Preliminary Study of Uncertainty-Driven Plasma Diffusion II

We have constructed a semiclassical collisional diffusion model. In this model, a field particle is treated as either a point charge or a spatially distributed charge. The test particle is treated as a distributed point charge with Gaussian distribution. It was shown that the collisional changes in velocity in our model is of the same order as the classical theory for a typical proton in a fusion plasma of T = 10 keV and n = 1020 m−3. It was also shown that the spatial extent of the distribution, or the quantum-mechanical uncertainty in position, for the test particle obtained in our model grows in time, and becomes of the order of the average interparticle separation Δ ≡ n−1/3 during a time interval τr ∼×107Δ /gth, where gth = √ 2T/m is the thermal speed, with m being the mass of the particle under consideration. The time interval is 3-4 order of magnitudes smaller than the collision time. This suggests that particle transport cannot be understood in the framework of classical mechanics, and that the quantum-mechanical distribution of individual particles in plasmas may cause the anomalous diffusio

Quantum Mechanical Plasma Scattering

We have solved the two-dimensional time-dependent Schödinger equation for a particle with and without the interparticle potential in a fusion plasma. It was shown that spatial extent of a free particle grows monotonically in time. Such expansion leads to a spatial extent or size of a proton of the order of the average interparticle separation Δl ≡ n−1/3 ∼ 2 × 10−7 m in a time interval of 106 × Δl/vth ∼ 10−7 sec for a plasma with a density n ∼ 1020 m−3 and a temperature T = mvth2/2 ∼ 10 keV. It was also shown that, under a Coulomb potential, the wavefunction of a charged particle first shrink and expand in time. In the expansion phase, at times t ≥ 10−10 sec, the size of particle in the presence of a Coulomb potential is much larger than that in the absence of it

Relativistic segmented contraction basis sets with core-valence correlation effects for atoms 57La through 71Lu : Sapporo-DK-nZP sets (n = D, T, Q)

For the 15 lanthanide atoms 57La through 71Lu, we report Sapporo-DK-nZP sets (n = D, T, Q), which are natural extensions of the Sapporo-(DK)-nZP sets for lighter atoms and efficiently incorporate the correlation among electrons in the N through P shells as well as the relativistic effect. The present sets well describe the correlation among the 4s and 4p electrons, which are important in the excitation of 4f electrons. Atomic test calculations of 57La, 58Ce, 59Pr, and 60Nd at configuration interaction with the Davidson correction level of theory confirm high performance of the present basis sets. Molecular test calculations are carried out for 57LaF and 70YbF diatomics at the coupled cluster level of theory. The calculated spectroscopic constants approach smoothly to the experimental values as the quality of the basis set increases

Design and Fabrication of Capacitive Silicon Nanomechanical Resonators with Selective Vibration of a High-Order Mode

This paper reports the design and fabrication of capacitive silicon nanomechanical resonators with the selective vibration of a high-order mode. Fixed-fixed beam capacitive silicon resonators have been successfully produced by the use of electron beam lithography, photolithography, deep reactive ion etching, and anodic bonding methods. All resonators with different vibration modes are designed to have the same resonant frequency for performance comparison. Measurement results show that higher-order mode capacitive silicon resonators can achieve lower insertion loss compared to that of lower-order mode capacitive silicon resonators. The motional resistance of the fourth mode vibration resonator is improved by 83%, 90%, and 93% over the third, second, and first mode vibration resonators, respectively