def divergence_sphi(self,r):
theta, phi = pi/2-self.xtal.gtheta, self.xtal.gphi
rot_in_xtal = lambda x: Physics.rot(x, (('y', -theta), ('z', phi)))
drag_in_xtal = lambda x: array(self.xtal.r) - array(x)
r=rot_in_xtal(self.photon.r)
r=drag_in_xtal(self.photon.r)
if self.xtal.source_lens_distance == "inf":
return 0.0
else:
return math.atan ( r[1] / r[0] )
def generate_position(self):
theta, phi = pi/2-self.xtal.gtheta, self.xtal.gphi
self.photon.r = self.random_position_on_surface()
# lambda functions to:
# 1. Convert from the crystal reference frame to the lens reference frame;
# 2. Rotate the photon WRT the lens axis till it corresponds to its defined xtal;
drag_out_xtal = lambda x: array(x) + array(self.xtal.r)
rot_out_xtal = lambda x: Physics.rot(x, (('y', -theta), ('z', -phi)))
# Set the photon position in the observer reference frame (rotation + translation)
self.photon.r=rot_out_xtal(self.photon.r)
self.photon.r=drag_out_xtal(self.photon.r)
def interaction(self):
"""Interaction between photon and xtal."""
# Lambda function for coordinate transformation
theta, phi = pi/2-self.xtal.gtheta, self.xtal.gphi
drag_in_xtal = lambda x: x-self.xtal.r
drag_out_xtal = lambda x: x+self.xtal.r
rot_in_xtal = lambda x: Physics.rot(x, (('z', phi), ('y', theta)))
rot_out_xtal = lambda x: Physics.rot(x, (('y', -theta), ('z', -phi)))
in_xtal = lambda x: rot_in_xtal(drag_in_xtal(x))
out_xtal= lambda x: drag_out_xtal(rot_out_xtal(x))
# Changing reference frame for photon and xtal
self.photon.k=rot_in_xtal(self.photon.k)
self.photon.r = in_xtal(self.photon.r)
self.xtal.g=rot_in_xtal(self.xtal.g)
self.int_history=[] # History init
# Photon adventure begins...
while self.isinside():
interaction_type=self.which_interaction()
self.interact(interaction_type)
if interaction_type==0: break # Photoabsorption: the photon dies in to xtal
# Photon adventure is over...
if interaction_type==0: pass # Dead photon (photo-absorption)
elif self.photon.knormalized[2]<=0.: # photon points towards focal plane... (no backscattering)
# Back to the original reference frame
self.photon.k=rot_out_xtal(self.photon.k)
self.photon.r=out_xtal(self.photon.r)
# transport the photon to the focal plane
self.photon.travelz(0.)
else: pass # Photon is backscattered and thus lost
# anyway the xtal goes backs to the previous reference frame
self.xtal.g=rot_out_xtal(self.xtal.g)
def divergence_stheta(self, r):
source_extension = 0.035
if self.xtal.source_lens_distance == "inf":
return 0.0
else:
theta, phi = pi/2-self.xtal.gtheta, self.xtal.gphi
rot_in_xtal = lambda x: Physics.rot(x, (('y', -theta), ('z', phi)))
drag_in_xtal = lambda x: array(self.xtal.r) - array(x)
r=rot_in_xtal(self.photon.r)
r=drag_in_xtal(self.photon.r)
if r[0] <= 0: s = math.sqrt(r[0]**2 + r[1]**2)
else: s = -math.sqrt(r[0]**2 + r[1]**2)
deltas = uniform (-source_extension/2 , source_extension/2 )
return math.atan(( s + deltas) / self.xtal.source_lens_distance)
def generator(self, Emin=1., Emax=1000., Exp=False, sphi=0., stheta=pi):
'''Generates randomly a photon that will go on to xtal.
Exp is the powerlaw spectral index (-2.1 for the Crab Nebula).
'''
theta, phi = pi/2-self.xtal.gtheta, self.xtal.gphi
# lambda functions #
drag_out_xtal = lambda x: array(x) + array(self.xtal.r)
rot_out_xtal = lambda x: Physics.rot(x, (('y', -theta), ('z', -phi)))
# Puts a photon an EPSILON under the xtal surface in a random 2D point
random_pos_on_surface=[uniform(-x/2., x/2.) for x in self.xtal.dim[:2]]
random_pos_on_surface.append(-EPSILON)
self.photon.r=random_pos_on_surface
# The photon position in observer reference frame (rotation + translation)
self.photon.r=rot_out_xtal(self.photon.r)
self.photon.r=drag_out_xtal(self.photon.r)
if self.photon.i !=1: self.photon.i=1.
# wavevector definition from source angular parameters
self.photon.k=Physics.makenormalvec(sphi, stheta)
# Energy calculation (powerlaw if Exp is False)
self.erandom((Emin, Emax), Exp=Exp)
