Magnetic Confinement Geometry Research Articles

Norman Rostoker

Norman Rostoker, a nuclear fusion innovator and, in his words, “somewhat a renegade” advocate of research independent of the US Department of Energy, died on 25 December 2014 in Irvine, California. At the time of his death, Tri Alpha Energy, the company he cofounded to advance work in field-reversed magnetic containment methods, was building its third-generation machine.Norman RostokerAIP ESVA, GIFT OF NORMAN ROSTOKERPPT|High resolutionBorn on 16 August 1925 in Toronto, Rostoker went to the University of Toronto, where he earned a BA in science in 1946 and a master’s degree in 1947. After receiving a DSc in physics from the Carnegie Institute of Technology in 1950, he worked there as a research physicist until 1953. His 1950 work on electrical resistivity of Earth, based on the Green function method, had widespread impact. Modern petroleum prospecting with low-frequency electromagnetic waves uses and expands on the physics in Rostoker’s work, and his Green function method was used in his later solid-state theory and in the foundation of plasma theory.In 1954 Rostoker added to what is now known as the Korringa-Kohn-Rostoker approximation, a Green function method still widely used in calculating the electronic band structure in solids. He broke ground on theories of the statistical mechanics of particles with Coulomb interactions and on the treatment of inhomogeneities, fluctuations, and cyclotron-radius effects in plasmas. Rostoker built on his solid-state work by translating the test-particle method into plasma physics, whereby a gas of charged particles is viewed as a group of “dressed” particles in which each one has its own shielding cloud. The concept simplifies basic property calculations and especially the particle-in-cell simulation approach.That foray into plasma physics led Rostoker into the practical side of plasma fusion research. He worked at the Armour Research Foundation and General Atomics before becoming a professor of physics at the University of California (UC), San Diego, in 1962. Starting in 1967 he was IBM Professor of Engineering at Cornell University, and in 1972 he joined the faculty at UC Irvine. He served as chair of the physics and astronomy department from 1973 to 1976.Rostoker believed that clean fusion should be an almost limitless, non- polluting energy source. Once he had developed the theoretical foundation, he began working to make the technology a reality. He had a gift for being able to apply theory to develop innovative fusion reactor technology.Among the first generation of fusion energy trailblazers, Rostoker saw early on the simplicity of field-reversed magnetic confinement geometries. Magnetic “bottles” are effective if the field lines do not penetrate solid surfaces but instead bend and close on themselves. Tokamaks implement the confining field in a toroidal chamber but require a current inside the plasma to give the field a helical twist. In field-reversed configurations, field lines are closed, so they provide good confinement, but the chamber is cylindrical, so it is easy to construct and maintain. The anomalous transport characteristic of tokamaks can be avoided, and a compact reactor design becomes viable.At Cornell and UC Irvine, Rostoker pursued the use of collective fields to accelerate ions in plasma. That work inspired a generation of students, some of whom went on to develop innovative plasma acceleration methods. Rostoker meanwhile combined accelerator physics with the plasma physics of a field-reversed geometry for use in a fusion reactor; in that alone he held 27 US patents. His laboratory team focused on devising new approaches to the central fusion problems and was able to translate theory into hardware.Fusion demands extremely high energy ions. In his most significant insight, Rostoker proposed that high-energy, large-orbit particles, such as those in accelerators, can “ride over” disruptive plasma turbulence and average their effects to nearly zero. With that approach, now known as Norman’s conjecture, researchers can thus get around plasma instabilities that interfere with other designs. Rostoker also wanted to use the boron–proton fusion reaction to devise a fusion reactor whose surrounding structure is not degraded by neutron capture. In 1998 Rostoker and his group at UC Irvine spun off Tri Alpha Energy to carry the efforts further. Unable to gain enough funding from the Department of Energy, Rostoker thereafter kept the company independently funded. He instituted a chair in applied physics in 2012 at UC Irvine.Rostoker was boundlessly resourceful in his humor and was able to soften even the most sullen of people at the tensest of times. He also showed unlimited generosity to his students, whom he attracted to UC Irvine from around the world. He personally picked up one of us (Tajima), fresh from Japan, at the John Wayne Airport in September 1973.© 2015 American Institute of Physics.

