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Copy pathAPLB_acc_LCApril_3D.py
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APLB_acc_LCApril_3D.py
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import numpy as np
from numba import jit
@jit(nopython=True)
def APLB_acc_LCApril_3D(lambda_0, s, a, P, Psi_0, phi_2, phi_3, t_0, z_0, x_0, y_0, beta_0, tau_p):
# initialize constants (SI units)
c = 2.99792458e8 # speed of light
m_e = 9.10938356e-31
q_e = 1.60217662e-19
e_0 = 8.85418782e-12
# calculate frequency properties
omega_0 = 2*np.pi*c/lambda_0
tau_0 = s*np.sqrt(np.exp(2/(s+1))-1)/omega_0
delta_omega = 2/tau_0
# amplitude factor
Amp = -1*np.sqrt(8*P/(np.pi*e_0*c))*a*c/(2*omega_0)
t_start = t_0 + z_0/c
t_end = +1e5*tau_0
# number of time steps per laser period
n = (lambda_0/(0.8e-6))*1000 # np.maximum(50, np.round(np.sqrt(P/(w_0**2))/(5e10))) # empirically chosen resolution based on field strength
num_t = np.int_(np.round(n*(t_end-t_start)/(lambda_0/c)))
time = np.linspace(t_start, t_end, num_t)
dt = time[1]-time[0]
omega = np.linspace((omega_0-4*delta_omega), (omega_0+4*delta_omega), 300)
omega_step = omega[1]-omega[0]
pulse_temp = np.exp(-((omega-omega_0)/delta_omega)**2)
pulse_prep = pulse_temp*np.exp(-1j*((phi_2/2)*(omega-omega_0)**2 + (phi_3/6)*(omega-omega_0)**3))
z_omega = a*tau_p*(omega-omega_0)
# initialize empty arrays
z = np.empty(shape=(len(time)))
x = np.empty(shape=(len(time)))
y = np.empty(shape=(len(time)))
v_z = np.empty(shape=(len(time)))
v_x = np.empty(shape=(len(time)))
v_y = np.empty(shape=(len(time)))
gamma = np.empty(shape=(len(time)))
KE = np.zeros(shape=(len(time)))
deriv2 = np.empty(shape=(len(time)))
deriv4 = np.empty(shape=(len(time)))
deriv6 = np.empty(shape=(len(time)))
# Set initial conditions
z[0] = beta_0*c*time[0] + z_0
x[0] = x_0
y[0] = y_0
v_z[0] = beta_0*c
v_x[0] = 0.0
v_y[0] = 0.0
gamma[0] = 1/np.sqrt(1-beta_0**2)
KE[0] = ((1/np.sqrt(1-beta_0**2))-1)*m_e*c**2/q_e
k_stop = -1
# do 5th order Adams-Bashforth finite difference method
for k in range(0, len(time)-1):
r = np.sqrt(x[k]**2 + y[k]**2)
Rt = np.sqrt(r**2 + (z[k] + 1j*a)**2)
Rtomega = np.sqrt(r**2 + (z[k] - z_omega + 1j*a)**2)
B_z_spec = -1*pulse_prep*(2*1j*Amp*np.exp(-omega*a/c)/(Rtomega)**2)*(np.sin(omega*Rt/c)*((2+(omega*r/c)**2)/Rtomega - 3*r**2/Rtomega**3)+np.cos(omega*Rt/c)*(3*omega*r**2/(Rtomega**2*c)-2*omega/c))/c
