# Laser-Induced Photon-Branched Chain Reaction

Authors: Renat R. Letfullin; Thomas F. George; Galen C. Duree
Journal: Laser Chemistry
 (2008)

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## Abstract

A promising avenue in the development of high-energy pulsed chemical HF/DF lasers and amplifiers is the utilization of a
photon-branched chain reaction initiated in a two-phase active medium, that is, a medium containing a laser working gas
and ultradispersed passivated metal particles. These particles are evaporated under the action of IR laser radiation which
results in the appearance of free atoms, their diffusion into the gas, and the development of a photon-branching chain
process, which involves photons as both reactants and products. The key obstacle here is the formation of a relatively
large volume (in excess of103cm3) of the stable active medium and filling this
volume homogeneously for a short time with a submicron monodisperse  metal aerosol, which has specified properties. In this paper, results are presented for an extensive study of laser initiation of a photon-branched chain reaction in a
gas-dispersed H2–F2
medium.


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## Body

## 1. Introduction

Theoretical investigations [1–9] have been
carried out for the problem of photon branching in a two-phase (consisting of a
gas and disperse particles) chemically active media. It has been shown that the
introduction of a certain concentration of ultradisperse particles into the
active medium of a chemical laser based on a chain reaction, and further their
(particles) evaporation by external infrared (IR) radiation, can result in the
generation of coherent radiation of energy considerably higher than the energy
of an initiating input pulse at same frequency. New laser photons generated in
the cavity can also participate directly in the laser-chemical reactions,
facilitating the formation of active centers of a chain reaction (free atoms). If
the number of emitted photons exceeds the number of those used in the
initiation process, one can speak of a new type of branched chain reaction: photon-branched chain reaction (PBCR). The
PBCR has practical interest because of it possible use in constructing powerful
pulsed HF/DF-lasers and amplifiers without external energy sources.The
first experimental results to achieve a photon-branched chain reaction in a
two-phase medium were published in [10]. The authors showed that during the
injection of a fine-disperse aluminum powder with particle diameters of 0.3 μm covered
by thin oxide film into a mixture of F2 +  H2 +  O2 +  He, the system remains stable. They observed the formation of free aluminum atoms
under the action of radiation of a chemical laser with intensities as high as
107 W/cm2, with a demonstration of the chemical mixture
ignition. Comparison of the output energy in the presence and absence of
disperse particles led to the conclusions that about 15% of the output energy is
due to a PBCR.The successes of the first experiments have given a
positive answer to the question of the feasibility of a photon-branched chain
chemical process in a two-phase active medium of an HF laser, and it has confirmed the
accuracy of the theoretical models of the chemical and vibration-relaxation
kinetics. We have developed a
relatively simple HF laser kinetic model [1, 2] which includes the most
important physical-chemical kinetics features under the assumption of
rotational-translational nonequilibrium, making it possible to calculate the
specific energy of the coherent radiation, the pulse duration, the effective
chain length of the reaction between fluorine and hydrogen, and the chemical
and engineering efficiencies of the laser. This model was supplemented with an electrodynamical
model [2–9] of the pulsed
laser based on a solution of the wave equation. The wave approach for the description of a pulsed
chemical HF laser amplifier based on a PBCR in an unstable telescopic cavity
enables the detection of interesting optical effects in an active two-phase
medium of H2–F2–O2–He
and Al particles and also of
the new properties of the laser. These effects, the optimal parameters and the
output performances of the laser and also some characteristics of an active medium,
are presented in Table 1.Table 1
Main properties and parameters of the HF-laser
amplifier based on a PBCR.
Here,r0 and  N0 are the radius and concentration of the dispersed
particles; I0 and  τin  are the intensity and duration of the initiating
radiation;  Eout  and  Esp  are the full (i.e., for
the whole volume of the laser active medium) and the specific (i.e., per unit
volume) energies of the output pulse of radiation; Pmax is the maximum generated power; kamp  is the energy gain
factor; τL  is the duration of the output pulse; τ1/2L  is the
output pulse duration at half of the maximum power; Ithr  is the threshold intensity for optical breakdown of
the active medium.
Observed effects and properties of the laserCalculated
optimal laser parametersOutput
characteristicsEffect of
autowave spreading of a PBCR throughout the volume of the active medium as self-supporting cylindrical zones of photon
branchingRatio of the
reagents as H2 : F2 =  1 : 2.
The range of
general pressures of the mixture is  P = 1–2.3 barEout=1.5×2.3KJEsp = 200–730 J/LPmax~1011WEffect of the
giant laser energy gain ofkamp  = Eout/Ein~1011, where Eout and Ein  are the output  and
input energies, respectivelyRanges of Al
particle radii and  concentrations are, respectively:r0 =   0.09–0.4 μm and N0 = 109–107 cm−3τL≈800 ns   τ1/2L=100 ns.Autonomous
generation: a self-contained laser   can
be initiated by a small submicrojoule master oscillator powered by an
accumulatorPerformances
of the master oscillator:
input signal intensityI0=104 W/cm2, energy of the input pulse Ein  =    2.18 ×  10−8 J, duration of the initiating pulse, τin=250 nskamp  =  Eout/Ein≈107–1011Property of
compactness, which is determined by the performances
of the main laser units: minimal linear
sizes of the cavity,~13  ×  14  ×  14 cm3; minimal energy of the master
oscillator, Ein  =  2.18 × 10−8 J; minimal initially excited volume, Vinmin =  10−7 cm3.  The volume of the active medium is about 2LGeometric
parameters of the unstable telescopic cavity are as follows: number of passes,Np  =  4;
range of cavity lengths, 13–50 cm; range of
magnification coefficients, β = 1.5–2; diameter of
the coupling aperture, d≤3 mmThe profile of the output pulse in the near-field zone is a torus, and
in the far-field zone, the profile is Gaussian-likeIt has been shown [3, 5–9] that the laser chemical reaction can be ignited in an
initial small focal volume of an active medium, and then spreads out of this
minimal volume spontaneously in the autowave regime, without external power
sources to subsequently fill the whole volume of the laser with a highly-intense
electromagnetic field with self-supporting cylindrical photon-branching zones
formed by the paths of the rays inside the unstable telescopic cavity. The
ignition of an autowave PBCR under the condition of external signal focusing
reduces strongly the input pulse energy necessary for initiation down to ~10−8 J and, thereby, enables a huge value of the energy gain of about 1011.
In a system of this kind, there is no danger of self-excitation, even for large values of the gain, because the medium is not inverted in advance, and the energy is reserved in the form of the free energy of reactants.A parametrical study [7–9] of a pulsed
chemical laser based on a PBCR initiated in a gaseous disperse
medium, composed of H2–F2–O2–He and Al
particles, by focused external IR radiation has been conducted. We see (Table 1) that both the observed effects of autowave spreading
of a PBCR under the condition of external signal focusing and the effect
of a huge laser energy gain of 1011 give the pulsed chemical HF laser the important properties of autonomy
and compactness. We have determined the performances of the main laser units:
the minimal linear size of the cavity, the minimal energy of the master
oscillator and its power source, and the dimensions of the system of gas
cylinders. We have also obtained the optimal composition of the reactants and
the pressure of the laser working mixture. For example, at a general pressure
of the working gases of  P = 2.3
bar, the optimal parameters of the dispersed component (Alparticles
with radius r0 =  0.09 μm and concentration N0 =  1.4 × 109 cm−3) and the composition of the working mixture, H2:F2=1:2, the
HF laser ensures an output energy up to ~1.5 kJ  in a pulse from a rather small
volume of about 2 L of active medium. A specific design was proposed for a
self-contained compact pulsed HF laser with small linear sizes of the unstable
telescopic cavity (~13 × 14 × 14 cm3, where the
diameter of the input (large) mirror is 14 cm), which can be initiated
by a small submicrojoule master oscillator powered by an accumulator. The wave studies of the spatiotemporal behavior
of the output laser radiation showed that the profile of the output pulse in
the near-field zone is a torus, whereas in the far-field zone, the profile is
Gaussian-like.For a
full-scale demonstration of the effect of photon-branching and design of a
chemical laser based on a PBCR, it is necessary to investigate the permissible
range of the concentration and size of disperse particles in the laser active
medium, its dynamics, and aging; to develop the technique of preparing the
gas-disperse medium of required properties. In this paper, we present an
overview of the optimal and permissible parameters of the disperse component of
HF active medium and give recommendations for the experimental realization of
PBCR in a chemically-active gas-disperse medium.


