QUANTUM gravitational effects are usually ignored in calculations of the formation and evolution of black holes. The justification for this is that the radius of curvature of space-time outside the event horizon is very large compared to the Planck length (Għ/c3)1/2 ≈ 10−33 cm, the length scale on which quantum fluctuations of the metric are expected to be of order unity. This means that the energy density of particles created by the gravitational field is small compared to the space-time curvature. Even though quantum effects may be small locally, they may still, however, add up to produce a significant effect over the lifetime of the Universe ≈ 1017 s which is very long compared to the Planck time ≈ 10−43 s. The purpose of this letter is to show that this indeed may be the case: it seems that any black hole will create and emit particles such as neutrinos or photons at just the rate that one would expect if the black hole was a body with a temperature of (κ/2π) (ħ/2k) ≈ 10−6 (M/M)K where κ is the surface gravity of the black hole1. As a black hole emits this thermal radiation one would expect it to lose mass. This in turn would increase the surface gravity and so increase the rate of emission. The black hole would therefore have a finite life of the order of 1071 (M/M)−3 s. For a black hole of solar mass this is much longer than the age of the Universe. There might, however, be much smaller black holes which were formed by fluctuations in the early Universe2. Any such black hole of mass less than 1015 g would have evaporated by now. Near the end of its life the rate of emission would be very high and about 1030 erg would be released in the last 0.1 s. This is a fairly small explosion by astronomical standards but it is equivalent to about 1 million 1 Mton hydrogen bombs. It is often said that nothing can escape from a black hole. But in 1974, Stephen Hawking realized that, owing to quantum effects, black holes should emit particles with a thermal distribution of energies — as if the black hole had a temperature inversely proportional to its mass. In addition to putting black-hole thermodynamics on a firmer footing, this discovery led Hawking to postulate 'black hole explosions', as primordial black holes end their lives in an accelerating release of energy.

Black Hole Explosions

A comprehensive review of zonal flow phenomena in plasmas is presented. While the emphasis is on zonal flows in laboratory plasmas, planetary zonal flows are discussed as well. The review presents the status of theory, numerical simulation and experiments relevant to zonal flows. The emphasis is on developing an integrated understanding of the dynamics of drift wave–zonal flow turbulence by combining detailed studies of the generation of zonal flows by drift waves, the back-interaction of zonal flows on the drift waves, and the various feedback loops by which the system regulates and organizes itself. The implications of zonal flow phenomena for confinement in, and the phenomena of fusion devices are discussed. Special attention is given to the comparison of experiment with theory and to identifying directions for progress in future research.

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Zonal flows in plasma—a review

The advent of ultraintense laser pulses generated by the technique of chirped pulse amplification (CPA) along with the development of high-fluence laser materials has opened up an entirely new field of optics. The electromagnetic field intensities produced by these techniques, in excess of ${10}^{18}\phantom{\rule{0.3em}{0ex}}\mathrm{W}∕{\mathrm{cm}}^{2}$, lead to relativistic electron motion in the laser field. The CPA method is reviewed and the future growth of laser technique is discussed, including the prospect of generating the ultimate power of a zettawatt. A number of consequences of relativistic-strength optical fields are surveyed. In contrast to the nonrelativistic regime, these laser fields are capable of moving matter more effectively, including motion in the direction of laser propagation. One of the consequences of this is wakefield generation, a relativistic version of optical rectification, in which longitudinal field effects could be as large as the transverse ones. In addition to this, other effects may occur, including relativistic focusing, relativistic transparency, nonlinear modulation and multiple harmonic generation, and strong coupling to matter and other fields (such as high-frequency radiation). A proper utilization of these phenomena and effects leads to the new technology of relativistic engineering, in which light-matter interactions in the relativistic regime drives the development of laser-driven accelerator science. A number of significant applications are reviewed, including the fast ignition of an inertially confined fusion target by short-pulsed laser energy and potential sources of energetic particles (electrons, protons, other ions, positrons, pions, etc.). The coupling of an intense laser field to matter also has implications for the study of the highest energies in astrophysics, such as ultrahigh-energy cosmic rays, with energies in excess of ${10}^{20}\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. The laser fields can be so intense as to make the accelerating field large enough for general relativistic effects (via the equivalence principle) to be examined in the laboratory. It will also enable one to access the nonlinear regime of quantum electrodynamics, where the effects of radiative damping are no longer negligible. Furthermore, when the fields are close to the Schwinger value, the vacuum can behave like a nonlinear medium in much the same way as ordinary dielectric matter expanded to laser radiation in the early days of laser research.

