(a) Show that the Boltzmann equation, in cylindrical coordinates, can be written as where the dot over...
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(a) Show that the Boltzmann equation, in cylindrical coordinates, can be written as
where the dot over the symbols stands for the time derivative operator d/dt and where
(b) Show, by direct substitution, that in the presence of an azimuthally symmetric magnetic field (in the z direction) a function of the form
is a solution of the Boltzmann equation under steady conditions, where the constant canonical momentum is given by pϕ = mr2ϕ̇ + qrAϕ, and where Aϕ denotes the ϕ component of the magnetic potential A, defined such that B = ∇ x A.
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