Circular symmetry | EPFL Graph Search

In geometry, circular symmetry is a type of continuous symmetry for a planar object that can be rotated by any arbitrary angle and map onto itself. Rotational circular symmetry is isomorphic with the circle group in the complex plane, or the special orthogonal group SO(2), and unitary group U(1). Reflective circular symmetry is isomorphic with the orthogonal group O(2). Two dimensions A 2-dimensional object with circular symmetry would consist of concentric circles and annular domains. Rotational circular symmetry has all cyclic symmetry, Zn as subgroup symmetries. Reflective circular symmetry has all dihedral symmetry, Dihn as subgroup symmetries. Three dimensions In 3-dimensions, a surface or solid of revolution has circular symmetry around an axis, also called cylindrical symmetry or axial symmetry. An example is a right circular cone. Circular symmetry in 3 dimensions has all pyramidal symmetry, Cnv as subgroups. A double-cone, bicone, cylinder, toroi

Investigation of the RF efficiency of Inductively Coupled Hydrogen Plasmas at 1MHz

Stefano Mattei, Minh Quang Tran

The power requirements of RF heated sources for negative hydrogen ions in fusion are substantial, which poses strong demands on the generators and components of the RF circuit. Consequently, an increase of the RF coupling efficiency would be highly beneficial. Fundamental investigations of the RF efficiency in inductively coupled hydrogen and deuterium discharges in cylindrical symmetry are conducted at the lab experiment CHARLIE. The experiment is equipped with several diagnostics including optical emission spectroscopy and a movable floating double probe to monitor the plasma parameters. The presented investigations are performed in hydrogen at a varying pressure between 0.3 and 10 Pa, utilizing a conventional helical ICP coil driven at a frequency of 1MHz and a fixed power of 520W for plasma generation. The coupling efficiency is strongly affected by the variation in pressure, reaching up to 85% between 1 and 3 Pa while dropping down to only 50% at 0.3 Pa, which is the relevant operating pressure for negative hydrogen ion sources for fusion. Due to the lower power coupling, also the measured electron density at 0.3 Pa is only 5 . 10(16) m(-3), while it reaches up to 2.5 . 10(17) m(-3) with increasing coupling efficiency. In order to gain information on the spatially resolved aspects of RF coupling and plasma heating which are not diagnostically accessible, first simulations of the discharge by an electromagnetic Particle-In-Cell Monte Carlo collision method have been conducted and are compared to the measurement data. At 1 Pa, the simulated data corresponds well to the results of both axially resolved probe measurements and radially resolved emission profiles obtained via OES. Thereby, information regarding the radial distribution of the electron density and mean energy is provided, revealing a radial distribution of the electron density which is well described by a Bessel profile.

Amer Inst Physics2017

Fundamental aspects to localize self-catalyzed III-V nanowires on silicon

William Craig Carter, Anna Fontcuberta i Morral, Martin George Friedl, Lea Ghisalberti, Wonjong Kim, Heidi Andrea Potts, Jelena Vukajlovic Plestina

III-V semiconductor nanowires deterministically placed on top of silicon electronic platform would open many avenues in silicon-based photonics, quantum technologies and energy harvesting. For this to become a reality, gold-free site-selected growth is necessary. Here, we propose a mechanism which gives a clear route for maximizing the nanowire yield in the self-catalyzed growth fashion. It is widely accepted that growth of nanowires occurs on a layerby-layer basis, starting at the triple-phase line. Contrary to common understanding, we find that vertical growth of nanowires starts at the oxide-substrate line interface, forming a ring-like structure several layers thick. This is granted by optimizing the diameter/height aspect ratio and cylindrical symmetry of holes, which impacts the diffusion flux of the group V element through the well-positioned group III droplet. This work provides clear grounds for realistic integration of III-Vs on silicon and for the organized growth of nanowires in other material systems.

2019

Vortex lattice structure in BaFe2(As0.67P0.33)(2) via small-angle neutron scattering

Jonathan White

We have observed a magnetic vortex lattice (VL) in BaFe2(As0.67P0.33)(2) (BFAP) single crystals by small-angle neutron scattering. With the field along the c axis, a nearly isotropic hexagonal VL was formed in the field range from 1 to 16 T, and no symmetry changes in the VL were observed. The temperature dependence of the VL signal was measured and confirms the presence of (non-d-wave) nodes in the superconducting gap structure for measurements at 5 T and below. The nodal effects were suppressed at high fields. At low fields, a VL reorientation transition was observed between 1 and 3 T, with the VL orientation changing by 45 degrees. Below 1 T, the VL structure was strongly affected by pinning and the diffraction pattern had a fourfold symmetry. We suggest that this (and possibly also the VL reorientation) is due to pinning to defects aligned with the crystal structure, rather than being intrinsic. The temperature dependence of the scaled intensity suggests that BFAP possesses at least one full gap and one nodal gap with circular symmetry. Judging from the symmetry, the node structure should take the form of an "accidental" circular line node, which is consistent with recent angle-resolved photoemission spectroscopy results.

Amer Physical Soc2014

Investigation of the RF efficiency of Inductively Coupled Hydrogen Plasmas at 1MHz

Stefano Mattei, Minh Quang Tran

Amer Inst Physics2017