Special EM processes and their role in Geant4-stepping (energy-loss processes and multiple scattering)

Transcription

1 The G4SteppingManager and its resposibilities ecapitulation Pre- point: itation Final remarks Special EM processes and their role in Geant4-ping (energy-loss processes and multiple scattering) Mihály Novák CEN EP-SFT (simulation group) Mihály Novák Geant4 Tutorial, Lund University, Lund, Sweden, 3-7 September, / 25

2 The G4SteppingManager and its resposibilities ecapitulation Pre- point: itation Final remarks Outline 1 The G4SteppingManager and its resposibilities Mihály Novák Geant4 Tutorial, Lund University, Lund, Sweden, 3-7 September, / 25

3 The G4SteppingManager and its resposibilities ecapitulation Pre- point: itation Final remarks Outline 1 The G4SteppingManager and its resposibilities 2 ecapitulation Mihály Novák Geant4 Tutorial, Lund University, Lund, Sweden, 3-7 September, / 25

4 The G4SteppingManager and its resposibilities ecapitulation Pre- point: itation Final remarks Outline 1 The G4SteppingManager and its resposibilities 2 ecapitulation 3 Pre- point: itation discrete part of the it continuous part of the itation Mihály Novák Geant4 Tutorial, Lund University, Lund, Sweden, 3-7 September, / 25

5 The G4SteppingManager and its resposibilities ecapitulation Pre- point: itation Final remarks Outline 1 The G4SteppingManager and its resposibilities 2 ecapitulation 3 Pre- point: itation discrete part of the it continuous part of the itation 4 Final remarks Mihály Novák Geant4 Tutorial, Lund University, Lund, Sweden, 3-7 September, / 25

6 The G4SteppingManager and its resposibilities ecapitulation Pre- point: itation Final remarks Contents 1 The G4SteppingManager and its resposibilities 2 ecapitulation 3 Pre- point: itation discrete part of the it continuous part of the itation 4 Final remarks Mihály Novák Geant4 Tutorial, Lund University, Lund, Sweden, 3-7 September, / 25

7 The G4SteppingManager and its resposibilities ecapitulation Pre- point: itation Final remarks General ping: G4SteppingManager A G4Track encapsulates both static (G4ParticleDefinition) and dynamic properties (energy, momentum, direction,etc.) of a particle Geant4 propagates such tracks: one track at a time, -by-: from the beginning: first with a primary or secondary track till the end: particle left the world, particle kinetic energy became zero, dropped below the (user defined) tracking it or the particle had a destructive interaction (, the user requested to kill the particle) properties of the track (currently under tracking) are updated after each secondary tracks are pushed into a track stack at each The G4SteppingManager is responsible to coordinate one implements a general ping algorithm: independent from the type of the particle and processes associated to the particle We will have a closer look at the itation part of this ping by focusing on charged particles with EM interactions: Ionization, Bremsstrahlung, Multiple Scattering (Why?) Mihály Novák Geant4 Tutorial, Lund University, Lund, Sweden, 3-7 September, / 25

8 The G4SteppingManager and its resposibilities ecapitulation Pre- point: itation Final remarks Contents 1 The G4SteppingManager and its resposibilities 2 ecapitulation 3 Pre- point: itation discrete part of the it continuous part of the itation 4 Final remarks Mihály Novák Geant4 Tutorial, Lund University, Lund, Sweden, 3-7 September, / 25

9 The G4SteppingManager and its resposibilities ecapitulation Pre- point: itation Final remarks Ionization and Bremsstrahlung are described as continuous-discrete interactions: secondary electron and gamma production with energy below the given production energy threshold E cut are not simulated explicitly instead, these low energy losses described as continuous energy losses along the (i.e. between the pre- and post- points) based on a mean value this mean value is the restricted stopping power i.e. mean energy loss in unit length de (E; E cut,...) = dx rest E cut 0 k dσ (E,..)dk (1) dk secondary electron and gamma production with energy above the given production energy threshold E cut are simulated explicitly as discrete interactions this discrete interaction probability is determined by the restricted cross section σ rest (E; E cut,...) = E E cut dσ (E,..)dk (2) dk that covers interactions only in which the secondary particle will have an energy above the production energy threshold Mihály Novák Geant4 Tutorial, Lund University, Lund, Sweden, 3-7 September, / 25