B_z_time = np.sum(B_z_spec*np.exp(1j*omega*time[k]))*omega_step/(delta_omega*np.sqrt(np.pi))
B_z_total = np.real(np.exp(1j*(Psi_0+np.pi/2))*B_z_time)
B_x_spec = -1*pulse_prep*(2*1j*Amp*np.exp(-omega*a/c))*(r*(z[k] - z_omega + 1j*a)/Rtomega**3)*(np.sin(omega*Rt/c)*(3/Rtomega**2 - (omega/c)**2) - 3*omega*np.cos(omega*Rt/c)/(Rtomega*c))*(x[k]/r)/c
B_x_time = np.sum(B_x_spec*np.exp(1j*omega*time[k]))*omega_step/(delta_omega*np.sqrt(np.pi))
B_x_total = np.real(np.exp(1j*(Psi_0+np.pi/2))*B_x_time)
B_y_spec = -1*pulse_prep*(2*1j*Amp*np.exp(-omega*a/c))*(r*(z[k] - z_omega + 1j*a)/Rtomega**3)*(np.sin(omega*Rt/c)*(3/Rtomega**2 - (omega/c)**2) - 3*omega*np.cos(omega*Rt/c)/(Rtomega*c))*(y[k]/r)/c
B_y_time = np.sum(B_y_spec*np.exp(1j*omega*time[k]))*omega_step/(delta_omega*np.sqrt(np.pi))
B_y_total = np.real(np.exp(1j*(Psi_0+np.pi/2))*B_y_time)
E_x_spec = pulse_prep*(2*1j*Amp*np.exp(-omega*a/c))*(1j*omega*r/(c*Rtomega)**2)*(np.sin(omega*Rt/c)/Rtomega - omega*np.cos(omega*Rt/c)/c)*(-y[k]/r)*c
E_x_time = np.sum(E_x_spec*np.exp(1j*omega*time[k]))*omega_step/(delta_omega*np.sqrt(np.pi))
E_x_total = np.real(np.exp(1j*(Psi_0+np.pi/2))*E_x_time)
E_y_spec = pulse_prep*(2*1j*Amp*np.exp(-omega*a/c))*(1j*omega*r/(c*Rtomega)**2)*(np.sin(omega*Rt/c)/Rtomega - omega*np.cos(omega*Rt/c)/c)*(x[k]/r)*c
E_y_time = np.sum(E_y_spec*np.exp(1j*omega*time[k]))*omega_step/(delta_omega*np.sqrt(np.pi))
E_y_total = np.real(np.exp(1j*(Psi_0+np.pi/2))*E_y_time)
dot_product = v_x[k]*E_x_total + v_y[k]*E_y_total
deriv2[k] = (-q_e/(gamma[k]*m_e))*(v_x[k]*B_y_total-v_y[k]*B_x_total-v_z[k]*dot_product/(c**2)) # Force in z
deriv4[k] = (-q_e/(gamma[k]*m_e))*(E_x_total+v_y[k]*B_z_total-v_z[k]*B_y_total-v_x[k]*dot_product/(c**2)) # Force in x
deriv6[k] = (-q_e/(gamma[k]*m_e))*(E_y_total+v_z[k]*B_x_total-v_x[k]*B_z_total-v_y[k]*dot_product/(c**2)) # Force in y
if k==0:
z[k+1] = z[k] + dt*v_z[k]
v_z[k+1] = v_z[k] + dt*deriv2[k]
x[k+1] = x[k] + dt*v_x[k]
v_x[k+1] = v_x[k] + dt*deriv4[k]
y[k+1] = y[k] + dt*v_y[k]
v_y[k+1] = v_y[k] + dt*deriv6[k]
elif k==1:
z[k+1] = z[k] + dt*(1.5*v_z[k]-0.5*v_z[k-1])
v_z[k+1] = v_z[k] + dt*(1.5*deriv2[k]-0.5*deriv2[k-1])
x[k+1] = x[k] + dt*(1.5*v_x[k]-0.5*v_x[k-1])
