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# Tag Archives: plasmasphere

## Debye length, plasma frequency and cyclotron frequency

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]