In a linear magnetised plasma device

PHYSICS · Multi-part · Fermi University Physics · Plasma Physics · Kinetic theory, collisions and transport · Kinetic theory, collisions and transport

Plasma Physics, Ch Transport across and along the field: ambipolar, classical, neoclassical and anomalous

Problem

In a linear magnetised plasma device, deuterium ions and electrons are held at fixed density

n = 1.0\times10^{19}\,\mathrm{m^{-3}}

and temperature

T_e = T_i = 10\,\mathrm{eV}

(Coulomb logarithm

\ln\Lambda = 10

) while the axial field

B

is changed. The measured electron heat diffusivity is

\chi_1 = 0.50\,\mathrm{m^2\,s^{-1}}

B_1 = 0.10\,\mathrm{T}

and

\chi_2 = 0.26\,\mathrm{m^2\,s^{-1}}

B_2 = 0.20\,\mathrm{T}

. A researcher argues: "Classical cross-field diffusivity scales as

\chi_\perp \propto r_{Le}^2\nu_{ei} \propto 1/B^2

. Doubling

B

should quarter

\chi

. We observe

\chi_2/\chi_1 = 0.52

, close to

1/2

rather than

1/4

; so classical theory is correct to within a factor of about two, and the cross-field heat transport in this device is essentially classical, just enhanced by some order-unity constant." ((a)) Using

D_\perp = r_{Le}^2\nu_{ei}(1 + T_i/T_e)

with

\nu_{ei} = 1/\tau_e

and Braginskii's

\tau_e

, compute the classical diffusivity predicted at

B_1

and at

B_2

. ((b)) Find the error(s) in the researcher's argument.

Browse the problem library