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Optics in the relativistic regime

Review of Charged Particle Dynamics. Beam Optics and Focusing Systems Without Space Charge. Linear Beam Optics with Space Charge. Self-Consistent Theory of Beams. Emittance Variation. Beam Physics Research from 1993 to 2007. Appendices. List of Frequently Used Symbols. Bibliography. Index.

Theory and Design of Charged Particle Beams

One of the scientific success stories of fusion research over the past decade is the development of the ExB shear stabilization model to explain the formation of transport barriers in magnetic confinement devices. This model was originally developed to explain the transport barrier formed at the plasma edge in tokamaks after the L (low) to H (high) transition. This concept has the universality needed to explain the edge transport barriers seen in limiter and divertor tokamaks, stellarators, and mirror machines. More recently, this model has been applied to explain the further confinement improvement from H (high)-mode to VH (very high)-mode seen in some tokamaks, where the edge transport barrier becomes wider. Most recently, this paradigm has been applied to the core transport barriers formed in plasmas with negative or low magnetic shear in the plasma core. These examples of confinement improvement are of considerable physical interest; it is not often that a system self-organizes to a higher energy state with reduced turbulence and transport when an additional source of free energy is applied to it. The transport decrease that is associated with ExB velocity shear effects also has significant practical consequences for fusion research. The fundamental physics involved in transport reduction is the effect of ExB shear on the growth, radial extent and phase correlation of turbulent eddies in the plasma. The same fundamental transport reduction process can be operational in various portions of the plasma because there are a number ways to change the radial electric field Er. An important theme in this area is the synergistic effect of ExB velocity shear and magnetic shear. Although the ExB velocity shear appears to have an effect on broader classes of microturbulence, magnetic shear can mitigate some potentially harmful effects of ExB velocity shear and facilitate turbulence stabilization.

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Effects of E×B velocity shear and magnetic shear on turbulence and transport in magnetic confinement devices

Dedication Foreword by Baruch Levush Preface Acknowledgements List of Contributors List of Acronyms and Abbreviations Chapter 1 Introduction and Overview Chapter 2 Historical Highlights Chapter 3 Klystrons Chapter 4 Traveling Waves Tubes (TWTs) Chapter 5 Gyro-Amplifiers Chapter 6 Crossed-Field Devices Chapter 7 Microfabricated MVEDs Chapter 8 Advanced Electron Beam Sources Chapter 9 How to Achieve Linear Amplification Chapter 10 Computational Modeling Chapter 11 Next-Generation Microwave Structures and Circuits Chapter 12 Advanced Materials Technologies for MVEDs Chapter 13 High Power Microwave (HPM) Sources Chapter 14 Affordable Manufacturing Chapter 15 Emerging Applications and Future Possibilities Index About the Editors Appendices

Modern Microwave and Millimeter-Wave Power Electronics

The L to H transition in the DIII‐D tokamak [Plasma Physics and Controlled Nuclear Fusion Research, 1986 (IAEA, Vienna, 1987), Vol. I, p. 159] is associated with two clear signatures: edge density fluctuations are abruptly suppressed (in ≊100 μsec), while the edge poloidal rotation velocity vθ increases, implying that the radial electric field Er becomes more negative. Detailed new spectroscopic profile measurements show that the changes in vθ and Er generate a region of sheared electric field and poloidal flow of width ≊3–5 cm. This region develops simultaneously with, and has the same spatial extent as, the edge fluctuation suppression zone as measured using a reflectometer system. Furthermore, the radial extent of the shear and fluctuation suppression zones encompass the location of the H‐mode edge transport barrier. These observations are consistent with recent theoretical models of the L–H transition, and a comparison with these theories is presented. Data are also presented on the evolution of edge parameters and density fluctuations after the transition: the shear and fluctuation suppression layers are maintained for the duration of the quiescent H‐mode phase, while relative density fluctuation levels decrease and interior plasma confinement gradually improves. Precursors to several different types of edge localized mode (ELMs) are also discussed.