10 The G4SteppingManager and its resposibilities ecapitulation Pre- point: itation Final remarks the discrete part of the interaction will imply a discrete it i.e. path length till the next discrete interaction, determined by the restricted cross section σ rest (E; E cut,...) the continuous part of the interaction will also imply a continuous it due to a maximum allowed along energy loss value due to this along energy loss, the particle kinetic energy will be different at the pre- and post- points Mihály Novák Geant4 Tutorial, Lund University, Lund, Sweden, 3-7 September, / 25

11 The G4SteppingManager and its resposibilities ecapitulation Pre- point: itation Final remarks Contents 1 The G4SteppingManager and its resposibilities 2 ecapitulation 3 Pre- point: itation discrete part of the it continuous part of the itation 4 Final remarks Mihály Novák Geant4 Tutorial, Lund University, Lund, Sweden, 3-7 September, / 25

12 The G4SteppingManager and its resposibilities ecapitulation Pre- point: itation Final remarks discrete part of the it Contents 1 The G4SteppingManager and its resposibilities 2 ecapitulation 3 Pre- point: itation discrete part of the it continuous part of the itation 4 Final remarks Mihály Novák Geant4 Tutorial, Lund University, Lund, Sweden, 3-7 September, / 25

13 The G4SteppingManager and its resposibilities ecapitulation Pre- point: itation Final remarks discrete part of the it First the interactions, that have discrete part, will propose a length: if the target atom density is N and the atomic interaction cross section of a process is σ (assumed to be constant along a at the moment!) according to the Beer-Lambert law, the p.d.f. of the corresponding interaction length x (i.e. the probability that the interaction will happen at x, x + dx is p(x)dx) p(x) = Nσ exp( xnσ) = x Exp(Nσ) (3) the mean or expected value of the interaction length x E(x) = 1 Nσ λ = 1 x Exp(Nσ) (4) Σ where λ is the mean free path and Σ = Nσ = 1/λ is the macroscopic cross section if there are M independent interactions with the corresponding atomic cross sections {σ i } M i=1, mean free paths {λ i = 1/Nσ i } M i=1, macroscopic cross sections {Σ i = Nσ i } M i=1 and the M interaction lengths as stochastic variables {s i } M i=1 such that s i Exp(Σ i ), then the shortest interaction length i.e. η = min{s 1,..., s M }, η Exp(Σ t ), where Σ t = M i=1 Σ i = M i=1 1/λ i is the total macroscopic cross section Mihály Novák Geant4 Tutorial, Lund University, Lund, Sweden, 3-7 September, / 25

14 The G4SteppingManager and its resposibilities ecapitulation Pre- point: itation Final remarks discrete part of the it Theorem If {s 1,..., s M } are independent random variables and i 1,..., M s i Exp(1/λ i), then η = min{s 1,..., s M } Exp( M i=1 1/λi) Proof. By definition, the cumulative distribution function of η as a random variable is equal to the probability that M P(η < x) = 1 P(η x) = 1 P(s 1 x,..., s N x) = 1 P(s i x) M M = 1 (1 P(s i < x)) = 1 (1 (1 e x/λ i )) = i=1 1 e x M i=1 1/λ i i=1 i=1 M = η = min{s 1,..., s M } Exp( 1/λ i) i=1 (5) Mihály Novák Geant4 Tutorial, Lund University, Lund, Sweden, 3-7 September, / 25