Fluid models of impurity transport via drift wave turbulence

Turbulent transport due to drift waves is a critical issue for fusion physics across all magnetic confinement geometries. Three-component fluid equations are used to find the eigenmodes and eigenfrequencies of a nonuniform, magnetized plasma with a four dimensional fluctuation vector composed of fluctuations of the electron density, the working gas ion density, the impurity density, and the electrostatic plasma potential. This structure of the eigenmodes and eigenvectors is shown for two collisionality regimes: (i) the collisional drift waves appropriate for the scrape-off-layer and the edge plasma in limiter discharges and (ii) the trapped electron mode taken in the limit of a Terry-Horton fluid description for the core plasma. From the eigenmodes and eigenvectors the part of the density and potential fluctuations that are out-of-phase is computed. The quasilinear particle fluxes are analyzed as a function of the power spectrum of the plasma potential fluctuations and the gradient parameters characterizing the Ohmic, H, and internal transport barrier confinement modes. A reversal in a direction of impurity flux is observed by changing the sign of the impurity density gradient length. After reversal, the impurity flux is directed outward and it is a favorable for fusion plasmas.

Rapid Fourier space solution of linear partial integro-differential equations in toroidal magnetic confinement geometries

Fluctuating quantities in magnetic confinement geometries often inherit a strong anisotropy along the field lines. One technique for describing these structures is the use of a certain set of Fourier components on the tori of nested flux surfaces. We describe an implementation of this approach for solving partial differential equations, like Poisson's equation, where a different set of Fourier components may be chosen on each surface according to the changing safety factor profile. Allowing the resolved components to change to follow the anisotropy significantly reduces the total number of degrees of freedom in the description. This can permit large gains in computational performance. We describe, in particular, how this approach can be applied to rapidly solve the gyrokinetic Poisson equation in a particle code, ORB5 (Jolliet et al., (2007) [5]), with a regular (non-field-aligned) mesh.

Energy Confinement Scaling Predictions for the Stabilized Tandem Mirror

The tandem mirror remains an attractive magnetic confinement geometry for fusion. The absence of toroidal curvature and relatively weak internal plasma parallel current gives the system strongly favorable stability and transport properties. Recent GAMMA-10 experiments demonstrate that sheared plasma rotation suppresses turbulent radial losses. Total energy confinement times calculated for the GAMMA-10 are found to be significantly larger than the corresponding empirical confinement times in toroidal devices. The tandem mirror appears to have a qualitatively different form of drift wave radial transport from that in toroidal devices.

First principles based simulations of instabilities and turbulence

It is now widely believed that low frequency turbulence developing from small-scale instabilities is responsible for the phenomenon of anomalous transport generally observed in magnetic confinement fusion experiments. The micro-instabilities are driven by gradients of equilibrium density, ion and electron temperatures and magnetic field strength. Gyrokinetic theory is based on the Vlasov–Maxwell equations and, consistent with the ordering, averages out the fast particle gyromotion, reducing the phase space from 6 to 5 dimensions. Solving the resulting equations is a non-trivial task. Difficulties are associated with the magnetic confinement geometry, the strong disparities in space and time scales perpendicular and parallel to B, the different time scales of ion and electron dynamics, and the complex nonlinear behaviour of the system. The main numerical methods are briefly presented together with some recent developments and improvements to the basic algorithms. Recent results are shown, with emphasis on the roles of zonal E × B flows, of parallel nonlinearity and of toroidal coupling on the saturation of ion temperature gradient (ITG) driven turbulence in tokamaks.

Transonic Magnetohydrodynamic Flows in Laboratory and Astrophysical Plasmas

Magnetohydrodynamic (MHD) waves control the dynamics of plasma, the main constituent of the universe. They occur as the natural response to global excitation. Frequency and wave forms are determined by the magnetic confinement geometry and distribution of background equilibrium variables. Hence, measurement of the spectrum of MHD waves gives direct information on the internal state of the plasma, provided a theoretical model is available to solve the forward and inverse spectral problems. This activity has been called MHD spectroscopy, [1, Goedbloed et al. Phys. Control. Fusion 35 B277 (1993)] in analogy with quantum mechanical spectroscopy which also involves eigenvalue problems of linear operators. The terminology also entails a program, viz. to improve the accuracy of our knowledge of plasmas, both in the laboratory and in astrophysics.While such a program is highly desirable a new angle to the study of MHD waves coming from the effects of transonic background flows requires a complete revision of all previous spectral results. Transonic flows in laboratory plasmas result from neutral beam heating (causing toroidal rotation) whereas they are commonplace for astrophysical plasmas (flows in coronal flux tubes, stellar winds, rotating accretion disks, jets emitted from radio galaxies, etc.). Such flows upset the standard theoretical approach to plasma dynamics, consisting of a separate study of equilibrium state and of the perturbations of this background. We will discuss a new approach to the dichotomy consisting of a study of the similarities of the nonlinear stationary flow patterns and the different linear waves structures that occur when the background speed traverses the full range of critical speeds (from "slow magnetosonic" to "Alfvén" to "fast magnetosonic"). This requires the development of new computational tools which yield a plethora of new waves and instabilities. We will illustrate this with results on tokomak and accretion disk plasmas.