## 2. Initiation of a Photon-Branched Chain Reaction in Aerosol

### 2.1. Kinetic Scheme

The initiation of a PBCR in an active medium of H2–F2-laser amplifier, containing
passivated fine aluminum particles covered by an oxide film with a thickness ~5–10 nm, occurs by the mechanism offered in [1, 2, 8]
for a pulsed HF generator. These aluminum particles are evaporated under
the action of laser radiation, resulting in the appearance of free Al atoms.
These atoms diffuse into the gas, and the photon-branching process begins. The
initiation can be described by the following scheme:(1)Al(solid)+nℏω→Al(gas),Al(gas)+F2(gas)→AlF+F. After the appearance of free F atoms, the atoms then
diffuse into the gas, and the chain reaction starts, leading to the formation
of vibrationally excited HF molecules and, further, to generation of new
photons:(2)F+H2→HF*+H,H+F2→HF*+F,HF*→HF+ℏω. Some of the emitted photons are absorbed, which leads to  the formation
of new free Al atoms, while other emitted photons contribute to the net laser
energy gain. The progressive growth of photons and free atoms takes place over
time, and all of the particles (photons and free F and Al atoms) participate in
active chain reactions. A reaction of this type is called a PBCR. This
idea has been validated by computer calculations based on the solution of a
system of differential equations of chemical kinetics, vibrational relaxation
transfer of laser radiation, and laser evaporation of particles [1–8].The advantages of using fine disperse particles of metals or other elements as the laser-active
media are as follows.(i)
High, in principle, concentrations of
free atoms.(ii)
Short time for producing high
concentration of free atoms.(iii)
Uniformity of filling large active
volumes with free atoms.(iv)
Universality
(ability to use various atoms).(v)
High
specific surface area of the particles, exceeding the area of the walls (e.g.,
a discharge chamber), which increases the rate of depopulation of the lower
active level. The properties of an
aerosol as an active medium of a pulsed chemical HF laser based on a
photon-branched reaction should satisfy a number of requirements, which can be
divided into two independent groups. These groups are as follows.(i)
The requirements imposed by the
conditions for sustaining the photon-branched chain reaction in an  H2–F2 mixture with fine disperse particles.(ii)
Those
imposed by the aerosol optics.


### 2.2. Laser Evaporation of Particles

The formation of active
centers of the chain reaction is achieved through the fast reaction of a
fluorine molecule with an evaporated aluminum atom from the surface of a
disperse particle under the action of external IR-laser radiation:(3)Al(gas)+F2→AlF+F.The characteristic time of
this reaction is≤10−9 s at the concentration [F2]≥1018 cm−3. Laser heating and evaporation of the disperse component can be
described within the approximation of free molecular flow, which is valid for
particles whose size
does not exceed the mean free path of molecules in a laser mixture (see, e.g.,
[8]): (4)4πr02dr0dtρ0=−η4πr02V¯s(Ts)ρs(Ts),43πr03ρ0CsdTsdt=σabsI−(Ts−Tg)∑MCM4πr02nmV¯M(Tg)+Levap4πr02dr0dtρ0. Here, Cs  and Levap  are, respectively, the specific heat and heat of
evaporation of aluminum; I is the radiation intensity inside the cavity; σabs is the cross-section of absorption of laser
radiation by an Al particle; Ts and Tg are
the temperatures of the aluminum particles and the laser active medium,
respectively; CM, V¯M,  and nM are, respectively, the molar specific heat,
average velocity, and concentration of the molecules of the Mth
component of the laser mixture; η is the accommodation coefficient; V¯s is the average velocity of the vapor
molecules; ρs(Ts) is the saturated vapor density of aluminum at  Ts.


### 2.3. Optimal Concentration of Particles

Formation of active centers
of the reaction chain and their spreading into the medium is thus possible around each fine
particle in the IR laser radiation field. The distribution of free atoms in the
active volume can become sufficiently homogeneous in a timeτh, which is limited by the duration of the laser chemical process (~1 microsecond),
provided that the condition Rev≤2Rdiff is satisfied, where Rev is the average distance between the particles, Rdiff~Dτh,
and D is the
diffusion coefficient
of the active centers in the laser medium. This sets the lower limit to the
required concentration of disperse particles as N0≈(1/Rev3).
Optimization of the aerosol parameters from the point of view of the laser chemical
process under the conditions of initiation of a pulsed HF amplifier was reported
in [8]. Calculations showed that the optimal concentration of aluminum
particles is NAl =  1.4 × 109 cm−3  for the radius r0=0.09 μm.


### 2.4. Optimal Particle Size

The optimal particle size is governed, for the
selected concentration, by the aerosol optics, so that the attenuation
coefficient of laser radiation representing scattering and absorption in a
disperse medium does not exceed the local active medium gainα. Calculations
of the optical characteristics of spherical disperse particles at a given
radiation wavelength λ were based on the Mie diffraction theory
and the single-scattering approximation [11].The Mie
formalism requires the use of two dimensionless input parameters,ρ=2πr0/ λ and δ=ρm, where m
is the relative value of the complex refractive index of the aerosol at the
wavelength λ. Computer
calculations of the dependences of the attenuation Katt,  scattering Ksc,  and absorption Kabs coefficients at the HF laser wavelength (λ =   3.3 μm) in the size
range r0  =    0.5–1 μm of aluminum particles (m =  3.2−29.5i  at 300 K)
were performed in [2, 8] and plotted in Figure 1. It is evident from Figure 1(a) that for particle radii r0>0.5 μm, the scattering coefficient Ksc is considerably greater than the absorption coefficient Kabs,
that is, lasing is impossible in such a strong scattering medium. Figure 1(b)
demonstrates, on a much larger scale, the region of intersection of the Ksc(r0) and Kabs(r0) curves.  The absorption of IR radiation predominates
over the scattering by aluminum particles, Kabs(r0)≥Ksc(r0), if r0≤0.15 μm. It follows
that the aerosol optics imposes stringent conditions on the maximum permissible
particle size in a two-phase active medium of the laser, which should satisfy
the condition ρ=2πr0/λ<1. An aluminum aerosol with the parameters r0 =  0.09–0.4 μm and NAl
=  107–109 cm−3  can be recommended as a model two-phase active medium of an HF laser based on a
PBCR.Dependencies of the attenuationKatt (1), scattering Ksc
(2), and absorption Kabs (3) coefficients at the HF-laser wavelength
(λ=3.3μm) for (a) the size r0 = 0.5–1 μm of aluminum particles (m
= 3.2–29.5i at 300 K) and (b) the region of intersection of curves
2 and 3 shown on an enlarged scale.
(a)(b)


