2-5. Suppose electrons obey the Boltzmann relation of Problem 1-5 in a cylindri- cally symmetric plasma column in which n(r) varies with a scale length A: that is, an/ar = -n/A. (a) Using E = -V6, find the radial electric field for given A. (b) For electrons, show that finite Larmor radius effects are large if ve is as large as vah- Specifically, show that r = 2A if vg = Van- (c) Is (b) also true for ions? Hint: Do not use Poisson's equation.
2-5. Suppose electrons obey the Boltzmann relation of Problem 1-5 in a cylindri- cally symmetric plasma column in which n(r) varies with a scale length A: that is, an/ar = -n/A. (a) Using E = -V6, find the radial electric field for given A. (b) For electrons, show that finite Larmor radius effects are large if ve is as large as vah- Specifically, show that r = 2A if vg = Van- (c) Is (b) also true for ions? Hint: Do not use Poisson's equation.
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Transcribed Image Text:2-5. Suppose electrons obey the Boltzmann relation of Problem 1-3 in a cylindri-
cally symmetric plasma column in which n(r) varies with a scale length A; that
is, an/ar = -n/A.
(a) Using E = -V$, find the radial electric field for given A.
(b) For electrons, show that finite Larmor radius effects are large if ve is as large
as vih. Specifically, show that r = 2A if vg =Vah-
(c) Is (b) also true for ions?
Hint: Do not use Poisson's equation.
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