Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Biasing Status Marc Verderi Laboratoire Leprince-Ringuet, Ecole polytechnique Geant4 Collaboration Meeting Plenary session 7 Chartres, 13th of September Introduction • This afternoon parallel session 8B will be devoted to biasing. • There are biasing activities in the EM group, with bremstralhung splitting. This will be presented by Daren this afternoon. • There are activities on designing geometry facility to help setting up or setting up automatically a biasing geometry for the case of geometry biasing (splitting technique also). By Alex. • Here, I will focus on new developments, not splitting based, but “importance sampling” based: ie changing the underneath physical laws. Introduction • Geant4 proposes biasing options – Geometrical importance sampling, Leading particle biasing, Radioactive decay biasing, G4WrapperProcess, Reverse MC • But misses others like – Exponential transform: 𝑝 ℓ = 𝜎 ⋅ 𝑒 −𝜎ℓ → 𝑝′ ℓ = 𝜎′ ⋅ 𝑒 −𝜎′ℓ • Change total cross-section • Make change direction dependent – forced interaction: • Force interaction in thin volume – forced flight (towards detector) • So called DXTRAN • Force scattering towards detector – Which are popular ones Thin detector Small detector DXTRAN sphere • These methods involve the replacement of the (analog) physical law by a biased one. A weight to compensate for the application of the biased law is computed (this weight is a critical aspect). • Such replacement capability was not developed in Geant4. Change of physical laws • Physical laws may be changed at several levels: Secondaries and /or scattered primary Primary Modify probability for interaction to occur: Biasing related to total-cross section, Regards quantities related to initial state only • • • • Change of total cross-section (exponential transform), Individual cross-section reshuffling (if total cross-section changed), Force Interaction, Force Free Flight (ie no interaction). Modify probabilities in the way the interaction occurs: Biasing related to final state • • • Differential cross-section biasing, So-called « Forced Flight » / DXTRANS : force primary to scatter towards a detector for tallying Individual cross-section reshuffling (favor some process, or favor some model). • Main focus was given for now to the change of interaction law – ie change of the natural exponential law Approach for including options (1/2) • Try to avoid “importing” options from other packages as they are – But review them as they have been developed for certain use-cases – Eg: forced interaction for thin detectors in MCNP will not be appropriate to a forced pion decay for a neutrino experiment like T2K (surviving pion will shower in the soil ⟹ just waste of time) MCNP Scheme One copy makes a forced free flight Primary is split pion Decay tunnel soil neutrino One copy makes the forced interaction muon • Need to “de-jargonize” – E.g. : exponential transform or path length biasing are the same techniques: ie change of the total X-section Approach for including options (2/2) • Try to “de-convolute” from implicit assumptions in these packages – Many techniques come from low energy domains for which “one track = one event = one ‘history’” • So can speak of “the” weight unambiguously – But in an HEP event, can consider doing something on one track –eg force Coulomb interaction in tracking chamber for tracking (in)efficiencyof a big event. – And “the” weight is not anymore defined that clearly • One biased track may define the weight for the entire event • Depends on how this event is then used • Try to see if techniques can be made more general – For example, transformation of interaction laws are made (to my knowledge) on the total cross-section – But in high energy problems, may want to force a specific process • e.g. photonuclear interaction to study gamma cluster (in)efficiency reconstruction – Corresponding formalism to compute the weight needed to be developed Formalism (in a nutshell) • Formalism first developed for the case of neutral particles – Ie, cross-sections are kept constant over a flight of length 𝓁 (no continuous actions) • If the physical law (exponential) for process 𝑖 is replaced by a biased one: 𝑝𝜑,𝑖 𝓁 = 𝜎𝑖 𝑒 −𝜎𝑖𝓁 → 𝑝𝑖 (𝓁) – The weight for a track travelling a step of length 𝓁 ending without interaction is: 𝑒 −𝜎𝑖𝓁 Probability for non𝑤𝑁𝐼 = = 𝑤𝑁𝐼,𝑖 interaction over length 𝓁 𝑃𝑁𝐼,𝑖 (𝓁) 𝑖 𝑖 – And, in the case the step ends with an interaction by process 𝑖, the weight is: 𝜎 𝑤𝑁𝐼 × 𝜎𝑖 𝑑 − log 𝑃𝑁𝐼,𝑖 (𝓁) 𝑑𝓁 – with 𝜎𝑖 = physical law) 𝑖 = “effective cross section” (coincides with 𝜎𝑖 for a • We note that – 𝑤𝑁𝐼 applies at any step; – It is the product of the non-interaction weight of each process: processes can be treated independently ! – In case an interaction occurs, only the cross-section and effective cross-section of the acting process are involved in the weight correction. • These remarks constitute the backbone of the design. Design for biasing of interaction law • Each discrete process is wrapped with a dedicated wrapper process • This wrapper methods are: – PostStepGPIL: • The wrapper has access to the cross-section of the wrapped process • It samples the biased law for limiting the step – AlongStepDoIt: • It applies in the AlongStepDoIt the weight for non-interaction • (These weights are multiplicative among processes) – PostStepDoIt: • If the process has limited the step, invoke PostStepDoIt of wrapped process to get final state • And includes the corresponding weight, ie the ratio of cross-section / effective cross-section in the particle change, before returning it to the stepping manager. • This approach solve conceptually the design aspect. • Other aspects (how to set and handle a biased law) are to be further discussed. Extension to charged particles • Laurent Desorgher has extended the formalism to the case of charged particles, to take into account the change of cross-section due to continuous action. – Weight correction applied is obtained by sampling of a variable which expectation value is the weight correction – Validated by toy MC in which the cross-section varies. Below plots are obtained mixing natural law, forced interaction and forced free flight ones. • Formalism for weight correction seems hence solid. • Other aspect not discussed here: Markovian MC. The Annecy mini-Workshop • We held a mini-workshop in Annecy, 14-16 May 2012 where we cover many aspects. • This afternoon session will continue with these discussions. Next ? • For biasing of interaction laws: – Need to define further the design: • Setting biased laws • Combine options – And define plans – Likely will be too short to deliver these options in 9.6 – Note we renew our request for a method from geometry to tell how much a track can travel in a volume • This is needed for the Forced Interaction technique. • Further options: – Regarding biasing of the final state – Ie : DXTRANS method, to force the scattering towards some detector – Need deep discussion: involves a concept of differential cross-section, that is unclear in Geant4. • All these will be discussed in the parallel session this afternoon.