106
H. J. Hilke and W. Riegler
Fig. 4.8 Longitudinal and transverse diffusion constants for low electric fields [33]. The dashdotted line denotes the thermal limit
As can be seen in Fig. 4.8, this minimum is approached for ‘cold gases’ like
Ar/CO 2 up to E~150 V/cm at 1 atm, for ‘hot gases’ like Ar/CH 4 only for much
lower fields.
Anisotropic Diffusion
So far, we have assumed isotropic diffusion. In 1967 it was found experimentally
[34], that the longitudinal diffusion D L along E can be different from the transversal
diffusion D T Subsequently it has been established that this is usually the case.
For ions this anisotropy occurs only at high E. As in a collision ions retain their
direction to a large extent, the instantaneous velocity has a preferential direction
along E. This causes diffusion to be larger longitudinally. However, this high field
region is beyond the drift fields used in practical detectors.
For electrons a semi-quantitative treatment [35], restricted to energy loss by
elastic collisions, shows that
D L /D T = (1 + γ ) / (1 + 2γ ) with γ = (ε 0 /v 0 ) (δv/δδ) .
(4.36)
It follows that longitudinal and transversal diffusion will be different, if the
collision rate v depends on the electron energy ε.
Figures 4.8, 4.9, 4.10 show measured diffusion for a drift of 1 cm for some
common gas mixtures [30, 33, 36]. Simulated diffusion curves are compiled in [33].
H. J. Hilke and W. Riegler
Fig. 4.8 Longitudinal and transverse diffusion constants for low electric fields [33]. The dashdotted line denotes the thermal limit
As can be seen in Fig. 4.8, this minimum is approached for ‘cold gases’ like
Ar/CO 2 up to E~150 V/cm at 1 atm, for ‘hot gases’ like Ar/CH 4 only for much
lower fields.
Anisotropic Diffusion
So far, we have assumed isotropic diffusion. In 1967 it was found experimentally
[34], that the longitudinal diffusion D L along E can be different from the transversal
diffusion D T Subsequently it has been established that this is usually the case.
For ions this anisotropy occurs only at high E. As in a collision ions retain their
direction to a large extent, the instantaneous velocity has a preferential direction
along E. This causes diffusion to be larger longitudinally. However, this high field
region is beyond the drift fields used in practical detectors.
For electrons a semi-quantitative treatment [35], restricted to energy loss by
elastic collisions, shows that
D L /D T = (1 + γ ) / (1 + 2γ ) with γ = (ε 0 /v 0 ) (δv/δδ) .
(4.36)
It follows that longitudinal and transversal diffusion will be different, if the
collision rate v depends on the electron energy ε.
Figures 4.8, 4.9, 4.10 show measured diffusion for a drift of 1 cm for some
common gas mixtures [30, 33, 36]. Simulated diffusion curves are compiled in [33].