def muonPopulationPitchAnglesModel(numMuons,injectionYMeanMm,injectionYSigmaMm,injectionTimeWidthNs,plot=True,debug=False) :
print ""
print "Params:"
print " Num mu+ = %i" % (numMuons)
print " n = %f" % (pitchAnglesOneMuon.fieldIndex)
print " Ring vertical acceptance = %f [mm]" % (pitchAnglesOneMuon.ringVerticalAcceptanceMm)
print " Gaussian vertical injection profile : Mean = %f [mm] : Sigma = %f [mm]" % (injectionYMeanMm,injectionYSigmaMm)
print ""
#
# Data containers
#
injectionYValsMm = list()
injectionMomentumValsGeV = list()
injectionTimeValsNs = list()
timeInRingValsNs = list()
decayTimeValsNs = list()
decayYValsMm = list()
decayPitchAngleValsDeg = list()
decayPitchAngle2ValsRad2 = list()
#
# Generate data
#
#Loop over mu+
for i_mu in range(0,numMuons) :
#Generate injection y (truncate around max acceptance)
while True :
injectionYMm = random.gauss(injectionYMeanMm,injectionYSigmaMm)
if abs(injectionYMm) < pitchAnglesOneMuon.ringVerticalAcceptanceMm : break
injectionYValsMm.append(injectionYMm)
#TODO TODO TODO Betatron amplitude depends on injection y and injection psi, here only modelling y dependences (e.g. assuming psi = 0)
#Generate momentum
pGeV = 3.09 #TODO Spread
injectionMomentumValsGeV.append(pGeV)
#Get boost from momentum
gamma = pGeV / pitchAnglesOneMuon.muonRestMassGeV
#Generate injection time
injectionTimeNs = random.uniform(0.,injectionTimeWidthNs)
#TODO spread, W function
injectionTimeValsNs.append(injectionTimeNs)
#Generate decay time (get dilated lifetime and generate decay from exponetial using this as time constant)
lifetimeNs = gamma * pitchAnglesOneMuon.muonRestLifetimeNs
timeInRingNs = -1. * lifetimeNs * math.log( random.uniform(0.,1.) )
timeInRingValsNs.append(timeInRingNs)
decayTimeNs = injectionTimeNs + timeInRingNs
decayTimeValsNs.append(decayTimeNs)
#Get y at decay time (vertical BO amplitude is displacement from orbit plane at injection)
#Only oscillate during time in ring (e.g. don't include injection time)
verticalBetatronAmplitudeMm = injectionYMm
decayYMm = pitchAnglesOneMuon.verticalBetatronPositionMm(verticalBetatronAmplitudeMm,pitchAnglesOneMuon.verticalBetatronPeriodNs,timeInRingNs)
decayYValsMm.append(decayYMm)
#Get pitch angle at time of decay, psi
psiRad = pitchAnglesOneMuon.verticalBetatronPitchAngleRad(verticalBetatronAmplitudeMm,pitchAnglesOneMuon.verticalBetatronPeriodNs,timeInRingNs)
decayPitchAngleValsDeg.append( math.degrees(psiRad) )
decayPitchAngle2ValsRad2.append(psiRad*psiRad)
#TODO generate full path, not just decay point to check pitch
#Dump debug info
if debug :
print "mu+ %i : Injection y = %f [mm] : Decay y = %f [mm] : Pitch angle = %f [deg]" \
% (i_mu,injectionYMm,decayYMm,math.degrees(psiRad))
#
# Plot injection profile
#
if plot :
plt.xlabel('Injection y [mm]',fontsize=20)
plt.hist(injectionYValsMm, normed=False, bins=50)
#plt.xlim([-100.,100.]) #Use when comparing to TDR Fig. 8.19
#plt.xticks(np.arange(-100.,101.,40.)) #Use when comparing to TDR Fig. 8.19