### 2.5. Lifetime of A Disperse Component

The main disadvantage of lasers
with two-phase active media is
the fast degradation of the disperse component and the consequent short
lifetime of the active medium with specified properties. Continuous variation
of the properties of the disperse phase with time results in a deterioration of
the output characteristics of a laser or in complete quenching of the laser
action.The first
attempt to model degradation of the disperse phase in a laser active medium was
made for the operating conditions in a pulsed chemical HF laser [12]. The degradation processes are practically the
same for all types of lasers with disperse media. We adopted an approximate
coagulation model [13] and assumed the Stokes law. In the first approximation,
we studied the time dependence
of the overall characteristics of an aerosol in a laser active medium,
including the average size and the total concentration of disperse particles,
and we also calculated the formation time and lifetime of a two-phase active
medium of an HF laser with the given parameters.The processes occurring in a gaseous
medium containing a disperse aerosol may be modeled on the assumption of
coagulation, precipitation, and (in the presence of electric charges)
electrostatic scattering of disperse particles. Aerosol coagulation was
described by the lognormal quasi-self-sustaining model of [14], based on an
approximation in which a lognormal model [15] and high-current sectional model,
conserving the square of the particle volume, [16] are adopted. Here, the particle size distribution is described by the
standard lognormal function.The
precipitation of particles was taken into account on the basis of the following
model assumptions. The active medium was taken to be ideally mixed, continuous,
incompressible, and characterized by a finite viscosity. The particle shape was
assumed to be spherical. All these assumptions were to apply the Stokes law to the
aerosol precipitation. The concentration of the disperse component remaining in
the medium after particle precipitation was calculated from(5)Nprec=N0exp(−vt)H, where H is the transverse size of the active
medium of the HF laser, assumed to be equal to the diameter of the larger
cavity mirror.An analysis of
the influence of the induced electrostatic charge of fine disperse particles of
a conducting aerosol on the rate of its degradation was made within the overall
framework of the problem of the lifetime of a two-phase active medium. The
formation of a metal aerosol is practically always accompanied by its charging,
for example, as a result of thermionic and photoemission of electrons. The
concentration of the aerosol remaining after electrostatic scattering of the
particles with the same charge and of the same size can be found from
expression:(6)Nesc=N01+4πq2BN0t, where B is average mobility of
the particles.Specific calculations were
carried out for a standard active mixture of the composition H2 : F2 : O2 : He
= 100 : 400 : 40 : 210 torr, into which an aluminum aerosol was injected in advance.
At the initial time t  =  0, the aerosol was assumed to be
quasi-monodisperse with the average initial radius r0  = 0.05 μm and
concentration N0 =  2 × 109 cm−3.Fast
coagulation, with the constantβ =  5 × 10−10 cm3s−1 (Figure 2) and sticking probability practically equal to unity for a submicron
aerosol, results in continuous enlargement of the particles with a certain size
distribution. The time for the
establishment of a self-sustaining lognormal particle size distribution in the investigated
two-phase active medium is about 25 seconds. Figure 2 shows the dependencies of coagulation
and electrostatic scattering constants on the particle size. We can see that an
increase in the average charge alters slightly the coagulation constant; this
effect is significant only for small (r<0.1 μm) particles. For an aerosol with r =  0.05 μm, the constants of these processes are
comparable, and the rate of electrostatic scattering of the charged particles
exceeds the rate of coagulation of the neutral particles only if the average
charge is q≥1.3e. Therefore, at the first instant,
such electrostatic scattering of submicron-charged particles competes with
their coagulation, which results in a rapid loss of the particles from the
volume of the active medium.Figure 2
Dependencies of the coagulation constant of neutral particlesβ, the coagulation constant of charged particles βq, and aerosol
electrostatic scattering constant βesc on the particle radius r for the
average induced unipolar charge q = e  (dashed curve), 1.1 e (dotted curve)
and 1.3 e  (chain curve).It follows from
Figure3(a) that during the first 50 seconds, there is a strong fall of the
concentration of the charged aerosol with the average unit charge per particle
down to the lowest value, ~108 cm−3 needed to sustain
the laser chemical reaction. An increase in the coagulation time results in
continuous spreading of the initial particle size distribution in the direction
of larger particles and in a fall of the aerosol, concentration because
electrostatic scattering is accelerated by the coagulation and precipitation of
the particles.Time dependencies of the concentrationNesc (a) of a unipolarlycharged
aerosol with the average unit elementary charge per particle
under electrostatic scattering conditions and (b) of the ratio of the change
in the total particle concentration N in the medium, which experiences
coagulation and precipitation, to the change in the concentration Nesc of
the particles which remain in the medium after electrostatic scattering,
plotted as a function of the average size rg of the particles participating in
these processes, calculated for q  = e (dashed curve), l.l e (dotted curve),
and 1.3 e (chain curve).
(a)(b)A comparison of the change, during the selected time step, in the
concentration of the particles remaining in the medium after electrostatic
scattering with the change in the total concentration of the particles in the
medium undergoing coagulation and precipitation shows (Figure3(b)) that,
beginning from the particle radius r~0.2 μm, such coagulation and
precipitation in an aerosol predominate strongly over electrostatic scattering,
irrespective of the particle charge. When the selected time step is relatively
large, t≥1000 seconds, so that the particles reach micron
sizes, and particle precipitation begins to predominate over coagulation, as
demonstrated in [13]. Therefore, in describing the gradual degradation of
two-phase active media of lasers, it is necessary to take into account all
three processes—electrostatic scattering, coagulation, and precipitation—which
compete in different ways during different time intervals.If the criteria
for optical transparency of the active medium to the laser radiation are
assumed to beIabs/I0≪1  and Isc/I0≪1 (Iabs, Isc, and I0 are the intensities of the absorbed, scattered, and
incident radiations), we can estimate the maximum permissible lifetime of a
two-phase active medium of the investigated laser. The strongest scattering of
the λ=3.3 μm radiation corresponds to the aluminum particle radius r = 0.6 μm and, consequently, the criteria selected by us can
be satisfied if the final size distribution n(r)  excludes almost completely particles of this radius.It follows from
Figure4 which gives the distributions n(r) calculated at different instants in
time, taking account all the processes resulting in the aging of a neutral
aluminum aerosol in the active medium of an HF laser, that the condition  n(r=0.6μm)/N0≪1 is well satisfied for t = 250 seconds. For a longer time
interval, for example, t = 300 seconds, numerical calculations give an aluminum
particle concentration ~3 × 103 cm−3 with the impermissible
radius r = 0.6 μm. The dashed curve in Figure 4 represents the
particle size distribution calculated ignoring precipitation. We can see that
the proportion of the large particles in the size distribution increases, and
consequently, the lifetime of an aerosol with the specified parameters
decreases further by 50 seconds.Figure 4
Particle size distributionn(r) at different limiting
time moments, calculated by taking account of coagulation and
precipitation (continuous curves) and ignoring precipitation
(dotted curve) of an aluminum aerosol in the active medium of
a pulsed HF laser.Thus, the above analysis of the
processes resulting in degradation of the disperse component of two-phase laser
active media allows us to draw the following main conclusions.(i)
The lifetime of two-phase active media with specified
properties is determined by electrostatic scattering, coagulation, and
precipitation of the aerosol when the real particle size distribution function
is taken into account.(ii)
An analysis of the optics and laser-chemical kinetics
makes it possible to recommend an aluminum aerosol with the parametersr0 =  0.09–0.4 μm and N = 107–109 cm−3 for a two-phase active medium of the
HF laser.(iii)
The calculated lifetime of the HF mixture with disperse Al particles, characterized by the
properties given above, is 250 seconds.


