RADIAL PROFILES OF EMISSION IN A HELIUM-SELENIUM DISCHARGE
2 function decreasing to zero at the walls, then 0 varies as r
, 4
For large dips in the selenium density profile the constant term in the series expansion for the selenium profile may be neglected
i ( / '
as a first approximation and so the total creation rate,V0«N ,A 2 Se
will be proportional to r^. Hence most of the selenium "created" 4
by 0^ appears near the tube walls - for an r dependence half of the selenium is produced within 0.1 R of the tube walls. Even if the selenium profile has such a small dip that its radial dependence is entirely neglected, half of the metal vapour comes from within 0.15R of the walls. There is no source term in equation (2.1) as this is implicit in the solution - the source of the metal vapour is at the tube walls. The boundary conditions affect the total amount of
metal vapour in the system, but not the profile shape- Thus,
inasmuch as the creation term 0 merely increases the flux of metal atoms from around the wall, the shape of the profile is unchanged from that established by 0 j.
While the foregoing argument merits closer treatment of 'the higher powers of r in the ionisation process, this second-order argument shows that deviation from a flat-profile ionisation process does not greatly distort the metal vapour profiles, justifying the claim ' that the dip is fairly independent of the detailed shape of the
electron density profiles.
It is interesting to compare equation (2.3) with the solution to equation (2.2) derived for a flat ionisation profile. Equation
(2.2) becomes
r^d^N^ Se . rdN^ Se r^N^ N f Se eo - ^ --- --- = O
dr dr D
The solution is a modified Bessel function: “se ' “seo 'f
which may be 'expanded:
1 r^ 1 2 r^
“se = “seo 64 “ '
This differs from (2.3) only in small terms of the fourth order upwards.
The profiles of upper-laser-level emission will be less dipped than those of the neutral ground state density because the pumping species, helium ions, is less concentrated at the walls than at the axis.
However, multiplication of the zero-order Bessel function assumed to describe the helium ion density (if the selenium ion density is small in comparison) by the expression for the ground-state dip' described by (2.3) shows the dip will still be evident at high enough values of a.
To calculate a typical value of a, equation (2.4) is used. We will assume here that only electron ionisation contributes to f. At a current of 400mA and a helium pressure of 10 Torr the axial
13 -3
electron density is taken to be 10 cm and the energy-averaged cross section for the electron ionisation of selenium is taken to be
diffusion coefficient of 300 cm^s ^ (see, for example. Table 6,1), a is about 20 which means the ratio of the intensity of emission from excited states observed at 0.7R divided by the axial intensity is about 2, This is of the order of the size of dip observed
(see Fig. 2.5 or Fig. 2.6).
From .the model the "hole" will be deeper at larger values of N^, corresponding to greater discharge currents, and at smaller D corresponding to greater pressures. Thus the model predicts the observations both in magnitude and in dependence on discharge parameters.
There are limitations to this simple model. An increase in the metal atom concentration at the sides of the tube will lower the electron temperature so reducing the value of f. Similarly at the walls the metal ion concentration may become comparable with the helium ion concentration which would affect the shape of the upper - laser-level pumping profiles.
2.6 Conclusion
The dip phenomenon depends, in the final analysis, on the high fractional ionisation of the metal which arises because of the
relatively low ionisation potential of selenium compared with that of helium. If the metal were only slightly ionised the neutral
diffusion gradient would not need to be high to balance the small radial ion flux. Since the buffer gases tend to have much higher ionisation potentials than the metal atoms in metal-rare-gas mixtures , the dip should be a feature of such discharges in general and not confined to helium-selenium systems.
The implications of the model and the experimental observations are that the power output of both Duffendack-and Penning-pumped positive -
column metal-vapour lasers will saturate with current because, as the electron density is increased, a greater fraction of the metal is found near the walls where a smaller fraction of rare gas ions or metastables exists to populate the upper laser levels. Hence the total number of laser level ions increases sublinearly with current and the axial concentration, in the most sensitive region of the tube for zero-order mode laser oscillation, will
saturate and even decrease at sufficiently high a. The onset of this sidelight sublinearity and laser power saturation with current was found to be coincident by Klein and Silfvast (12) which is in accordance with the model.
Unfortunately the efficacy of the solution of increasing the .oven temperature is limited because the axial density of metal
vapour will be maintained only at the expense of creating a very dense metal-vapour sheath. Since electrons ionise more easily in the sheath, the axial electric field will decrease so reducing the
overall production rate of rare-gas ions or metastable atoms near the axis. A similar situation will exist for any such positive-column system where a radial electric field can drive the highly ionised metal vapour to the wall.
Owing to tlie complicating effect of molecular selenium which 7
probably exists in such discharges , the possible involvement of 17
selenium metastable levels in He-Se Duffendack reactions and the incomplete spectroscopic literature available on selenium, the remainder of this work describes a more detailed investigation
of the hole effect using a hélium-cadmium discharge. Cadmium
was selected because the system is simple in design and construction and is well-documented and because a comparison is afforded between the Penning and the Duffendack pumped levels. (There is no disadvantage in
observing charge-exchange levels which have not in fact been made to lase in the positive column because the general features of
such a discharge are common to all such systems, and so He-Cd serves as a model for all positive-column metal-vapour lasers.)