plt.show()
plt.xlabel('Injection momentum [GeV]')
plt.hist(injectionMomentumValsGeV, normed=False, bins=50)
plt.show()
plt.xlabel('Injection time [ns]')
plt.hist(injectionTimeValsNs, normed=False, bins=50)
plt.show()
#
# Plot decay profile
#
if plot :
plt.xlabel('Decay y [mm]')
n, bins, patches = plt.hist(decayYValsMm, normed=False, bins=50)
#(mu, sigma) = norm.fit(decayYValsMm) #Fit Gaussian
#plt.title( "Gaussian fit : Mean = %f, sigma = %f [mm]" % (mu,sigma) )
#plt.plot(bins, mlab.normpdf(bins,mu,sigma), 'r--', linewidth=2) #Plot the fit
plt.show()
plt.xlabel('Decay time in ring [ns]')
plt.hist(timeInRingValsNs, normed=False, bins=50)
plt.show()
plt.xlabel('Decay absolute time [ns]')
plt.hist(decayTimeValsNs, normed=False, bins=50)
plt.show()
plt.xlabel('Decay pitch angle [deg]')
plt.hist(decayPitchAngleValsDeg, normed=False, bins=50)
plt.show()
plt.xlabel('Decay pitch angle squared [rad^2]')
plt.hist(decayPitchAngle2ValsRad2, normed=False, bins=50)
plt.show()
#
# Plot decay y vs t
#
if plot :
plt.title('')
plt.xlabel('Decay time [ns]')
plt.ylabel('Decay y [mm]')
plt.plot(decayTimeValsNs,decayYValsMm,"b.")
plt.xlim([0,1000])
plt.show()
plt.title('')
plt.xlabel('Time in ring [ns]')
plt.ylabel('Decay y [mm]')
plt.plot(timeInRingValsNs,decayYValsMm,"b.")
plt.xlim([0,1000])
plt.show()
#
# Plot decay pitch angle vs t
#
if plot :
plt.title('')
plt.xlabel('Decay time [ns]')
plt.ylabel('Decay pitch angle [deg]')
plt.plot(decayTimeValsNs,decayPitchAngleValsDeg,"b.")
plt.xlim([0,1000])
plt.show()
plt.title('')
plt.xlabel('Time in ring [ns]')
plt.ylabel('Decay pitch angle [deg]')
plt.plot(timeInRingValsNs,decayPitchAngleValsDeg,"b.")
plt.xlim([0,1000])
plt.show()
#
# Plot decay pitch angle vs y
#
if plot :
plt.title('')
plt.xlabel('Decay y [mm]')
plt.ylabel('Decay pitch angle [deg]')
plt.plot(decayYValsMm,decayPitchAngleValsDeg,"b.")
plt.show()
#
# Calculate pitch correction
#
pitchCorrection, pitchCorrectionPpb = pitchAnglesOneMuon.pitchCorrection(decayPitchAngle2ValsRad2)
print ""
print "Results:"
print " Pitch correction = %f [ppb]" % (pitchCorrectionPpb)
print ""
#
# Done
#
#Return results
return pitchCorrectionPpb
psiValsDeg = list()
psi2ValsRad2 = list()
#Loop over steps
for i in range(0,numSteps) :
#Get t
t = t0Ns + ( float(i) * stepSizeNs )
tValsNs.append(t)
#Get y
y = pitchAnglesOneMuon.verticalBetatronPositionMm(verticalBetatronAmplitudeMm,pitchAnglesOneMuon.verticalBetatronPeriodNs,t)
yValsMm.append(y)
#Get pitch angle, psi = atan(dy/dz)
psiRad = pitchAnglesOneMuon.verticalBetatronPitchAngleRad(verticalBetatronAmplitudeMm,pitchAnglesOneMuon.verticalBetatronPeriodNs,t)
psiValsDeg.append( math.degrees(psiRad) )
psi2ValsRad2.append(psiRad*psiRad)
#
# Calculate pitch correction for this injection y value
#
pitchCorrection, pitchCorrectionPpb = pitchAnglesOneMuon.pitchCorrection(psi2ValsRad2)
pitchCorrectionValsPpb.append(pitchCorrectionPpb)
#
# Plot decay y vs t
#