def GetDrag(self, h, V):
""" Function to compute the drag force, modelled on an
Atlas V launch vehicle as a function of Mach no."""
#CONSTANTS:
gamma = 1.14
R = 287
T, rho = atmosphere.Atmosphere(h)
A = np.sqrt(gamma * R * T)
M = V / A
if M <= 1.25:
Cd = -0.0415 * M**3 + 0.3892 * M**2 - 0.2614 * M + 0.303
elif M > 1.25 and M <= 4:
Cd = -0.049 * M**4 + 0.5664 * M**3 - 2.3265 * M**2 + 3.8512 * M - 1.6625
elif M > 4 and M <= 10:
Cd = -0.0037 * M**3 + 0.0695 * M**2 - 0.4105 * M + 0.9732
elif M > 10:
Cd = 0.255
D = 0.5 * rho * V**2 * self.A * Cd
return D
def __init__(self,X_max,N_max,d0,earth_emergence,azimuth=0,
ckarray='gg_t_delta_theta_2020_normalized.npz',tel_area = 1):
self.atmosphere = at.Atmosphere()
self.gga = CherenkovPhotonArray(ckarray)
self.tel_area = tel_area
self.reset_shower(X_max,N_max,d0,earth_emergence,azimuth=0)
def __init__(self, time_span, rocket):
if isinstance(rocket, Rocket.Rocket) is False:
print(
'Error <in ModelWorld>: "rocket" must be an object of Rocket!')
exit(-1)
if time_span[0] < 0 or time_span[1] < 0:
print(
'Error <in ModelWorld>: incorrect time interval! Time cannot be negative!'
)
exit(-1)
self.t_start = time_span[0]
self.t_end = time_span[1]
self.atmo = Atmo.Atmosphere()
self.main_rocket = copy.copy(rocket)
self.rocket = copy.copy(rocket)
def initialize_run(self):
# ## Create atmosphere: attributes are self.atm.gas, self.atm.cloud and self.atm.layerProperty
self.atm = atm.Atmosphere(self.planet,
mode=self.mode,
config=self.config,
log=self.log,
**self.kwargs)
self.atm.run()
# ## Read in absorption modules: to change absorption, edit files under /constituents'
self.alpha = alpha.Alpha(mode=self.mode,
config=self.config,
log=self.log,
**self.kwargs)
# ## Next compute radiometric properties - initialize bright and return data class
self.bright = bright.Brightness(mode=self.mode,
log=self.log,
**self.kwargs)
self.data_return = data_handling.DataReturn()
# ## Create fileIO class
self.fIO = fileIO.FileIO(self.output_type)
class Shower():
"""A class for generating extensive air shower profiles and their Cherenkov
outputs. The shower can either be a Gaisser Hillas shower or a Griessen
Shower.
Parameters:
X_max: depth at shower max (g/cm^2)
N_max: number of charged particles at X_max
h0: height of first interaction (meters)
X0: Start depth
theta: Polar angle of the shower axis with respect to vertical. Vertical
is defined as normal to the Earth's surface at the point where the axis
intersects with the surface.
phi: azimuthal angle of axis intercept (radians) measured from the x
axis. Standard physics spherical coordinate convention. Positive x axis is
North, positive y axis is west.
profile: Shower type, either 'GN' for Greisen, or GH for Gaisser-Hillas.
direction: Shower direction, either 'up' for upward going showers, or 'down'
for downward going showers.
"""
earth_radius = 6.371e6
Lambda = 70
atm = at.Atmosphere()
axis_h = np.linspace(0,atm.maximum_height,10000)
axis_rho = atm.density(axis_h)
axis_delta = atm.delta(axis_h)
axis_Moliere = 96. / axis_rho
Moliere_data = np.load('lateral.npz')
t_Moliere = Moliere_data['t']
AVG_Moliere = Moliere_data['avg']
def __init__(self,X_max,N_max,h0,theta,direction,phi=0,type='GH'):
self.type = type
self.reset_shower(X_max,N_max,h0,theta,direction,phi,type)
def reset_shower(self,X_max,N_max,h0,theta,direction,phi=0,type='GH'):
'''Set necessary attributes and perform calculations
'''
self.input_X_max = X_max
self.N_max = N_max
self.h0 = h0
self.direction = direction
self.theta = theta
self.axis_r, self.axis_start_r = self.set_axis(theta,h0)
self.axis_X, self.axis_dr, self.X0 = self.set_depth(self.axis_r,
self.axis_start_r)
self.X_max = X_max + self.X0
self.axis_nch = self.size(self.axis_X)
self.axis_nch[self.axis_nch<1.e3] = 0
self.i_ch = np.nonzero(self.axis_nch)
self.shower_X = self.axis_X[self.i_ch]
self.shower_r = self.axis_r[self.i_ch]
self.shower_Moliere = self.axis_Moliere[self.i_ch]
self.shower_t = self.stage(self.shower_X)
self.shower_avg_M = np.interp(self.shower_t,self.t_Moliere,self.AVG_Moliere)
self.shower_rms_w = self.shower_avg_M * self.shower_Moliere
def h_to_axis_R_LOC(self,h,theta):
'''Return the length along the shower axis from the point of Earth
emergence to the height above the surface specified
Parameters:
h: array of heights in meters
theta: polar angle of shower axis (radians)
returns: r (same size as h), an array of distances along the shower
axis_sp.