15 The G4SteppingManager and its resposibilities ecapitulation Pre- point: itation Final remarks discrete part of the it usually, the total macroscopic cross section Σ t = M i=1 Σ i = N M i=1 σ i is computed and used to sample the path length η to the next discrete interaction point from the exponential distribution, η Exp(Σ t ) then at the post- point, the type of the discrete interaction is sampled based on the discrete probabilities p(proc = i) = Σ i /Σ t in Geant4, each discrete process will propose an interaction length s i Exp(Σ i 1/λ i ) based on their own macroscopic cross section Σ i then the shortest η = min{s 1,..., s M } will be selected as discrete it, which is (based on the proof given in the previous slide) equivalent to the previous one moreover, with this Geant4 already selects the discrete interaction at the pre- point that will(if any 1 ) happen at the post- point i.e. after travelling the path η 1 there are several cases when the discrete interaction does not happen at all, we will discuss them soon one by one Mihály Novák Geant4 Tutorial, Lund University, Lund, Sweden, 3-7 September, / 25

16 The G4SteppingManager and its resposibilities ecapitulation Pre- point: itation Final remarks discrete part of the it In case of particles, that have Ionization and Bremsstrahlung: due to the secondary production threshold, the corresponding restricted macroscopic cross sections Σ rest (E; E cut,...) are used to propose the discrete it due to the continuous part, i.e. the along energy losses, the pre- point E pre and post- point E post kinetic energies will be different the cross section is not constant along the, that must be accounted: a fictive, delta interaction is introduced for each interaction such that, the sum of the real Σ r i (E) and this delta interaction Σ δ i (E) cross section is constant along the i.e. does not depend on the particle energy and Σ r i (E) Σ const i along the Σ r i (E) + Σ δ i (E) = Σ i( E) Σ const i = constant along the (6) along the, which implies that Σ const i = max{σ i(e)} i.e. maximum this constant macroscopic cross section Σ const i is used to sample the discrete interaction length(to a real or delta interaction) at the pre- point at the post- point, after the along energy loss is already accounted, the probability that the delta interaction happen is p(δ) = 1 Σ r i (E post )/Σ const i Mihály Novák Geant4 Tutorial, Lund University, Lund, Sweden, 3-7 September, / 25

17 The G4SteppingManager and its resposibilities ecapitulation Pre- point: itation Final remarks continuous part of the itation Contents 1 The G4SteppingManager and its resposibilities 2 ecapitulation 3 Pre- point: itation discrete part of the it continuous part of the itation 4 Final remarks Mihály Novák Geant4 Tutorial, Lund University, Lund, Sweden, 3-7 September, / 25

18 The G4SteppingManager and its resposibilities ecapitulation Pre- point: itation Final remarks continuous part of the itation So far, the discrete interaction its have been considered: each discrete process (or discrete part of the process) proposed a length the shortest among these was selected as the current candidate length the corresponding process was selected as the current candidate process a flag to indicate that the current candidate length was proposed by the discrete part of the current candidate process possible energy loss along the was considered At this point, G4SteppingManager will ask each continuous part of the processes to propose their own its one by one: starts with the previous settings regarding the candidate length, process, and type flag (discrete) each proposed continuous it is compared to the current candidate one if the current continuous it is shorter than the current candidate, the candidate length, process and type flag (continuous) are updated Mihály Novák Geant4 Tutorial, Lund University, Lund, Sweden, 3-7 September, / 25

