Damping of transversal plasma-electron oscillations and waves in low-collision electron-ion plasmas
Previously developed method for finding asymptotic solutions of Vlasov equations using two-dimensional (in coordinate x and time t) Laplace transform is here applied to consider transversal oscillations and waves in low-collision quasi-neutral (n_i \simeq n_e) Maxwellian electron-ion plasmas. We obtain two branches of electron waves: the ubiquitous one of high-frequency and high-velocity oscillations and the unusual low-velocity one. Taking into account Coulomb collisions in the limit m_e << m_i, \bar{v_i} << \bar{v_e}, and T_e m_e << T_i m_i results in expressions for transversal plasma-electron oscillation/wave decrements with a damping of the low-velocity electron branch \sim n_i^{1/3}/\bar{v}_e^{4/3}, where n_i is the ion density and \bar{v}_e is the mean electron velocity. It ought to rehabilitate Vlasov principal value prescription for relevant integrals, but to supplement it with representation of an asymptotical solution as a sum of exponents (not a single one). "Non-damping" kinematical waves in low-collision plasma transform in the damping ones at reasonably chosen iteration process.
Some notes on ideology of waves in plasmas
Our last three papers provide an occasion to make some brief notes on ideology of waves in plasmas and to rehabilitate Vlasov prescription to calculate relevant logarithmically divergent integrals in the principal value sense. In this approach asymptotical solutions of plasma oscillations are selected according to self-consistent boundary physical conditions. Landau damping is absent in this case by definition. Boundary electrical field together with conditions of absence of unphysical backward and kinematical waves define single-valued dependence of boundary distribution function on electron velocity \vec{v} in the case of transversal waves and on the surface break of the normal electrical field in the case of longitudinal oscillations. We have proposed physically more justified modified iteration procedure of collisional damping calculation and demonstrated some results of damping decrements calculations in a low-collision electron-ion plasma. Dispersion smearing of both longitudinal and transversal high-frequency waves, for which the smearing decrement \delta_x is proportional to \Delta\omega/(\omega\sqrt{\omega^2-\omega_L^2}), might be the main cause of waves amplitude damping in collisionless plasmas imitating Landau damping.
Effect of Aeration and Agitation Regimes on Lipase Production by Newly Isolated Rhodotorula mucilaginosa–MTCC 8737 in Stirred Tank Reactor Using Molasses as Sole Production Medium
The influence of media and process parameters (aeration and agitation) on fermentation broth rheology and biomass formation has been studied in 1.5-l stirred tank reactor for lipase production using Rhodotorula mucilaginosa MTCC 8737. Molasses, as sole production medium, is used for lipase production by varying aeration (1, 2, and 3 vvm) and agitation speeds (100, 200, and 300 rpm). Maximum lipase activity of 72 U/ml was obtained during 96 h of fermentation at 2 vvm, 200 rpm, pH 7, and 25 ± 2°C temperature. Lipase production kinetics with respect to dry cell weight of biomass showed YP/S of 25.71 U/mg, specific product formation of 10.9 U/mg DC, and YX/S 2.35 mg/mg. Maximum lipase activity (MC 2) of 56 U/ml was observed at 1% molasses, and a further increase in the molasses concentration of (%) 1.5 and 2 inhibited the product formation of lipase with 15 and 8.5 U/ml, respectively. The production kinetics of molasses media showed YP/X was 14 U/mg DC, YP/S 16 U/mg, and YX/S 1.14 mg/mg during 96 h of bioreactor operation. The kLa values for all batches (MC 1–MC 4) at 96 h of fermentation were 32, 28, 21, and 19/h, and the |oxygen transfer rate were 54.4, 56, 35.7, and 17.29 mg/l h, respectively. Increase in molasses concentration resulted in decreased lipase activity by increase in viscosity of the fermentation broth.