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# tol-mc.py
# Monte-Carlo Simulation of a basic muon time-of-flight experiment
# @author: bryan newbold
# @email: bnewbold@mit.edu
# @date: oct 2006
from pylab import *;
from scipy import *;
# default number of tries to run...
max_tries = 10**2
# default geometry
h = 100.0 # cm
h_err = 1.0 # cm
Tw = 15.5*2.54 # inches->cm
Tw_err = .5*2.54
Tl = 23.5*2.54
Tl_err = 1.*2.54
Tpmtl = 19.*2.54
Tpmtl_err = 1.*2.54
Bw = 42.
Bw_err = 4./10 # mm->cm
Bl = 53.
Bl_err = 1.
Bpmtl = 20.
Bpmtl_err = 1.
n_scint = 1.5 # index of refraction of scintillators
C_ = 2.99792458*10**10 # speed of light in cm
# shortcuts to random number generators
ur = lambda: rand();
gr = lambda: randn();
aTx = lambda: ur()*Tl
aTy = lambda: ur()*Tw
#aphi = lambda: arccos( sqrt(ur()))
aomega = lambda: ur()*2*pi
aBx = lambda x,p,o,h: x+h*sin(o)*tan(p)
aBy = lambda y,p,o,h: y+h*cos(o)*tan(p)
#aP = lambda p: 100.*cos(p)
aP = lambda p,mc: ((mc/2.99) + gr() * 0.02) * C_
aTime = lambda x,y,pmt,w: n_scint/(C_)*sqrt((x+pmt)**2 + (w/2 - y)**2)
if not vars().has_key('phi_table'):
phi_table = zeros((1000,1),typecode='f')
for i in frange(0., pi/2,0.00001):
m = (2*i + sin(2*i))/pi
phi_table[int(1000*(m - (m%.001)))] = i
phi_table[-1] = pi/2
def aphi():
n = ur();
return phi_table[int(1000*(n-(n%.001)))][0];
def run(tries=max_tries, h=h, h_err=h_err,printstuff=True,mean_c=2.93):
num_events=0;
if(printstuff): print "Going to make %d tries..." % tries
events=zeros((tries,7),typecode='f')
while tries>0:
tries = tries-1;
Tx,Ty,phi,omega=aTx(),aTy(),aphi(),aomega();
Bx = aBx(Tx,phi,omega,h)
if((Bx < 0.) or (Bx > Bl)):
continue;
By = aBy(Ty + abs(Tw-Bw)/2,phi,omega,h)
if((By < 0.) or (By > Bw)):
continue;
P = aP(phi,mean_c)
dL = (h/cos(phi));
dT = -1 *aTime(Tx,Ty + abs(Tw-Bw)/2,Tpmtl,Tw) \
+ aTime(Bx,By,Bpmtl,Bw) \
+ dL/P;
events[num_events] = (Tx,Ty,Bx,By,P,dT,dL);
num_events = num_events +1;
if num_events>0:
if(printstuff): print "... %d valid events!" % num_events;
return events[0:num_events];
else:
if(printstuff): print "No valid events!"