'''
cos_EM = np.cos(np.pi-theta)
R = self.earth_radius
r_CoE= h + R # distance from the center of the earth to the specified height
r = R*cos_EM + np.sqrt(R**2*cos_EM**2-R**2+r_CoE**2)
return r
def set_axis(self,theta,h0):
'''Create a table of distances along the shower axis
'''
axis_r = self.h_to_axis_R_LOC(self.axis_h, theta)
axis_start_r = self.h_to_axis_R_LOC(self.h0, theta)
return axis_r, axis_start_r
def set_depth(self,axis_r,axis_start_r):
'''Integrate atmospheric density over selected direction to create
a table of depth values.
'''
axis_dr = axis_r[1:] - axis_r[:-1]
axis_deltaX = np.sqrt(self.axis_rho[1:]*self.axis_rho[:-1])*axis_dr / 10# converting to g/cm^2
if self.direction == 'up':
axis_X = np.concatenate((np.array([0]),np.cumsum(axis_deltaX)))
elif self.direction == 'down':
axis_X = np.concatenate((np.cumsum(axis_deltaX[::-1])[::-1],
np.array([0])))
axis_dr = np.concatenate((np.array([0]),axis_dr))
X0 = np.interp(axis_start_r,axis_r,axis_X)
return axis_X, axis_dr, X0
def size(self,X):
"""Return the size of the shower at a slant-depth X
Parameters:
X: the slant depth at which to calculate the shower size [g/cm2]
Returns:
N: the shower size
"""
if self.type == 'GH':
value = self.GaisserHillas(X)
elif self.type == 'GN':
value = self.Greisen(X)
return value
def GaisserHillas(self,X):
'''Return the size of a GH shower at a given depth.
'''
x = (X-self.X0)/self.Lambda
g0 = x>0.
m = (self.X_max-self.X0)/self.Lambda
n = np.zeros_like(x)
n[g0] = np.exp( m*(np.log(x[g0])-np.log(m)) - (x[g0]-m) )
return self.N_max * n
def Greisen(self,X,p=36.62):
'''Return the size of a Greisen shower at a given depth.
'''
X[X < self.X0] = self.X0
Delta = X - self.X_max
W = self.X_max-self.X0
eps = Delta / W
s = (1+eps)/(1+eps/3)
i = np.nonzero(s)
n = np.zeros_like(X)
n[i] = np.exp((eps[i]*(1-1.5*np.log(s[i]))-1.5*np.log(s[i]))*(W/p))
return self.N_max * n
def stage(self,X,X0=36.62):
"""Return the shower stage at a given slant-depth X. This
is after Lafebre et al.
Parameters:
X: atmosphering slant-depth [g/cm2]
X0: radiation length of air [g/cm2]
Returns:
t: shower stage
"""
return (X-self.X_max)/X0
class UpwardShower():
"""A class for generating upward shower profiles and their Cherenkov
outputs. The shower can either be a Gaisser Hillas shower or a Griessen
Shower.
