Experimental vertical stability studies for ITER performance and design

Operating experimental devices have provided key inputs to the design process for ITER axisymmetric control. In particular, experiments have quantified controllability and robustness requirements in the presence of realistic noise and disturbance environments, which are difficult or impossible to characterize with modelling and simulation alone. This kind of information is particularly critical for ITER vertical control, which poses the highest demands on poloidal field system performance, since the consequences of loss of vertical control can be severe. This work describes results of multi-machine studies performed under a joint ITPA experiment (MDC-13) on fundamental vertical control performance and controllability limits. We present experimental results from Alcator C-Mod, DIII-D, NSTX, TCV and JET, along with analysis of these data to provide vertical control performance guidance to ITER. Useful metrics to quantify this control performance include the stability margin and maximum controllable vertical displacement. Theoretical analysis of the maximum controllable vertical displacement suggests effective approaches to improving performance in terms of this metric, with implications for ITER design modifications. Typical levels of noise in the vertical position measurement and several common disturbances which can challenge the vertical control loop are assessed and analysed.United States Department of Energy (DE-FC02-04ER54698, DEAC52- 07NA27344, and DE-FG02-04ER54235

Exact solution of the envelope equations for a matched quadrupole-focused beam in the zero space-charge limit

The Kapchinskij-Vladimirskij equations are widely used to study the evolution of the beam envelopes in a periodic system of quadrupole focusing cells. In this paper, we analyze the case of a matched beam. Our model is analogous to that used by Courant and Snyder [E.D. Courant and H.S. Snyder, Ann. Phys. 3, 1 (1958)] in obtaining a first-order approximate solution for a synchrotron. Here, we treat a linear machine and obtain an exact solution. The model uses a full occupancy, piecewise-constant focusing function and neglects space charge. There are solutions in an infinite number of bands as the focus strength is increased. We show that all these bands are stable. Our explicit results for the phase advance {sigma} and the envelope a(z) are exact for all phase advances except multiples of 180{sup o}, where the behavior is singular. We find that the peak envelope size is minimized at {sigma} = 90{sup o}. Actual operation in the higher bands would require very large, very accurate field strengths and would produce significantly larger envelope excursions

Stable propagation of an electron beam in gas

Conditions for the stable propagation of a pinched electron beam in low pressure gas (p approximately 0.1 to 100 torr) are described. The observed window of good propagation around p approximately 2 torr air is interpreted as the quenching of the two-stream mode by sufficiently high plasma density and collision frequency, and the simultaneous suppression of the resistive hose mode by sufficiently rapid generation of electrical conductivity from breakdown ionization

Theoretical issues in Spheromak research

This report summarizes the state of theoretical knowledge of several physics issues important to the spheromak. It was prepared as part of the preparation for the Sustained Spheromak Physics Experiment (SSPX), which addresses these goals: energy confinement and the physics which determines it; the physics of transition from a short-pulsed experiment, in which the equilibrium and stability are determined by a conducting wall (``flux conserver``) to one in which the equilibrium is supported by external coils. Physics is examined in this report in four important areas. The status of present theoretical understanding is reviewed, physics which needs to be addressed more fully is identified, and tools which are available or require more development are described. Specifically, the topics include: MHD equilibrium and design, review of MHD stability, spheromak dynamo, and edge plasma in spheromaks

On coupling fluid plasma and kinetic neutral physics models

The coupled fluid plasma and kinetic neutral physics equations are analyzed through theory and simulation of benchmark cases. It is shown that coupling methods that do not treat the coupling rates implicitly are restricted to short time steps for stability. Fast charge exchange, ionization and recombination coupling rates exist, even after constraining the solution by requiring that the neutrals are at equilibrium. For explicit coupling, the present implementation of Monte Carlo correlated sampling techniques does not allow for complete convergence in slab geometry. For the benchmark case, residuals decay with particle number and increase with grid size, indicating that they scale in a manner that is similar to the theoretical prediction for nonlinear bias error. Progress is reported on implementation of a fully implicit Jacobian-free Newton–Krylov coupling scheme. The present block Jacobi preconditioning method is still sensitive to time step and methods that better precondition the coupled system are under investigation. Keywords: Divertor modeling, Charge exchange, Ionization, Recombination, Implicit, Newton–Krylov, UEDGE, DEGAS2, EIRENE, SOLPS, MSC: 00-01, 99-0