Modifications in turbulence and edge electric fields at the L–H transition in the DIII‐D tokamak

The relativistic dynamics of electrons subjected to the electromagnetic field of an intense, ultrashort laser pulse in vacuum is studied theoretically. The effects of both finite pulse duration and beam focusing are taken into account. It is found that when the quiver amplitude of the electrons driven by the laser field exceeds the focal spot radius of a Gaussian beam, the restoring force acting on the charge decays exponentially, and the electrons are scattered away from the focus. This physical process, known as ponderomotive scattering, effectively terminates the interaction within a laser wavelength, and the electrons can escape with very high energy, as the normalized laser field is of the order of or greater than unity. The relation between the scattering angle and the escape energy is derived analytically from the conservation of canonical momentum and energy in the photon field. For a linearly polarized laser field, the interaction produces two jets of high energy electrons. The theory is supplemented by detailed two-dimensional computer simulations.

Nonlinear ponderomotive scattering of relativistic electrons by an intense laser field at focus

Experimental results are presented on the first W-band gyrotron Traveling-Wave Tube (gyro-TWT) developed to exploit the 94 GHz atmospheric window for long-range, high-resolution radar applications. The gyro-TWT is designed to operate in the higher order TE01 mode and is driven by a 100 kV, 5 A electron beam with a pitch angle of v⊥/vz=1 and velocity spread of Δvz/vz=5%. Large-signal simulations predict 140 kW output power at 92 GHz with 28% efficiency, 50 dB saturated gain, and 5% bandwidth. The stability of the amplifier against spurious oscillations has been checked with linear codes. To suppress the potential gyro-BWO interactions involving the TE02, TE11, and TE21 modes, the interaction circuit with a cutoff frequency of 91 GHz has been loaded with loss so that the single-path, cold-circuit attenuation is 90 dB at 93 GHz. A coaxial input coupler with 3% bandwidth is employed with a predicted and measured coupling of 1 dB and 2 dB, respectively. The operating voltage is limited to below 75 kV because of oscillations encountered at higher voltages in this initial embodiment. Preliminary test at Vb=60 kV and Ib=3.7 A yielded 59 kW saturated output power at 92.2 GHz with 42 dB gain, 26.6% efficiency, and a 3 dB bandwidth of 1.2 GHz (1.3%).

Theory and experiment of a 94 GHz gyrotron traveling-wave amplifier

This work presents one of the most powerful methods of plasma diagnosis in exquisite detail to guide researchers in the theory and measurement techniques of light scattering in plasmas. Light scattering in plasmas is essential in the research and development of fusion energy, environmental solutions, and electronics. Referred to as the 'Bible' by researchers, the work encompasses fusion and industrial applications essential in plasma research. It is the only comprehensive resource specific to the plasma scattering technique. This title provides a wide-range of experimental examples and discussion of their principles with worked examples to assist researchers in applying the theory. It offers computing techniques for solving basic equations that help researchers compare data to the actual experiment. It provides new material on advances on the experimental side, such as the application of high density plasmas of inertial fusion. It contains worked out examples of the scattering technique for easier comprehension of theory.

Neville C. Luhmann

Papers

Modern Microwave and Millimeter-Wave Power Electronics

Modifications in turbulence and edge electric fields at the L–H transition in the DIII‐D tokamak

Nonlinear ponderomotive scattering of relativistic electrons by an intense laser field at focus

Theory and experiment of a 94 GHz gyrotron traveling-wave amplifier

Plasma Scattering of Electromagnetic Radiation: Theory and Measurement Techniques