Parameters:
X_max: depth at shower max (g/cm^2)
N_max: number of charged particles at X_max
d0: height of first interaction (meters)
earth_emergence: angle the primary particle makes with the tangent line of
the Earth's surface as it emerges (radians)
azimuth: azimuthal angle of Earth emergence (radians)
n_stage: number of depth steps for calculating Cherenkov light
ckarray: filename of the Cherenkov distribution table
tel_area: surface area of the orbital telescopes (m^2)
"""
earth_radius = 6.371e6
Lambda = 70
atm = at.Atmosphere()
axis_h = np.linspace(0,atm.maximum_height,1000)
axis_rho = atm.density(axis_h)
axis_delta = atm.delta(axis_h)
def __init__(self,X_max,N_max,d0,earth_emergence,azimuth=0,
ckarray='gg_t_delta_theta_2020_normalized.npz',tel_area = 1):
self.atmosphere = at.Atmosphere()
self.gga = CherenkovPhotonArray(ckarray)
self.tel_area = tel_area
self.reset_shower(X_max,N_max,d0,earth_emergence,azimuth=0)
def reset_shower(self,X_max,N_max,d0,earth_emergence,azimuth=0):
'''Set necessary attributes and perform calculations
'''
self.X_max = X_max
self.N_max = N_max
self.d0 = d0
self.earth_emergence = earth_emergence
self.zenith = np.pi / 2 - earth_emergence
self.azimuth = azimuth
self.axis_cem = np.cos(np.pi - self.zenith)
self.crunch_numbers()
def crunch_numbers(self):
'''This function performs all the calculations in order.
'''
self.set_shower_axis()
self.select_shower_steps()
self.calculate_gg()
self.calculate_yield()
def h_to_axis_R_LOC(self,h,cos_EM):
'''Return the length along the shower axis from the point of Earth
emergence to the height above the surface specified
Parameters:
h: array of heights in meters
cos_EM: cosine of the Earth emergence angle plus 90 degrees
returns: r (same size as h), an array of distances along the shower axis_sp.
'''
R = self.earth_radius
r_CoE= h + R # distance from the center of the earth to the specified height
r = R*cos_EM + np.sqrt(R**2*cos_EM**2-R**2+r_CoE**2)
return r
def flat_earth_difference(self,r,EM,CEM):
'''Calculate the difference in height between a flat earth height and
the corrected height as as an inclined upward shower goes through the
atmosphere.
Parameters:
r: distance along the track (m)
EM: earth emergence angle (rad)
CEM: cosine of the earth emergence angle + pi/2 radians
returns: the difference in atmospheric height (between flat and round
earth) at the given length along the track.
'''
calculate the height correction
R = self.earth_radius
h_flat = r * np.sin(EM)
h_true = np.sqrt(r**2 + R**2 -2*r*R*CEM) - R
return h_true - h_flat
def set_shower_axis(self):
'''Create a table of 10000 distances and depths along the shower axis
to interpolate into across its whole atmospheric path
'''
self.axis_r = self.h_to_axis_R_LOC(self.axis_h, self.axis_cem)
self.axis_dr = self.axis_r[1:] - self.axis_r[:-1]
axis_deltaX = np.sqrt(self.axis_rho[1:]*self.axis_rho[:-1])*self.axis_dr / 10# converting to g/cm^2
self.axis_X = np.concatenate((np.array([0]),np.cumsum(axis_deltaX)))
self.axis_dr = np.concatenate((np.array([0]),self.axis_dr))
def select_shower_steps(self):
'''Select the depth indices steps where the shower is producing light,
i.e. where there are charged particles, then invoke the orbital counter
class to calculate angles and distances to hypothetical telescopes.
'''
self.axis_start_r = self.h_to_axis_R_LOC(self.d0, self.axis_cem)
self.X0 = np.interp(self.axis_start_r,self.axis_r,self.axis_X)
self.X_max += self.X0
self.axis_nch = self.size(self.axis_X)
self.axis_nch[self.axis_nch<1.e-1] = 0
self.axis_t = self.stage(self.axis_X)
self.i_ch = np.nonzero(self.axis_nch)
self.n_stage = np.size(self.i_ch)
axis_r = self.axis_r[self.i_ch] - self.axis_start_r
tel_r = self.h_to_axis_R_LOC(525.e3, self.axis_cem) - self.axis_start_r
self.OC = OrbitalCounters(axis_r,100,100.e3,tel_r)
def size(self,X):
"""Return the size of the shower at a slant-depth X
Parameters:
X: the slant depth at which to calculate the shower size [g/cm2]
Returns:
N: the shower size
"""
x = (X-self.X0)/self.Lambda
g0 = x>0.
m = (self.X_max-self.X0)/self.Lambda
n = np.zeros_like(x)
n[g0] = np.exp( m*(np.log(x[g0])-np.log(m)) - (x[g0]-m) )
return self.N_max * n
def stage(self,X,X0=36.62):
"""Return the shower stage at a given slant-depth X. This
is after Lafebre et al.
Parameters:
X: atmosphering slant-depth [g/cm2]
X0: radiation length of air [g/cm2]
Returns:
t: shower stage
"""
return (X-self.X_max)/X0
def calculate_gg(self):
'''This function sets the class attribute gg which is the value of
the normalized Cherenkov distribution for each stage going to each
telescope.
