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.