### 2.6. Aerosol-Evaporation Reactor Cavity

In the previous sections, we have determined the
aerosol properties satisfying the laser active medium and their dynamics over
time. We have considered, also, the first experiments on the formation of a
gaseous disperse medium of a pulsed chemical H2–F2 laser.
However, there remains an unsolved
problem of generating a relatively large volume (in excess of 103 cm3)
of the active medium of such a laser amplifier and filling this volume
homogeneously with a submicron monodisperse metal aerosol which has specified
properties. An analysis of the aerosol optics and laser-chemical kinetics of
the relevantPBCR shows that the ranges of the permissible parameters of
the disperse component in which oscillation is possible in an HF laser are as
follows: the radius of passivated
aluminum particles should be r0 = 0.09–0.4 μm, and their concentration should
be N0 = 109–107 cm−3.The simplest method for the formation of a two-phase
active medium is atomization of a previously prepared fine powder. However,
when this method is used, it is impossible to ensure the optimal parameters of
the dispersion, size, and concentration of the particles, and also the
homogeneity of the filling (because, e.g., of particle agglomeration). Moreover, coagulation, gravitational precipitation,
and electrostatic scattering of the injected particles result in continuous
variation of the parameters of the disperse component and, consequently, in
deterioration of the output characteristics of the laser amplifier or even
suppression of lasing. An analysis of the degradation processes in a two-phase
active medium of an HF laser shows that, within these ranges of the parameters,
the lifetime of the active mixture containing disperse aluminum particles isτcoag=250 seconds.Experiments [10] have demonstrated stability of a
fluorine-hydrogen mixture with an injected highly disperse component (Al
particles with r0  = 0.2–1 μm and concentration N0 =  105 cm−3) against spontaneous self-inflammation and
that a chain reaction can be initiated by evaporating such particles by IR
laser radiation. On the other hand, these experiments reveal that in order to
achieve lasing and a full-scalePBCR,  it is necessary to employ
improved methods for the formation of a gas-disperse medium with the required
parameters and for homogeneous filling of large working volumes in a short
time. For example, in a time interval t<τcoag=250 seconds, it is
necessary to form an aerosol with specified properties and to inject a gaseous
mixture into the active volume of the laser. The time needed to fill this
volume with an H2–F2 mixture, and to ensure its
homogeneous mixing amounts is,
3-4 minutes in the
experiments, and consequently, no more than 10 seconds remain for the formation of the aerosol.A solution to this problem, proposed below, involves
adoption of a fundamentally new method for the preparation of a two-phase
active medium of a pulsed HF laser in an aerosol reactor coupled structurally
to an unstable telescopic cavity. The use of such a closed HF
oscillator-amplifier system, based on aPBCR and containing a device for
the generation of a homogeneous aerosol, reduces considerably the time needed
for the formation of a two-phase active medium and ensures that the disperse
component has the necessary parameters. On the other hand, this system requires an
external-pulsed energy source, and it is promising primarily for experimental
research on the implementation of aPBCR and investigation of this
reaction. The method may be of practical interest also for the improvement of
metal vapor lasers and the nascent new aerosol laser technologies [17].The basic design of the proposed laser amplifier with a two-phase active
medium is shown in Figure5. This laser
amplifier consists of an unstable telescopic cavity (1), which is structurally coupled to an aerosol reactor (2). The front cavity mirror has an
aperture for coupling to a master oscillator (3). The aerosol reactor is in the form of a demountable
cylindrical chamber made of heat-resistant quartz glass. Plasma deposition or
some other method is used to deposit, on the inner wall of this chamber, an
aluminum film (4) of the
required thickness. This metal film can extend over the whole length of the
aerosol reactor (Figure 5(a)), or it may form a closed ring of limited length
at the center of the internal wall of the quartz glass chamber (Figure 5(b)).
The aerosol chamber variant with a limited length of the evaporated film is
preferable from the point of view of preventing contamination of the end walls
of the chamber by the metal, which is not permissible when the chamber is used
inside the laser cavity to generate a two-phase active medium. The metal film
is subjected to a homogeneous electromagnetic field generated in a solenoid (5) and evaporated, so that it mixes with
the atmosphere of a low-pressure carrier gas (helium). The reactor contains
also a power supply and a capacitor bank. The linear dimensions of the chamber
are governed by the cavity parameters.Simplified basic designs of a laser with (a) an aerosolevaporation
reactor and (b) an aerosol reactor with a limited length
of the evaporated film :d1,2 are the cavity mirror diameters; lc is
the cavity length; F is the focal length of the output mirror; l is the
reactor length; (1) unstable telescopic cavity; (2) aerosol reactor; (3)
master oscillator; (4) evaporated film; (5) solenoid; (6) gassupply
pipes.
(a)(b)Let us now
consider the formation of a two-phase laser active medium in the aerosol
reactor. A bank of capacitors with a calculated capacitanceC is
discharged over a short time interval by closing the circuit. The discharge
excites the solenoid, which has the following parameters: its length is lL, the number of turns is NL, the wire cross-section is SL, and the resistance of the primary winding is R1. A homogeneous magnetic flux Φ  is generated inside a closed region surrounded
by the primary winding whose inductance is L1.  This flux is sufficient for the evaporation,
over a short time interval, of the metal film, where the film acts also as a
secondary winding whose resistance is R2. The metal vapor spreads in the surrounding cold gaseous He, then
condenses to submicron metal particles. The metal can be prevented from
reaching the end faces of the chamber, and the region with aluminum vapor can
be filled homogeneously if the film is evaporated under the conditions of
laminar flow of the carrier gas through pipes (6) placed at the ends of the chamber (2). A small amount of oxidant (O2) injected into the
reactor after condensation of the metal vapor produces an oxide film on the
surfaces of the aluminum particles. Such an oxide film is 5–10 nm thick and
prevents spontaneous self-inflammation of the fluorine-hydrogen working mixture
of the laser. The necessary average size
of the resultant particles and their concentration are ensured by varying the
thickness of the initial metal film and by suitable selection of the electric
parameters of the apparatus. The aerosol chamber variant with a limited length
of the evaporated film (Figure 5(b)) has an additional advantage that it is possible to vary the aerosol
parameters by altering the evaporated film length.The evaporation of an aluminum
film with a given massm0 =  0.1 g requires an energy ΔE=Levm0≈1088J. Calculations show that a solenoid with a primary
winding made of copper wire 4 mm in diameter and containing NL=50 turns, in combination with a capacitor of capacitance C =  10 μF subjected to a voltage Uc
=  50 kV, can ensure evaporation of this film over a time τev=1/(2γ)≈0.217 millisecond. The same results can be obtained for a lower
voltage across the capacitor, for example, Uc = 18 kV, if the
selection is made of a solenoid with a primary winding consisting of wires with
a small diameter (1.5 mm) when the number of turns is NL =  4. The energy stored
in the capacitor is then EC = 1620 J, which is sufficient to
evaporate the film and to compensate for the energy lost in heating the wires
in the primary winding and for the heat lost to the ambient gas and to the
chamber walls. The variant with a small number of primary winding turns in the
solenoid corresponds to an aerosol reactor with an evaporated film of finite
length (Figure 5(b)), which is preferable for intracavity use.Discharge of a capacitor which stores this energy
results in slight heat dissipation in the primary winding of the solenoid as
well. Consequently, the primary winding temperature rises byΔT=EC/CpmCu≈40°C, where Cp  and mcu
are the specific heat and mass of a copper wire in the primary winding. Film
evaporation is accompanied also by the loss of heat to the ambient gas and to
the quartz-glass chamber walls. Let us ignore the energy lost as a result of
heat conduction in the gas and estimate the upper limit to the heat lost to the
chamber walls from the film being evaporated. The depth Δh of penetration of heat into
quartz glass over the course of diffusive heat exchange with the heated film
during the total evaporation time τev≈0.217 millisecond is Δh=2χτev≈2 × 10−5 m, where χ  is the thermal diffusivity of quartz glass.
The energy lost through the chamber walls in the case of a four-turn solenoid
does not exceed ΔQ=Δm1CplΔT1≈500J, where Δm1  is the mass of the heated
chamber wall, Cgl is the specific heat of quartz glass, and ΔT1  is the temperature drop at the
film-glass interface. The newly-formed aluminum vapor expands adiabatically
inside the reactor and experiences a condensation  “jump” accompanied by the
formation of clusters with critical radius rcr
and high
concentration (Table 2) in a short time of τ≈1  microsecond. The evolution of these clusters at
various ambient gas pressures is illustrated in Figure 6 and Table 2. It
follows from our calculations that the time t*  needed for the
formation, over the course of condensation, of particles with final radius r0 is  ~50–150 microseconds,
which corresponds to the time of attainment of the balance between the masses
of the evaporated film on one hand and of the clusters and vapor on the other.
The growth of these particles in the range of radii from  rcr to r0≈0.1 μm occurs at a practically constant and maximum
concentration N0 (Figure 6(b)), which makes it easier to
satisfy the condition on  r0 for a two-phase active medium of
an HF laser. For large particles, 0.1μm<r0≤rmax=0.5μm, the particle
(cluster) concentration N0 rapidly falls to ~105 cm−3, and the attenuation of the generated IR radiation is then
slight. It follows that condensation of the aluminum vapor in 50–150 microseconds
produces a polydisperse aerosol with a distribution of the particle radii close
to a “step” (Figure 6(b)). The width of this step matches the particle radius
range of rcr≈1nm≤r0≤0.1μm.Table 2
Results of numerical calculations of the formation of
a two-phase active medium and of the output characteristics of an HF laser.  Here,PHe is the buffer
(carrier) gas pressure; rcr  and  r0 are the
critical and final radii of the condensed particles; N0 is the particle
concentration; t*  is the time needed for the formation of
particles with the final radius r0; Eout  and Esp  are the total and specific energies of the output
radiation pulses; Pmax  is the maximum output power; τp is the
duration of the output pulse; and kamp  is the energy gain.
PHe/torr104rcr/μmr0/μm10−7N0/cm−3t*/μsEout /JEsp/J L−110−10Pmax/Wτp/ns10−4kamp3009.40.27651341076141.231.97367.14009.50.1981080.51465192.262.07169.7600110.1581357.61485194.921.5737.69.9(a) Evolution of clusters in time and (b) distribution of the
concentration of the particles formed by the condensation of Al vapor,
described in terms of the particle sizeNp(rp), calculated for helium buffer
(carrier) gas pressures PHe  =  600 torr (1), 400 torr (2), and 300 torr (3).
(a)(b)A fast reaction of aluminum with oxygen added to helium
occurs on the surfaces of the growing clusters:4Al+3O2→2Al2O3. The result is a
dense protective Al2O3 film, 5–0 nm thick, on
the particle surfaces. This film prevents spontaneous self-inflammation of the
working mixture of the laser during the dark reactions. It was demonstrated
experimentally in [10] that mixing of passivated aluminum particles—~0.5 μm in diameter and with a concentration ~105 cm—with a
laser-active mixture of the composition H2 : F2 : O2 : He
= 50 : 114 : 11 : 635 torr does not increase the rate of accumulation of the HF
molecules, and such a mixture has the required long-term stability.


