108
H. J. Hilke and W. Riegler
This reduction is essential for most TPCs with their long drift distances.
A more rigorous treatment of averages [19] shows that different ratios apply to
low and high B:
D(0)/D(B) = 1 + ω 2 τ 2
1
for low B, and
D(0)/D(B) = C + ω 2 τ 2
2
for high B.
(4.38)
This behaviour was indeed verified [37], by measuring D(B) over a wide range of
B. In an Ar/CH 4 (91/9%) mixture the data could be fitted with τ 1 = 40 ps, τ 2 = 27
ps and C = 2.8. The high field behaviour is approached above about 3 kg, close to
ωτ = 1.
The longitudinal diffusion remains unchanged: D L (ω) = D L (0).
The effects of E and B combine if both fields are present.
4.2.2.3 Electron Attachment
In the presence of electronegative components or impurities in the gas mixture, the
drifting electrons may be absorbed by the formation of negative ions. Halogenides
(e.g. CF 4 ) and oxygen have particularly strong electron affinities. Two-body and
three-body attachment processes are distinguished [38].
In the two-body process, the molecule may or may not be broken up:
e − + AX → Ax − ∗ → A (or A ∗ ) + X −
or X − ∗
or
e − + AX → Ax − ∗ → AX
−
+ energy.
(4.39)
The attachment rate R is proportional to the density N:
R = cσ N
(4.40)
for an electron velocity c and attachment cross-section σ The rate constants of freons
and many other halogen-containing compounds are known [39].
The best known three-body process is the Bloch-Bradbury process [40]. In this
process, an electron is attached to a molecule through the stabilizing action of
another molecule. It is important for the attachment of electrons with energy below
1 eV to O 2 , forming an excited unstable state with a lifetime τ of the order of
10 −10 s. A stable ion will be formed only if the excitation energy is carried away
during τ by another molecule. The attachment rate is proportional to the square of
the gas pressure, as it depends on the product of the concentrations of oxygen and
of the stabilizing molecules [19]:
R = τ c e c 2 σ 1 σ 2 N (O 2 ) N (X) .
(4.41)
H. J. Hilke and W. Riegler
This reduction is essential for most TPCs with their long drift distances.
A more rigorous treatment of averages [19] shows that different ratios apply to
low and high B:
D(0)/D(B) = 1 + ω 2 τ 2
1
for low B, and
D(0)/D(B) = C + ω 2 τ 2
2
for high B.
(4.38)
This behaviour was indeed verified [37], by measuring D(B) over a wide range of
B. In an Ar/CH 4 (91/9%) mixture the data could be fitted with τ 1 = 40 ps, τ 2 = 27
ps and C = 2.8. The high field behaviour is approached above about 3 kg, close to
ωτ = 1.
The longitudinal diffusion remains unchanged: D L (ω) = D L (0).
The effects of E and B combine if both fields are present.
4.2.2.3 Electron Attachment
In the presence of electronegative components or impurities in the gas mixture, the
drifting electrons may be absorbed by the formation of negative ions. Halogenides
(e.g. CF 4 ) and oxygen have particularly strong electron affinities. Two-body and
three-body attachment processes are distinguished [38].
In the two-body process, the molecule may or may not be broken up:
e − + AX → Ax − ∗ → A (or A ∗ ) + X −
or X − ∗
or
e − + AX → Ax − ∗ → AX
−
+ energy.
(4.39)
The attachment rate R is proportional to the density N:
R = cσ N
(4.40)
for an electron velocity c and attachment cross-section σ The rate constants of freons
and many other halogen-containing compounds are known [39].
The best known three-body process is the Bloch-Bradbury process [40]. In this
process, an electron is attached to a molecule through the stabilizing action of
another molecule. It is important for the attachment of electrons with energy below
1 eV to O 2 , forming an excited unstable state with a lifetime τ of the order of
10 −10 s. A stable ion will be formed only if the excitation energy is carried away
during τ by another molecule. The attachment rate is proportional to the square of
the gas pressure, as it depends on the product of the concentrations of oxygen and
of the stabilizing molecules [19]:
R = τ c e c 2 σ 1 σ 2 N (O 2 ) N (X) .
(4.41)