E-folding time

We expect an efficient a — Q-dynamo to be at work in the merger remnant. The differential rotation will wind up initial poloidal into a strong toroidal field ( Q-effect ), the fluid instabilities/convection will transform toroidal fields into poloidal ones and vice versa ( a—effect ). Usually, the Rossby number, Ro = is adopted as a measure of the efficiency of dynamo action in a star. In the central object we find Rossby numbers well below unity, 0.4, and therefore expect an efficient amplification of initial seed magnetic fields. A convective dynamo amplifies initial fields exponentially with an e-folding time given approximately by the convective overturn time, rc ss 3 ms the saturation field strength is thereby independent of the initial seed field (Nordlund et al. 1992). 

Data for vibrational-translational energy transfer are usually presented as a relaxation-time-pressure product pr, where r refers to the e-folding time... 

Figure 8 Oxidation of SO2 to SO4 in the Pinatubo stratospheric cloud. The total SO2 mass curve indicates the loss of SO2 by oxidation to sulfate aerosol according to an initial loading of 17 Tg of SO2 (after Read et at. (1993), and 3 Tg lower than the TOMS-only estimate of Bluth et al. (1992)) and a 33 d e-folding time. The circles indicate satellite measurements of stratospheric SO2 burden from Read et al. (1993). The total aerosol mass curve is obtained by modeling the aerosol mass generated by sulfate oxidation and an e-folding time for aerosol loss of 1 yr. The squares show estimates of the stratospheric aerosol mass from Baran et al. (1993). Daily rates of SO2 conversion and aerosol production are shown by the two other curves (labeled).

The residence time (or renewal time) is defined by the e-folding time, 1/e. In this example it is the time required for the difference between the concentration and its initial value to reach 63% of the difference between the initial and final values. The process of renewing the water in the pool is 63% of the way to completion. 

Thus, species A decays to He of its initial concentration in time t = /k. This time is referred to as the e-folding time of the reaction, or the mean lifetime of A against this reaction. 

If the time response is redefined as equal to the e-folding time, when 6 — X (20) may be simplified to... 

Fig. 5. Theoretical heat-transfer e-folding time and warm-temperature mass-transfer time, Model II gas thermometer. Cold-volume temperature change = 0.5°K.

Fig. 7. Measured e-folding time response, Model II gas thermometers.

Because P is negative, a is pure imaginary and the perturbations are unstable with e-folding time. The inertial instability develops in regions where the absolute vorticity fa has sign opposite to /. This derivation reduces to that for the stable inertial oscillation in the special case in which M = 0 and P = p. 

For instance, period (Pd), which is e-fold time, or time to change by a factor of e can be used and (1) becomes... 

The reactor is made critical with the rod to be calibrated in its most fully inserted position. The rod is then withdrawn a known amount and, after waiting for the flux to be represented by the dominant term ( 90 sec for most practical values of reactivity), the e-folding time of the reactor flux is measured. A control rod other than the one being calibrated is then used to return the reactor to criticality at a low flux. The rod being calibrated is then again withdrawn a known amount and the above procedure repeated. The reactivity equivalents of the periods can then be found from the computed curve (Fig. 3.6). 

Reactor critical at Reactor supercritical at Resulting e-folding time... 

---