Optical and Quantum Electronics

, Volume 14, Issue 1, pp 25–40 | Cite as

Kinetic modelling of a fast-axial-flow CO2 laser

  • R. E. BeverlyIII
Papers

Abstract

A six-temperature Boltzmann-equilibrium kinetics model has been developed for simulating the performance of fast-axial-flow, longitudinal-discharge CO2 lasers. The model includes the effects of electrical excitation, VV and VT collisional relaxation, thermal energy transport, distributed optical losses, and coherent radiation extraction for a CO2/N2/He/H2O mixture. Numerical predictions from the model are compared with experimental results obtained with a 2.5 kW device.

Nomenclature and values

Boltzmann factors

T

gas kinetic temperature

Tα

vibrational temperature of a vibrational mode

a

= exp (-θa/Ta)

b

= exp (-θb/Tb)

n

= exp (-θn/Tn)

s

= exp (-θs/Ts)

w

= exp (-θw/Tw)

b

= exp (-θb/T)

¯n

= exp (-θn/T)

¯w

= exp (-θw/T)

Characteristic temperatures

θr

characteristic temperature of a vibrational mode

θa

= 3380 K

θn

= 3354 K

θw

= 2295 K

θs

= 1997 K

θb

= 960 K

θwb

=θw-θb=1335K

θaw

=θa-θw=1085K

θnw

=θn-θw=1059K

θab

=θa-3θb=500K

θsb

=θs-2θb=77K

θan

=θa-θn=26K

θr

characteristic temperature of rotational mode = 0.556K

Energy defect factors

A

= exp (-θan/T)

B

= exp (-θsb/T)

C

= exp (-θab/T)

D

= exp (-θnw/T)

F

= exp (-θaw/T)

G

= exp (-θaw/T)

Gas heating factors

Cβ

specific heat at constant pressure (J K−1 mol−1)

Ch

= 20.79

Cn

= 29.11

Cc

= 36.63

Cw

= 33.26

Eα

characteristic energy density (Jcm−3)

Fe

gas discharge direct heating rate (J cm−3 s−1)

fα

molar fraction ofα species

P

total gas pressure (Pa)

Radiation intensities

bδJ

scattering loss per cm inside the resonator

IδJ

collimated light intensity (W cm−2)

IδJ+

collimated photon intensity in the +z direction

IδJ-

collimated photon intensity in the —z direction

αδJO

small-signal gain of gas medium (cm−1)

αδJO

spatially averaged small-signal gain (cm−1)

αδJ

spatially-dependent gain of gas medium (cm−1)

αi

absorptivity of the1th mirror

αδJint

homogenized cavity loss of the internal elements per cm

IδJ+,IδJ-

average cavity loss per cm for photons travelling in the+z and —z directions, respectively

ΔNδJ

population inversion density (cm−3)

τi

transmissivity of the ith mirror

Subscripts

a

asymmetric stretch mode (ASM) of CO2

b

bending mode (BM) of CO2

c

CO2

h

He

n

N2

s

symmetric stretch mode (SSM) of CO2

w

H2O

0

denotes initial condition atz = 0

Transition rates

kαβ

reaction rate coefficient in cm3 perβ particle per second

Nα

number ofα particles per cm3

N

total number density of gas in particles per cm3

Rα

VT transition rate in number of transitions per second

Nαβ

VV transition rate due to collisions betweenα andβ particles

Electrical properties

E

electric field (V cm−1)

I

discharge current (A)

j

discharge current density (A cm−2)

Uα

electrical pumping term (s−1)

Wα

power density entering theα mode (W cm−3)

γα

fraction of electrical power density which excites theαth level

Stimulated emission

A21δJ

spontaneous transition probability rate between upper and lower laser levels (s−1)

ΔvG

Gaussian bandwidth (half linewidth at half maximum) (cm−1)

ΔvL

Lorentzian bandwidth (half linewidth at half maximum) (cm−1)

J′

rotational quantum number of upper laser level (must be odd)

J

rotational quantum number of lower laser level (must be even)

Mc

CO2 mass (amu)

NδJ′

population density of upper laser level (particles cm−3)

NδJ

population density of lower laser level (particles cm−3)

P

denotes P-branch transition (J′=J-1)

QδJ

common rotational factor of the stimulated emission factor

R

denotes R-branch transition (J′ =J + 1)

S21δJ

stimulated transition probability rate (s−1)

ψJ

fraction of molecules in theJth rotational level

δ

P or R (specifies branch for rotational transition)

Γ

stimulated emission term (s−1)

ГδJ

stimulated emission factor

¯v0

laser radiation wave number (cm−1)

vO

value of line shape factor at line centre (cm)

φδJO

stimulated emission cross-section (cm2)

Laser cavity

z

downstream distance from the entrance to the discharge tube

ν

gas flow velocity (cm s−1)

LM

distance between the mirrors (cm)

lpc

length of the discharge positive column (cm)

lflow

length of the gas flow per discharge tube (cm)

Nt

number of discharge tubes

dt

discharge tube diameter (cm)

Adis

= (π/4)dt2 = cross-sectional area of the gas discharge (cm2)

Constants

k

= 1.3805 × 10−23 J K−1

h

= 6.6256 × 10−34J s

c

= 2.9979 × 1010 cm s−1

NA

= 6.0225 × 1023 particles mol−1 (Avagadro's number)

NL

= 2.6517 × 1014 particles Pa−1 (Loschmidt's number)

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Copyright information

© Chapman and Hall Ltd 1982

Authors and Affiliations

  • R. E. BeverlyIII
    • 1
  1. 1.ColumbusUSA

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