1986 00 00 Fusion Technology - Vol 10 No 2 - Houlberg and Lacatski

Magazine Overview

Title: Fusion Technology
Issue: Vol. 10, No. 2
Date: September 1986
Publisher: American Nuclear Society
Country: USA
Language: English
ISSN: 0748-1896

Article: Assessment of a Compact Torsatron Reactor, ATFSR

This article, authored by Wayne A. Houlberg, James T. Lacatski, and Nermin A. Uckan, evaluates the confinement and engineering issues of a small, moderate-aspect-ratio torsatron reactor, designated ATFSR. The study uses the Advanced Toroidal Facility (ATF) design as a starting point due to its relatively low aspect ratio and high beta capabilities.

Introduction to Torsatron Reactors

The authors highlight the inherent advantages of stellarator/torsatron reactors, including steady-state operation without net plasma current, which minimizes cyclic stresses and fatigue. Other benefits include disruption-free operation, natural divertor capabilities, the ability to start up on existing magnetic surfaces, and potential for modular construction. Torsatrons, specifically, offer improved access compared to stellarators due to requiring only / helical windings to produce a poloidal harmonic of l, as opposed to 2/ in stellarators.

The primary issues addressed for reactor relevance are plasma beta (efficient use of magnetic fields), engineering aspects (size, access, shielding), and energy confinement for ignition or high-Q operation. The ATF, currently under construction, is expected to provide access to the second stability regime due to its moderate aspect ratio, shear, and magnetic axis shift. The ATFSR concept aims to leverage the lower aspect ratio and higher beta capabilities of ATF for more compact reactor designs.

ATFSR Design and Parameters

The ATFSR is conceived as a scaled-up version of ATF, with an average plasma minor radius of 1 meter. The study relaxes the blanket/shield thickness constraint, recognizing it as a potential problem area, to achieve an ignition machine. The paper emphasizes the evaluation of confinement, which significantly impacts minimum size projections.

Table I compares various stellarator/torsatron power reactor designs, including the ATFSR, detailing parameters such as plasma radius, major radius, aspect ratio, plasma volume, average density, average beta, magnetic field strength, first-wall loading, thermal power, and net plant efficiency. The ATFSR is noted for its relatively small major radius (7.0 m) and aspect ratio (7.0).

Table II provides dimensionless and scaled parameters for ATF and ATFSR. For ATFSR, the major radius is 7.0 m, average minor radius is 1.0 m, and the helical coil current is 14.6 MA. The magnetic field on axis is 5.0 T.

Magnetic Properties and Stability

The ATF torsatron is described as an l=2 design with m=12 toroidal field periods and additional vertical field (VF) coils. The magnetic field strength is approximated by B = Bo[1-e cos θ - en cos (lφ - mθ)]. The helical ripple (en) is defined by en = Eno + Ena(p/ā)², where p is the radial coordinate. The aspect ratio of ATFSR is 7.0, with a helical ripple at the edge (Eha) of 0.22 and a transform at the edge (ta) of 0.90.

The paper discusses the MHD stability properties of the ATF configuration, which are expected to apply to ATFSR as well. The equilibrium limit is constrained by the Shafranov shift being less than ~50% of the minor radius. The stability boundary is determined by low-n internal ideal instabilities near the plasma edge. An average beta of 9% is chosen as the reference operating point for ATFSR, though there is uncertainty about this upper limit.

Engineering Challenges: Blanket and Shielding

A significant engineering challenge identified for ATFSR is the limited space between the plasma and the helical field (HF) coils (ΔS = 0.4 m). This space is insufficient for a blanket and shield, given a 0.1-m dewar and a 0.05-m first-wall thickness. To accommodate an efficient shielding material, ΔS would need to be increased to 0.6 to 0.7 m. Options to relax this tight spacing include using thinner, higher current density coils, employing lower aspect ratio HF coils, or designing a larger scale device.

Table III details the ATFSR blanket, shield, and coil parameters. The coil shield thickness (ΔS) is 0.4 m, and the blanket/shield thickness (ABS) is 1.5 m. The field at the coil (Bmax) is 10 T, with a maximum current density of 15 MA/m².

