Table of contents

A stability criterion, independent of Ohm's law is obtained for cylindrical plasmas by means of the study of near-by equilibria. This criterion is the same as that given by the energy principle (Bernstein et al., 1958) except is some particular cases. These cases often lead to new instabilities.

The cyclotron radiation of electrons having a two-dimensional Maxwellian distribution and which are in a magnetic field is considered. Formulae are derived for the intensity of the radiation and coefficient of absorption. These are found to be in good agreement with the numerical calculations of Beard and Baker (1961).

A method of storing an accelerated beam for accelerators with alternating magnetic field is proposed and its experimental realization on a 15 MeV betatron is described. The lifetime of the beam for an energy of 11 MeV was measured as 0.15 sec when the vacuum was 10^-7 tor; the decay of the beam is caused mainly by radiation losses.

A differential equation is obtained for the profile of a beam with finite emittance and space-charge. Various special cases are considered and profiles for a non-accelerated beam are given. A phase-space distribution consistent with the non-accelerated case is determined explicitly as far as its Fourier transform.

The physical properties of electron and plasma streams are discussed and classified in terms of three general dimensionless parameters. For electrons these parameters are; α_e, the ratio of stream kinetic energy to the thermal energy of transverse motions; β_e, the ratio of the electron pressure to the magnetic pressure produced by the longitudinal electron current; and ν_e, the line density multiplied by the classical electron radius. These three parameters have the quite general relation of α_eβ_eν_e approximately equal to 1. This general relation is used as the basis of an elementary and a descriptive study of electron beams and plasma streams.

A microwave interferometer which is suitable for the measurement of the electron density in the positive column of a gas discharge is described. The discharge tube is placed in the waveguide structure. The construction of the interferometer is such that reflexions of the e.m. signal on the plasma boundary are very small. The propagation constant was solved numerically from the wave equation, under the assumption that the electron density distribution ove the cross section of the discharge tube has the form of a parabola. The influence of the glass wall of the discharge tube was taken into account. Measurements are in good agreement with work of other authors.

The relationship is investigated between laminar and turbulent theories of the structure of a collisionless shock wave. For p_e ≫ p_i, where p_i, p_e are the ion and electron pressures, a laminar structure of the shock wave may be constructed in terms of the `solitary' wave with thickness of the order of the Debye length. When p_i ≳ p_e the principal part within the shock front is played by scattering of ions by small-scale field fluctuations which result from anisotropic instability. The thickness of the front is in order of magnitude

Δ ∼ (c/Ω₀)(m_i/m_e)(1/(M-1)²) (M - 1 < 1),

where c is the velocity of light, Ω₀ = 4πne²/m_i, m_i, m_e are the ion and electron masses, and M is the Mach number.

It is shown that at sufficiently high currents the phase oscillations of a bunch of accelerated particles becomes unstable and the criterion for stability is derived. It is necessary to take this loss of stability into account when designing the r.f. equipment for storage systems.

The article describes briefly the design of the first strong focusing ring accelerator to be built in the Soviet Union. The design parameters and the results obtained during the start-up of the accelerator are presented.

A short description is given of some of the characteristics of accelerators having a vertically increasing field. The requirements which must be satisfied for an accelerator of optimum performance are discussed and so also are such questions as the existence of equilibrium orbits, the stability of the betatron oscillations and the process by which particles are accelerated in this type of accelerator.