results for au:Paul_E in:physics
Tight tolerances have been a leading driver of cost in recent stellarator experiments, so improved definition and control of tolerances can have significant impact on progress in the field. Here we relate tolerances to the shape gradient representation that has been useful for shape optimization in industry, used for example to determine which regions of a car or aerofoil most affect drag, and we demonstrate how the shape gradient can be computed for physics properties of toroidal plasmas. The shape gradient gives the local differential contribution to some scalar figure of merit (shape functional) caused by normal displacement of the shape. In contrast to derivatives with respect to quantities parameterizing a shape (e.g. Fourier amplitudes), which have been used previously for optimizing plasma and coil shapes, the shape gradient gives spatially local information and so is more easily related to engineering constraints. We present a method to determine the shape gradient for any figure of merit using the parameter derivatives that are already routinely computed for stellarator optimization. Examples of shape gradients for plasma and electromagnetic coil shapes are given. We also derive and present examples of an analogous representation of the local sensitivity to magnetic field errors; this magnetic sensitivity can be rapidly computed from the shape gradient. The shape gradient and magnetic sensitivity can both be converted into local tolerances, which inform how accurately the coils should be built and positioned, where trim coils and structural supports for coils should be placed, and where magnetic material and current leads can best be located. Both sensitivity measures provide insight into shape optimization, enable systematic calculation of tolerances, and connect physics optimization to engineering criteria that are more easily specified in real space than in Fourier space.
We present a method for stellarator coil design via gradient-based optimization of the coil-winding surface. The REGCOIL (Landreman 2017 Nucl. Fusion 57 046003) approach is used to obtain the coil shapes on the winding surface using a continuous current potential. We apply the adjoint method to calculate derivatives of the objective function, allowing for efficient computation of analytic gradients while eliminating the numerical noise of approximate derivatives. We are able to improve engineering properties of the coils by targeting the root-mean-squared current density in the objective function. We obtain winding surfaces for W7-X and HSX which simultaneously decrease the normal magnetic field on the plasma surface and increase the surface-averaged distance between the coils and the plasma in comparison with the actual winding surfaces. The coils computed on the optimized surfaces feature a smaller toroidal extent and curvature and increased inter-coil spacing. A technique for visualization of the sensitivity of figures of merit to normal surface displacement of the winding surface is presented, with potential applications for understanding engineering tolerances.
Neoclassical transport in the presence of non-axisymmetric magnetic fields causes a toroidal torque known as neoclassical toroidal viscosity (NTV). The toroidal symmetry of ITER will be broken by the finite number of toroidal field coils and by test blanket modules (TBMs). The addition of ferritic inserts (FIs) will decrease the magnitude of the toroidal field ripple. 3D magnetic equilibria with toroidal field ripple and ferromagnetic structures are calculated for an ITER steady-state scenario using the Variational Moments Equilibrium Code (VMEC). Neoclassical transport quantities in the presence of these error fields are calculated using the Stellarator Fokker-Planck Iterative Neoclassical Conservative Solver (SFINCS). These calculations fully account for $E_r$, flux surface shaping, multiple species, magnitude of ripple, and collisionality rather than applying approximate analytic NTV formulae. As NTV is a complicated nonlinear function of $E_r$, we study its behavior over a plausible range of $E_r$. We estimate the toroidal flow, and hence $E_r$, using a semi-analytic turbulent intrinsic rotation model and NUBEAM calculations of neutral beam torque. The NTV from the $\rvert n \rvert = 18$ ripple dominates that from lower $n$ perturbations of the TBMs. With the inclusion of FIs, the magnitude of NTV torque is reduced by about 75% near the edge. We present comparisons of several models of tangential magnetic drifts, finding appreciable differences only for superbanana-plateau transport at small $E_r$. We find the scaling of calculated NTV torque with ripple magnitude to indicate that ripple-trapping may be a significant mechanism for NTV in ITER. The computed NTV torque without ferritic components is comparable in magnitude to the NBI and intrinsic turbulent torques and will likely damp rotation, but the NTV torque is significantly reduced by the planned ferritic inserts.
We present the screenplay of a physics show on particle physics, by the Physikshow of Bonn University. The show is addressed at non-physicists aged 14+ and communicates basic concepts of elementary particle physics including the discovery of the Higgs boson in an entertaining fashion. It is also demonstrates a successful outreach activity heavily relying on the university physics students. This paper is addressed at anybody interested in particle physics and/or show physics. This paper is also addressed at fellow physicists working in outreach, maybe the experiments and our choice of simple explanations will be helpful. Furthermore, we are very interested in related activities elsewhere, in particular also demonstration experiments relevant to particle physics, as often little of this work is published. Our show involves 28 live demonstration experiments. These are presented in an extensive appendix, including photos and technical details. The show is set up as a quest, where 2 students from Bonn with the aid of a caretaker travel back in time to understand the fundamental nature of matter. They visit Rutherford and Geiger in Manchester around 1911, who recount their famous experiment on the nucleus and show how particle detectors work. They travel forward in time to meet Lawrence at Berkeley around 1950, teaching them about the how and why of accelerators. Next, they visit Wu at DESY, Hamburg, around 1980, who explains the strong force. They end up in the LHC tunnel at CERN, Geneva, Switzerland in 2012. Two experimentalists tell them about colliders and our heroes watch live as the Higgs boson is produced and decays. The show was presented in English at Oxford University and University College London, as well as Padua University and ICTP Trieste. It was 1st performed in German at the Deutsche Museum, Bonn (5/'14). The show has eleven speaking parts and involves in total 20 people.