Appleton–Hartree equation

The Appleton–Hartree equation, sometimes also referred to as the Appleton–Lassen equation is a mathematical expression that describes the refractive index for electromagnetic wave propagation in a cold magnetized plasma. The Appleton–Hartree equation was developed independently by several different scientists, including Edward Victor Appleton, Douglas Hartree and German radio physicist H. K. Lassen. Lassen's work, completed two years prior to Appleton and five years prior to Hartree, included a more thorough treatment of collisional plasma; but, published only in German, it has not been widely read in the English speaking world of radio physics.

The dispersion relation can be written as an expression for the frequency (squared), but it is also common to write it as an expression for the index of refraction ${\displaystyle n^{2}=\left({\frac {ck}{\omega }}\right)^{2}}$ .

The equation is typically given as follows:

or, alternatively, with damping term Z = 0 and rearranging terms:

${\displaystyle n}$ = complex refractive index

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