Fundamentals of Plasma Physics

20 Chapter 1. Basic concepts

1.12 A quantitative perspective

Relevant physical constants are

e= 1. 6 × 10 −^19 Coulombs

me= 9. 1 × 10 −^31 kg

mp/me= 1836

ε 0 = 8. 85 × 10 −^12 Farads/meter.

The temperature is measured in units of electron volts, so thatκ= 1. 6 × 10 −^19 Joules/volt;
i.e.,κ=e.Thus, the Debye length is

λD =

√

ε 0 κT

ne^2

=

√

ε 0

e

√

TeV

n

= 7. 4 × 103

√

TeV

n

meters. (1.34)

We will assume that the typical velocity is related to the temperatureby

1

2

mv^2 =

3

2

κT. (1.35)

For electron-electron scatteringμ=me/ 2 so that the small angle scattering cross-section
is

σ∗ =

1

2 π

(

e 2

ε 0 mv^2 / 2

) 2

ln

(

λD/bπ/ 2

)

=

1

2 π

(

e^2

3 ε 0 κT

) 2

lnΛ (1.36)

where

Λ =

λD

bπ/ 2

=

√

ε 0 κT

ne^2

4 πε 0 mv^2 / 2

e^2

= 6πnλ^3 D (1.37)

is typically a very large number corresponding to there being a macroscopically large num-
ber of particles in a sphere having a radius equal to a Debye length;different authors will
have slightly different numerical coefficients, depending on how they identifyvelocity with
temperature. This difference is of no significance because one is taking thelogarithm.