19 ange ρ = 1mm. For the case of a particle range > ρ the StepFunction Pre- point: itation Final remarks provides it for the size S by the following formula:! " ρ S = α + ρ (1 α ) 2. (7.4) The G4SteppingManager and its resposibilities ecapitulation continuous part of the itation In the opposite case of a small range Sfollowing =. The figure below shows the In case of particles, that have Ionization continuous ecapitulation Pre- point: and itationbremsstrahlung the osibilities ratio /range e range becomes lower than ρ (parameter finalange). Default final- as a function of range if itation is determined only Forit function is used: by the expression (7.4). ρ = 1mm. the case of a particle range > ρ the StepFunction The G4SteppingManager and its resposibilities ecapitulation Pre- point: itation s,s that Ionization and(parameter Bremsstrahlung the following continuous until the range becomes lower than finalange). ithave for the size S bydefault thefinal-following formula: continuous part For the case of a particle range > the StepFunction ange = 1mm. is used: When the particle range > fl finalange: provides it for the size S by the following formula:! ρ "Bremsstrahlung In cases of particles,) 2that. have Ionization and the following continuous nge range = + (1 (7.4) (1 α ) Sit α + ρused: 2. range = function is When the particle > fl (7.4) finalange: = 0.2 In the opposite case of a small range S =. The figure below the until the shows range becomes lower than (parameter finalange). Default final s: = 1mm. the StepFunction ratio /range as a functionvalue: of range if isange determined only For the case of a particle range > - default flitation = 1.0[mm] 1 S provides it for the size S by the following formula: by the expression (7.4). opposite case small range S =. The figure below shows the - of adoverange S = + (1 ) 2. (7.4) The G4SteppingManager and its resposibilities ecapitulation - default value: = 0.2 ep/range as a function of range ifopposite itation isthedetermined only Pre- point: itation In the case of a small range S =. figure below shows the ratio /range as a function of range if itation is determined only continuous part - (7.4). at high energies: S (7.4). by the expression expression until the range becomes lower than (parameter finalange). Default final range 1 ange 1mm. For the case of a particle > the StepFunction In case of particles, that have Ionization and= Bremsstrahlung therange following continuous doverange provides it for the size S by the following formula: it function is used: S = + (1 ) 2. (7.4) When the particle range < fl : In the opposite case of a small range S =. The figure below shows the low energies: S = ratio /range until the range becomes lower than (parameter finalange). Default final- as a function of range if itation is determined only range doverange ange 1 ager and its resposibilities ecapitulation Pre- point: itation = 1mm. For the case of a particle range > by the expression (7.4). the StepFunction doverange The G4SteppingManager and its resposibilities ecapitulation Pre- point: itation of provides particles, that Ionization and(parameter Bremsstrahlung the following continuous finalange until the range becomes lower than finalange). ithave for the size S bydefault thefinal-following formula: finalange continuous part For the case of a particle range > the StepFunction ange = 1mm. it function is used: When the particle range > fl finalange: range provides it for the size S by the following formula: In cases of particles, that. have Ionization and Bremsstrahlung the followingpre- continuous doverange The G4SteppingManager ecapitulation range = and + (1 2overwritten (7.4) an UI command: its resposibilities point: itation range The parameters of StepFunction can using (1 Sit be)+ 2 particle. range (7.4) = ) the function is used: When > fl finalange: lt value: =continuous 0.2 In the opposite case of a small range S =. The figure below the until the shows range becomes lower than(parameter finalange). Default finalpart finalange = 1mm. the StepFunction ratio /range as a functionvalue: of range if isange determined only For the case of a particle range > - default flitation = distribution 1.0[mm] /process/eloss/stepfunction mm Figure: 1 h energies: S provides it for the size S by the following formula: by the expression (7.4). Transverse range In of simulation particles, have andfigure Bremsstrahlung the the following continuous To provide more accurate ofthat particle ranges in physics constructors The parameters of StepFunction can be overwritten using an UI command: In the opposite case small range S =. The below shows -case Ionization of adoverange S = + (1 ) 2. (7.4) G4EmStandardPhysics option3 and G4EmStandardPhysics option4 more strict it function used: When the particle range > can flthe overwritten finalange: be - default value: = 0.2 parameters StepFunction ratio /range as a function ofisrange ifopposite itation is determined In the casethe of a Seoul, small range epublic S =of. The figure below shows Nova k Geant4 Tutorial, of Korea, 8-10only Dec, 2016using an UI command: 16 / 16 itation is Miha ly chosen for different particle types. ratio /range as a function of range if itation is determined only default value: fl = 1.0[mm] at high energies: S by the expression (7.4). ping power. the expression (7.4). from the restricted d by range, computed /process/eloss/stepfunction mm Figure: Transverse distribution/process/eloss/stepfunction mm doverange Miha ly Nova k Geant4 Tutorial, Seoul, epublic of Korea, 8-10 Dec, / 16 until the range becomes than more (parameter finalange). Default final-of particle Tolower provide accurate simulation ranges in physics constructors un Time Energy Loss Computation doverange ange = 1mm. For the case of a particle range > the StepFunction - default value: = 0.2 To provide option3 and G4EmStandardPhysics option4 more strict more accurate simulation of particle ranges in physics constructors provides it for theg4emstandardphysics size S by the following formula: The computation of the mean energy loss after a given is done by using itation is chosen for different particle types. at high energies: S S = + (1 ) 2 the de/dx, -ange,. (7.4) G4EmStandardPhysics option3 and G4EmStandardPhysics more strict16 / 25 and Inverseange tables. The de/dx table is used if Miha ly Nova k Geant4 Tutorial, Lund University, Lund, Sweden, 3-7 option4 September, 2018 based on particle restricted range When the range range, < fl : computed from the restricted ping power. Based on restricted range, computed from the restricted ping power! range 1 range doverange 1

