Page 87 - High Power Laser Handbook

56 G a s , C h e m i c a l , a n d F r e e - E l e c t r o n L a s e r s Chemical Lasers 57

These processes are quite rapid. At pressures of interest in flowing
devices, these processes substantially perturb the nascent fraction
produced by the pumping reactions. More detailed discussions of HF
and DF kinetic rates in general can be found in Cohen and Bott.
11
It follows that for HF and DF devices, deactivation and energy
transfer processes are quite important and substantially influence the
design of these lasers. Specifically, they determine how high a partial
pressure of HF or DF one can practically achieve in a laser device;
they also dictate that if one wants to construct a high-power device, it
is advantageous to have a high flow velocity to allow power extrac-
tion before deactivation depletes the excited species. To further illus-
trate this point, let us assume that the only process considered is a
simple deactivation loss of HF(v = 1) by HF at room temperature:

HF(v = 1) + HF(v = 0) → HF(v = 0) + HF(v = 0) (3.17)

3
12
This process has a typical rate constant k = 1 x 10 mole/s-cm . Even
at room temperature and an HF partial pressure of 1 torr (molar den-
–8
3
sity is 5.5 x 10 mole/cm ), the corresponding 1/e decay time is only
5
18 µsec in the absence of other gases. At a velocity of 10 cm/s, the 1/e
decay occurs in a flow distance of only 1.8 cm. This example illus-
trates the difficulty in pressure scaling and the motivation to flow at
high velocity. It also illustrates the need to mix and extract power
quickly in order to be competitive with deactivation losses.
3.3.5 Fluid Mechanics and Nozzle Design
The enhanced gain associated with Doppler broadening and favor-
able partial inversion at low temperatures makes it advantageous to
operate HF and DF CW devices at temperatures far below those
required to thermally dissociate fluorine. This is achieved by rapidly
expanding the combustor flow in converging (subsonic) and then
diverging (supersonic) nozzle geometries, which freezes the dissocia-
tion fraction while drastically dropping the pressure, static tempera-
ture, and density. In order to understand issues associated with such
flowing laser devices, the following general review of concepts asso-
ciated with one-dimensional fluid mechanics should be helpful.
At a given location, a gas is characterized by the fluid parameters
and the relative mole fractions of the gas components. Variables
include (1) static temperature T, (2) static pressure P, (3) density ρ,
and (4) gas velocity U. Knowledge of the stoichiometry allows one to
also calculate the average molecular weight W, the heat capacities at
constant pressure C and temperature C , the specific heat ratio γ =
P
V
C /C , and the speed of sound c. The gas equation of state, which is
P
V
usually well approximated by the ideal gas law, allows calculation of
the mass density and local molecular concentrations of the various
gas constituents based on temperature and pressure.