Uniqueness of roots up to conjugacy for some affine and finite type Artin groups

Let $G$ be one of the Artin groups of finite type ${\mathbf B}_n={\mathbf C}_n$, and affine type $\tilde{\mathbf A}_{n-1}$ and $\tilde{\mathbf C}_{n-1}$. In this paper, we show that if $\alpha$ and $\beta$ are elements of $G$ such that $\alpha^k=\beta^k$ for some nonzero integer $k$, then $\alpha$ and $\beta$ are conjugate in $G$. For the Artin group of type $\mathbf A_n$, this was recently proved by J. Gonz\'alez-Meneses. In fact, we prove a stronger theorem, from which the above result follows easily by using descriptions of those Artin groups as subgroups of the braid group on $n+1$ strands. Let $P$ be a subset of $\{1,...,n\}$. An $n$-braid is said to be \emph{$P$-pure} if its induced permutation fixes each $i\in P$, and \emph{$P$-straight} if it is $P$-pure and it becomes trivial when we delete all the $i$-th strands for $i\not\in P$. Exploiting the Nielsen-Thurston classification of braids, we show that if $\alpha$ and $\beta$ are $P$-pure $n$-braids such that $\alpha^k=\beta^k$ for some nonzero integer $k$, then there exists a $P$-straight $n$-braid $\gamma$ with $\beta=\gamma\alpha\gamma^{-1}$. Moreover, if $1\in P$, the conjugating element $\gamma$ can be chosen to have the first strand algebraically unlinked with the other strands. Especially in case of $P=\{1,...,n\}$, our result implies the uniqueness of root of pure braids, which was known by V. G. Bardakov and by D. Kim and D. Rolfsen.Comment: 15 pages, 8 figures; version published by Math.

Non-classical correlations from dissociation time entanglement

We discuss a strongly entangled two-particle state of motion that emerges naturally from the double-pulse dissociation of a diatomic molecule. This state, which may be called dissociation-time entangled, permits the unambiguous demonstration of non-classical correlations by violating a Bell inequality based on switched single particle interferometry and only position measurements. We apply time-dependent scattering theory to determine the detrimental effect of dispersion. The proposed setup brings into reach the possibility of establishing non-classical correlations with respect to system properties that are truly macroscopically distinct.Comment: 8 pages, 2 figures; corresponds to published versio

2D measurements of plasma electron density using coherence imaging with a pixelated phase mask

In this paper, the pixelated phase mask (PPM) method of interferometry is applied to coherence imaging (CI)—a passive, narrowband spectral imaging technique for diagnosing the edge and divertor regions of fusion plasma experiments. Compared to previous CI designs that use a linear phase mask, the PPM method allows for a higher possible spatial resolution. The PPM method is also observed to give a higher instrument contrast (analogous to a more narrow spectrometer instrument function). A single-delay PPM instrument is introduced as well as a multi-delay system that uses a combination of both pixelated and linear phase masks to encode the coherence of the observed radiation at four different interferometer delays simultaneously. The new methods are demonstrated with measurements of electron density ne, via Stark broadening of the Hγ emission line at 434.0 nm, made on the Magnum-PSI linear plasma experiment. A comparison of the Abel-inverted multi-delay CI measurements with Thomson scattering shows agreement across the 3 × 1019 1 × 1020 m−3 only. Accurate and independent interpretation of single-delay CI data at lower ne was not possible due to Doppler broadening and continuum emission

Development of an 11-channel multi wavelength imaging diagnostic for divertor plasmas in MAST Upgrade

Divertor detachment and alternative divertor magnetic geometries are predicted to be promising approaches to handle the power exhaust of future fusion devices. In order to understand the detachment process caused by volumetric losses in alternative divertor magnetic geometries, a Multi-Wavelength Imaging (MWI) diagnostic has recently been designed and built for the Mega Amp Spherical Tokamak Upgrade. The MWI diagnostic will simultaneously capture 11 spectrally filtered images of the visible light emitted from divertor plasmas and provide crucial knowledge for the interpretation of observations and modeling efforts. This paper presents the optical design, mechanical design, hardware, and test results of an 11-channel MWI system with a field of view of 40°. The optical design shows better than 5 mm FWHM spatial resolution at the plasma on all 11 channels across the whole field of view. The spread of angle of incidence on the surface of each filter is also analyzed to inform the bandwidth specification of the interference filters. The results of the initial laboratory tests demonstrate that a spatial resolution of better than 5 mm FWHM is achieved for all 11 channels, meeting the specifications required for accurate tomography.</p