Test particle simulations for transport in toroidal plasmas

The authors derive the guiding center equations of motion from the phase space Euler–Lagrange formulation for the motion of a charged particle in toroidal magnetic confinement geometry. The guiding center equations are numerically solved together with the Monte Carlo Coulomb collisional pitch angle scattering. The numerically calculated microscopic diffusion coefficients for various values of collisionality ν* in the case of no electrostatic potential agree well with the results of neoclassical theory. The diffusion coefficient is then measured in the presence of a model electrostatic drift wave fluctuation and an equilibrium potential. The diffusion coefficient increases with increasing fluctuation amplitude while the equilibrium potential diminishes the diffusion processes through both the orbit squeezing and the Er×B shear flow of the poloidal velocity.

Forming and maintaining a potential well in a quasispherical magnetic trap

The formation and maintenance of an electrostatic potential well by injecting electrons into a quasispherical cusped magnetic confinement geometry is studied experimentally, as a function of plasma fill density and of the energy and current of the injected electrons. A model is developed to analyze the experiment. It is found that the potential is comparable to the energy of the injected electrons at low density, and decreases as an increasing density of cold plasma fills the device because of ionization or wall bombardment. Implications for fusion based on electrostatic/magnetic confinement are discussed.

Kinetic stability of large-scale MHD modes

Two independent particle methods, which are based on the Vlasov fluid model, have been developed to examine the modification of magnetohydrodynamic instabillities due to finite orbit effects. The relative cost and accuracy of the methods, the dispersion functional analysis and initial value method, are discussed and the results of applying the methods to a field-reversed, magnetic confinement geometry are presented.

Beam Probe Space-Potential Measurement in a Minimum-B Field

A measurement of plasma space potential in a minimum-B magnetic field has been made with a particle beam probe. The diagnostic technique is an extension of conventional heavy ion beam probing in that, among other features, the probing beam is neutral rather than ionized cesium and the parallel-plate electrostatic energy analyzer is fully characterized in a new manner which permits its use in complex magnetic confinement geometries.

Ion source operation with different magnetic confinement geometries

A comparison has been made between the longitudinal line cusp and the ‘‘continuous’’ checkerboard magnet geometries. We find that the checkerboard arrangement can provide a larger uniform density profile with approximately 20% less plasma density than the longitudinal line cusp. Results seem to indicate that the reduction in plasma density is closely related to the containment of primary ionizing electrons by the permanent magnets. A new magneto-electrostatic containment scheme was generated by using an internal magnetic cage system. The overall efficiency of this ion source was increased when it was operated with a xenon or argon plasma.

Confinement and related transport in extrap geometry

The properties of the plasma dynamic equilibrium are investigated for the Extrap magnetic confinement geometry. The temperatures achieved so far in the high-β pinches are much lower than the predicted values. Here, it is shown that the particle containment in Extrap may be improved as compared to the other pinches due to the electrostatic confinement. An analytic solution for the profiles of the plasma parameters are found under the assumption that the energy is lost primarily in the radial direction by heat conduction and convection. An estimate of the radial particle confinement time is given, showing favourable scaling with plasma density and temperature. The conventional assumption of a uniform current density is shown to be unjustified in the case of an inhomogeneous electron temperature. An analytical expression is found for the pinch radius at different mechanisms of the heat transport.

Plasma and Engineering Parameters for a Fusion Powered Rocket

With the advent of hard superconductors, thermonuclear fusion reactors can be seriously considered as a continuous power source for high-powered interplanetary missions. Assuming a solution will be forthcoming to solve the plasma instability and confinement problems, a preliminary study is presented showing the relationship of pertinent plasma parameters. The set of equations describing these pertinent parameters indicates a typical 25 megawatt net power motor could be expected to operate at a plasma ion density of ~1014/cm3 and an average ion temperature of ~105 kev. The plasma would be confined by a magnetic field of approximately 50 kilogauss, with a total motor weight of approximately 25,000 lbs. The reacting plasma is assumed within a multipolar magnetic confinement geometry. The power lost to neutrons by most fusion reactors shows that 3He-D is the unique fusion reaction suitable for space propulsion. The relationship of plasma particle density, ion temperature, and confining magnetic field to total fusion power is presented. The significant plasma losses of bremsstrahlung and gyromagnetic radiation are discussed and equations describing their relationship to the plasma parameters are calculated. The consequences resulting from different values of ß (the ratio of plasma to magnetic confinement pressures) are investigated. All equations are derived with ß as a dependent variable. Necessary average plasma containment time is studied to indicate the magnitude of required average plasma confinement time. The rate of generation of both DD and DT neutrons is investigated over the range of interest.