' $ Multiple Sattering in GEANT4, latest dev elopmen ts 1 - PowerPoint PPT Presentation

' $ Multiple S attering in GEANT4, latest dev elopmen ts 1 Multiple S attering in GEANT4, latest dev elopmen ts L � aszl� o Urb � an, Cen tral Res.Inst.Ph ys., Budap est 1 O t 2002 Abstra t hanges in the MSC mo del in G4, tests/v alidation i.e. G4/data omparisons + some G3 results & % G4 W orkshop CERN L.Urb� an(CRIP ,Budap est) 1 O t 2002

' $ Multiple S attering in GEANT4, latest dev elopmen ts 2 Change in MSC sin e Gean t4 V4.1 Mo di�ed angle distribution fun tion : g ( u ) = q [ pg ( u ) + (1 p ) g ( u )℄ + (1 q ) g ( u ) (1) � � 1 2 3 where u = os� g ( u ) = exp [ � a (1 u )℄ for u [ u ; 1℄ � 2 1 1 0 � g ( u ) = [( b u ) ℄ for u [ � 1 ; u ℄ � 2 2 2 0 g ( u ) = 3 3 are normalization onstan ts, a; b; ; u and the w eigths p; q are i 0 mo del parameters. & % G4 W orkshop CERN L.Urb� an(CRIP ,Budap est) 1 O t 2002

' $ Multiple S attering in GEANT4, latest dev elopmen ts 3 Where this fun tional form omes from? 2 a� g ( u ) is Gaussian for small � , g ( u ) = exp [ � ℄ � 1 1 2 g ( u ) has a Rutherford-lik e tail for b 1 and 2 � � � 2 � g = onstan t for simpli it y 3 (the �rst t w o ome from the ph ysi s) & % G4 W orkshop CERN L.Urb� an(CRIP ,Budap est) 1 O t 2002

' $ Multiple S attering in GEANT4, latest dev elopmen ts 4 Determination of the parameters All of them are fun tions of the v ariable � = �=t , where � is the transp ort mean free path, t is the (true) path length. Requiremen ts for g ( u ): 1. g ( u ) and the 1st deriv ativ e should b e on tin uous at u = u 0 2. theoreti al mean v alue of u = os� should b e repro du ed b y g ( u ) 3. angle distribution of 15.7 MeV e- after thin Au foils should b e repro du ed (�t) 2 2 2 4. � = < u > � < u > should b e appro ximately agree with theory & % G4 W orkshop CERN L.Urb� an(CRIP ,Budap est) 1 O t 2002

' $ Multiple S attering in GEANT4, latest dev elopmen ts 5 The (simple) fun tional form of the mo del parameters an b e found in the o de, there are altogether 5 onstan ts, whi h determine the mo del ompletely . This new v ersion agrees b etter with the exp erimen tal data than � the results of v ersion 4.1 (and than the results of GEANT3 in some ases). � This new v ersion giv es a w eak er step/ ut dep enden e than the v ersion 4.1 F ollo w some tests whi h sho w the qualit y of the results. Most of them are G4 sim ulation ompared to exp. data, but in some ases GEANT3 results are sho wn as w ell. & % G4 W orkshop CERN L.Urb� an(CRIP ,Budap est) 1 O t 2002

' $ Multiple S attering in GEANT4, latest dev elopmen ts 6 Angle distributions, Gean t4 V4.1 with new MSC Angular distribution of 15.7 MeV e- after Au foils -1 10 G4 (18.66 mg/cm2) -2 10 G4 (37.28 mg/cm2) -3 10 -4 10 -5 10 -6 10 -7 10 0 5 10 15 20 25 30 angle(deg) = ) G4 = data from Ref. 1. & % G4 W orkshop CERN L.Urb� an(CRIP ,Budap est) 1 O t 2002

' $ Multiple S attering in GEANT4, latest dev elopmen ts 7 Angle distributions, GEANT3 (MSC Moliere) Angular distribution of 15.7 MeV e- after Au foils -1 10 G3 (18.66 mg/cm2) -2 10 G3 (37.28 mg/cm2) -3 10 -4 10 -5 10 -6 10 -7 10 0 5 10 15 20 25 30 angle(deg) = ) G3 � data, agreemen t sligh tly b etter for G4 & % G4 W orkshop CERN L.Urb� an(CRIP ,Budap est) 1 O t 2002

' $ Multiple S attering in GEANT4, latest dev elopmen ts 8 Depth-dose distribution of 500 k eV e- in Al Energy deposit of 0.5 MeV e- in Al as a function of depth 2.25 G4 4.1+new MSC 2 1.75 1.5 1.25 1 0.75 0.5 0.25 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 t/r0 r - range of the 500 k eV e- in Al, data tak en from Ref. 2. 0 = ) G4 = data within errors (G3 giv es shorter distribution) & % G4 W orkshop CERN L.Urb� an(CRIP ,Budap est) 1 O t 2002

' $ Multiple S attering in GEANT4, latest dev elopmen ts 9 T ransmission of 25 k eV e- through Al foils transmission coeff. of 25 keV e- (Al) % 100 80 data from Ref. 3 G4 4.1 + new MSC lowenergy MC of Ref. 4 60 40 20 0 0 200 400 600 800 1000 1200 1400 t(microg/cm2) = ) G4 = l.e. MC of Ref. 4 � data from Ref. 3. & % G4 W orkshop CERN L.Urb� an(CRIP ,Budap est) 1 O t 2002