### 2.7. Beam Stability of A Chemically-Active Aerosol

The off-resonant initiation
mechanism of a PBCR by laser evaporation of ultradisperse metal particles
injected into a laser active medium imposes restrictions from below and above
on the radiation intensity of the master oscillator. On the one hand, the
intensity of the input radiation should be sufficient for effective evaporation
of submicron metal particles, and on the other hand, it should be below the
threshold intensity of the optical breakdown of an H2–F2 laser gas-disperse active medium. The kinetics of plasma formation in the laser
infrared radiation field has been studied for gas-disperse fluorine containing
media in [8].The
limiting factors for maximum values of the output energy of HF/DF laser based
on a PBCR are only the beam stability of the laser active medium and the cavity
mirrors. The thresholds for optical breakdown are as follows.(i)
Beam stability of metallic
mirrors from molybdenum and copper, at a pulse duration of 100 nanoseconds,Ethr~100 J/cm2,  that is, Ithr~109 W/cm2 (Ethr and Ithr are threshold energy and
intensity).(ii)
Optical breakdown threshold
of the laser active medium isIthr~1010 W/cm2
(τthr~10 nanoseconds).(iii)
Optical breakdown threshold
of raw air isIthr~2⋅109W/cm2.(iv)
Optical breakdown threshold
of purified air isIthr≥1010W/cm2.


## 2.1. Kinetic Scheme

The initiation of a PBCR in an active medium of H2–F2-laser amplifier, containing
passivated fine aluminum particles covered by an oxide film with a thickness ~5–10 nm, occurs by the mechanism offered in [1, 2, 8]
for a pulsed HF generator. These aluminum particles are evaporated under
the action of laser radiation, resulting in the appearance of free Al atoms.
These atoms diffuse into the gas, and the photon-branching process begins. The
initiation can be described by the following scheme:(1)Al(solid)+nℏω→Al(gas),Al(gas)+F2(gas)→AlF+F. After the appearance of free F atoms, the atoms then
diffuse into the gas, and the chain reaction starts, leading to the formation
of vibrationally excited HF molecules and, further, to generation of new
photons:(2)F+H2→HF*+H,H+F2→HF*+F,HF*→HF+ℏω. Some of the emitted photons are absorbed, which leads to  the formation
of new free Al atoms, while other emitted photons contribute to the net laser
energy gain. The progressive growth of photons and free atoms takes place over
time, and all of the particles (photons and free F and Al atoms) participate in
active chain reactions. A reaction of this type is called a PBCR. This
idea has been validated by computer calculations based on the solution of a
system of differential equations of chemical kinetics, vibrational relaxation
transfer of laser radiation, and laser evaporation of particles [1–8].The advantages of using fine disperse particles of metals or other elements as the laser-active
media are as follows.(i)
High, in principle, concentrations of
free atoms.(ii)
Short time for producing high
concentration of free atoms.(iii)
Uniformity of filling large active
volumes with free atoms.(iv)
Universality
(ability to use various atoms).(v)
High
specific surface area of the particles, exceeding the area of the walls (e.g.,
a discharge chamber), which increases the rate of depopulation of the lower
active level. The properties of an
aerosol as an active medium of a pulsed chemical HF laser based on a
photon-branched reaction should satisfy a number of requirements, which can be
divided into two independent groups. These groups are as follows.(i)
The requirements imposed by the
conditions for sustaining the photon-branched chain reaction in an  H2–F2 mixture with fine disperse particles.(ii)
Those
imposed by the aerosol optics.


## 2.2. Laser Evaporation of Particles

The formation of active
centers of the chain reaction is achieved through the fast reaction of a
fluorine molecule with an evaporated aluminum atom from the surface of a
disperse particle under the action of external IR-laser radiation:(3)Al(gas)+F2→AlF+F.The characteristic time of
this reaction is≤10−9 s at the concentration [F2]≥1018 cm−3. Laser heating and evaporation of the disperse component can be
described within the approximation of free molecular flow, which is valid for
particles whose size
does not exceed the mean free path of molecules in a laser mixture (see, e.g.,
[8]): (4)4πr02dr0dtρ0=−η4πr02V¯s(Ts)ρs(Ts),43πr03ρ0CsdTsdt=σabsI−(Ts−Tg)∑MCM4πr02nmV¯M(Tg)+Levap4πr02dr0dtρ0. Here, Cs  and Levap  are, respectively, the specific heat and heat of
evaporation of aluminum; I is the radiation intensity inside the cavity; σabs is the cross-section of absorption of laser
radiation by an Al particle; Ts and Tg are
the temperatures of the aluminum particles and the laser active medium,
respectively; CM, V¯M,  and nM are, respectively, the molar specific heat,
average velocity, and concentration of the molecules of the Mth
component of the laser mixture; η is the accommodation coefficient; V¯s is the average velocity of the vapor
molecules; ρs(Ts) is the saturated vapor density of aluminum at  Ts.


## 2.3. Optimal Concentration of Particles

Formation of active centers
of the reaction chain and their spreading into the medium is thus possible around each fine
particle in the IR laser radiation field. The distribution of free atoms in the
active volume can become sufficiently homogeneous in a timeτh, which is limited by the duration of the laser chemical process (~1 microsecond),
provided that the condition Rev≤2Rdiff is satisfied, where Rev is the average distance between the particles, Rdiff~Dτh,
and D is the
diffusion coefficient
of the active centers in the laser medium. This sets the lower limit to the
required concentration of disperse particles as N0≈(1/Rev3).
Optimization of the aerosol parameters from the point of view of the laser chemical
process under the conditions of initiation of a pulsed HF amplifier was reported
in [8]. Calculations showed that the optimal concentration of aluminum
particles is NAl =  1.4 × 109 cm−3  for the radius r0=0.09 μm.


