Warning $T_e$ stands for $k_B T_e$!
Debye length:
$$ \lambda_D = \sqrt{\frac{\epsilon_0 T_e}{e^2 n}} $$How to remember the formula:
Electron plasma frequency:
$$ w_p = \sqrt{\frac{n e^2}{\epsilon_0 m_e}} $$How to remember the formula:
1eV = 1.602176565(35)×10−19 J
kB×T[Kelvin]=T[Joules]=1.602×10−19×T[eV],
e = 1.602e-19
epsilon_0 = 8.8542e-12 #F/m
m_e = 9.1094e-31
k_b = 1.3807e-23
import numpy as np
T = 10 * e
n = 1e7
debye = np.sqrt(epsilon_0 * T / (e**2 * n))
debye
7.4343569272229804
wp = np.sqrt(n * e**2 / (epsilon_0 * m_e))
wp
178378.68647273269
wp / (2 * np.pi)
28389.849694374814
28 kHz = fréquence d'oscillation des électrons du soleil
Nd = n * debye**3
Nd
4108944014.0460491
"{:.1e}".format(Nd)
'4.1e+09'
T = 10 * e
n = 1e23
debye = np.sqrt(epsilon_0 * T / (e**2 * n))
debye
7.4343569272229817e-08
wp = np.sqrt(n * e**2 / (epsilon_0 * m_e))
wp
17837868647273.266
"{:.1e}".format(wp / (2 * np.pi))
'2.8e+12'
2.8 THz dans un éclair!
Nd = n * debye**3
Nd
41.089440140460518
"{:.1e}".format(Nd)
'4.1e+01'
"In the {} setting, the debye length is {:.2e} m, the electron oscillation pulsation is {:.2e}, or a frequency of {:.2e} Hz and the number of particles in a debye cube is {:.2e}".format("lightning", debye, wp, wp/(2*np.pi), Nd)
'In the lightning setting, the debye length is 7.43e-08 m, the electron oscillation pulsation is 1.78e+13, or a frequency of 2.84e+12 Hz and the number of particles in a debye cube is 4.11e+01'
T = 1e4 * e
n = 1e20
debye = np.sqrt(epsilon_0 * T / (e**2 * n))
debye
7.4343569272229809e-05
wp = np.sqrt(n * e**2 / (epsilon_0 * m_e))
wp
564082935282.9021
"{:.1e}".format(wp / (2 * np.pi))
'9.0e+10'
Nd = n * debye**3
Nd
41089440.140460506
"In the {} setting, the debye length is {:.2e} m, the electron oscillation pulsation is {:.2e}, or a frequency of {:.2e} Hz and the number of particles in a debye cube is {:.2e}".format("magnetic fusion", debye, wp, wp/(2*np.pi), Nd)
'In the magnetic fusion setting, the debye length is 7.43e-05 m, the electron oscillation pulsation is 5.64e+11, or a frequency of 8.98e+10 Hz and the number of particles in a debye cube is 4.11e+07'
T = k_b * 10000
n = 1e17
T / e
0.8618601747815231
debye = np.sqrt(epsilon_0 * T / (e**2 * n))
debye
2.1825380030026764e-05
wp = np.sqrt(n * e**2 / (epsilon_0 * m_e))
wp
17837868647.27327
"{:.1e}".format(wp / (2 * np.pi))
'2.8e+09'
Nd = n * debye**3
Nd
1039.645895990164
"In the {} setting, the debye length is {:.2e} m, the electron oscillation pulsation is {:.2e}, or a frequency of {:.2e} Hz and the number of particles in a debye cube is {:.2e}".format("magnetic fusion", debye, wp, wp/(2*np.pi), Nd)
'In the magnetic fusion setting, the debye length is 2.18e-05 m, the electron oscillation pulsation is 1.78e+10, or a frequency of 2.84e+09 Hz and the number of particles in a debye cube is 1.04e+03'