Fast-ion physics in SPARC

Potential loss of energetic ions including alphas and radio-frequency tail ions due to classical orbit effects and magnetohydrodynamic instabilities (MHD) are central physics issues in the design and experimental physics programme of the SPARC tokamak. The expected loss of fusion alpha power due to ripple-induced transport is computed for the SPARC tokamak design by the ASCOT and SPIRAL orbit-simulation codes, to assess the expected surface heating of plasma-facing components. We find good agreement between the ASCOT and SPIRAL simulation results not only in integrated quantities (fraction of alpha power loss) but also in the spatial, temporal and pitch-angle dependence of the losses. If the toroidal field (TF) coils are well-aligned, the SPARC edge ripple is small (0.15–0.30 %), the computed ripple-induced alpha power loss is small ( ${\sim } 0.25\,\%$ ) and the corresponding peak surface power density is acceptable ( $244\ \textrm{kW}\ \textrm {m}^{-2}$ ). However, the ripple and ripple-induced losses increase strongly if the TF coils are assumed to suffer increasing magnitudes of misalignment. Surface heat loads may become problematic if the TF coil misalignment approaches the centimetre level. Ripple-induced losses of the energetic ion tail driven by ion cyclotron range of frequency (ICRF) heating are not expected to generate significant wall or limiter heating in the nominal SPARC plasma scenario. Because the expected classical fast-ion losses are small, SPARC will be able to observe and study fast-ion redistribution due to MHD including sawteeth and Alfvén eigenmodes (AEs). SPARC's parameter space for AE physics even at moderate $Q$ is shown to reasonably overlap that of the demonstration power plant ARC (Sorbom et al., Fusion Engng Des., vol. 100, 2015, p. 378), and thus measurements of AE mode amplitude, spectrum and associated fast-ion transport in SPARC would provide relevant guidance about AE behaviour expected in ARC.

Solution for Nonlinear Three-Dimensional Intercept Problem with Minimum Energy

Classical orbit intercept applications are commonly formulated and solved as Lambert-type problems, where the time-of-flight (TOF) is prescribed. For general three-dimensional intercept problems, selecting a meaningful TOF is often a difficult and an iterative process. This work overcomes this limitation of classical Lambert’s problem by reformulating the intercept problem in terms of a minimum-energy application, which then generates both the desired initial interceptor velocity and the TOF for the minimum-energy transfer. The optimization problem is formulated by using the classical Lagrangianfandgcoefficients, which map initial position and velocity vectors to future times, and a universal time variablex. A Newton-Raphson iteration algorithm is introduced for iteratively solving the problem. A generalized problem formulation is introduced for minimizing the TOF as part of the optimization problem. Several examples are presented, and the results are compared with the Hohmann transfer solution approaches. The resulting minimum-energy intercept solution algorithm is expected to be broadly useful as a starting iterative for applications spanning: targeting, rendezvous, interplanetary trajectory design, and so on.

New Observational Techniques and Precise Orbit Determination of Artificial Satellites

Modern observational techniques using ground-based and space-based instrumentation have enabled the measurement of the distance between the instrument and satellite to better than one centimeter. Such high precision instrumentation has fostered applications with centimeter-level requirements for satellite position knowledge. The determination of the satellite position to such accuracy requires a comparable modeling of the forces experienced by the satellite, especially when classical orbit determination methods are used. Geodetic satellites, such as Lageos, in conjunction with high precision ground-based laser ranging, have been used to improve for modeling of forces experienced by the satellite. Space-based techniques, such as Global Positioning System (GPS), offer alternatives, including kinematic techniques which require no modeling of the satellite forces, or only rudimentary models. This paper will describe the various techniques and illustrate the accuracies achieved with current satellites, such as TOPEX/POSEIDON, GPS/MET and the expectations for some future satellites.