def __call__(self, angpos, zenith, wavelength, feed, pol_index):
seps = separations(angpos, zenith)
x = np.pi*self.diameter/wavelength*np.sin(seps)
out = (2*bessel_j1(x)/x) # (Voltage Beam)
out[np.degrees(seps) > self.sep_limit] = 0.
return out
def solve(self):
dist = self.rr.reshape((-1,1,1))
time = self.tt.reshape((1,-1,1))
beta = self.beta_n.reshape((1,1,-1))
term1 = 2/(self.RR**2-1)*((dist[:,:,0]**2)/4.+time[:,:,0])
term2 = self.RR**2/(self.RR**2-1)*np.log(dist[:,:,0])
term3 = 3*self.RR**4-4*self.RR**4*np.log(self.RR)-2*self.RR**2-1
term4 = 4*(self.RR**2-1)**2
term5 = (bessel_j1(beta*self.RR))**2*np.exp(-(beta**2)*time)
term6 = bessel_j1(beta)*bessel_y0(beta*dist)-bessel_y1(beta)*bessel_j0(beta*dist)
term7 = beta*((bessel_j1(beta*self.RR))**2-(bessel_j1(beta))**2)
term8 = term5*term6/term7
self.PP = term1-term2-term3/term4+np.pi*term8.sum(axis=2)
def root_function_first_derivative(self, beta):
"""
it needs a treshold value of beta and two functions to calculate analytical values,
one close to singularity \beta=0, the other at larger values of \betta
"""
J1B = bessel_j1(beta)
Y1B = bessel_y1(beta)
J1BR = bessel_j1(beta * self.RR)
Y1BR = bessel_y1(beta * self.RR)
J1B_prime = bessel_jvp(1, beta)
Y1B_prime = bessel_yvp(1, beta)
J1BR_prime = self.RR * bessel_jvp(1, beta * self.RR)
Y1BR_prime = self.RR * bessel_yvp(1, beta * self.RR)
return J1BR_prime * Y1B + J1BR * Y1B_prime - J1B_prime * Y1BR - J1B * Y1BR_prime
def root_function(self, beta):
"""
This is the function that outputs values of root function
defined in Everdingen solution. At singularity point of \beta = 0,
it outputs its value at limit.
"""
beta = toarray(beta)
res = np.empty(beta.shape)
res[beta == 0] = -self.RR / np.pi + 1 / (np.pi * self.RR)
J1B = bessel_j1(beta[beta > 0])
Y1B = bessel_y1(beta[beta > 0])
J1BR = bessel_j1(beta[beta > 0] * self.RR)
Y1BR = bessel_y1(beta[beta > 0] * self.RR)
res[beta > 0] = J1BR * Y1B - J1B * Y1BR
return res
def calcPcs(u):
if u <= 0.0:
return 1.0
res = 2. * bessel_j1(u) / u
return res