'''
self.gg = np.empty_like(self.OC.travel_length)
for i in range(self.OC.travel_length.shape[0]):
for j in range(self.OC.travel_length.shape[1]):
if self.axis_t[self.i_ch][j]>self.gga.t[0] and self.axis_t[self.i_ch][j]<self.gga.t[-1]:
self.gg[i,j] = self.gga.interpolate(self.axis_t[self.i_ch][j],self.axis_delta[self.i_ch][j],self.OC.tel_q[i,j])
else:
self.gg[i,j] = 0
def calculate_yield(self):
'''This function calculates the number of Cherenkov photons at each
telescope using the normalized angular distribution values interpolated
from the table.
'''
alpha_over_hbarc = 370.e2 # per eV per m, from PDG
tel_dE =1.377602193180103 # Energy interval calculated from Cherenkov wavelengths
chq = CherenkovPhoton.cherenkov_angle(1.e12,self.axis_delta[self.i_ch])
cy = alpha_over_hbarc*np.sin(chq)**2*tel_dE
tel_factor = self.axis_nch[self.i_ch] * self.axis_dr[self.i_ch] * cy
self.ng = self.gg * self.OC.tel_omega * tel_factor
self.ng_sum = self.ng.sum(axis = 1)
class Shower():
"""A class for generating extensive air shower profiles and their Cherenkov
outputs. The shower can either be a Gaisser Hillas shower or a Griessen
Shower. The Cartesian origin is at the point where the shower axis intersects
with the Earth's surface.
Parameters:
X_max: depth at shower max (g/cm^2)
N_max: number of charged particles at X_max
h0: height of first interaction above the ground level (meters)
X0: Start depth
theta: Polar angle of the shower axis with respect to vertical. Vertical
is defined as normal to the Earth's surface at the point where the axis
intersects with the surface.
direction: Shower direction, either 'up' for upward going showers, or 'down'
for downward going showers.
phi: azimuthal angle of axis intercept (radians) measured from the x
axis. Standard physics spherical coordinate convention. Positive x axis is
North, positive y axis is west.
ground_level: Height above sea level of center of shower footprint (meters)
type: Shower type, either 'GN' for Greisen, or GH for Gaisser-Hillas.
"""
earth_radius = 6.371e6
c = value('speed of light in vacuum')
Lambda = 70
atm = at.Atmosphere()
Moliere_data = np.load('lateral.npz')
t_Moliere = Moliere_data['t']
AVG_Moliere = Moliere_data['avg']
theta_upper_limit = np.pi / 2
theta_lower_limit = 0.
def __init__(self,
X_max,
N_max,
h0,
theta,
direction,
phi=0.,
ground_level=0.,
type='GH'):
if theta < self.theta_lower_limit or theta > self.theta_upper_limit:
raise Exception("Theta value out of bounds")
self.reset_shower(X_max, N_max, h0, theta, direction, phi,
ground_level, type)
def reset_shower(self, X_max, N_max, h0, theta, direction, phi,
ground_level, type):
'''Set necessary attributes and perform calculations
'''
self.type = type
self.input_X_max = X_max
self.N_max = N_max
self.h0 = h0
self.direction = direction
self.theta = theta
self.phi = phi
self.axis_h = np.linspace(ground_level, self.atm.maximum_height, 10000)
self.axis_rho = self.atm.density(self.axis_h)
self.axis_delta = self.atm.delta(self.axis_h)
self.axis_h -= ground_level
self.axis_Moliere = 96. / self.axis_rho
axis_midh = np.sqrt(self.axis_h[1:] * self.axis_h[:-1])
self.axis_dh = np.empty_like(self.axis_h)
self.axis_dh[1:-1] = np.abs(axis_midh[:-1] - axis_midh[1:])
self.axis_dh[-1] = self.axis_dh[-2]
self.axis_dh[0] = self.axis_dh[1]
self.ground_level = ground_level
self.earth_radius += ground_level # adjust earth radius
self.axis_r = self.h_to_axis_R_LOC(self.axis_h, theta)
self.axis_start_r = self.h_to_axis_R_LOC(h0, theta)
self.axis_X, self.axis_dr, self.X0 = self.set_depth(
self.axis_r, self.axis_start_r)
self.X_max = X_max + self.X0
self.axis_nch = self.size(self.axis_X)
self.axis_nch[self.axis_nch < 1.e3] = 0
self.i_ch = np.nonzero(self.axis_nch)[0]
self.shower_X = self.axis_X[self.i_ch]
self.shower_r = self.axis_r[self.i_ch]
self.shower_dr = self.axis_dr[self.i_ch]
self.shower_nch = self.axis_nch[self.i_ch]
self.shower_Moliere = self.axis_Moliere[self.i_ch]
self.shower_delta = self.axis_delta[self.i_ch]
self.shower_h = self.axis_h[self.i_ch]
self.shower_dh = self.axis_dh[self.i_ch]
self.shower_t = self.stage(self.shower_X, self.X_max)
self.shower_avg_M = np.interp(self.shower_t, self.t_Moliere,
self.AVG_Moliere)
self.shower_rms_w = self.shower_avg_M * self.shower_Moliere
@classmethod
def h_to_axis_R_LOC(cls, h, theta):
'''Return the length along the shower axis from the point of Earth
emergence to the height above the surface specified
Parameters:
h: array of heights (m above sea level)
theta: polar angle of shower axis (radians)
returns: r (m) (same size as h), an array of distances along the shower
axis_sp.