## 2.4. Optimal Particle Size

The optimal particle size is governed, for the
selected concentration, by the aerosol optics, so that the attenuation
coefficient of laser radiation representing scattering and absorption in a
disperse medium does not exceed the local active medium gainα. Calculations
of the optical characteristics of spherical disperse particles at a given
radiation wavelength λ were based on the Mie diffraction theory
and the single-scattering approximation [11].The Mie
formalism requires the use of two dimensionless input parameters,ρ=2πr0/ λ and δ=ρm, where m
is the relative value of the complex refractive index of the aerosol at the
wavelength λ. Computer
calculations of the dependences of the attenuation Katt,  scattering Ksc,  and absorption Kabs coefficients at the HF laser wavelength (λ =   3.3 μm) in the size
range r0  =    0.5–1 μm of aluminum particles (m =  3.2−29.5i  at 300 K)
were performed in [2, 8] and plotted in Figure 1. It is evident from Figure 1(a) that for particle radii r0>0.5 μm, the scattering coefficient Ksc is considerably greater than the absorption coefficient Kabs,
that is, lasing is impossible in such a strong scattering medium. Figure 1(b)
demonstrates, on a much larger scale, the region of intersection of the Ksc(r0) and Kabs(r0) curves.  The absorption of IR radiation predominates
over the scattering by aluminum particles, Kabs(r0)≥Ksc(r0), if r0≤0.15 μm. It follows
that the aerosol optics imposes stringent conditions on the maximum permissible
particle size in a two-phase active medium of the laser, which should satisfy
the condition ρ=2πr0/λ<1. An aluminum aerosol with the parameters r0 =  0.09–0.4 μm and NAl
=  107–109 cm−3  can be recommended as a model two-phase active medium of an HF laser based on a
PBCR.Dependencies of the attenuationKatt (1), scattering Ksc
(2), and absorption Kabs (3) coefficients at the HF-laser wavelength
(λ=3.3μm) for (a) the size r0 = 0.5–1 μm of aluminum particles (m
= 3.2–29.5i at 300 K) and (b) the region of intersection of curves
2 and 3 shown on an enlarged scale.
(a)(b)


## 2.5. Lifetime of A Disperse Component

The main disadvantage of lasers
with two-phase active media is
the fast degradation of the disperse component and the consequent short
lifetime of the active medium with specified properties. Continuous variation
of the properties of the disperse phase with time results in a deterioration of
the output characteristics of a laser or in complete quenching of the laser
action.The first
attempt to model degradation of the disperse phase in a laser active medium was
made for the operating conditions in a pulsed chemical HF laser [12]. The degradation processes are practically the
same for all types of lasers with disperse media. We adopted an approximate
coagulation model [13] and assumed the Stokes law. In the first approximation,
we studied the time dependence
of the overall characteristics of an aerosol in a laser active medium,
including the average size and the total concentration of disperse particles,
and we also calculated the formation time and lifetime of a two-phase active
medium of an HF laser with the given parameters.The processes occurring in a gaseous
medium containing a disperse aerosol may be modeled on the assumption of
coagulation, precipitation, and (in the presence of electric charges)
electrostatic scattering of disperse particles. Aerosol coagulation was
described by the lognormal quasi-self-sustaining model of [14], based on an
approximation in which a lognormal model [15] and high-current sectional model,
conserving the square of the particle volume, [16] are adopted. Here, the particle size distribution is described by the
standard lognormal function.The
precipitation of particles was taken into account on the basis of the following
model assumptions. The active medium was taken to be ideally mixed, continuous,
incompressible, and characterized by a finite viscosity. The particle shape was
assumed to be spherical. All these assumptions were to apply the Stokes law to the
aerosol precipitation. The concentration of the disperse component remaining in
the medium after particle precipitation was calculated from(5)Nprec=N0exp(−vt)H, where H is the transverse size of the active
medium of the HF laser, assumed to be equal to the diameter of the larger
cavity mirror.An analysis of
the influence of the induced electrostatic charge of fine disperse particles of
a conducting aerosol on the rate of its degradation was made within the overall
framework of the problem of the lifetime of a two-phase active medium. The
formation of a metal aerosol is practically always accompanied by its charging,
for example, as a result of thermionic and photoemission of electrons. The
concentration of the aerosol remaining after electrostatic scattering of the
particles with the same charge and of the same size can be found from
expression:(6)Nesc=N01+4πq2BN0t, where B is average mobility of
the particles.Specific calculations were
carried out for a standard active mixture of the composition H2 : F2 : O2 : He
= 100 : 400 : 40 : 210 torr, into which an aluminum aerosol was injected in advance.
At the initial time t  =  0, the aerosol was assumed to be
quasi-monodisperse with the average initial radius r0  = 0.05 μm and
concentration N0 =  2 × 109 cm−3.Fast
coagulation, with the constantβ =  5 × 10−10 cm3s−1 (Figure 2) and sticking probability practically equal to unity for a submicron
aerosol, results in continuous enlargement of the particles with a certain size
distribution. The time for the
establishment of a self-sustaining lognormal particle size distribution in the investigated
two-phase active medium is about 25 seconds. Figure 2 shows the dependencies of coagulation
and electrostatic scattering constants on the particle size. We can see that an
increase in the average charge alters slightly the coagulation constant; this
effect is significant only for small (r<0.1 μm) particles. For an aerosol with r =  0.05 μm, the constants of these processes are
comparable, and the rate of electrostatic scattering of the charged particles
exceeds the rate of coagulation of the neutral particles only if the average
charge is q≥1.3e. Therefore, at the first instant,
such electrostatic scattering of submicron-charged particles competes with
their coagulation, which results in a rapid loss of the particles from the
volume of the active medium.Figure 2
Dependencies of the coagulation constant of neutral particlesβ, the coagulation constant of charged particles βq, and aerosol
electrostatic scattering constant βesc on the particle radius r for the
average induced unipolar charge q = e  (dashed curve), 1.1 e (dotted curve)
and 1.3 e  (chain curve).It follows from
Figure3(a) that during the first 50 seconds, there is a strong fall of the
concentration of the charged aerosol with the average unit charge per particle
down to the lowest value, ~108 cm−3 needed to sustain
the laser chemical reaction. An increase in the coagulation time results in
continuous spreading of the initial particle size distribution in the direction
of larger particles and in a fall of the aerosol, concentration because
electrostatic scattering is accelerated by the coagulation and precipitation of
the particles.Time dependencies of the concentrationNesc (a) of a unipolarlycharged
aerosol with the average unit elementary charge per particle
under electrostatic scattering conditions and (b) of the ratio of the change
in the total particle concentration N in the medium, which experiences
coagulation and precipitation, to the change in the concentration Nesc of
the particles which remain in the medium after electrostatic scattering,
plotted as a function of the average size rg of the particles participating in
these processes, calculated for q  = e (dashed curve), l.l e (dotted curve),
and 1.3 e (chain curve).
(a)(b)A comparison of the change, during the selected time step, in the
concentration of the particles remaining in the medium after electrostatic
scattering with the change in the total concentration of the particles in the
medium undergoing coagulation and precipitation shows (Figure3(b)) that,
beginning from the particle radius r~0.2 μm, such coagulation and
precipitation in an aerosol predominate strongly over electrostatic scattering,
irrespective of the particle charge. When the selected time step is relatively
large, t≥1000 seconds, so that the particles reach micron
sizes, and particle precipitation begins to predominate over coagulation, as
demonstrated in [13]. Therefore, in describing the gradual degradation of
two-phase active media of lasers, it is necessary to take into account all
three processes—electrostatic scattering, coagulation, and precipitation—which
compete in different ways during different time intervals.If the criteria
for optical transparency of the active medium to the laser radiation are
assumed to beIabs/I0≪1  and Isc/I0≪1 (Iabs, Isc, and I0 are the intensities of the absorbed, scattered, and
incident radiations), we can estimate the maximum permissible lifetime of a
two-phase active medium of the investigated laser. The strongest scattering of
the λ=3.3 μm radiation corresponds to the aluminum particle radius r = 0.6 μm and, consequently, the criteria selected by us can
be satisfied if the final size distribution n(r)  excludes almost completely particles of this radius.It follows from
Figure4 which gives the distributions n(r) calculated at different instants in
time, taking account all the processes resulting in the aging of a neutral
aluminum aerosol in the active medium of an HF laser, that the condition  n(r=0.6μm)/N0≪1 is well satisfied for t = 250 seconds. For a longer time
interval, for example, t = 300 seconds, numerical calculations give an aluminum
particle concentration ~3 × 103 cm−3 with the impermissible
radius r = 0.6 μm. The dashed curve in Figure 4 represents the
particle size distribution calculated ignoring precipitation. We can see that
the proportion of the large particles in the size distribution increases, and
consequently, the lifetime of an aerosol with the specified parameters
decreases further by 50 seconds.Figure 4
Particle size distributionn(r) at different limiting
time moments, calculated by taking account of coagulation and
precipitation (continuous curves) and ignoring precipitation
(dotted curve) of an aluminum aerosol in the active medium of
a pulsed HF laser.Thus, the above analysis of the
processes resulting in degradation of the disperse component of two-phase laser
active media allows us to draw the following main conclusions.(i)
The lifetime of two-phase active media with specified
properties is determined by electrostatic scattering, coagulation, and
precipitation of the aerosol when the real particle size distribution function
is taken into account.(ii)
An analysis of the optics and laser-chemical kinetics
makes it possible to recommend an aluminum aerosol with the parametersr0 =  0.09–0.4 μm and N = 107–109 cm−3 for a two-phase active medium of the
HF laser.(iii)
The calculated lifetime of the HF mixture with disperse Al particles, characterized by the
properties given above, is 250 seconds.


