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Registered Member #1667
Joined: Sat Aug 30 2008, 09:57PM
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Posts: 373
Pinky's Brain wrote ...
Isn't the lower (partial) pressure of the N2 in fact a necessity to use slower capacitors?
The upper level life-time is given empirically by t=(36ns)/(1+p/(77 mbar)).
I'd have to look up what the contributions to the lifetime are but evidently, collisions play a major role. These can also occur with other gas molecules or atoms so the partial pressure might not be as significant as the total pressure.
Registered Member #543
Joined: Tue Feb 20 2007, 04:26PM
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Posts: 4992
In the case of nitrogen the problem is that the lifetime of the upper state, which really sets the width of the laser pulse in this case, is inversely dependent on pressure according to the formula [1]:
t = 36/(1+p/58)
where t is the lifetime of the upper lasing level in nanoseconds and p is the pressure in the discharge tube in torr. (ref: Patel, Rev. Sci. Inst., below)
Hence in a 'normal' N2 laser operating at 30-60 torr the lifetime of the upper lasing level is about 20 nS. In a TEA laser the higher pressure reduces the lifetime of the upper energy state to about 2.5 nS. The pulse width of the TEA laser is hence reduced to about 1 nS. Now, construction of a 'normal' N2 laser is difficult enough given that particular attention must be paid to keep inductances very low. Consider the capacitors used - although tempting one cannot use regular 0.045" thick PCB for an N2 laser since the self-inductance of the board is quite high which slows the discharge and hence it fails to work. In the TEA nitrogen laser the situation is ten times worse so that extreme measures must be taken to keep inductances low! Consider the characteristic impedance of a Blumlein transmission line given by [2]:
Z = (377/e1/2) * (s/L)
where Z is the impedance of the line in ohms, s the thickness of the dielectric and e the dielectric constant of the capacitor material, and L the width of the conductors in the transmission line.
The ultra-fast discharge required for a TEA laser dictates that we keep the dielectric as thin as possible which, of course, leads to problems with dielectric breakdown due to the high voltages required. Using the first formula we find that the lifetime of the ULL is 2.5ns so that logically our transmission line must discharge within that time. This dictates a maximum length for the transmission line based on the speed at which it discharges [5]:
L = (c * tp) / e1/2
where c is the speed of light (3*108 m/s) and tp the length of the pulse. Since the later parameter must be kept to 2.5ns or less this dictates that the transmission line must not exceed 43cm where a dielectric with an e of 3 is used (Of course if polyethylene, mylar, or other materials are used for the caps this number will change accordingly). High dielectric materials will dictate a shorter width of the transmission line. Anything over this figure will result in energy being wasted since population inversion will end with the ULL lifetime.
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TEA lasers
