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.
Solving non-linear equations of longitudinal and transverse electron waves in collisionless Maxwellian plasma
We have considered an expansion of solutions of the non-linear equations for both longitudinal and transverse waves in collisionless Maxwellian plasma in series of non-damping overtones of the field E(x,t) and electron velocity distribution function f=f(0) +f(1) where f(0) is background Maxwellian electron distribution function and f(1) is perturbation. The electrical field and perturbation f(1) are presented as a series of non-damping harmonics with increasing frequencies of the order n and the same propagation speed. It is shown presence of recurrent relations for arising overtones. Convergence of the series is provided by a power law parameter series convergence. There are proposed also successive procedures of cutting off the distribution function f(1) to the condition of positivity f near the singularity points where kinetic equation becomes inapplicable. In this case, at poles absence the solution reduces to non-damping Vlasov waves (oscillations). In the case of transverse waves, dispersion equation has two roots, corresponding to the branches of fast electromagnetic and slow electron waves. There is noted a possibility of experimental testing appearing exotic results with detecting frequencies and amplitudes of n-order overtones.
NMR characteristics of intracellular K in the rat salivary gland: a 39K NMR study using double-quantum filtering.
Intracellular K of the perfused rat mandibular salivary gland was measured by 39K NMR spectroscopy at 8.45 T. Multiple-quantum NMR arising from multiple-exponential decay was used to eliminate the resonance due to extracellular K in the perfused gland at 25 degrees C. The resonance due to intracellular K consisted of two Lorentzian signals stemming from the [spin 1/2 to -1/2] coherence (sharp resonance) and the [spin -1/2 to -3/2], [spin 3/2 to 1/2] coherences (broad resonance). The transverse relaxation time (T2) corresponding to the [spin 1/2 to -1/2] coherence was ca. 2.5 ms, and that corresponding to the [spin -1/2 to -3/2], [spin 3/2 to 1/2] coherences was ca. 0.4 ms. The relaxation time of the double-quantum coherence of rank 3 (originating from product operators like Ix2Iz) was determined to be ca. 0.2 ms. These results suggest the possibility of the presence of a single homogeneous population of intracellular K with a correlation time of ca. 2.5 x 10(-8) s and a quadrupolar coupling constant of ca. 1.4 MHz.