## 2.6. Aerosol-Evaporation Reactor Cavity

In the previous sections, we have determined the
aerosol properties satisfying the laser active medium and their dynamics over
time. We have considered, also, the first experiments on the formation of a
gaseous disperse medium of a pulsed chemical H2–F2 laser.
However, there remains an unsolved
problem of generating a relatively large volume (in excess of 103 cm3)
of the active medium of such a laser amplifier and filling this volume
homogeneously with a submicron monodisperse metal aerosol which has specified
properties. An analysis of the aerosol optics and laser-chemical kinetics of
the relevantPBCR shows that the ranges of the permissible parameters of
the disperse component in which oscillation is possible in an HF laser are as
follows: the radius of passivated
aluminum particles should be r0 = 0.09–0.4 μm, and their concentration should
be N0 = 109–107 cm−3.The simplest method for the formation of a two-phase
active medium is atomization of a previously prepared fine powder. However,
when this method is used, it is impossible to ensure the optimal parameters of
the dispersion, size, and concentration of the particles, and also the
homogeneity of the filling (because, e.g., of particle agglomeration). Moreover, coagulation, gravitational precipitation,
and electrostatic scattering of the injected particles result in continuous
variation of the parameters of the disperse component and, consequently, in
deterioration of the output characteristics of the laser amplifier or even
suppression of lasing. An analysis of the degradation processes in a two-phase
active medium of an HF laser shows that, within these ranges of the parameters,
the lifetime of the active mixture containing disperse aluminum particles isτcoag=250 seconds.Experiments [10] have demonstrated stability of a
fluorine-hydrogen mixture with an injected highly disperse component (Al
particles with r0  = 0.2–1 μm and concentration N0 =  105 cm−3) against spontaneous self-inflammation and
that a chain reaction can be initiated by evaporating such particles by IR
laser radiation. On the other hand, these experiments reveal that in order to
achieve lasing and a full-scalePBCR,  it is necessary to employ
improved methods for the formation of a gas-disperse medium with the required
parameters and for homogeneous filling of large working volumes in a short
time. For example, in a time interval t<τcoag=250 seconds, it is
necessary to form an aerosol with specified properties and to inject a gaseous
mixture into the active volume of the laser. The time needed to fill this
volume with an H2–F2 mixture, and to ensure its
homogeneous mixing amounts is,
3-4 minutes in the
experiments, and consequently, no more than 10 seconds remain for the formation of the aerosol.A solution to this problem, proposed below, involves
adoption of a fundamentally new method for the preparation of a two-phase
active medium of a pulsed HF laser in an aerosol reactor coupled structurally
to an unstable telescopic cavity. The use of such a closed HF
oscillator-amplifier system, based on aPBCR and containing a device for
the generation of a homogeneous aerosol, reduces considerably the time needed
for the formation of a two-phase active medium and ensures that the disperse
component has the necessary parameters. On the other hand, this system requires an
external-pulsed energy source, and it is promising primarily for experimental
research on the implementation of aPBCR and investigation of this
reaction. The method may be of practical interest also for the improvement of
metal vapor lasers and the nascent new aerosol laser technologies [17].The basic design of the proposed laser amplifier with a two-phase active
medium is shown in Figure5. This laser
amplifier consists of an unstable telescopic cavity (1), which is structurally coupled to an aerosol reactor (2). The front cavity mirror has an
aperture for coupling to a master oscillator (3). The aerosol reactor is in the form of a demountable
cylindrical chamber made of heat-resistant quartz glass. Plasma deposition or
some other method is used to deposit, on the inner wall of this chamber, an
aluminum film (4) of the
required thickness. This metal film can extend over the whole length of the
aerosol reactor (Figure 5(a)), or it may form a closed ring of limited length
at the center of the internal wall of the quartz glass chamber (Figure 5(b)).
The aerosol chamber variant with a limited length of the evaporated film is
preferable from the point of view of preventing contamination of the end walls
of the chamber by the metal, which is not permissible when the chamber is used
inside the laser cavity to generate a two-phase active medium. The metal film
is subjected to a homogeneous electromagnetic field generated in a solenoid (5) and evaporated, so that it mixes with
the atmosphere of a low-pressure carrier gas (helium). The reactor contains
also a power supply and a capacitor bank. The linear dimensions of the chamber
are governed by the cavity parameters.Simplified basic designs of a laser with (a) an aerosolevaporation
reactor and (b) an aerosol reactor with a limited length
of the evaporated film :d1,2 are the cavity mirror diameters; lc is
the cavity length; F is the focal length of the output mirror; l is the
reactor length; (1) unstable telescopic cavity; (2) aerosol reactor; (3)
master oscillator; (4) evaporated film; (5) solenoid; (6) gassupply
pipes.
(a)(b)Let us now
consider the formation of a two-phase laser active medium in the aerosol
reactor. A bank of capacitors with a calculated capacitanceC is
discharged over a short time interval by closing the circuit. The discharge
excites the solenoid, which has the following parameters: its length is lL, the number of turns is NL, the wire cross-section is SL, and the resistance of the primary winding is R1. A homogeneous magnetic flux Φ  is generated inside a closed region surrounded
by the primary winding whose inductance is L1.  This flux is sufficient for the evaporation,
over a short time interval, of the metal film, where the film acts also as a
secondary winding whose resistance is R2. The metal vapor spreads in the surrounding cold gaseous He, then
condenses to submicron metal particles. The metal can be prevented from
reaching the end faces of the chamber, and the region with aluminum vapor can
be filled homogeneously if the film is evaporated under the conditions of
laminar flow of the carrier gas through pipes (6) placed at the ends of the chamber (2). A small amount of oxidant (O2) injected into the
reactor after condensation of the metal vapor produces an oxide film on the
surfaces of the aluminum particles. Such an oxide film is 5–10 nm thick and
prevents spontaneous self-inflammation of the fluorine-hydrogen working mixture
of the laser. The necessary average size
of the resultant particles and their concentration are ensured by varying the
thickness of the initial metal film and by suitable selection of the electric
parameters of the apparatus. The aerosol chamber variant with a limited length
of the evaporated film (Figure 5(b)) has an additional advantage that it is possible to vary the aerosol
parameters by altering the evaporated film length.The evaporation of an aluminum
film with a given massm0 =  0.1 g requires an energy ΔE=Levm0≈1088J. Calculations show that a solenoid with a primary
winding made of copper wire 4 mm in diameter and containing NL=50 turns, in combination with a capacitor of capacitance C =  10 μF subjected to a voltage Uc
=  50 kV, can ensure evaporation of this film over a time τev=1/(2γ)≈0.217 millisecond. The same results can be obtained for a lower
voltage across the capacitor, for example, Uc = 18 kV, if the
selection is made of a solenoid with a primary winding consisting of wires with
a small diameter (1.5 mm) when the number of turns is NL =  4. The energy stored
in the capacitor is then EC = 1620 J, which is sufficient to
evaporate the film and to compensate for the energy lost in heating the wires
in the primary winding and for the heat lost to the ambient gas and to the
chamber walls. The variant with a small number of primary winding turns in the
solenoid corresponds to an aerosol reactor with an evaporated film of finite
length (Figure 5(b)), which is preferable for intracavity use.Discharge of a capacitor which stores this energy
results in slight heat dissipation in the primary winding of the solenoid as
well. Consequently, the primary winding temperature rises byΔT=EC/CpmCu≈40°C, where Cp  and mcu
are the specific heat and mass of a copper wire in the primary winding. Film
evaporation is accompanied also by the loss of heat to the ambient gas and to
the quartz-glass chamber walls. Let us ignore the energy lost as a result of
heat conduction in the gas and estimate the upper limit to the heat lost to the
chamber walls from the film being evaporated. The depth Δh of penetration of heat into
quartz glass over the course of diffusive heat exchange with the heated film
during the total evaporation time τev≈0.217 millisecond is Δh=2χτev≈2 × 10−5 m, where χ  is the thermal diffusivity of quartz glass.
The energy lost through the chamber walls in the case of a four-turn solenoid
does not exceed ΔQ=Δm1CplΔT1≈500J, where Δm1  is the mass of the heated
chamber wall, Cgl is the specific heat of quartz glass, and ΔT1  is the temperature drop at the
film-glass interface. The newly-formed aluminum vapor expands adiabatically
inside the reactor and experiences a condensation  “jump” accompanied by the
formation of clusters with critical radius rcr
and high
concentration (Table 2) in a short time of τ≈1  microsecond. The evolution of these clusters at
various ambient gas pressures is illustrated in Figure 6 and Table 2. It
follows from our calculations that the time t*  needed for the
formation, over the course of condensation, of particles with final radius r0 is  ~50–150 microseconds,
which corresponds to the time of attainment of the balance between the masses
of the evaporated film on one hand and of the clusters and vapor on the other.
The growth of these particles in the range of radii from  rcr to r0≈0.1 μm occurs at a practically constant and maximum
concentration N0 (Figure 6(b)), which makes it easier to
satisfy the condition on  r0 for a two-phase active medium of
an HF laser. For large particles, 0.1μm<r0≤rmax=0.5μm, the particle
(cluster) concentration N0 rapidly falls to ~105 cm−3, and the attenuation of the generated IR radiation is then
slight. It follows that condensation of the aluminum vapor in 50–150 microseconds
produces a polydisperse aerosol with a distribution of the particle radii close
to a “step” (Figure 6(b)). The width of this step matches the particle radius
range of rcr≈1nm≤r0≤0.1μm.Table 2
Results of numerical calculations of the formation of
a two-phase active medium and of the output characteristics of an HF laser.  Here,PHe is the buffer
(carrier) gas pressure; rcr  and  r0 are the
critical and final radii of the condensed particles; N0 is the particle
concentration; t*  is the time needed for the formation of
particles with the final radius r0; Eout  and Esp  are the total and specific energies of the output
radiation pulses; Pmax  is the maximum output power; τp is the
duration of the output pulse; and kamp  is the energy gain.
PHe/torr104rcr/μmr0/μm10−7N0/cm−3t*/μsEout /JEsp/J L−110−10Pmax/Wτp/ns10−4kamp3009.40.27651341076141.231.97367.14009.50.1981080.51465192.262.07169.7600110.1581357.61485194.921.5737.69.9(a) Evolution of clusters in time and (b) distribution of the
concentration of the particles formed by the condensation of Al vapor,
described in terms of the particle sizeNp(rp), calculated for helium buffer
(carrier) gas pressures PHe  =  600 torr (1), 400 torr (2), and 300 torr (3).
(a)(b)A fast reaction of aluminum with oxygen added to helium
occurs on the surfaces of the growing clusters:4Al+3O2→2Al2O3. The result is a
dense protective Al2O3 film, 5–0 nm thick, on
the particle surfaces. This film prevents spontaneous self-inflammation of the
working mixture of the laser during the dark reactions. It was demonstrated
experimentally in [10] that mixing of passivated aluminum particles—~0.5 μm in diameter and with a concentration ~105 cm—with a
laser-active mixture of the composition H2 : F2 : O2 : He
= 50 : 114 : 11 : 635 torr does not increase the rate of accumulation of the HF
molecules, and such a mixture has the required long-term stability.


