Herbert L Berk

Bio: Herbert L Berk is an academic researcher from University of Texas at Austin. The author has contributed to research in topics: Instability & Tokamak. The author has an hindex of 50, co-authored 227 publications receiving 7631 citations. Previous affiliations of Herbert L Berk include Lawrence Livermore National Laboratory & General Atomics.

Chapter 5: Physics of energetic ions

Abstract: This chapter reviews the progress accomplished since the redaction of the first ITER Physics Basis (1999 Nucl Fusion 39 2137-664) in the field of energetic ion physics and its possible impact on burning plasma regimes New schemes to create energetic ions simulating the fusion-produced alphas are introduced, accessing experimental conditions of direct relevance for burning plasmas, in terms of the Alfvenic Mach number and of the normalised pressure gradient of the energetic ions, though orbit characteristics and size cannot always match those of ITER Based on the experimental and theoretical knowledge of the effects of the toroidal magnetic field ripple on direct fast ion losses, ferritic inserts in ITER are expected to provide a significant reduction of ripple alpha losses in reversed shear configurations The nonlinear fast ion interaction with kink and tearing modes is qualitatively understood, but quantitative predictions are missing, particularly for the stabilisation of sawteeth by fast particles that can trigger neoclassical tearing modes A large database on the linear stability properties of the modes interacting with energetic ions, such as the Alfven eigenmode has been constructed Comparisons between theoretical predictions and experimental measurements of mode structures and drive/damping rates approach a satisfactory degree of consistency, though systematic measurements and theory comparisons of damping and drive of intermediate and high mode numbers, the most relevant for ITER, still need to be performed The nonlinear behaviour of Alfven eigenmodes close to marginal stability is well characterized theoretically and experimentally, which gives the opportunity to extract some information on the particle phase space distribution from the measured instability spectral features Much less data exists for strongly unstable scenarios, characterised by nonlinear dynamical processes leading to energetic ion redistribution and losses, and identified in nonlinear numerical simulations of Alfven eigenmodes and energetic particle modes Comparisons with theoretical and numerical analyses are needed to assess the potential implications of these regimes on burning plasma scenarios, including in the presence of a large number of modes simultaneously driven unstable by the fast ions

Universal Eigenmode in a Strongly Sheared Magnetic Field

Abstract: It is shown, contrary to previous work, that in the presence of large shear ($\frac{{L}_{S}}{{R}_{P}}l\frac{{R}_{P}}{{a}_{i}}$) an unstable universal eigenmode exists. The criterion for the stabilization of this mode for long wavelengths (${k}_{\ensuremath{\perp}}{a}_{i}\ensuremath{\lesssim}1$) is $\frac{{L}_{S}}{{R}_{P}}l{(\frac{M}{m})}^{\frac{1}{3}}$ which is more restrictive than the usual criterion for stabilization of the transient (convective) modes ordinarily considered.

Theoretical Interpretation of Alfvén Cascades in Tokamaks with Nonmonotonic q Profiles

Abstract: Alfv\'en spectra in a reversed-shear tokamak plasma with a population of energetic ions exhibit a quasiperiodic pattern of primarily upward frequency sweeping (Alfv\'en cascade). Presented here is an explanation for such asymmetric sweeping behavior which involves finding a new energetic particle mode localized around the point of zero magnetic shear.

Physics and Applications of Bismuth Ferrite

Abstract: 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.

Theory of plasma transport in toroidal confinement systems

Abstract: 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.

Waves and turbulence on a beta-plane

Abstract: 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).

Percolation, statistical topography, and transport in random media

Abstract: 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.

Chapter 1: Overview and summary

Abstract: 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.