Accelerators

All accelerators employ electric fields to accelerate stable charged particles (electrons, protons, or heavier ions) to high energies. The simplest machine would be a d.c. high-voltage source (called a Van der Graaff accelerator), which can, however, only achieve beam energies of about 20 MeV. To do better, one has to employ a high frequency a.c. voltage and carefully time a bunch of particles to obtain a succession of accelerating kicks. This is done in the linear accelerator, with a succession of accelerating elements (called drift tubes) in line, or by arranging for the particles to traverse a single (radio-frequency) voltage source repeatedly, as in the cyclic accelerator.

Linear accelerators (linacs)

Figure 11.1 shows a sketch of a proton linac. It consists of an evacuated pipe containing a set of metal drift tubes, with alternate tubes attached to either side of a radio-frequency voltage. The proton (hydrogen ion) source is continuous, but only those protons inside a certain time bunch will be accelerated. Such protons traverse the gap between successive tubes when the field is from left to right, and are inside a tube (therefore in a field-free region) when the voltage changes sign. If the increase in length of each tube along the accelerator is correctly chosen then as the proton velocity increases under acceleration the protons in a bunch receive a continuous acceleration. Typical fields are a few MeV per metre of length. Such proton linacs, reaching energies of 50 MeV or so, are used as injectors for the later stages of cyclic accelerators.

In this book, the term solar dynamo refers to the complex of mechanisms that cause the magnetic phenomena in the solar atmosphere. Usually, however, that complex is broken down into three components: (1) the generation of strong, large-scale fields of periodically reversing polarity, (2) the rise of these fields to the photosphere, and (3) the processing in, spreading across, and removal from the photosphere of magnetic flux. Components (2) and (3) are discussed in Chapters 4–6; in this chapter, we concentrate on aspect (1). Even on this limited topic, there is a stream of papers, but, as Rüdiger (1994) remarked, “it is much easier to find an excellent… review about the solar dynamo… than a working model of it.”

In dynamo theory, the mean, large-scale solar magnetic field is usually taken to be the axially symmetric component of the magnetic field that can be written, without loss of generality, as the sum of a toroidal (i.e., azimuthal) component Bφ ≡ (0, Bφ, 0) and a poloidal component, which is restricted to meridional planes: Bp ≡ (Br, 0, Bθ′), where θ′ is the colatitude. The poloidal component is usually pictured as if a dipole field aligned with the rotation axis were its major component, which is a severe restriction.

All solar-cycle dynamo models rely on the differential rotation v0(r, θ′) to pull out the magnetic field into the toroidal direction, as sketched in Fig. 6.10a; about this mechanism there is no controversy.

Introduction

On the main sequence, it has long been known that large mean rotational velocities are common among the early-type stars and that these velocities decline steeply in the F-star region, from 150 km s−1 to less than 10 km s−1 in the cooler stars (see Figure 1.6). As was shown in Section 6.3.2, the observed projected velocities indicate that the mean value of the total angular momentum 〈J〉 closely follows the simple power law 〈J〉 α M2 for stars earlier than spectral type F0, which corresponds to about 1.5M⊙ (see Figure 6.7). The difficulty is not to account for such a relation, which probably reflects the initial distribution of angular momentum, but to explain why it does not apply throughout the main sequence. It has been suggested that the break in the mean rotational velocities beginning at about spectral type F0 might be due to the systematic occurrence of planets around the low-mass stars (M ≲ 1.5M⊙), with most of the initial angular momentum being then transferred to the planets. Although this explanation has retained its attractiveness well into the 1960s, there is now ample evidence that it is not the most likely cause of the remarkable decline of rotation in the F-star region along the main sequence. Indeed, following Schatzman's (1962) original suggestion, there is now widespread agreement that this break in the rotation curve can be attributed to angular momentum loss through magnetized winds and/or sporadic mass ejections from stars with deep surface convection zones.

Introduction

As indicated in Chapters 1 and 2, we are faced in nature with several types of fundamental interaction or field between particles. Each field has its distinct characteristics, such as space–time transformation properties (vector, tensor, scalar etc.), a particular set of conservation rules that are obeyed by the interaction and a characteristic coupling constant that determines the magnitude of the collision cross-sections or decay rates mediated by the interaction.

