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.
rPET detectors design and data processing
Small animal PET systems based on rotating planar detectors posses some interesting advantages for high sensitivity, high resolution imaging. We have designed the rPET detectors based on MLS crystals assembled on a 30times30 matrix optically coupled to a flat-panel PS-PMT. Weighted position readout circuits pre-process the 64 signals from the 8times8 anodes matrix, which are digitized using a charge-integrating converter. The amplification electronics, including the trigger output for coincidence detection, and the high voltage supply are integrated in a three PCBs stack that forms the base attached to the back of the PMT. The whole assembly is enclosed in a light tight, lead (Pb) shielded aluminum box. The detectors are mounted on a rotating gantry with more than 180 degrees rotation span. The digitized events are screened and histogramed, and a modified center of gravity algorithm removes from the position calculation those signals with poor signal to noise ratio. Apparent mean crystal size on the 511 keV field-flood images is 0.6 mm, mean peak-to-valley ratio is better than 8, and intrinsic resolution is 1.5 mm at the central row, with the energy window wide open. Sensitivity (CPS) for a pair of these detectors set in coincidence at 160 mm distance is 1%