The calculation of characteristic Debye length, plasma frequency and cyclotron frequency of electrons in the ionosphere, the plasmasphere, the outer magnetosphere and the solar wind.
clc;clear all; me = 9.109E-31; %[kg] Electron rest mass mp = 1.673E-27; %[kg] Proton rest mass eps0 = 8.8542E-12; %[A*s/(V*m)] Permittivity e = 1.602E-19; %[C] Elementary charge Re = 6.37E6; %[m] Earth’s radius Md = 8E15; %[T*m3] Earth’s magnetic dipole moment
Ionosphere
n = 1E12; %[m-3] Electron density kTe = 0.1; %[eV] Thermal energy r = Re + 3E5; %[km] Radial distance from the Earth’s center wp = (e^2*n/(eps0*me))^0.5/(2*pi); %[Hz] Plasma frequency lD = (eps0*kTe/(n*e))^0.5; %[m] Debye length B = 2*Md/r^3; %[T] Earth’s magnetic field Fc = e*B/(2*pi*me); %[Hz] Cyclotron frequency fprintf('Debye length %4.2d [m]\n',lD); fprintf('Plasma frequency %4.2d [Hz]\n',wp); fprintf('Cyclotron frequency %4.2d [Hz]\n\n',Fc);
Debye length 2.35e-003 [m] Plasma frequency 8.98e+006 [Hz] Cyclotron frequency 1.51e+006 [Hz]
Plasmasphere
n = 1E7; %[m-3] Electron density kTe = 1; %[eV] Thermal energy r = 5*Re; %[km] Radial distance from the Earth’s center wp = (e^2*n/(eps0*me))^0.5/(2*pi); %[Hz] Plasma frequency lD = (eps0*kTe/(n*e))^0.5; %[m] Debye length B = 2*Md/r^3; %[T] Earth’s magnetic field Fc = e*B/(2*pi*me); %[Hz] Cyclotron frequency fprintf('Debye length %4.2d [m]\n',lD); fprintf('Plasma frequency %4.2d [Hz]\n',wp); fprintf('Cyclotron frequency %4.2d [Hz]\n\n',Fc);
Debye length 2.35e+000 [m] Plasma frequency 2.84e+004 [Hz] Cyclotron frequency 1.39e+004 [Hz]
Outer magnetosphere
n = 1E6; %[m-3] Electron density kTe = 50; %[eV] Thermal energy r = 7*Re; %[km] Radial distance from the Earth’s center wp = (e^2*n/(eps0*me))^0.5/(2*pi); %[Hz] Plasma frequency lD = (eps0*kTe/(n*e))^0.5; %[m] Debye length B = 2*Md/r^3; %[T] Earth’s magnetic field Fc = e*B/(2*pi*me); %[Hz] Cyclotron frequency fprintf('Debye length %4.2d [m]\n',lD); fprintf('Plasma frequency %4.2d [Hz]\n',wp); fprintf('Cyclotron frequency %4.2d [Hz]\n\n',Fc);
Debye length 5.26e+001 [m] Plasma frequency 8.98e+003 [Hz] Cyclotron frequency 5.05e+003 [Hz]
Solar wind
n = 1E6; %[m-3] Electron density kTe = 5; %[eV] Thermal energy wp = (e^2*n/(eps0*me))^0.5/(2*pi); %[Hz] Plasma frequency lD = (eps0*kTe/(n*e))^0.5; %[m] Debye length B = 1E-8; %[T] Earth’s magnetic field Fc = e*B/(2*pi*me); %[Hz] Cyclotron frequency fprintf('Debye length %4.2d [m]\n',lD); fprintf('Plasma frequency %4.2d [Hz]\n',wp); fprintf('Cyclotron frequency %4.2d [Hz]\n\n',Fc);
Debye length 1.66e+001 [m] Plasma frequency 8.98e+003 [Hz] Cyclotron frequency 2.80e+002 [Hz]
Small Satellites 
Just a minor point: the ‘wp’ name for the plasma frequency implies slightly that this is an omega value, but given the divisor of 2 pi, it might actually be clearer to name it something like ‘fp’.
That is, if I’m understanding correctly!
I think you are right. It was a long ago I wrote this code and I forgot the reason I for using such a notion.
To be safe you always look to the units 🙂 Good luck!