (logical vol.) (rec, cyl) (universes) Lattice (rec, hex) Reflections 3 types Neutron albedo Viewer Debugger Built-in: 2-D Interactive X-Windows External: Vised Moritz Built-in: 3-D Interactive OpenGL OpenInventor RayTracer External: WIRED VRML DAWN Overlap tools Built-in: ne External: Custom (X11) Debugger built in Built-in: 2-D Interactive Tcl/Tl 3-D Interactive OpenGL External: Built-in Built-in: 2,3-D Command PS via Angel External: Angel PS Setup GUI Vised Moritz GGE Tcl/Tl CAD STEP via GUI STEP via Tool Fields (E/B) 2.6.D Moving Solid Objects 2.6.D

53 Sources Source MCNPX GEANT4 FLUKA MARS PHITS Fixed General Explicit Distribution Dep. Dist. External User Sub. SSW/SSR GPS Eigenvalue Burnup (2.6.A)

54 Physics Capabilities Physics MCNPX GEANT4 FLUKA MARS PHITS Particles Charged particles Energy loss Scatter Straggling XTR/Cheren. CSDA Bethe-Bloch Rossi Vavilov CSDA Bethe-Bloch Lewis Urban CSDA Bethe-Bloch Moliere improved Custom /yes CSDA Bethe-Bloch Moliere improved Custom CSDA Bethe-Bloch Moliere Vavilov Baryons Neutron Low High Proton Low High Other Cont. (ENDF) Models Cont. (ENDF) Models Model List: Bertini ISABEL CEM INCL FLUKA89>3 GeV LAQGSM (2.6.C) Cont. (ENDF) Models Models Models Model list: Hadron-nucleous GHEISHA* INUCL(Bertini) BIC CHIPS QGS/FTF>8 GeV Multigroup(72) Models Models Models Model list: PEANUT(GINC) +DPM+Glauber Cont. (ENDF) Models Models Models Model list: Custom CEM LAQGSM DPMJET Cont. (ENDF) Models Models Models Model list: Bertini JAM>3 GeV Leptons Electrons Muon Neutrino Other ITS 3.0 CSDA/decay Production Decay Models/EEDL, EADL Models Production Decay Custom Models Models Decay Custom Models Models Models ITS 3.0 CSDA/decay Models Models

55 Physics Capabilities, cont. Mesons Models Models Models Models Models Photons Optical x-ray/g Photonuclear ITS 3.0 Libraries (IAEA) CEM Models or EPDL97, EADL CHIPS Custom+EPDL97 PEANUT VMDM Custom Custom CEM ITS 3.0 Ions ISABEL LAQGSM (2.6.C) AAM EDM BLIC RQMD-2.4 DPMJET-3 LAQGSM JQMD JAMQMD > 3 GeV/u Delayed n, (2.6.C) α,,?, n

56 Tallies/Scores/Edits (Results) Tallies MCNPX GEANT4 FLUKA MARS PHITS Standard Flux Volume Surface Point/ring Current Charge Kinetic energy Particle density Reaction rates Energy deposition Rapidity DPA Momentum Pulse-height Termination Modifiers HTAPE3X Partial 9 Limited Limited (user) User input?? 2 Star (inelastic) Some 2 (neutrons). Partial 2 2 Special Mesh Coincidence Residuals Activation Event logs rec, cyl, sph 2.5.D rec, cyl?? rec, cyl rec, cyl, sph rec,cyl

57 Tallies/Scores/Edits (Results) cont. Convergence Tests 10 Error Error Error Error Results Viewer Built-in: 1-D, 2-D Custom X-Windows External: IDL Tecplot GNUplot PAW Built-in: External: JAS PI Open Scientist PAW Built-in: ne External: Custom (X11) GNUplot PAW ROOT Built-in: Custom External: PAW Built-in: Angel External: Angel

58 Variance Reduction Variance Reduction MCNPX GEANT4 FLUKA MARS PHITS Population control Region biasing Weight cutoff Weight window mesh Energy biasing Modified sampling Source biasing Implicit capture Exp. transform Production biasing Angular bias DXTRAN RDM?? DXTRAN Viewer 2-D contour

59 Radioactive decay in Geant4 and Fluka Enjoy the code and the practical exercise

60 Conclusions? Use data to validate MC MC comparison is important and useful As always trust, but do not forget a critical view data!= information!= knowledge!= wisdom!= truth MC