v_x[k+1] = v_x[k] + dt*(1.5*deriv4[k]-0.5*deriv4[k-1])
y[k+1] = y[k] + dt*(1.5*v_y[k]-0.5*v_y[k-1])
v_y[k+1] = v_y[k] + dt*(1.5*deriv6[k]-0.5*deriv6[k-1])
elif k==2:
z[k+1] = z[k] + dt*((23/12)*v_z[k]-(4/3)*v_z[k-1]+(5/12)*v_z[k-2])
v_z[k+1] = v_z[k] + dt*((23/12)*deriv2[k]-(4/3)*deriv2[k-1]+(5/12)*deriv2[k-2])
x[k+1] = x[k] + dt*((23/12)*v_x[k]-(4/3)*v_x[k-1]+(5/12)*v_x[k-2])
v_x[k+1] = v_x[k] + dt*((23/12)*deriv4[k]-(4/3)*deriv4[k-1]+(5/12)*deriv4[k-2])
y[k+1] = y[k] + dt*((23/12)*v_y[k]-(4/3)*v_y[k-1]+(5/12)*v_y[k-2])
v_y[k+1] = v_y[k] + dt*((23/12)*deriv6[k]-(4/3)*deriv6[k-1]+(5/12)*deriv6[k-2])
elif k==3:
z[k+1] = z[k] + dt*((55/24)*v_z[k]-(59/24)*v_z[k-1]+(37/24)*v_z[k-2]-(3/8)*v_z[k-3])
v_z[k+1] = v_z[k] + dt*((55/24)*deriv2[k]-(59/24)*deriv2[k-1]+(37/24)*deriv2[k-2]-(3/8)*deriv2[k-3])
x[k+1] = x[k] + dt*((55/24)*v_x[k]-(59/24)*v_x[k-1]+(37/24)*v_x[k-2]-(3/8)*v_x[k-3])
v_x[k+1] = v_x[k] + dt*((55/24)*deriv4[k]-(59/24)*deriv4[k-1]+(37/24)*deriv4[k-2]-(3/8)*deriv4[k-3])
y[k+1] = y[k] + dt*((55/24)*v_y[k]-(59/24)*v_y[k-1]+(37/24)*v_y[k-2]-(3/8)*v_y[k-3])
v_y[k+1] = v_y[k] + dt*((55/24)*deriv6[k]-(59/24)*deriv6[k-1]+(37/24)*deriv6[k-2]-(3/8)*deriv6[k-3])
else:
z[k+1] = z[k] + dt*((1901/720)*v_z[k]-(1387/360)*v_z[k-1]+(109/30)*v_z[k-2]-(637/360)*v_z[k-3]+(251/720)*v_z[k-4])
v_z[k+1] = v_z[k] + dt*((1901/720)*deriv2[k]-(1387/360)*deriv2[k-1]+(109/30)*deriv2[k-2]-(637/360)*deriv2[k-3]+(251/720)*deriv2[k-4])
x[k+1] = x[k] + dt*((1901/720)*v_x[k]-(1387/360)*v_x[k-1]+(109/30)*v_x[k-2]-(637/360)*v_x[k-3]+(251/720)*v_x[k-4])
v_x[k+1] = v_x[k] + dt*((1901/720)*deriv4[k]-(1387/360)*deriv4[k-1]+(109/30)*deriv4[k-2]-(637/360)*deriv4[k-3]+(251/720)*deriv4[k-4])
y[k+1] = y[k] + dt*((1901/720)*v_y[k]-(1387/360)*v_y[k-1]+(109/30)*v_y[k-2]-(637/360)*v_y[k-3]+(251/720)*v_y[k-4])
v_y[k+1] = v_y[k] + dt*((1901/720)*deriv6[k]-(1387/360)*deriv6[k-1]+(109/30)*deriv6[k-2]-(637/360)*deriv6[k-3]+(251/720)*deriv6[k-4])
gamma[k+1] = 1/np.sqrt(1-(v_z[k+1]**2+v_x[k+1]**2+v_y[k+1]**2)/c**2)
KE[k+1] = (gamma[k+1]-1)*m_e*c**2/q_e
if (time[k] > 300*tau_0 and np.mean(np.abs(np.diff(KE[k-np.int(10*n):k+1]))/(KE[k+1]*dt)) < 1e7):
k_stop = k+1
break
return time[:k_stop], z[:k_stop], x[:k_stop], y[:k_stop], v_z[:k_stop], v_x[:k_stop], v_y[:k_stop], KE[:k_stop]