'''
cos_EM = np.cos(np.pi - theta)
R = cls.earth_radius
r_CoE = h + R # distance from the center of the earth to the specified height
r = R * cos_EM + np.sqrt(R**2 * cos_EM**2 - R**2 + r_CoE**2)
return r
@classmethod
def theta_normal(cls, h, theta):
''' Convert a polar angle (at a given height) with respect to the z axis
to a polar angle with respect to vertical in the atmosphere (at that
height)
Parameters:
h: array of heights (m above sea level)
theta: array of polar angle of shower axis (radians)
Returns:
The cosine(s) of the corrected angles(s)
'''
r = cls.h_to_axis_R_LOC(h, theta)
cq = ((cls.earth_radius + h)**2 + r**2 -
cls.earth_radius**2) / (2 * r * (cls.earth_radius + h))
return cq
def set_depth(self, axis_r, axis_start_r):
'''Integrate atmospheric density over selected direction to create
a table of depth values.
Parameters:
axis_r: distances along the shower axis
axis_start_r: distance along the axis where the shower starts
returns:
axis_X: depths at each axis distances (g/cm^2)
axis_dr: corresponding spatial distance associated with each depth (m)
X0: start depth (g/cm^2)
'''
axis_dr = axis_r[1:] - axis_r[:-1]
axis_deltaX = np.sqrt(
self.axis_rho[1:] *
self.axis_rho[:-1]) * axis_dr / 10 # converting to g/cm^2
if self.direction == 'up':
axis_X = np.concatenate((np.array([0]), np.cumsum(axis_deltaX)))
elif self.direction == 'down':
axis_X = np.concatenate(
(np.cumsum(axis_deltaX[::-1])[::-1], np.array([0])))
axis_dr = np.concatenate((np.array([0]), axis_dr))
X0 = np.interp(axis_start_r, axis_r, axis_X)
return axis_X, axis_dr, X0
def size(self, X):
"""Return the size of the shower at a slant-depth X
Parameters:
X: the slant depth at which to calculate the shower size [g/cm2]
Returns:
N: the shower size (# of charged particles)
"""
if self.type == 'GH':
value = self.GaisserHillas(X)
elif self.type == 'GN':
value = self.Greisen(X)
return value
def GaisserHillas(self, X):
'''Return the size of a GH shower at a given depth.
Parameters:
X: depth
Returns:
# of charged particles
'''
x = (self.axis_X - self.X0) / self.Lambda
g0 = x > 0.
m = (self.X_max - self.X0) / self.Lambda
n = np.zeros_like(x)
n[g0] = np.exp(m * (np.log(x[g0]) - np.log(m)) - (x[g0] - m))
return self.N_max * n
def Greisen(self, X_in, p=36.62):
'''Return the size of a Greisen shower at a given depth.
Parameters:
X_in: depth
Returns:
# of charged particles
'''
X = [x if x > self.X0 else self.X0 for x in X_in]
Delta = X - self.X_max
W = self.X_max - self.X0
eps = Delta / W
s = (1 + eps) / (1 + eps / 3)
i = np.nonzero(s)
n = np.zeros_like(X)
n[i] = np.exp(
(eps[i] * (1 - 1.5 * np.log(s[i])) - 1.5 * np.log(s[i])) * (W / p))
return self.N_max * n
@classmethod
def stage(cls, X, X_max, X0=36.62):
"""Return the shower stage at a given slant-depth X. This
is after Lafebre et al.
Parameters:
X: atmosphering slant-depth [g/cm2]
X0: radiation length of air [g/cm2]
Returns:
t: shower stage
"""
return (X - X_max) / X0
