110
H. J. Hilke and W. Riegler
The positive ions produced in the avalanche have too little energy to contribute
to the ionization in the avalanche. They will move slowly to the cathode(s), where
they get neutralized but where rare gas ions may also liberate additional electrons.
The addition of the quencher reduces this risk significantly, as its recombination
energy can be dissipated in other ways, e.g. by disintegration. This explains why
more complex molecules provide higher protection.
Up to a certain value A p , one has a proportional regime: the signal produced will
on average be proportional to the number of primary electrons. The amplification
will rise approximately exponentially with voltage. The azimuthal extension of the
avalanche around the wire will grow with amplification and eventually the avalanche
will surround the wire.
When the field is raised above this proportional regime, space charge effects
will set in. The space charge of the positive ions—moving only very slowly
compared to the electrons—will reduce the field at the head of the avalanche and the
amplification will rise more slowly with voltage and will no longer be proportional
to the primary ionization. In addition, space charge effects will depend on the track
angle with respect to the wire and on the density of the primary ionization. This is
the so-called limited proportionality regime.
Increasing the field further, the positive space charge may produce additional
effects. Near the avalanche tail the electric field is increased. If the absorption of
UV photons in the quench gas is high, the photons may ionize this high field region
and start a limited streamer moving backwards by starting avalanches further and
further away from the sense wire. As the electric field at large radius weakens,
this development will stop after typically 1–3 mm. The total charge is almost
independent of the primary charge starting the streamer. The process depends quite
strongly on experimental conditions. An example is presented in Fig. 4.11, which
shows a steep step from the proportional regime [41]. In the narrow transition zone
one finds a rapid change of the ratio of streamer/proportional signal rates. In other
experimental conditions a smoother transition has been observed.
If the absorption of the UV photons is weak, photons travel further and
avalanches may be started over the full length of the wire, leading to the Geiger
mode, if the discharge is limited by external means.
4.2.3.2 Gas Gain
With multiplication, the number n of electrons will grow on a path ds by
dn = n α ds,
(4.44)
where α is the first Townsend coefficient. Ionization growth is obviously proportional
to the gas density p and depends on the ionization cross-sections, which are a
function of the instantaneous energy ε of the electrons. This energy itself is a
function of E/p. The relationship between α and E is, therefore, given in the form α/p
as function of E/p or for a specific temperature as α/p(E/p). Figure 4.12 gives some
H. J. Hilke and W. Riegler
The positive ions produced in the avalanche have too little energy to contribute
to the ionization in the avalanche. They will move slowly to the cathode(s), where
they get neutralized but where rare gas ions may also liberate additional electrons.
The addition of the quencher reduces this risk significantly, as its recombination
energy can be dissipated in other ways, e.g. by disintegration. This explains why
more complex molecules provide higher protection.
Up to a certain value A p , one has a proportional regime: the signal produced will
on average be proportional to the number of primary electrons. The amplification
will rise approximately exponentially with voltage. The azimuthal extension of the
avalanche around the wire will grow with amplification and eventually the avalanche
will surround the wire.
When the field is raised above this proportional regime, space charge effects
will set in. The space charge of the positive ions—moving only very slowly
compared to the electrons—will reduce the field at the head of the avalanche and the
amplification will rise more slowly with voltage and will no longer be proportional
to the primary ionization. In addition, space charge effects will depend on the track
angle with respect to the wire and on the density of the primary ionization. This is
the so-called limited proportionality regime.
Increasing the field further, the positive space charge may produce additional
effects. Near the avalanche tail the electric field is increased. If the absorption of
UV photons in the quench gas is high, the photons may ionize this high field region
and start a limited streamer moving backwards by starting avalanches further and
further away from the sense wire. As the electric field at large radius weakens,
this development will stop after typically 1–3 mm. The total charge is almost
independent of the primary charge starting the streamer. The process depends quite
strongly on experimental conditions. An example is presented in Fig. 4.11, which
shows a steep step from the proportional regime [41]. In the narrow transition zone
one finds a rapid change of the ratio of streamer/proportional signal rates. In other
experimental conditions a smoother transition has been observed.
If the absorption of the UV photons is weak, photons travel further and
avalanches may be started over the full length of the wire, leading to the Geiger
mode, if the discharge is limited by external means.
4.2.3.2 Gas Gain
With multiplication, the number n of electrons will grow on a path ds by
dn = n α ds,
(4.44)
where α is the first Townsend coefficient. Ionization growth is obviously proportional
to the gas density p and depends on the ionization cross-sections, which are a
function of the instantaneous energy ε of the electrons. This energy itself is a
function of E/p. The relationship between α and E is, therefore, given in the form α/p
as function of E/p or for a specific temperature as α/p(E/p). Figure 4.12 gives some