- #1

Firben

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## Homework Statement

In a so called z-pinch the plasma is determined by:B =B

_{0}r/a θ

^{^}

where a is the pinch radius

Calculate the drift velocity due a inhomogenous magnetic field and a bended magnetic field in ions with charge q and mass M in the pinch. Assume that that the ions in the plasma has a isotropic speed distribution with the speed sqrt(KT/M) per degree of freedom

## Homework Equations

V

_{∇B}= μ/(qB

^{2})*(B x ∇B)

V

_{R}= (mv

_{||}

^{2})/(qBR

_{c}

^{2})*(R

_{c}x B)

## The Attempt at a Solution

From the solution manual i don't understand how they calculate the

perpendicular and

horizontal speed.

This is what i don't get:

Isotropic distribution of ions:

1/2M<v

_{_}

^{2}> = 2* KT/M <----- Why multiply with 2 ?

and

1/2M<v

_{||}

^{2}> = 1 * KT/M <----- Why multiply with 1 ?

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