The fact that the strength of the gravitational interaction between two protons, for example, is only 10−38 of their electrical interaction has always been a puzzle and a challenge, and many attempts have been made to understand the interrelation between the different fields. In the last decades, the belief has grown that the strong, weak, electromagnetic and gravitational interactions are but different aspects of a single universal interaction, which would be manifested at some colossally high energy. At the everyday energies met with in laboratory studies in particle physics, it is necessary to assume that this symmetry is badly broken, at these mass or energy scales which are puny relative to the unification energy.

The first successful attempt to unify two apparently different interactions was achieved by Clerk Maxwell in 1865. He showed that electricity and magnetism could be unified into a single theory involving a vector field (the electromagnetic field) interacting between electric charges and currents.

The main object in writing this book has been to present the subject of elementary particle physics at a level suitable for advanced physics undergraduates or to serve as an introductory text for graduate students.

Since the first edition of this book was produced over 25 years ago, and the third edition over 10 years ago, there have been many revolutionary developments in the subject, and this has necessitated a complete rewriting of the text in order to reflect these changes in direction and emphasis. In comparison with the third edition, the main changes have been in the removal of much of the material on hadron–hadron interactions as well as most of the mathematical appendices, and the inclusion of much more detail on the experimental verification of the Standard Model of particle physics, with emphasis on the basic quark and lepton interactions. Although much of the material is presented from the viewpoint of the Standard Model, one extra chapter has been devoted to physics outside of the Standard Model and another to the role of particle physics in cosmology and astrophysics.

Many – indeed most – texts on this subject place particular emphasis on the power and beauty of the theoretical description of high energy processes. However, progress in this field has in fact depended crucially on the close interplay of theory and experiment. Theoretical predictions have challenged the ingenuity of experimentalists to confirm or refute them, and equally there have been long periods when unexpected experimental discoveries have challenged our theoretical description of high energy phenomena.

In this final chapter we present a synopsis of the observational constraints on dynamo processes in stars with convective envelopes that complements our review of studies of the solar dynamo in Chapter 7. We do not try to summarize the rapidly growing literature on mathematical and numerical models of stellar dynamos, but rather we attempt to capture the observational constraints on dynamos in a set of propositions, following Schrijver (1996). You will encounter some speculative links that attempt to bring together different facets of empirical knowledge, but we shall always distinguish conclusions from hypotheses.

Throughout this book, we use the term dynamo in a comprehensive sense, implying the ensemble of processes leading to the existence of a magnetic field in stellar photospheres, which evolves on times scales that are very short compared to any of the time scales for stellar evolution or for large-scale resistive dissipation of magnetic fields. Such a dynamo involves the conversion of kinetic energy in convective flows into magnetic energy.

Solar magnetic activity is epitomized by the existence of small-scale (compared to the stellar surface area), long-lived (compared to the time scale of the convective motions in the photosphere), highly structured magnetic fields in the photosphere, associated with nonthermally heated regions in the outer atmosphere, in which the temperatures significantly exceed that of the photosphere. Other cool stars exhibit similar phenomena, which are collectively referred to as stellar magnetic activity.

Outer-atmospheric imaging

The nearest cool star confronted us with the reality that cool stars have extremely inhomogeneous outer atmospheres. This was first confirmed for stars other than the Sun by the modulation of broadband signals, caused by starspots, and later by the discovery of the quasi-periodic variation in the Ca II H+K signal of some cool stars by Vaughan et al. (1981) caused by the rotation of an inhomogeneously covered stellar surface. Insight in stellar dynamos requires observational data on the properties of stellar active regions and their emergence patterns. For instance, we would like to know the sizes of stellar active regions and their lifetimes, the details of the structure of starspots, the emission scale height at different temperatures, and so on. In fact, we would like to know the entire three-dimensional geometrical structure of the outer atmospheres of cool stars. For that knowledge to be obtained, stellar surfaces should somehow be imaged by sounding the atmosphere from the photosphere on out. We would like to learn all this not merely for stars with activity levels similar to that of the Sun, but also for other stars, from the extremely active, tidally interacting binary systems for which much of the surface seems to be covered by areas as bright as solar active regions with a small fraction being even brighter, down to the very slowly rotating giant stars whose average coronal brightness is well below that of a solar coronal hole.