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Christopher Bowman

Publications and source records attributed to Christopher Bowman.

6 recordsLinked to original sources

An improved understanding of the roles of atomic processes and power balance in divertor target ion current loss during detachment

The process of divertor detachment, whereby heat and particle fluxes to divertor surfaces are strongly diminished, is required to reduce heat loading and erosion in a magnetic fusion reactor to acceptable levels. In this paper the physics leading to the decrease of the total divertor ion current (It), or 'roll-over', is experimentally explored on the TCV tokamak through characterization of the location, magnitude and role of the various divertor ion sinks and sources including a complete analysis of particle and power balance. These first measurements of the profiles of divertor ionisation and hydrogenic radiation along the divertor leg are enabled through novel spectroscopic techniques. Over a range in TCV plasma conditions (plasma current and electron density, with/without impurity-seeding) the $I_t$ roll-over is ascribed to a drop in the divertor ion source; recombination remains small or negligible farther into the detachment process. The ion source reduction is driven by both a reduction in the power available for ionization, Precl, and concurrent increase in the energy required per ionisation, $E_{ion}$: often described as 'power starvation' (or 'power limitation'). The detachment threshold is found experimentally (in agreement with analytic model predictions) to be $\sim P_{recl}/I_t {E_{ion}} \sim 2$, corresponding to a target electron temperature, $T_t \sim E_{ion}/γ$ where $γ$ is the sheath transmission coefficient. The target pressure reduction, required to reduce the target ion current, is driven both by volumetric momentum loss as well as upstream pressure loss. The measured evolution through detachment of the divertor profile of various ion sources/sinks as well as power losses are quantitatively reproduced through full 2D SOLPS modelling through the detachment process as the core density is varied.

physics.plasm-ph

The cellular second fundamental theorem of invariant theory for classical groups

We prove that the centralizer algebras of the symplectic and orthogonal group acting on tensor space are cellular algebras over the integers. We do this by providing an axiomatic framework for studying quotient towers for towers of diagram algebras. Our framework covers the centralizer algebras of the general linear group acting on mixed tensor space as well. We also provide descriptions of the kernels of the homomorphisms from the diagrammatic versions of the algebras to the centralizer algebras on tensor space, which constitute versions of the second fundamental theorem of invariant theory.

math.RT

Diagram algebras, dominance triangularity, and skew cell modules

We present an abstract framework for the axiomatic study of diagram algebras. Algebras that fit this framework possess analogues of both the Murphy and seminormal bases of the Hecke algebras of the symmetric groups. We show that the transition matrix between these bases is dominance unitriangular. We construct analogues of the skew Specht modules in this setting. This allows us to propose a natural tableaux theoretic framework in which to study the infamous Kronecker problem.

math.RT

Multiplicity-free Kronecker products of characters of the symmetric groups

We provide a classification of multiplicity-free inner tensor products of irreducible characters of symmetric groups, thus confirming a conjecture of Bessenrodt. Concurrently, we classify all multiplicity-free inner tensor products of skew characters of the symmetric groups. We also provide formulae for calculating the decomposition of these tensor products.

math.RT

Kleshchev's decomposition numbers for diagrammatic Cherednik algebras

We construct a family of graded isomorphisms between certain subquotients of diagrammatic Cherednik algebras as the quantum characteristic, multicharge, level, degree, and weighting are allowed to vary; this provides new structural information even in the case of the classical q-Schur algebra. This also allows us to prove some of the first results concerning the (graded) decomposition numbers of these algebras over fields of arbitrary characteristic.

math.RT

The partition algebra and the Kronecker coefficients

We propose a new approach to study the Kronecker coefficients by using the Schur-Weyl duality between the symmetric group and the partition algebra. We explain the limiting behavior and associated bounds in the context of the partition algebra. Our analysis leads to a uniform description of the Kronecker coefficients when one of the indexing partitions is a hook or a two-part partition.

math.RT