i am wondering about Plasma frequency magnitude. According to the image i want to plot that graph.
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$\begingroup$ Suspected source of the plot: physics.stackexchange.com/q/366916 $\endgroup$– Tom NeiserCommented Jan 22, 2020 at 19:19
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2 Answers
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Everything shown in the plot is in normalized units. That is, the frequency, $\omega$, is normalized to the plasma frequency, $\omega_{p}$, and the wave number, $k$, is normalized to the inertial length or skin depth, $c/\omega_{p}$.
So you need only redefine the dispersion relation to: $$ \frac{ \omega }{ \omega_{p} } = \sqrt{ 1 + \left( \frac{ k \ c }{ \omega_{p} } \right)^{2} } \tag{0} $$ then basically plot this like you were plotting: $$ Y = \sqrt{ 1 + X^{2} } \tag{1} $$
The dashed line just goes to: $$ \frac{ \omega }{ \omega_{p} } = \frac{ k \ c }{ \omega_{p} } \tag{2} $$
answered Jan 22, 2020 at 15:53
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$\begingroup$ This is correct. The equation in the legend may have been confusing, $\omega=\sqrt{\omega_p^2 + c^2 k^2}$. When you write this in code, it's best to work in dimensionless variables, so what was plotted was indeed $Y(X)$ above $\endgroup$ Commented Jan 22, 2020 at 19:31
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I’m not really sure what you are trying to ask but if you look at where k=0, your frequency becomes the plasma frequency I.e. the y-intercept of your graph.
answered Jan 22, 2020 at 11:10
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$\begingroup$ i want to plot the dispersion law, but i do not know what should i replace for ''n'' and ''k''?! ''n'' is parameter in the omega p. $\endgroup$– user109707Commented Jan 22, 2020 at 11:24
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$\begingroup$ Can you please put all this in the original question clearly? $\endgroup$ Commented Jan 22, 2020 at 11:26
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$\begingroup$ according to that image, i want to convert the dispersion law (w=sqrt(c^2*k^2)+wp^2) into matlab and get the same graph, but after plotting the figure is not similar to the attached image! Also wp^2=ne^2/mebsilon zero. can you give me guideline for plotting? $\endgroup$– user109707Commented Jan 22, 2020 at 11:37