The Wall Boundary Condition
At the Wall, the exchange of electrons occurs through the following mechanisms:
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Loss of electrons due to a net flux of electrons from the plasma bulk to the wall.
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Loss of electrons due to the random motion of electrons within the mean free path of the wall.
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Gain of electrons due to secondary emission; a wall emits an electron with some probability when it is struck by an ion or other excited species.
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Gain of electrons due to thermionic emission.
The resulting equation for the normal component of the electron flux at the wall is given by:
(4-8)
and for the normal component of the electron energy density:
(4-9)
here:
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re is the reflection coefficient (usually 0).
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νe,th is the thermal velocity (SI unit: m/s).
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γi is the secondary emission coefficient from the ith positive ion species.
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Γi is the ion flux of the ith positive ion species at the wall (SI unit: 1/(m2·s)).
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Γt is the thermal emission flux (SI unit: 1/(m2·s)).
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is the mean energy of the ith species of secondary electrons (SI unit: V).
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is the mean energy of thermally emitted electrons (SI unit: V).
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n is the outward normal.
The thermal velocity is defined as:
.
When the Include migration effects is activated the first term on the right-hand side of Equation 4-8 becomes:
and the first term on the right-hand side of Equation 4-9 becomes:
where E is the electric field on the wall.