def energy_radiated_approx(self, trajectory, gamma, x, y, distance):
N = trajectory.nb_points()
n_chap = np.array([x - trajectory.x * codata.c, y - trajectory.y * codata.c, distance - trajectory.z * codata.c])
R = np.sqrt( n_chap[0]**2 + n_chap[1]**2 + n_chap[2]**2 )
n_chap[0,:] /= R
n_chap[1,:] /= R
n_chap[2,:] /= R
E = np.zeros((3,), dtype=np.complex)
integrand = np.zeros((3, N), dtype=np.complex)
A1 = (n_chap[1] * trajectory.v_z - n_chap[2] * trajectory.v_y)
A2 = (-n_chap[0] * trajectory.v_z + n_chap[2] * trajectory.v_x)
A3 = (n_chap[0] * trajectory.v_y - n_chap[1] * trajectory.v_x)
Alpha2 = np.exp(0. + 1j * self.photon_frequency * (trajectory.t + R / codata.c))
integrand[0] -= (n_chap[1] * A3 - n_chap[2] * A2) * Alpha2
integrand[1] -= (- n_chap[0] * A3 + n_chap[2] * A1) * Alpha2
integrand[2] -= (n_chap[0] * A2 - n_chap[1] * A1) * Alpha2
for k in range(3):
E[k] = np.trapz(integrand[k], trajectory.t)
#E[k] = integrate.simps(integrand[k], trajectory.t)
E *= self.photon_frequency * 1j
terme_bord = np.full((3), 0. + 1j * 0., dtype=np.complex)
Alpha_1 = (1.0 / (1.0 - n_chap[0][-1] * trajectory.v_x[-1]
- n_chap[1][-1] * trajectory.v_y[-1] - n_chap[2][-1] * trajectory.v_z[-1]))
Alpha_0 = (1.0 / (1.0 - n_chap[0][0] * trajectory.v_x[0]
- n_chap[1][0] * trajectory.v_y[0] - n_chap[2][0] * trajectory.v_z[0]))
terme_bord += ((n_chap[1][-1] * A3[-1] - n_chap[2][-1] * A2[-1]) * Alpha_1 *
np.exp(1j * self.photon_frequency * (trajectory.t[-1] + R[-1] / codata.c)))
terme_bord -= ((n_chap[1][0] * A3[0] - n_chap[2][0] * A2[0]) * Alpha_0 *
np.exp(1j * self.photon_frequency * (trajectory.t[0] + R[0] / codata.c)))
E += terme_bord
return E
# energy radiated without the the far filed approxiamation
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