3. 3 Plasma sheath
Why plasma sheath? Consider thermal velocity (eT/m)^1/2
It is at least 100x higher for electrons than for ions
Plasma sheath – Debye sheath
sx
density of e- / ions in the sheath:
in weakly ionized plasma with eVfewe T
0i Tat grounded or floating wall (low
potential drop), collisionless
velocity of ions at sheath
edge (Bohm velocity):
density at the sheath edge: 0s 0.5nn 
electron and ion flux has to equal at floating wall Bsi un
Bu
eb
e
8 b
s4
1
e
Tk
eV
e
m
Tk
n









M
πm
e
Tk
Vw
2
ln
2
eb
calculation for Ar discharge with Te = 2 eV, n=108 cm-3:
floating potential approx. 5Te =10 V,
sheath thickness approx. 5lD = 0.37 mm
Plasma sheath – Child-Langmuir sheath
high-voltage sheath (when a voltage is
applied)
Then, current density j, voltage drop V0 and
sheath thickness d are related by the ChildLangmuir
Law of Space-Charge-Limited Diodes
following previous example with
assumptionV0 = 400 V: d = 30lD,
total sheath thickness 35lD, i.e. about 1 cm
Sheath can be artificially divided into Debye sheath
which contains electrons and high-voltage ChildLangmuir
sheath which has ions only.