## Collective Effects

In this last chapter we consider three special types of collective interactions, the generation of anomalous collisions and diffusion in an otherwise collisionless plasma, col-lisionless shock waves, and the acceleration of plasma particles to high energies. This selection of topics is guided by practical needs in space physics. Of course, all chapters of this book include collective effects. But the present chapter selects those effects which fall somewhat outside the main course of the...

## Upstream Waves and Shock Reformation

The reflected ion beams in the foreshock region are a source of free energy and drive several ion-ion beam instabilities. The two beams involved in the interaction are the dense but cold incident solar wind and the warm reflected ion beam, which is only a little less dense than the solar wind. The dominant ion beam instability in the fore-shock is the right-hand resonant instability (see Fig. 5.10). The mode is an Alfven-cyclotron mode, which scatters the ion beam into the diffuse ion...

## Loss Cone Instabilities

Aside from the lower- and upper-hybrid waves, the electrostatic electron- and ion-cyclotron waves are the most important electrostatic waves in homogeneous magnetized plasmas. They cover a wide range of cyclotron harmonics and, because of being principle plasma resonances, they contribute to energy exchange between waves and particles. In the following we discuss a few ways to drive these waves unstable. Since these waves, except for the lowest harmonics, are purely of kinetic origin, the...

## Modified Two Stream Instability

The instabilities considered so far are driven by either field-aligned currents or field-aligned beams. Magnetic fields have little effect on these electrostatic instabilities. The only exception is the electrostatic current-driven ion-cyclotron instability, which has a frequency close to the ion-cyclotron frequency and where the wave propagates nearly perpendicular to the magnetic field. A similar current-driven instability exists also for currents which flow perpendicular to the magnetic...

## Spontaneous Cherenkov Emission

An illustrative example of wave amplification is the Cherenkov emission. We already know from Sec. 10.2 of the companion book, Basic Space Plasma Physics, that inverse Landau damping leads to amplification of plasma waves. This process depends on the shape of the equilibrium distribution function. It is a process in which plasma wave emission is induced by the overpopulation of a higher level, very similar to Laser emission, and is called induced emission. Before we come to consider some of the...

## Collisionless Tearing Mode

When the plasma is collisionless, reconnection can evolve only as kinetic instability with ion inertia as the force which mixes the magnetic fields. The resulting instability is the collisionless tearing instability. As in the case of resistive tearing consider a planar current sheet (see Fig. 7.7), but no resistivity. A small disturbance in the position of the distribution of the current filaments along x will cause the filaments to attract each other and magnetic islands will start to form...

## Microscopic Double Layers

Another important observation is that the solution of the Korteweg-de Vries equation for the potential does not necessarily require the potentials on both sides to be the same. This gives the possibility for the description of microscopic double layers in terms of asymmetric solitons. The two particular families of solitons for which double layers seem to be possible are the ion-acoustic soliton and a pure electron fluid soliton, the electron-acoustic soliton arising from the electron-acoustic...

## Cyclotron Resonance

Hence, it is easy to imagine that particles of the right species with a particular parallel velocity will see a constant perpendicular electric wave field in their frame of reference and will undergo strong interaction with the wave. This is the nature of cyclotron resonance. In order to provide unstable conditions one must chose a distribution function such that it has an excess of particles with a higher momentum than the wave. These particles will be retarded by the wave and decelerated in...

## Lower Hybrid Drift Collision Frequency

The last instability important for the excitation of anomalous collisions is the lower-hybrid drift instability. The quasilinear saturation level of this instability is given in Eq. (8.75). We recall that the lower-hybrid drift instability is caused by transverse currents, not by the field-aligned currents discussed so far. This instability will therefore be most important for interrupting perpendicular currents, which exist in extended current layers subject to reconnection. One can expect...

## Rankine Hugoniot Conditions

The Rankine-Hugoniot conditions do neither provide any information about the formation of shocks nor about the intrinsic dissipative processes which are at work in the shock transition layer. Moreover, they are based on the one-fluid model of the plasma, which is a very rough approximation to reality. Therefore, they hold only sufficiently far away from the shock front itself, deep in the ideal magnetohydrodynamic regions to both sides of the shock front. Prescribing the inflow parameters the...

## Ion Acoustic Solitons

The first example of solitons relevant for space plasmas are acoustic solitons. We consider a one-dimensional system in which ion-acoustic waves have been excited by, for example, a field-aligned current instability. In the one-dimensional field-aligned case the physics is independent of the magnetic field. Normalizing all quantities, E eEl(meksTe)1 2wpe (or 0 e0 kBTe), x x D, and t wpit, and assuming Boltzmann-distributed electrons, the equations describing the evolution of the plasma are When...

## Maser Instability

Propagating plasma waves contribute to redistribution of energy and to transport of information. The various instabilities discussed so far generate waves which are trapped in the plasma. But there is also radiation which can escape from the plasma. Such radiation is observed from natural plasmas, like the solar corona, magnetized stars, the large planets like Jupiter, and also from the magnetosphere. Radiation is emitted by accelerated electrons moving in the curved magnetic field. This gyro...

## Critical Mach Numbers

The limit of extremely high Mach numbers given above is unrealistic. When the Mach number of a collisionless shock becomes too large, the character of the shock transition changes from laminar to turbulent. This change has to do with the process which dissipates the inflowing kinetic and magnetic energies in order to increase the entropy during shock transition and to generate irreversibility. Laminar shock waves are steepened magnetohydrodynamic waves with breaking of the wave inhibited by...

## Inverse Landau Damping

A system consisting only of electrons will be subject to Langmuir oscillations or, when including thermal effects, to propagating Langmuir waves with a dispersion given by Fig. 4.1. Gentle beam plasma configuration for the bump-in-tail instability. Fig. 4.1. Gentle beam plasma configuration for the bump-in-tail instability.

## Resistive Tearing Mode

So far we have avoided to touch the problem of how reconnection sets on. The instability envisaged must work in a plasma where at least the magnetic field is inhomoge-neous, changing its direction across the current sheet. This inhomogeneity implies that the currents flowing across the field are also inhomogeneous. Thus the instability is by nature a macroinstability, but it is not necessarily a magnetohydrodynamic instability. Since, in addition, a dissipative region is required around the...

## Preface

This book is the second volume of our introductory text on Space Plasma Physics. The first volume is published under the title Basic Space Plasma Physics and covers the more fundamental aspects, i.e., single particle dynamics, fluid equilibria, and waves in space plasmas. This second volume extends the material to the more advanced fields of plasma instabilities and nonlinear effects. Actually, there are already a number of monographs, where the general nonlinear plasma methods are described in...