N2 laser gain medium depletion

The main causes of a reduction of the generation energy at a high repetition rate are as follows: (i) a decrease in the active medium gain coefficient due to an increase in the translational gas temperature; (ii) slow relaxation of the vibrational excited states of the ground electronic state. Vibrational relaxation in N2 lasers is maximally effective upon the collision of molecules with the discharge cell walls.   The repetition rate is increased along with the reduction in the discharge channel diameter...  "Pulsed Gas Lasers with Longitudinal Discharge and Their Application in Medicine", Provorov, et. al.

What's the reason for the decline of my N2 laser output at high repetition rate?  Is it because the N2 gets too hot and affects the transitions between levels, and consequently their relative populations, ie. too much of the gas is stuck in an energy level which cannot be excited?   Or, are there too many residual ions from the previous pulses, lowering the breakdown voltage, and consequently the pulse strength?    Noodling with the ideal gas law shows that the increasing pressure is within two torr of the initial pressure, so I doubt it is moving the gas enough away from the optimal E/p to make a difference.

N2 energy level diagram.  Lasing at 337.1 nm is due to the ( C 3 Π u  ) -> ( B 3 Π g) transition (the electronic ground state is labeled X 1 Σ +g). 

Credit:  http://raptor.physics.wisc.edu/download2.htm

The upper las​ing​ level (ULL) has a lifetime (τ) that is pressure dependent, [ τ = 36/(1+(p/58)) ] (p is pressure in torr).  The ULL, labeled in the diagram as  C 3 Π u has a lifetime of ~18 ns at 60 torr, and for the lower lasing level (LLL), B 3 Π g, τ ~10 μs.   For the metastable state (A 3 Σ u), guesses of τ in the literature range from .01 to 2s.  My guess is that it's temperature dependent. 

First, a test of the temperature dependence.   Here is a measurement of the N2 laser's power variation with temperature.

Experiment specifics:

• I evacuated the tube and added N2 ;  Pressure 5-8 kPa. Volume:  40.84 cm3. Average ambient temp: ~294 K. 8.0765×1019 molecules.

• Repetition rate:  17 pps.

• Average output power was measured using a photodiode with an optical filter in front.  Photodiode reponse at 337.1 nm:  7.14 A/W, and the filter transmittance at 337.1 nm:  60%  (both estimated from the manufacturer's curves, reproduced below).

• Gas temperature was measured with an infrared thermometer.

I found that power decreased with increase of the temperature of the N2, and that the power was restored after allowing the tube to cool down to its original temperature.  Time of power decline to 50% of initial power was measured to be 5 min 33 sec, when the temperature reached 30°C.   However, after first cooling the tube with ice to 16.6°C, it took 7 min 9 sec to decline to 50% of the initial power, and a total of 11 min 15 sec to decline to the minimum power reached in the first measurement, again at approximately 30°C.

With a blower continuously cooling the tube, maintaining a stable temperature of 23.5°C, power stabilized at 75% of the initial power, and remained at that level.

Experimental set-up.  Cooling the tube with a blower.

With the metastable A 3 Σ u state having a long lifetime, the ground state may not have enough molecules to keep a high power beam going.  Molecules can be de-excited from an energy level by collisions; with the walls of the tube, or with other gasses.  Next I will do the same tests with some He added to the N2, to see if collisions between N2 and He help to repopulate the ground state.

Addenda:

Photodiode response curve.  BaseLine ChromTech Research Centre model HS1010CE.

Narrow pass filter transmittance chart.  Omega model 340BP10.