return [];
def plot_events(events, xres=16,yres=16):
if(size(events[0]) != 7):
print "Passed matrix is no good...";
return;
figure();
# TOP part
subplot(211);
x = arange(0.,Tl,Tl/xres);
y = arange(0.,Tw,Tw/yres);
X,Y = meshgrid(x,y);
Z = zeros((xres,yres));
for i in events:
Z[int(i[1] * yres/Tw),int(i[0] * xres/Tl)] +=1;
contourf(X,Y,Z);
title("Distribution on Top Paddle (counts per %.3g cm^2)" \
% (Tl/xres * Tw/yres));
xlabel("Paddle Length (%g cm +/- %g cm)" % (Tl,Tl_err));
ylabel("Paddle Width (%g cm +/- %g cm)" % (Tw,Tw_err));
colorbar();
# BOTTOM part
subplot(212);
x = arange(0.,Bl,Bl/xres);
y = arange(0.,Bw,Bw/yres);
X,Y = meshgrid(x,y);
Z = zeros((xres,yres));
for i in events:
Z[int(i[3] * yres/Bw),int(i[2] * xres/Bl)] +=1;
contourf(X,Y,Z);
title("Distribution on Bottom Paddle (counts per %.3g cm^2)" \
% (Bl/xres * Tw/yres));
xlabel("Paddle Length (%g cm +/- %g)" % (Bl,Bl_err));
ylabel("Paddle Width (%g cm +/- %g cm)" % (Bw,Bw_err));
colorbar();
def plot_events_3d(events):
if(size(events[0] != 6)):
print "Passed matrix is no good...";
return;
figure();
return;
def plot_deltaT_h(heights=frange(33.,233,50.),num_events=1000,err=3,c=2.93):
points = zeros((size(heights),6),typecode='f');
points[:,0] = list(heights[:]);
times = frange((int(err)));
dL = frange((int(err)));
actP = frange((int(err)));
for i in points:
for r in range(0,size(times)):
events = run(int(num_events),h=i[0],printstuff=False,mean_c=c);
times[int(r)] = mean(events[:,5]);
dL[int(r)] = mean(events[:,6]);
actP[int(r)] = mean(events[:,4]);
i[1] = mean(times);
i[2] = std(times);
i[3] = mean(dL);
i[4] = mean(actP)
i[5] = std(actP)
stuff = fittodata_linear(points[:,0],points[:,1],[1.,1.],err=points[:,2],ret_all=True)
plotfit(stuff)
v = stuff['params']
ax = gca()
title("Change in delta-T with average h");
xlabel("Average h in cm");
ylabel("Average delta-T");
txt = text(0.65,.22,"delta-T/h: %g \noffset: %g \nmean muon speed: %g cm/s\nmonte carlo input speed:%g +/- %g cm/s"
% (v[0],v[1],1/v[0],mean(points[:,4]),mean(points[:,5])),
horizontalalignment='center',
verticalalignment='center',
transform = ax.transAxes)
stuff = fittodata_linear(points[:,3],points[:,1],[1.,1.],err=points[:,2],ret_all=True)
plotfit(stuff)
vc = stuff['params']
ax=gca()
title('Change in mean delta-T with change in mean L')
xlabel('Mean Length of flight')
ylabel('Mean time gap between events')
txt = text(0.65,.22,"delta-T/h: %g \noffset: %g \nmean muon speed: %g cm/s\nmean muon speed corrected: %g cm/s\nmonte carlo input speed:%g +/- %g cm/s"
% (v[0],v[1],1/v[0],1/vc[0],mean(points[:,4]),mean(points[:,5])),
horizontalalignment='center',
verticalalignment='center',
transform = ax.transAxes)
def plot_L_vs_h(heights=r_[18.5:218.5:8.],num_events=400,err=2,c=2.93):
points = zeros((size(heights),5),typecode='f');
for i in range(0,size(heights)):
points[i,0] = heights[i];
times = r_[0.:int(err)];
dL = r_[0.:int(err)];
for i in range(0,size(heights)):
for r in range(0,size(times)):
events = run(int(num_events),h=points[i,0],printstuff=False,mean_c=c);
times[int(r)] = mean(events[:,5]);
dL[int(r)] = mean(events[:,6]);
points[i,1] = mean(times);
points[i,2] = std(times);
points[i,3] = mean(dL);
points[i,4] = std(dL);
x = points[:,0].tolist(); x = array(x)
y = points[:,3].tolist(); y = array(y)
err = points[:,4].tolist(); err = array(err)
plotfit(fittodata_linear(x,y,[3.,-1.],err=err,ret_all=True))
title("Change in mean L with h");
xlabel("h in cm");
ylabel("Mean L");
figure();
plot(x,y-x);
return (x,y,err);
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