Some GEANT4

exercises…

GEANT4 simulation of the diamond test setup

Task:to understand and improve the built setup…

• are the electrons MIP?• is the ionization homogeneous in diamond?• can be geometry improved?

&Gate

PA

discr

discr

delay

ADCSr90

PM1

PM2

diamond

Scint.

SrY

E, MeV

Sr

Y

Sr

Emip = 1.5 MeV dE/dx = 5.57 MeV/cm R = 0.2 cm

MIP

GEANT4 geometry + sourceR

EAL

GEA

NT

setup_geometry.cc :

G4UserLimits *l = new G4UserLimits();// Sets a max Step length in the

diamond :G4double maxStep = 0.005*mm; l->SetMaxAllowedStep(maxStep);

diamond_log->SetUserLimits(l);

Source:

G4GeneralParticleSource or G4RadioactiveDecay or your own...

setup_PrimaryGeneratorAction.cc

setup_PhysicsListLE.cc:……………………

void setup_PhysicsListLE::SetCuts(){ SetCutValue(0.01*mm, "gamma"); SetCutValue(0.01*mm, "e-"); SetCutValueForOthers(defaultCutValue); DumpCutValuesTable();}

setup_diamHit.hh :

class setup_diamHit : public G4VHit{public: ….private: G4int trackID; G4double edep; G4ThreeVector pos; G4String pname; ……}

setup_diamSD.hh :class setup_diamSD : public G4VSensitiveDetector{public: … G4bool ProcessHits(G4Step*, G4TouchableHistory*);private: setup_diamHitsCollection* diamCollection;};

setup_EventAction.cc :void setupEventAction::EndOfEventAction(const G4Event* anEvent){ setupRootManager* sRM = setupRootManager::getInstance();

// get information from setup_diamHitsCollection, setup_diamHitsCollection,...

// and fill root histo/ntuple/tree…sRM->fillE(Eini,diamEnergy,scintEnergy);sRM->FillSomethingElse(…)

};

setup_RootManager.hh :class setupRootManager{ //singletonpublic: ... static setupRootManager* getInstance(); void fillX(double dE,

double x, double y, double z, int psN); void fillE(double iE, double dE, double sE); …private: static setupRootManager* instance; TFile* f; TNtuple* ntupleX; TNtuple* ntupleE; …};

Diamond –spectrum(energy deposition)for any e-

Diamond –spectrum(energy deposition)for triggered e-

Initial electrons -spectrumfor “diamond” e-

Initial electrons -Spectrumfor “triggered” e-

energy spectra

all electrons in diamond

triggered electrons in diamond

depth distributions

No step limits:=> Step size is defined by a process…

max Step length = 10 m :=> Step size is defined by the limit

step limits influence - 0.3 MeV e-

More games…

ROOT :)

histogram fitting…

Simple?..TH1F * signal = new TH1F(…);F1 * g1 = new TF1("g1", myFunc, min, max, npar);signal->Fit("g1","VR");

If the function is not so simple?...

Signal = Gaus1 + Landau * Gauss2

Fit parameters:p[0] = Norm(Gauss1)p[1] = Mean(Gauss1) - fixedp[2] = Sigma(Gauss1) – fixedp[3] = Width(Langau)p[4] = MPV(Langau)p[5] = Area(Langau)p[6] = Sigma(Gauss2)

Simple fitting for the complicated case…Function:TF1 * glg = new TF1("glg", gaulangaufun, 50, 400, 7);

Proper initial parameters:p[0] = 100.; p[1] = 139.1; p[2] = 17.7; // from noise gaussp[3] = 5.; p[4] = 180.; p[5] = 20000.; p[6] = 30.; // signalglg->SetParameters(p);

And fit it:signal->Fit("glg","VR");