## 2.7. Beam Stability of A Chemically-Active Aerosol

The off-resonant initiation
mechanism of a PBCR by laser evaporation of ultradisperse metal particles
injected into a laser active medium imposes restrictions from below and above
on the radiation intensity of the master oscillator. On the one hand, the
intensity of the input radiation should be sufficient for effective evaporation
of submicron metal particles, and on the other hand, it should be below the
threshold intensity of the optical breakdown of an H2–F2 laser gas-disperse active medium. The kinetics of plasma formation in the laser
infrared radiation field has been studied for gas-disperse fluorine containing
media in [8].The
limiting factors for maximum values of the output energy of HF/DF laser based
on a PBCR are only the beam stability of the laser active medium and the cavity
mirrors. The thresholds for optical breakdown are as follows.(i)
Beam stability of metallic
mirrors from molybdenum and copper, at a pulse duration of 100 nanoseconds,Ethr~100 J/cm2,  that is, Ithr~109 W/cm2 (Ethr and Ithr are threshold energy and
intensity).(ii)
Optical breakdown threshold
of the laser active medium isIthr~1010 W/cm2
(τthr~10 nanoseconds).(iii)
Optical breakdown threshold
of raw air isIthr~2⋅109W/cm2.(iv)
Optical breakdown threshold
of purified air isIthr≥1010W/cm2.


## 3. Conclusions

The results presented in this
paper lead to the following main conclusions.(i)
An analysis of the
aerosol optics, based on the exact Mie diffraction theory, and the laser chemical kinetics of a PBCR have
been used to determine the range of the maximal permissible parameters of the
disperse component, which is capable of supporting the operation of a pulsed
chemical HF laser with a two-phase active medium, with particle radiusr0 = 0.09–0.4 μm  and particle
concentration N0 = 109–107 cm−3.(ii)
In this range of aerosol
parameters, the lifetime of the active medium of the HF laser with the disperse
Al particles is governed by the coagulation, precipitation, and electrostatic
scattering of particles occurring in the time range of~103 seconds.(iii)
The first experiments demonstrated the stability of a
fluorine-hydrogen mixture with an injected fine disperse component (Al
particles of radiusr0  = 0.2–1 μm with concentration  N0=105cm−3) under the conditions when spontaneous
combustion is possible. It was also shown that a chain reaction could be
initiated by the evaporation of particles under the action of IR radiation. The
corresponding numerical calculations let us conclude that in some experiments,
conducted in [13], the photon-branched chain reaction has been observed for the
first time. For a full-scale demonstration of the effect of the photon-branched
chain reaction, it is necessary to improve the technique of preparing the
gas-disperse medium as discussed above.(iv)
The optical
breakdown of a chemically active aerosol at the wavelength of the generated
radiation (λg=3.3μm) is characterized by the threshold intensity Ithr = 1–3 × 1010 W/cm2.



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*Source: 839873-2009-03-08.xml*