20 The G4SteppingManager and its resposibilities ecapitulation Pre- point: itation Final remarks Contents 1 The G4SteppingManager and its resposibilities 2 ecapitulation 3 Pre- point: itation discrete part of the it continuous part of the itation 4 Final remarks Mihály Novák Geant4 Tutorial, Lund University, Lund, Sweden, 3-7 September, / 25

21 The G4SteppingManager and its resposibilities ecapitulation Pre- point: itation Final remarks So far a candidate physics length has been selected that is: the current minimum of the lengths, proposed by all discrete and continuous processes, was selected as candidate length it is assumed at this point, that the particle will travel this path length as a straight line along it s original direction: to the post- point where the selected discrete interaction takes place that discrete interaction proposed the shortest length to the post- point where no discrete interaction takes place if a continuous interaction proposed the shortest length However, there are one or two special continuous processes left: transportation (always), multiple scattering (possible). The end of the itation depends: if the particle does not have Coulomb scattering (A.) if the particle has Coulomb scattering and its described by a single scattering model i.e. as a discrete process (B.) if the particle has Coulomb scattering and its described by a multiple scattering model i.e. as a continuous process (C.) Mihály Novák Geant4 Tutorial, Lund University, Lund, Sweden, 3-7 September, / 25

22 The G4SteppingManager and its resposibilities ecapitulation Pre- point: itation Final remarks Particles, that do not have Coulomb scattering (A.): the only remaining (continuous) process is the transportation (the last in the list!) the above candidate physical length will be selected as proposed by the physics since all discrete and all but one (transportation) continuous processes have already proposed their lengths regarding the physics interactions(transportation is still to be called), the particle is supposed to be transported the selected distance from the pre- point along its original direction the last continuous process, transportation will be asked to propose its it: if the particle can be propagated along its original direction to the selected distance without hitting volume boundary, then the transportation process will accept the proposed length (and it will propagate the particle to its proposed post- point) otherwise, the particle will be transported to the volume boundary and the proposed length will be shortened by transportation process accordingly Mihály Novák Geant4 Tutorial, Lund University, Lund, Sweden, 3-7 September, / 25

