Collisional relaxation time

A somewhat different aspect of the control of reactant species is the precise knowledge of reactant states that is often possible. For example, it is possible to assure that atomic ions (e.g., O are in their ground electronic states by virtue of having sufficient collisional relaxation time between formation and reaction. In favorable cases (e.g., N2 ) it is possible to assure that molecular ions are in their ground electronic and vibrational states. 

The simplest such collision operator is the lattice BGK (Bhatnagar-Gross-Krook) model [77], Cij = -Sij/x, where the collisional relaxation time t is related to the viscosity. Here we will work within the more general framework of the multirelaxation time (MRT) model [110], for which the lattice BGK model is a special case. 

Many optical studies have employed a quasi-static cell, through which the photolytic precursor of one of the reagents and the stable molecular reagent are slowly flowed. The reaction is then initiated by laser photolysis of the precursor, and the products are detected a short time after the photolysis event. To avoid collisional relaxation of the internal degrees of freedom of the product, the products must be detected in a shorter time when compared to the time between gas-kinetic collisions, that depends inversely upon the total pressure in the cell. In some cases, for example in case of the stable NO product from the H + NO2 reaction discussed in section B2.3.3.2. the products are not removed by collisions with the walls and may have long residence times in the apparatus. Study of such reactions are better carried out with pulsed introduction of the reagents into the cell or under crossed-beam conditions. 

The time constant r, appearing in the simplest frequency equation for the velocity and absorption of sound, is related to the transition probabilities for vibrational exchanges by 1/r = Pe — Pd, where Pe is the probability of collisional excitation, and Pd is the probability of collisional de-excitation per molecule per second. Dividing Pd by the number of collisions which one molecule undergoes per second gives the transition probability per collision P, given by Equation 4 or 5. The reciprocal of this quantity is the number of collisions Z required to de-excite a quantum of vibrational energy e = hv. This number can be explicitly calculated from Equation 4 since Z = 1/P, and it can be experimentally derived from the measured relaxation times. 

The possibility of deactivation of vibrationally excited molecules by spontaneous radiation is always present for infrared-active vibrational modes, but this is usually much slower than collisional deactivation and plays no significant role (this is obviously not the case for infrared gas lasers). CO is a particular exception in possessing an infrared-active vibration of high frequency (2144 cm-1). The probability of spontaneous emission depends on the cube of the frequency, so that the radiative life decreases as the third power of the frequency, and is, of course, independent of both pressure and temperature the collisional life, in contrast, increases exponentially with the frequency. Reference to the vibrational relaxation times given in Table 2, where CO has the highest vibrational frequency and shortest radiative lifetime of the polar molecules listed, shows that most vibrational relaxation times are much shorter than the 3 x 104 /isec radiative lifetime of CO. For CO itself radiative deactivation only becomes important at lower temperatures, where collisional deactivation is very slow indeed, and the specific heat contribution of vibrational energy is infinitesimal. Radiative processes do play an important role in reactions in the upper atmosphere, where collision rates are extremely slow. 

Since (1) and (2) will have different collisional efficiencies, the result will be a composite relaxation time for A, given by... 

Thus far we have dealt with the idealized case of isolated molecules that are neither -subject to external collisions nor display spontaneous emission. Further, we have V assumed that the molecule is initially in a pure state (i.e., described by a wave function) and that the externally imposed electric field is coherent, that is, that the " j field is described by a well-defined function of time [e.g., Eq. (1.35)]. Under these. circumstances the molecule is in a pure state before and after laser excitation and S remains so throughout its evolution. However, if the molecule is initially in a mixed4> state (e.g., due to prior collisional relaxation), or if the incident radiation field is notlf fully coherent (e.g., due to random fluctuations of the laser phase or of the laser amplitude), or if collisions cause the loss of quantum phase after excitation, then J phase information is degraded, interference phenomena are muted, and laser controi. is jeopardized. < f... 

From inspecting the atomic database of the EIRENE code [31], which is used in many applications to a large number of different tokamaks, including for the ITER design, in particular its collisional-radiative models for molecules, it was clear that matters can be more complicated. The relaxation time for establishing a vibrational distribution of the ground state molecule is comparable to the transport time of the molecule, hence the applicability of local collisional-radiative approximations is questionable. Furthermore, one of the two atoms created in dissociative recombination is electronically excited, and, hence, can be ionized very effectively even at low divertor plasma temperatures (instead of radiative decay). In this case, the whole chain of reactions would be just an enhanced ( molecular activated ) dissociation (MAD, i.e., dissociative excitation of those H]]", which have been produced... 

ADAS is centred on generalized collisional-radiative (GCR) theory. The theory recognizes relaxation time-scales of atomic processes and how these relate to plasma relaxation times, metastable states, secondary collisions etc. Attention to these aspects - rigorously specified in generalized collisional-radiative theory - allow an atomic description suitable for modeling and analyzing spectral emission from most static and dynamic plasmas in the fusion and astrophysical domains [3,4]. 

The formation of the triplet state can be directly followed in time through the observation of the transient triplet-triplet (T-T) absorption in flash or modulated photolysis or by the observation of the phosphorescence emission. A typical radiative lifetime of phosphorescence for simple carbonyls is 10 3 s. Therefore, it is extremely difficult to observe the "unrelaxed" phosphorescence emission without collisional relaxation, unless the triplet lifetime is significantly shortened by a competing radiationless process. Under these conditions, the correspondingly low quantum yield of phosphorescence makes such measurement rather difficult. Usually, "relaxed" phosphorescence from a molecule such as biacetyl is observed. Therefore, only the transient T-T absorption can provide useful data in the gas phase, although a determination of the absolute yield is rather involved and difficult. 

Short-range forces will give a collisional contribution that may be calculated in a similar way to energy relaxation times. 

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