Development of an 11-channel multi wavelength imaging diagnostic for divertor plasmas in MAST Upgrade

Divertor detachment and alternative divertor magnetic geometries are predicted to be promising approaches to handle the power exhaust of future fusion devices. In order to understand the detachment process caused by volumetric losses in alternative divertor magnetic geometries, a Multi-Wavelength Imaging (MWI) diagnostic has recently been designed and built for the Mega Amp Spherical Tokamak Upgrade. The MWI diagnostic will simultaneously capture 11 spectrally filtered images of the visible light emitted from divertor plasmas and provide crucial knowledge for the interpretation of observations and modeling efforts. This paper presents the optical design, mechanical design, hardware, and test results of an 11-channel MWI system with a field of view of 40°. The optical design shows better than 5 mm FWHM spatial resolution at the plasma on all 11 channels across the whole field of view. The spread of angle of incidence on the surface of each filter is also analyzed to inform the bandwidth specification of the interference filters. The results of the initial laboratory tests demonstrate that a spatial resolution of better than 5 mm FWHM is achieved for all 11 channels, meeting the specifications required for accurate tomography

Development of an 11-channel multi wavelength imaging diagnostic for divertor plasmas in MAST Upgrade

Divertor detachment and alternative divertor magnetic geometries are predicted to be promising approaches to handle the power exhaust of future fusion devices. In order to understand the detachment process caused by volumetric losses in alternative divertor magnetic geometries, a Multi-Wavelength Imaging (MWI) diagnostic has recently been designed and built for the Mega Amp Spherical Tokamak Upgrade. The MWI diagnostic will simultaneously capture 11 spectrally filtered images of the visible light emitted from divertor plasmas and provide crucial knowledge for the interpretation of observations and modeling efforts. This paper presents the optical design, mechanical design, hardware, and test results of an 11-channel MWI system with a field of view of 40°. The optical design shows better than 5 mm FWHM spatial resolution at the plasma on all 11 channels across the whole field of view. The spread of angle of incidence on the surface of each filter is also analyzed to inform the bandwidth specification of the interference filters. The results of the initial laboratory tests demonstrate that a spatial resolution of better than 5 mm FWHM is achieved for all 11 channels, meeting the specifications required for accurate tomography

Characterisation of detachment in the MAST-U Super-X divertor using multi-wavelength imaging of 2D atomic and molecular emission processes

In this work, we provide the first 2D spatially resolved description of radiative detachment in MAST-U Super-X L-mode divertor plasmas. The Super-X magnetic configuration was designed to achieve reduced heat- and particle loads at the divertor target compared to conventional exhaust solutions. We use filtered camera imaging to reconstruct 2D emissivity profiles in the poloidal plane for multiple atomic and molecular emission lines and bands. A set of deuterium fuelling scans is discussed that, together, span attached to deeply detached divertor states observed in MAST-U. Emissivity profiles facilitate separate analysis of locked-mode induced split branches of the scrape-off layer. Molecular deuterium Fulcher band emission front tracking reveals that the deuterium electron-impact ionisation front, for which it serves a proxy, detaches at different upstream electron densities in the split branches. Upon detachment of this ionisation front, Balmer emission attributed to molecular activated recombination appears near-target. We report a simultaneous radial broadening of the emission leg, consistent with previous SOLPS-ITER modelling. With increased fuelling this emission region detaches, implying electron temperatures below ${\sim}{\,}1{\,}$eV. In this phase, 2D Balmer line ratio reconstruction indicates an onset of volumetric direct electron-ion recombination near-target. At the highest fuelling rates this emission region moves off-target, suggesting a drop in near-wall electron density accompanying the low temperatures