Fine Space Resolution Research Articles

Stage‐parallel preconditioners for implicit Runge–Kutta methods of arbitrarily high order, linear problems

AbstractFully implicit Runge–Kutta methods offer the possibility to use high order accurate time discretization to match space discretization accuracy, an issue of significant importance for many large scale problems of current interest, where we may have fine space resolution with many millions of spatial degrees of freedom and long time intervals. In this work, we consider strongly A‐stable implicit Runge–Kutta methods of arbitrary order of accuracy, based on Radau quadratures. For the arising large algebraic systems we introduce efficient preconditioners, that (1) use only real arithmetic, (2) demonstrate robustness with respect to problem and discretization parameters, and (3) allow for fully stage‐parallel solution. The preconditioners are based on the observation that the lower‐triangular part of the coefficient matrices in the Butcher tableau has larger in magnitude values, compared to the corresponding strictly upper‐triangular part. We analyze the spectrum of the corresponding preconditioned systems and illustrate their performance with numerical experiments. Even though the observation has been made some time ago, its impact on constructing stage‐parallel preconditioners has not yet been done and its systematic study constitutes the novelty of this article.

Optical properties of nanoporous silica frustules of a diatom determined using a 10 µm microfiber probe

A microfiber spectroscopic method was developed to reveal the photonic crystalline characteristics of a cylindrical frustule of the diatom Melosira variance. The spectroscopy apparatus used was composed of two quartz fibers with fine ends, approximately 10 µm in diameter, set on micromanipulators to control the position of the fine ends of each fiber, which were focused at the edge of a frustule. The method had fine space resolution and sensitivity toward the propagation direction of incident light, which is suitable for analyzing photonic crystallinity. A typical absorption was observed at wavelengths of 400–500 nm, which corresponded to a quasi-stop band calculated by a finite-difference time-domain (FDTD) method for a three-dimensional (3D) slab model constructed based on an SEM image of the frustule. These results suggest that the photonic crystalline characteristics of the frustule can assist the absorption of incident light near 420 nm, which is crucial for the efficient photosynthesis of the diatom.

Particle and energy balance in the SOL generated by a limiter in a RFP plasma

The plasma outer region of the RFP experiment ETA BETA II has been extensively investigate. In particular by an insertable graphite limiter, instrumented with thermocouples and Langmuir probes, the energy and particle fluxes in the shadow of the limiter have been measured at different insertions. The results are compared with those obtained by small-size calorimeter/Langmuir probes inserted to investigate, with fine space resolution, the outer region without limiter. Almost 80% of the power to the limiter is estimated to be carried by fast suprathermal electrons flowing along the magnetic field line direction. From an energy balance equation, applied in the SOL locally generated, the connection length of the limiter has been derived. Thus particle balance has been applied to determine the particle diffusion coefficient at the plasma edge.

Picosecond Time Measuremnts with a Linear Accelerator and RF Separator

A picosencond time measurement method is described based on the microwave properties of beams from electron linear accelerators or from possible remodulated external proton beams at proton synchrotrons. A conventional RF separator (RFS) is used operating at the same frequency as the microwave structure of beams and driven by the same master oscillator which modulates the beam. For example, the 2856 MHz microwave at SLAC corresponds to 350 psec between beam RF buckets; accelerated electrons with an RF phase bite of about 5 degrees are time structured and correspondingly have about 5 psec time spread in every 350 psec interval. Charged particles produced in interactions or decays originate with this time structure. An RFS is placed at the last stage of a double focussing spectrometer, providing a lever arm between it and the final (few mm) small spot size focus. Reference calibration charged particles are timed by setting the RFS relative phase to null deflections. Other observed particles arriving at different times than this standardare deflected a few tenths ofa anm per psec of delay. A multi-wire proportional chamber (IMPC) having a 0.05 mm space resolution can provide time measurements with sub-picosecond resolution. The technique is used in an experiment to search for changes in the velocity of light with high energy photons at SLAC. The devised timing method is presented and the properties of a new, fine space resolution MWPC is demonstrated.