…. And get:FCN=140.264 FROM MIGRAD STATUS=FAILED 611 CALLS 612 TOTAL EDM=30.8846 STRATEGY= 1 ERR MATRIX NOT POS-DEF EXT PARAMETER APPROXIMATE STEP FIRST NO. NAME VALUE ERROR SIZE DERIVATIVE 1 p0 1.72541e+01 9.99999e-01 -0.00000e+00 -1.74731e-03 2 p1 1.39100e+02 fixed 3 p2 1.77000e+01 fixed 4 p3 4.91314e+00 1.79039e+00 0.00000e+00 -4.07711e+00 5 p4 1.86918e+02 2.33982e+00 0.00000e+00 -4.67063e-03 6 p5 9.58479e+03 1.44047e+02 0.00000e+00 -3.45415e-09 7 p6 2.74389e+01 2.34762e+00 0.00000e+00 8.24991e-02

To try to improve the fit…

To improve:signal->Fit("glg","EVR"); // „better error estimation“

… And it takes ~8 times loneger…

…. And get: FCN=140.208 FROM MINOS STATUS=PROBLEMS 4058 CALLS 5120 TOTAL EDM=0.358165 STRATEGY= 1 ERR MATRIX NOT POS-DEF EXT PARAMETER PARABOLIC MINOS ERRORS NO. NAME VALUE ERROR NEGATIVE POSITIVE 1 p0 1.74193e+01 1.29294e+00 1.08485e+00 2 p1 1.39100e+02 fixed 3 p2 1.77000e+01 fixed 4 p3 4.87816e+00 1.56382e-03 5 p4 1.86941e+02 6.02893e-03 6 p5 9.58141e+03 1.62875e+02 7 p6 2.73866e+01 1.06973e+00 9.57228e-01

going back to MINUIT…

Actually:

ROOT uses MINUIT:signal->Fit("glg","VR"); <=> gMinuit->mnexcm("MIGRAD", arglist ,2,ierflg);signal->Fit("glg",“EVR"); <=> gMinuit->mnexcm("MIGRAD", arglist ,2,ierflg);

+ gMinuit->mnexcm("MINOS", arglist ,npar,ierflg);

Then what is wrong?Probably, too many things are predefined?

To use TMinuit class directly (only necessary and optimal things)?

going back to MINUIT…

Everything (almost) as in Fortran:

TMinuit *gMinuit = new TMinuit(7); gMinuit->SetFCN(fcn); // just Chi2

arglist[0] = 1;gMinuit->mnexcm("SET ERR", arglist, 1, ierflg); // UD = 1 for chisqr

// Set starting values and step sizes for parameters Double_t vstart[7] = {100, 139.1, 17.7, 5., 180., 20000., 30.}; Double_t step[7] = {1 , 1 , 0.1, .02, .1, 50, .3}; gMinuit->mnparm(0, "PNorm", vstart[0], step[0], 0,0, ierflg);…………………………………..

arglist[0] = 1000; arglist[1] = .01; // with set maxcall and tolerancegMinuit->mnexcm("MIGRAD", arglist ,2,ierflg);

arglist[0] = 200; arglist[1] = 5; // with set maxcall and npargMinuit->mnexcm("MINOS", arglist ,2,ierflg);

and we’ve finally got…

FCN=140.388 FROM MINOS STATUS=SUCCESSFUL 357 CALLS 1062 TOTAL EDM=0.000510439 STRATEGY= 1 ERR MATRIX NOT POS-DEF EXT PARAMETER PARABOLIC MINOS ERRORS NO. NAME VALUE ERROR NEGATIVE POSITIVE 1 PNorm 1.72476e+01 2.44167e+00 2 PMean 1.39100e+02 fixed 3 PSigma 1.77000e+01 fixed 4 LSigma 4.91366e+00 1.52320e-02 5 LMPV 1.86905e+02 2.15345e-01 -5.77136e-01 5.10611e-01 6 LNorm 9.57911e+03 1.02587e+02 7 GSigna 2.73663e+01 8.55687e-02

Chi2

LMPV