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With the increasingly urgent need to find solutions to the impending energy crisis, there is growing interest within the fusion community in revisiting the concept of the fusion–fission hybrid reactor. But how soon could such reactors be realized, and could they meet the challenges of the coming century?

This report summarizes the findings and recommendations of the second Committee of Visitors (COV) whose charge was to review the manner in which the U. S. Department of Energy’s Office of Fusion Energy Science (OFES) manages certain programs under its charter. The specific programs reviewed by this COV involve confinement innovation and basic plasma sciences. The charge letter from the Department of Energy is included as Appendix A.

We have carried out a detailed analysis that compares steady state versus pulsed tokamak reactors. The motivations are as follows. Steady state current drive has turned out to be more difficult than expected - it takes too many watts to drive an Ampere, which has a negative effect on power balance and economics. This is partially compensated by the recent development of high temperature REBCO superconductors, which offers the promise of more compact, lower cost tokamak reactors, both steady state and pulsed. Of renewed interest is the reduction in size of pulsed reactors because of the possibility of higher field OH transformers for a given required pulse size. Our main conclusion is that pulsed reactors may indeed be competitive with steady state reactors and this issue should be re-examined with more detailed engineering level studies.

This is the report of a panel set up by the U.S. Department of Energy Fusion Energy Sciences Advisory Committee (FESAC) in response to a charge letter on October 5, 2000, from Dr. Mildred Dresselhaus, then Director of the DOE's Office of Science. In that letter, Dr. Dresselhaus asked the FESAC to investigate the subject of burning plasma science. The report addresses several topics, including the scientific issues to be addressed by a burning plasma experiment and its major supporting elements, identification of issues that are generic to toroidal confinement, and the role of the Next-Step Options (NSO) Program.

The analytic theory presented in Paper I is converted into a form convenient for numerical analysis. A fast and accurate code has been written using this numerical formulation. The results are presented by first defining a reference set of physical parameters based on experimental data from high performance discharges. Numerically obtained scaling relations of maximum achievable elongation versus inverse aspect ratio are obtained for various values of poloidal beta, wall radius and feedback capability parameter in ranges near the reference values. It is also shown that each value of maximum elongation occurs at a corresponding value of optimized triangularity, whose scaling is also determined as a function of inverse aspect ratio. The results show that the theoretical predictions of maximum elongation are slightly higher than experimental observations for high performance discharges as measured by high average pressure. The theoretical optimized triangularity values are noticeably lower. We suggest that the explanation is associated with the observation that high performance involves not only MHD considerations, but also transport as characterized by confinement time. Operation away from the MHD optimum may still lead to higher performance if there are more than compensatory gains in the confinement time. Unfortunately, while the empirical scaling of the confinement time with the elongation has been determined, the dependence on the triangularity has still not been quantified. This information is needed in order to perform more accurate overall optimizations in future experimental designs.

A highly elongated plasma is desirable in order to increase plasma pressure and energy confinement to maximize fusion power output. However, there is a limit to the maximum achievable elongation which is set by vertical instabilities driven by the \\(n=0\\) MHD mode. This limit can be increased by optimizing several parameters characterizing the plasma and the wall. The purpose of our study is to explore how and to what extent this can be done. Specifically, we extend many earlier calculations of the \\(n=0\\) mode and numerically determine scaling relations for the maximum elongation as a function of dimensionless parameters describing (1) the plasma profile (\\(\\beta_p\\) and \\(l_i\\)), (2) the plasma shape (\\(\\epsilon\\) and \\(\\delta\\)), (3) the wall radius (\\(b/a\\)) and (4) most importantly the feedback system capability parameter \\(\\gamma\\tau_w\\). These numerical calculations rely on a new formulation of \\(n=0\\) MHD theory we recently developed [Freidberg et. al. 2015; Lee et. al. 2015] that reduces the 2-D stability problem into a 1-D problem. This method includes all the physics of the ideal MHD axisymmetric instability while reducing the computation time significantly, so that many parameters can be explored during the optimization process. Perhaps the most useful final result is a simple analytic fit to the simulations which gives the maximum elongation and corresponding optimized triangularity as functions \\(\\kappa(\\epsilon,\\beta_p,l_i,b/a,\\gamma\\tau_w)\\) and \\(\\delta(\\epsilon,\\beta_p,l_i,b/a,\\gamma\\tau_w)\\). The scaling relations we present include the effects of the optimal triangularity and the finite aspect ratio on the maximum elongation, and can be useful for determining optimized plasma shapes in current experiments and future tokamak designs.

We present a new fast solver to calculate fixed-boundary plasma equilibria in toroidally axisymmetric geometries. By combining conformal mapping with Fourier and integral equation methods on the unit disk, we show that high-order accuracy can be achieved for the solution of the equilibrium equation and its first and second derivatives. Smooth arbitrary plasma cross-sections as well as arbitrary pressure and poloidal current profiles are used as initial data for the solver. Equilibria with large Shafranov shifts can be computed without difficulty. Spectral convergence is demonstrated by comparing the numerical solution with a known exact analytic solution. A fusion-relevant example of an equilibrium with a pressure pedestal is also presented.

Using a two-dimensional fluid description, we investigate the nonlinear radial-longitudinal dynamics of intense beams in storage rings and cyclotrons. With a multiscale analysis separating the time scale associated with the betatron motion and the slower time scale associated with space-charge effects, we show that the longitudinal-radial vortex motion can be understood in the frame moving with the charged beam as the nonlinear advection of the beam by the \\(\\mathbf{E}\\times\\mathbf{B}\\) velocity field, where \\(\\mathbf{E}\\) is the electric field due to the space charge and \\(\\mathbf{B}\\) is the external magnetic field. This interpretation provides simple explanations for the stability of round beams and for the development of spiral halos in elongated beams. By numerically solving the nonlinear advection equation for the beam density, we find that it is also in quantitative agreement with results obtained in PIC simulations.

Session 1377 The New Discipline of Nuclear Engineering Jeffrey P. Freidberg Massachusetts Institute of Technology I.

This document is the product of a stellarator community workshop, organized by the National Stellarator Coordinating Committee and referred to as Stellcon, that was held in Cambridge, Massachusetts in February 2016, hosted by MIT. The workshop was widely advertised, and was attended by 40 scientists from 12 different institutions including national labs, universities and private industry, as well as a representative from the Department of Energy. The final section of this document describes areas of community wide consensus that were developed as a result of the discussions held at that workshop. Areas where further study would be helpful to generate a consensus path forward for the US stellarator program are also discussed. The program outlined in this document is directly responsive to many of the strategic priorities of FES as articulated in “Fusion Energy Sciences: A Ten-Year Perspective (2015–2025)” [ 1 ]. The natural disruption immunity of the stellarator directly addresses “Elimination of transient events that can be deleterious to toroidal fusion plasma confinement devices” an area of critical importance for the US fusion energy sciences enterprise over the next decade. Another critical area of research “Strengthening our partnerships with international research facilities,” is being significantly advanced on the W7-X stellarator in Germany and serves as a test-bed for development of successful international collaboration on ITER. This report also outlines how materials science as it relates to plasma and fusion sciences, another critical research area, can be carried out effectively in a stellarator. Additionally, significant advances along two of the Research Directions outlined in the report; “Burning Plasma Science: Foundations—Next-generation research capabilities”, and “Burning Plasma Science: Long pulse—Sustainment of Long-Pulse Plasma Equilibria” are proposed.