Axisymmetric, High-β, Steady-State Plasma Torus: A "Wind-Tunnel" to Develop Whole Device Models
The development of experimentally-validated whole device models is a grand challenge of fusion energy science and a major goal of integrated simulation research. As explained in the 2009 Joint FES/ASCR Workshop Report [1], extreme-scale computing power will allow “improved versions” of large-scale simulations “to produce an experimentally validated integrated simulation capability for scenario modeling of the whole device.” Whole device models will integrate multi-scale physics (e.g. turbulence and transport, local and nonlocal coupling), magnetic geometry (e.g. anisotropy between parallel and perpendicular dynamics, interfaces between closed and open field lines), nonlinear and electromagnetic dynamics (e.g. instability-induced energy transfer, particle kinetics and resonances), and carefully designed validation experiments. This scientific challenge is unquestionably “grand.” Workshop participants called integrated predictive modeling both “urgent” and “one of the most difficult and least understood problems in fusion energy research” [1]. This white paper presents a cost-effective and near-term research step that makes progress towards this grand challenge by considering the simpler task of experimentally validated integrated simulation of a steady-state, high-β plasma torus confined by a simple axisymmetric current ring. Using our nation’s only toroidal confinement device with superconducting magnets, we can now make unparalleled measurements of fusion-relevant plasmas confined for several minutes and use these measurements for critical validation studies. We call this approach a “plasma wind tunnel”, because it is analogous to using low-cost instrumented objects in wind tunnels to validate CFD and turbulent hydrodynamics for various aerodynamical applications. In a manner of speaking, we want to follow in the footsteps of the Wright brothers. Just as the Wright brothers validated the means to predict lift and drag in their wind tunnel, we should build confidence in our whole-plasma capabilities by first demonstrating success with a fusion-relevant plasma torus that has the least complicated magnetic geometry and the least complicated particle kinetics. We believe the axisymmetric current ring is both the simplest magnetized plasma torus that can be used for whole-plasma modeling, and, also, the simplest plasma torus that incorporates features of any fusion device: multi-scale and boundary layer physics, nonlinear stability and turbulence phenomena, and important kinetic effects and particle resonances. Steady-state high-β plasmas have proven to be relatively easy to produce in the laboratory [2-7], and gyro-kinetic and gyro-fluid models have been successfully applied to this geometry, yielding important insights into the fundamental nonlinear turbulent transport processes [8-12]. Like a tokamak, the plasma torus confined by a current ring is sustained by sources of heat, particles, and toroidal momentum and involves turbulent transport across boundary layers, upgradient turbulent pinches [13,14], nonlinear fast particle dynamics [15], filamentary “blobs” [16], and turbulent cascades [17]. Unlike a tokamak, turbulent transport does not always lead to plasma loss. Instead turbulence causes self-organization, centrally-peaked profiles, and either an inward particle or an inward thermal pinch [11, 12] as the plasma approaches a state of minimum entropy production [18].
Transport induced by large scale convective structures in a dipole-confined plasma.
Convective structures characterized by E×B motion are observed in a dipole-confined plasma. Particle transport rates are calculated from density dynamics obtained from multipoint measurements and the reconstructed electrostatic potential. The calculated transport rates determined from the large-scale dynamics and local probe measurements agree in magnitude, show intermittency, and indicate that the particle transport is dominated by large-scale convective structures.
LYAPUNOV-BASED TRANSFER BETWEEN ELLIPTIC KEPLERIAN ORBITS
We present a study of the transfer of satellites between elliptic Keplerian orbits using Lyapunov stability theory specific to this problem. The construction of Lyapunov functions is based on the fact that a non-degenerate Keplerian orbit is uniquely described by its angular momentum and Laplace (- Runge-Lenz) vectors. We suggest a Lyapunov function, which gives a feedback controller such that the target elliptic orbit becomes a locally asymptotically stable periodic orbit in the closed-loop dynamics. We show how to perform a global transfer between two arbitrary elliptic orbits based on the local transfer result. Finally, a second Lyapunov function is presented that works only for circular target orbits.