23 The G4SteppingManager and its resposibilities ecapitulation Pre- point: itation Final remarks Particles, that have Coulomb scattering and its described by a single scattering model i.e. as a discrete process (B.): elastic scattering was already accounted in the it since it is included in the list of discrete processes therefore, everything is the same as in the previous case (A.) since the only remaining (continuous) process is the transportation (the last in the list!) A. and B. C. Post- point (r1): with many Coulomb Sc C. Post- point (r1): with many Coulomb Sc C. Post- point (r1): with many Coulomb Sc r1 = r0 + d0st r1 = r0 + dtrsg d0 st = sg st d0 st st d0 sg Æ st st st dtr d0 sg Æ st [dtrsg]z [dtrsg]xy st Post- point (r1): Pre- point (r0) w/o single Coulomb Sc Post- point (r1): Pre- point (r0) w/o single Coulomb Sc Post- point (r1): Pre- point (r0) w/o single Coulomb Sc Post- point (r1): Pre- point (r0) w/o single Coulomb Sc MSc model gives sg, dtr and r1 in one Mihály Novák Geant4 Tutorial, Lund University, Lund, Sweden, 3-7 September, / 25

24 The G4SteppingManager and its resposibilities ecapitulation Pre- point: itation Final remarks Particles, that have Coulomb scattering and its described by a multiple scattering model i.e. as a continuous process (C.): elastic scattering was removed from the list of discrete interactions = elastic scattering is not included in the current it s t therefore, the current candidate length s t does not contains the effects of (possible many) elastic scattering with elastic scattering, the particle would stop (probably many times) along the currently selected path length s t and the direction of propagation would change each time therefore, the particle would travel the currently selected path length to the next interaction along a curved, zig-zagged trajectory instead of a straight line the real post- point location, the distance (straight line) between the pre- and post points (geometrical length s g ) and final direction of propagation is provided by the Multiple Scattering model Mihály Novák Geant4 Tutorial, Lund University, Lund, Sweden, 3-7 September, / 25

25 The G4SteppingManager and its resposibilities ecapitulation Pre- point: itation Final remarks therefore, before the transportation (the last), the last but one continuous process, multiple scattering is asked to provide its itation: multiple scattering can further it the current candidate path length s t after its own itation, multiple scattering will change the current true length s t to the geometrical length s g by computing the corresponding transport distance and transport direction d tr after the multiple scattering (last but one), the last continuous process, transportation s continuous itation is invoked, by providing the transport distance s g instead of the true length s t form this point everything is the same as in case of A. and B. Mihály Novák Geant4 Tutorial, Lund University, Lund, Sweden, 3-7 September, / 25

26 The G4SteppingManager and its resposibilities ecapitulation Pre- point: itation Final remarks Contents 1 The G4SteppingManager and its resposibilities 2 ecapitulation 3 Pre- point: itation discrete part of the it continuous part of the itation 4 Final remarks Mihály Novák Geant4 Tutorial, Lund University, Lund, Sweden, 3-7 September, / 25

27 The G4SteppingManager and its resposibilities ecapitulation Pre- point: itation Final remarks using production cuts is NOT mandatory in Genat4: interactions (e.g. Ionization) can be described as pure discrete interaction (the appropriate model, process need to be selected) using multiple scattering model is NOT mandatory neither: single scattering models, processes for elastic scattering are available in Geant4 that will be pure discrete using pure discrete processes in the simulation gives exact solution of the transport problem: but feasible only at low energies! (below few 100 kev) in general, at high energies we need to use condensed history approximation and production cuts to be able to solve the transport problem within acceptable computational time these approximations make the transport simulation more complex and naturally introduce some user defined parameters, settings understanding more details of these approximations helps the user to provide settings that are the most suitable for their applications Geant4 provides several predefined physics lists prepared and maintained by expert physics developers for special application areas Mihály Novák Geant4 Tutorial, Lund University, Lund, Sweden, 3-7 September, / 25

28 The G4SteppingManager and its resposibilities ecapitulation Pre- point: itation Final remarks Questions... Mihály Novák Geant4 Tutorial, Lund University, Lund, Sweden, 3-7 September, / 25