Axel Togawa
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- I don't understand the role of "drift velocity" in the derivation of the "polarization drift"
When studying a particle in slowly time varying, uniform electric field E, and in a constant, uniform magnetic field \textbf{B}, I found many texts where I can't understand the derivation of the "polarization drift" \textbf{v}_p, in particular I quote as reference this book I found online ([1], Pag.93) where they take as expression for the "drift velocity ExB" \textbf{v}_E = \frac{\textbf{E}\times\textbf{B}}{B^2}, which is the same formula used in the case where \textbf{E} = cost, why? The assumption to find this expression is that \frac{d\textbf{v}_E}{dt} = 0 but that is not true in this scenario.
I could consider that the variation in time is small, so \frac{d\textbf{v}_E}{dt} \approx 0, but then they find the expression for the polarization drift as \textbf{v}_p = -\frac{m}{q}\frac{\dot{\textbf{v}}_E\times \textbf{B}}{B^2} (where \dot{\textbf{v}}_E = \frac{d\textbf{v}_E}{dt}).
So why is \textbf{v}_E sometimes considered constant and sometimes not?
[1] "Introduction to Plasma Physics C17, Lecture Notes, John Howard": https://people.physics.anu.edu.au/~jnh112/AIIM/c17/chap04.pdf
I could consider that the variation in time is small, so \frac{d\textbf{v}_E}{dt} \approx 0, but then they find the expression for the polarization drift as \textbf{v}_p = -\frac{m}{q}\frac{\dot{\textbf{v}}_E\times \textbf{B}}{B^2} (where \dot{\textbf{v}}_E = \frac{d\textbf{v}_E}{dt}).
So why is \textbf{v}_E sometimes considered constant and sometimes not?
[1] "Introduction to Plasma Physics C17, Lecture Notes, John Howard": https://people.physics.anu.edu.au/~jnh112/AIIM/c17/chap04.pdf