Download Biasing Status

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.