' $ Multiple S attering in GEANT4, latest dev elopmen ts 10 T ransmission of 1 MeV e- through Al la y ers transmission coeff. of 1 MeV e- (Al) ctran % 100 80 data taken from Ref.3 G4 4.1+new MSC,fr 0.01 G4 4.1+new MSC,fr 1.0 GEANT3 60 40 20 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 t/r0 = ) G4 results loser to data than G3 results, fr = 0.01 � data , fr = 1 (no b oundary algorithm) sligthly small o e�s but transmission is not to o sensitiv e to the v alue of fr. & % G4 W orkshop CERN L.Urb� an(CRIP ,Budap est) 1 O t 2002

' $ Multiple S attering in GEANT4, latest dev elopmen ts 11 Ba ks attering of e-/e+ small uts (1 k eV) b oth in G4 and G3 GEANT4 sim ulation is lose to data, GEANT3 6 = data .... GEANT4 - step limitation when en tering a v olume + go o d MSC angle distribution GEANT3 - far from data ev en in the ase of using step limit = ) angle distribution is not go o d enough ... & % G4 W orkshop CERN L.Urb� an(CRIP ,Budap est) 1 O t 2002

' $ Multiple S attering in GEANT4, latest dev elopmen ts 12 Ba ks attering of e- from Au, energy dep enden e backscattering coeff. of e- (Gold) 100 % 90 data from Ref. 3 G4 4.1+new MSC,fr 0.01 80 G4 4.1+new MSC,fr def GEANT3 stmx=1 mic 70 GEANT3 def 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 kin. energy(keV) = G4 results loser to data than G3 results, fr = 0.01 data ) � ba ks attering o e�. is sensitiv e to the v alue of fr. & % G4 W orkshop CERN L.Urb� an(CRIP ,Budap est) 1 O t 2002

' $ Multiple S attering in GEANT4, latest dev elopmen ts 13 Ba ks attering of 40 k eV e- from C, angle dep enden e backscattering coeff. of 40 keV e- (C) 80 % data from Ref. 3 70 G4 4.1+new MSC,fr 0.01 G4 4.1+new MSC,fr def 60 GEANT3 stmx=0.01 range GEANT3 def 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 angle of incidence(deg) = G4 results loser to data than G3 results, fr = 0.01 data ) � ba ks attering o e�. is sensitiv e to the v alue of fr. & % G4 W orkshop CERN L.Urb� an(CRIP ,Budap est) 1 O t 2002

' $ Multiple S attering in GEANT4, latest dev elopmen ts 14 Ba ks attering of 35 k eV e+ from Au, angle dep enden e backscattering coeff. of 35 keV e+ (Au) 100 % data from Ref. 5 90 G4 4.1+new MSC,fr 0.01 GEANT3 stmx=0.01 range 80 70 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 angle of incidence(deg) = ) G4 with fr = 0.01 � data, G3 giv es zero ba ks attering for e+, probable reason: annihilation ross se tion is to o big at lo w energy in GEANT3. & % G4 W orkshop CERN L.Urb� an(CRIP ,Budap est) 1 O t 2002

' $ Multiple S attering in GEANT4, latest dev elopmen ts 15 Ba ks attering of 60 k eV e- from di�. materials, Z dep enden e backscattering coeff. of 60 keV e- for diff. materials 80 % data of Ref. 3 70 G4 4.1+new MSC,fr 0.01 G4 4.1+new MSC,fr def 60 GEANT3 def GEANT3 stmx=0.01 range 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 100 atomic number (Z) = ) G4 with f r = 0 : 01 � data, G3 results far from data. & % G4 W orkshop CERN L.Urb� an(CRIP ,Budap est) 1 O t 2002

' $ Multiple S attering in GEANT4, latest dev elopmen ts 16 Ba ks attering of 1 MeV e- from di�. materials Energy and angle distribution of backscattered electrons (T0=1 MeV) 2500 0.08 Au Au 2250 0.07 Sn Sn Fe 2000 Fe 0.06 Al Al 1750 0.05 1500 1250 0.04 1000 0.03 750 0.02 500 0.01 250 0 0 0 0.25 0.5 0.75 1 100 120 140 160 180 MeV deg G4 sim ulation , 0.001 mm uts. Ni e agreemen t with data of Rester and Derri kson(ref.6, not sho wn here) & % G4 W orkshop CERN L.Urb� an(CRIP ,Budap est) 1 O t 2002

' $ Multiple S attering in GEANT4, latest dev elopmen ts 17 Step dep enden e of MSC in G4 4.1 and G4 with new MSC Step dependence of MSC, angle distr. of 2 MeV e- after 1 mm Si 1.2 1.2 1 10 steps 1 10 steps 5 steps 5 steps 0.8 2 steps 0.8 2 steps 0.6 0.6 0.4 0.4 0.2 0.2 0 0 0 20 40 60 80 0 20 40 60 80 deg deg = ) step dep enden e is w eak er with new MSC & % G4 W orkshop CERN L.Urb� an(CRIP ,Budap est) 1 O t 2002