Fundamentals of Plasma Physics

1.8 Small v. large angle collisions in plasmas 11

so thatrmax≃ 7 λD.
Thus, the largest spherical volume that could spontaneously become fully depleted of
electrons has a radius of a few Debye lengths, but this would require the highly unlikely
situation of having all the electrons initially moving in the outward radial direction. We
conclude thatthe plasma is quasi-neutral over scale lengths much larger than the Debye
length. When a biased electrode such as a wire probe is inserted into a plasma, the plasma
screens the field due to the potential on the electrode in the same way that the test charge
potential was screened. The screening region is called thesheath,which is a region of
non-neutrality having an extent of the order of a Debye length.

1.8 Small v. large angle collisions in plasmas

We now consider what happens to the momentum and energy of a test particle of charge
qTand massmTthat is injected with velocityvTinto a plasma. This test particle will
make a sequence of random collisions with the plasma particles (called “field” particles
and denoted by subscriptF);these collisions will alter both the momentum and energy of
the test particle.

b
/ 2

small

angle

scattering

cross section 
b
^2 /2

for large angle scattering

/ 2 scattering

b



differentialcross section 2 
bdb

for small angle scattering

Figure 1.3: Differential scattering cross sections for large and small deflections

Solution of the Rutherford scattering problem in the center of mass frame shows (see