BiFeO3 is perhaps the only material that is both magnetic and a strong ferroelectric at room temperature. As a result, it has had an impact on the field of multiferroics that is comparable to that of yttrium barium copper oxide (YBCO) on superconductors, with hundreds of publications devoted to it in the past few years. In this Review, we try to summarize both the basic physics and unresolved aspects of BiFeO3 (which are still being discovered with several new phase transitions reported in the past few months) and device applications, which center on spintronics and memory devices that can be addressed both electrically and magnetically.

Physics and Applications of Bismuth Ferrite

The dissipation induced by coulomb-collisional scattering provides an irreducible minimum, and thus a useful standard for comparison, for transport processes in a hot, magnetically confined plasma. The kinetic description of this dissipation is provided by an equation of the Fokker-Planck form. As in the standard transport theory for a neutral gas, approximate solution of the Fokker-Planck equation permits the calculation of transport coefficients, which linearly relate the fluxes of particles, energy, and electric charge, to the density and temperature gradients, and to the electric field. The transport relations are useful in studying the confinement properties of present and future experimental devices for research in controlled thermonuclear fusion. The transport theory for a magnetized plasma (in which the Larmor radius is much smaller than gradient scale lengths describing the plasma fluid) departs from the theory for a neutral gas in several fundamental ways. Thus, transport coefficients for a magnetized plasma can be calculated even when the collisional mean free path is much longer than the gradient scale length (as would pertain in thermonuclear regimes). Such transport coefficients are generally nonlocal, being defined in terms of averages over surfaces with macroscopic dimensions. Furthermore, when the mean free path is long, the magnetized-plasma transport coefficients depend crucially upon the magnetic field geometry, the effects of which must be treated at the kinetic level of the Fokker-Planck equation. The results display several novel couplings between collisional dissipation and the electromagnetic field. The present review of magnetized-plasma transport theory is intended to be as widely accessible as possible. Thus the relevant features of magnetic confinement in closed (toroidal) systems, and of charged particles in spatially varying fields, are derived, at least in outline, from first principles. Although consideration is given to "classical" transport in which most field geometric effects are omitted, major emphasis is placed on the "neoclassical" theory which has been developed over the last decade. Neoclassical transport coefficients are specifically relevant to a magnetically confined plasma, rather than to just a magnetized plasma; their unusual features, such as nonlocality and geometry dependence, become particularly important in the high temperature regime of proposed thermonuclear reactors. The area of neoclassical theory which seems most complete---its application to axisymmetric tokamak-type confinement systems---is correspondingly stressed.

/pdf/theory-of-plasma-transport-in-toroidal-confinement-systems-3zu124w3dl.pdf

Theory of plasma transport in toroidal confinement systems

Two-dimensional eddies in a homogeneous fluid at large Reynolds number, if closely packed, are known to evolve towards larger scales. In the presence of a restoring force, the geophysical beta-effect, this cascade produces a field of waves without loss of energy, and the turbulent migration of the dominant scale nearly ceases at a wavenumber kβ = (β/2U)½ independent of the initial conditions other than U, the r.m.s. particle speed, and β, the northward gradient of the Coriolis frequency.The conversion of turbulence into waves yields, in addition, more narrowly peaked wavenumber spectra and less fine-structure in the spatial maps, while smoothly distributing the energy about physical space.The theory is discussed, using known integral constraints and similarity solutions, model equations, weak-interaction wave theory (which provides the terminus for the cascade) and other linearized instability theory. Computer experiments with both finite-difference and spectral codes are reported. The central quantity is the cascade rate, defined as
 \[
 T = 2\int_0^{\infty} kF(k)dk/U^3\langle k\rangle ,
 \]
 where F is the nonlinear transfer spectrum and 〈k〉 the mean wavenumber of the energy spectrum. (In unforced inviscid flow T is simply U−1d〈k〉−1/dt, or the rate at which the dominant scale expands in time t.) T is shown to have a mean value of 3·0 × 10−2 for pure two-dimensional turbulence, but this decreases by a factor of five at the transition to wave motion. We infer from weak-interaction theory even smaller values for k [Lt ] kβ.After passing through a state of propagating waves, the homogeneous cascade tends towards a flow of alternating zonal jets which, we suggest, are almost perfectly steady. When the energy is intermittent in space, however, model equations show that the cascade is halted simply by the spreading of energy about space, and then the end state of a zonal flow is probably not achieved.The geophysical application is that the cascade of pure turbulence to large scales is defeated by wave propagation, helping to explain why the energy-containing eddies in the ocean and atmosphere, though significantly nonlinear, fail to reach the size of their respective domains, and are much smaller. For typical ocean flows, . In addition the cascade generates, by itself, zonal flow (or more generally, flow along geostrophic contours).

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112075001504

Waves and turbulence on a beta-plane

A review of classical percolation theory is presented, with an emphasis on novel applications to statistical topography, turbulent diffusion, and heterogeneous media. Statistical topography involves the geometrical properties of the isosets (contour lines or surfaces) of a random potential $\ensuremath{\psi}(\mathrm{x})$. For rapidly decaying correlations of $\ensuremath{\psi}$, the isopotentials fall into the same universality class as the perimeters of percolation clusters. The topography of long-range correlated potentials involves many length scales and is associated either with the correlated percolation problem or with Mandelbrot's fractional Brownian reliefs. In all cases, the concept of fractal dimension is particularly fruitful in characterizing the geometry of random fields. The physical applications of statistical topography include diffusion in random velocity fields, heat and particle transport in turbulent plasmas, quantum Hall effect, magnetoresistance in inhomogeneous conductors with the classical Hall effect, and many others where random isopotentials are relevant. A geometrical approach to studying transport in random media, which captures essential qualitative features of the described phenomena, is advocated.

