sheath, Δz sh , is of the order of the Debye length, λ D ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
T e =4πn sh e 2
p
, where T e is the
electron temperature, n sh is the plasma density in the sheath and e is the elementary
charge.
For α 6 ¼ π/2 the thickness of the sheath starts to depend on the ion gyro-radius,
ρ i ¼ Mc=eB
ð
Þ
ffiffiffiffiffiffiffiffiffiffiffi
T i =M
p
(here T i is the ion temperature, c is the speed of light, B is the
strength of the magnetic field, and M is the ion mass) and for α ( 1, Δz sh ~ ρ i since
in the edge plasma, the Debye length is usually small in comparison with ρ i . In this
case, one can split the sheath into the magnetic presheath and the Debye sheath with
the thicknesses ~ρ i and ~λ D respectively.
What is important for many aspects of edge plasma physics is that for smooth
transition of electrostatic potential from the sheath region into the plasma interior,
the average ion velocity along the magnetic field lines for such plasma flow
relatively far away from the surface, V
ðÀ1Þ
k
, is limited by the so-called BohmChodura [1, 2] sheath criterion:
V
ðÀ1Þ
k
! V crit ,
ð4:1Þ
where the critical velocity V crit is determined by the plasma parameters (see also [3]).
Fig. 4.1 Electrostatic
potential φ(z) within the
sheath plugs most of the free
streaming electron flux to
maintain ambipolar
plasma flow
Fig. 4.2 (left) Direction of the magnetic field and the coordinates which will be used. (right)
Magnetic presheath, with the width ~ρ i , and Debye sheath with the width ~λ D for the case α ( 1
74
4 Sheath Physics
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
T e =4πn sh e 2
p
, where T e is the
electron temperature, n sh is the plasma density in the sheath and e is the elementary
charge.
For α 6 ¼ π/2 the thickness of the sheath starts to depend on the ion gyro-radius,
ρ i ¼ Mc=eB
ð
Þ
ffiffiffiffiffiffiffiffiffiffiffi
T i =M
p
(here T i is the ion temperature, c is the speed of light, B is the
strength of the magnetic field, and M is the ion mass) and for α ( 1, Δz sh ~ ρ i since
in the edge plasma, the Debye length is usually small in comparison with ρ i . In this
case, one can split the sheath into the magnetic presheath and the Debye sheath with
the thicknesses ~ρ i and ~λ D respectively.
What is important for many aspects of edge plasma physics is that for smooth
transition of electrostatic potential from the sheath region into the plasma interior,
the average ion velocity along the magnetic field lines for such plasma flow
relatively far away from the surface, V
ðÀ1Þ
k
, is limited by the so-called BohmChodura [1, 2] sheath criterion:
V
ðÀ1Þ
k
! V crit ,
ð4:1Þ
where the critical velocity V crit is determined by the plasma parameters (see also [3]).
Fig. 4.1 Electrostatic
potential φ(z) within the
sheath plugs most of the free
streaming electron flux to
maintain ambipolar
plasma flow
Fig. 4.2 (left) Direction of the magnetic field and the coordinates which will be used. (right)
Magnetic presheath, with the width ~ρ i , and Debye sheath with the width ~λ D for the case α ( 1
74
4 Sheath Physics