Confinement Model with Radial Electric Field Effects

The confinement properties of ATFSR are analyzed using the POPCON option in the WHIST transport code, incorporating models for the radial electric field. The particle and energy transport equations are adapted from tokamak analyses, with the radial electric field effects included in the radial fluxes.

The particle balance is described by ∂na/∂t + (1/V'(ρ)) ∂[V'(ρ)Γα]/∂ρ = Spa, and the ion energy balance by Σ(3/2) ∂(naTi)/∂t + (1/V'(ρ)) ∂[V'(ρ)Qα + ΓαTi]/∂ρ = Qea + Sea – ZaΓαφ'. The electron energy balance equation is similar, with specific terms for radiative losses and energy exchange.

The particle and heat fluxes are assumed to have neoclassical and anomalous contributions. The neoclassical fluxes are derived from models for particles trapped in helical ripples (ncr) and toroidally trapped particles (nca), along with an anomalous term (an). The integral formulation of Shaing provides a smooth fit to these fluxes.

The analysis incorporates the effect of the radial electric field, which strongly influences particle drifts in nonaxisymmetric plasmas. This leads to an algebraic equation for the radial electric field that is highly nonlinear. The paper discusses two methods for incorporating this field: assuming a parabolic profile or solving self-consistently from neoclassical particle fluxes.

Confinement Results and Discussion

A Gaussian heating profile simulating ion cyclotron resonant heating (ICRH) was used to evaluate auxiliary power needs for startup. Pellet fueling maintained deuterium and tritium densities.

Figure 4 shows steady-state contours for an assumed electric potential profile (ξ = 4). Ignition (Pfus = 0) occurs at <βτ> = 8%, with a fusion power output of ~300 MW. The reference operating values from Table I are achieved at the intersection of the ignition curve and the <βτ> = 9% contour. With assumptions for recirculating power fraction, thermal conversion efficiency, and blanket energy multiplication, the electron energy confinement time is estimated at ~0.5 s, and the ion energy confinement time is ~5 s, resulting in a global energy confinement time of 0.9 s.

For a case with ξ = 2, the ignition curve is raised, requiring ~50 MW of steady-state auxiliary power and yielding a global energy confinement time of 0.7 s. At ξ = 3, ignition occurs at the 9% beta curve, providing a single-point operating window.

At lower temperatures, neoclassical ion particle losses dominate, leading to a negative ambipolar electric potential. At higher temperatures, electron losses dominate, resulting in a positive potential. The transition zone involves small potentials and electric fields where resonant neoclassical helical ripple losses are significant.

Figure 5 illustrates steady-state contours with self-consistent electric field evolution through the transition zone and ξ = 4 thereafter. The potential is forced to asymptotically approach ξ = 4 at high temperatures, where neoclassical ripple-induced fluxes are reduced and more vulnerable to anomalous losses.

The study emphasizes that the ATFSR represents a preliminary scale-up of ATF, aiming for a more compact reactor. While the design offers high beta capabilities, challenges remain, particularly regarding the space for blanket and shielding. The authors suggest that lower aspect ratio coil designs or increased coil current density could address these issues. The physics involved extends into an experimentally untried regime, and further exploration of these phenomena is needed.

Conclusion

The ATFSR concept presents a promising path towards a compact fusion reactor by leveraging the high beta capabilities of low-aspect-ratio torsatrons. However, significant engineering challenges, primarily related to integrating adequate shielding within the compact design, need to be overcome. The paper concludes that further theoretical and experimental investigations are crucial to validate the predicted physics and refine the design for future fusion power plants.

Recurring Themes and Editorial Stance

The recurring themes in this issue revolve around advanced fusion reactor concepts, specifically focusing on the torsatron configuration. The articles explore the technical challenges and potential advantages of compact, high-beta designs like the ATFSR. There is a clear emphasis on the interplay between plasma physics (confinement, stability) and engineering constraints (size, shielding, coil design). The editorial stance appears to be one of scientific inquiry and exploration of alternative fusion approaches beyond traditional tokamaks, highlighting the ongoing research and development in the field of fusion energy.