/pdf/percolation-statistical-topography-and-transport-in-random-1ddemlupey.pdf

Percolation, statistical topography, and transport in random media

The ITER Physics Basis presents and evaluates the physics rules and methodologies for plasma performance projections, which provide the basis for the design of a tokamak burning plasma device whose goal is to demonstrate the scientific and technological feasibility of fusion energy for peaceful purposes. This Chapter summarizes the physics basis for burning plasma projections, which is developed in detail by the ITER Physics Expert Groups in subsequent chapters. To set context, the design guidelines and requirements established in the report of ITER Special Working Group 1 are presented, as are the specifics of the tokamak design developed in the Final Design Report of the ITER Engineering Design Activities, which exemplifies burning tokamak plasma experiments. The behaviour of a tokamak plasma is determined by the interaction of many diverse physics processes, all of which bear on projections for both a burning plasma experiment and an eventual tokamak reactor. Key processes summarized here are energy and particle confinement and the H-mode power threshold; MHD stability, including pressure and density limits, neoclassical islands, error fields, disruptions, sawteeth, and ELMs; power and particle exhaust, involving divertor power dispersal, helium exhaust, fuelling and density control, H-mode edge transition region, erosion of plasma facing components, tritium retention; energetic particle physics; auxiliary power physics; and the physics of plasma diagnostics. Summaries of projection methodologies, together with estimates of their attendant uncertainties, are presented in each of these areas. Since each physics element has its own scaling properties, an integrated experimental demonstration of the balance between the combined processes which obtains in a reactor plasma is inaccessible to contemporary experimental facilities: it requires a reactor scale device. It is argued, moreover, that a burning plasma experiment can be sufficiently flexible to permit operation in a steady state mode, with non-inductive plasma current drive, as well as in a pulsed mode where current is inductively driven. Overall, the ITER Physics Basis can support a range of candidate designs for a tokamak burning plasma facility. For each design, there will remain a significant uncertainty in the projected performance, but the projection methodologies outlined here do suffice to specify the major parameters of such a facility and form the basis for assuring that its phased operation will return sufficient information to design a prototype commercial fusion power reactor, thus fulfilling the goal of the ITER project.

https://iopscience.iop.org/article/10.1088/0029-5515/39/12/301/pdf

Chapter 1: Overview and summary

: Report is a review of research and studies of fusion with low neutron emission (advanced) fuels (such as Deuterium with Helium 3); it is an assessment of the feasibility of developing advanced fuels as a fusion power source for space propulsion and electrical power generation.

Advanced fusion power: A preliminary assessment

Fusion: funding alternatives.

For an MHD stable system, we investigate the interplay between drift wave (ETG and gyro-Bohm) radial transport and axial losses in the GAMMA-10 experimental facility and the proposed kinetically stabilized tandem mirror (KSTM) fusion reactor. Numerical coefficients in the models are taken to be consistent with tokamak and stellarator databases. The trade off between radial losses and the Pastukhov end losses is examined. We propose the use of a genetic algorithm to optimize the fusion power amplification Q = P
 fusion/P
 injected as a function of the key system parameters.

Global Energy Confinement Scaling Predictions for Tandem Mirrors

The nonlinear dynamics of a linearly unstable mode in a driven kinetic system is investigated to determine scaling of the saturated fields near the instability threshold. To leading order, this problem reduces to solving an integral equation with a temporally nonlocal cubic term. This equation can exhibit a self-similar solution that blows up in a finite time. When the blow-up occurs, higher nonlinearities become important and the mode saturates due to plateau formation arising from particle trapping in the wave. Otherwise, the simplified equation gives a regular solution that leads to a different saturation scaling reflecting the closeness to the instability threshold.

/pdf/nonlinear-dynamics-of-a-driven-mode-near-marginal-stability-27xdohhcle.pdf

Nonlinear dynamics of a driven mode near marginal stability

Measurements of high-frequency oscillations in JET [Joint European Torus], JT-60U, Alcator C-Mod, DIII-D, and TFTR [Tokamak Fusion Test Reactor] plasmas are contributing to a new understanding of fast ion-driven instabilities relevant to Advanced Tokamak (AT) regimes. A model based on the transition from a cylindrical-like frequency-chirping mode to the Toroidal Alfven Eigenmode (TAE) has successfully encompassed many of the characteristics seen in experiments. In a surprising development, the use of internal density fluctuation diagnostics has revealed many more modes than has been detected on edge magnetic probes. A corollary discovery is the observation of modes excited by fast particles traveling well below the Alfven velocity. These observations open up new opportunities for investigating a ''sea of Alfven Eigenmodes'' in present-scale experiments, and highlight the need for core fluctuation and fast ion measurements in a future burning-plasma experiment.

/pdf/observation-of-energetic-particle-driven-modes-relevant-to-n55q9tyouq.pdf

Herbert L Berk

Papers

Advanced fusion power: A preliminary assessment

Fusion: funding alternatives.

Global Energy Confinement Scaling Predictions for Tandem Mirrors

Nonlinear dynamics of a driven mode near marginal stability

Observation of Energetic Particle Driven Modes Relevant to Advanced Tokamak Regimes