def integrand_no_phi(t_inner, t_outer):
amp = electric_field.amplitude**2
envelopes = electric_field.get_electric_field_envelope(
t_outer) * electric_field.get_electric_field_envelope(t_inner)
kernel = ide.gaussian_kernel_LEN(t_outer - t_inner,
tau_alpha=tau_alpha)
cosines = np.cos(electric_field.omega_carrier *
(t_outer - t_inner))
return amp * envelopes * kernel * cosines
def double_kick_v3(beta, delta_t, omega_alpha, tau_alpha):
"""previous a is 1"""
kernel = ide.gaussian_kernel_LEN(delta_t, tau_alpha=tau_alpha)
first = (1 + beta)**4
second = (beta**2) * (np.abs(kernel)**2)
third = (2 * beta * ((1 + beta)**2) *
np.real(kernel * np.exp(1j * omega_alpha * delta_t)))
return first + second - third
def double_kick(beta, delta_t, omega_alpha, tau_alpha):
"""previous a is 1 + beta"""
kernel = ide.gaussian_kernel_LEN(delta_t, tau_alpha=tau_alpha)
pre = (1 + beta)**2
kernel_squared = (beta * np.abs(kernel))**2
interference = (-2 * beta * (1 + beta) *
np.real(kernel * np.exp(1j * omega_alpha * delta_t)))
return pre * (pre + kernel_squared + interference)
return sim
if __name__ == "__main__":
with logman as logger:
td = np.linspace(0, 1000 * asec, 1000)
test_mass = 1 * electron_mass_reduced
test_charge = 1 * electron_charge
test_width = 1 * bohr_radius
hyd_kern_prefactor = 128 * (bohr_radius**7) / (3 * (pi**2))
gau_kern_prefactor = np.sqrt(pi) * (test_width**2)
kernel_gaussian = gau_kern_prefactor * ide.gaussian_kernel_LEN(
td, tau_alpha=ide.gaussian_tau_alpha_LEN(test_width, test_mass))
kernel_hydrogen = ide.hydrogen_kernel_LEN(
td, kernel_prefactor=ide.hydrogen_kernel_prefactor_LEN())
si.vis.xy_plot(
"kernel_comparison",
td,
np.abs(kernel_gaussian),
np.real(kernel_gaussian),
np.imag(kernel_gaussian),
np.abs(kernel_hydrogen),
np.real(kernel_hydrogen),
np.imag(kernel_hydrogen),
line_labels=[
r"Abs Gaussian",
r"Re Gaussian",
import ide as ide
FILE_NAME = os.path.splitext(os.path.basename(__file__))[0]
OUT_DIR = os.path.join(os.getcwd(), "out", FILE_NAME)
PLOT_KWARGS = dict(target_dir=OUT_DIR, img_format="png", fig_dpi_scale=5)
if __name__ == "__main__":
with si.utils.LogManager(
"simulacra", "ionization", stdout_logs=True, stdout_level=logging.DEBUG
) as logger:
tau_alpha = 4 * electron_mass * (bohr_radius ** 2) / hbar
print(f"tau alpha: {tau_alpha / asec:3f}")
time_diffs = np.linspace(0, 10 * tau_alpha, 1000)
kernel = ide.gaussian_kernel_LEN(time_diffs, tau_alpha=tau_alpha)
comp_cosh = 1 / np.cosh(time_diffs / tau_alpha)
si.vis.xy_plot(
"kernel_vs_time_diff",
time_diffs,
np.abs(kernel),
np.real(kernel),
np.imag(kernel),
comp_cosh,
line_labels=[
r"$ \left|K\right| $",
r"$ \mathrm{Re} \, K $",
r"$ \mathrm{Im} \, K $",
"$ 1 / \cosh(t-t') $",
if __name__ == "__main__":
with logman as logger:
p = ion.potentials.SincPulse(pulse_width=200 * asec, phase=pi / 2)
times = np.linspace(-100 * asec, 100 * asec, 1000)
si.vis.xy_plot(
"test",
times,
p.get_electric_field_amplitude(times),
x_unit="asec",
**PLOT_KWARGS,
)
tau_alpha = ide.gaussian_tau_alpha_LEN(test_width=1 * bohr_radius,
test_mass=electron_mass)
dt = np.linspace(0, 3 * tau_alpha, 1000)
k = ide.gaussian_kernel_LEN(time_difference=dt, tau_alpha=tau_alpha)
si.vis.xy_plot(
"kernel",
dt,
np.abs(k),
np.real(k),
np.imag(k),
x_unit="asec",
**PLOT_KWARGS,
)
imag_min_t = dt[np.argmin(np.imag(k))]
print(tau_alpha / asec)
print(imag_min_t / asec)
print(imag_min_t / tau_alpha)