Table of contents

The external electron beam of the C.E.A. was focused vertically and bent upward by a 6-ft deflecting magnet. The deflected and undeflected beams were allowed to drift 20 ft through a vacuum pipe producing a separation of about 32 in. Accurate measurements of this separation were made by surveying the spots produced by the beams on glass slides. Combining this measurement of angular deflexion with a precise mapping of the field of the deflecting magnet yielded a calibration of the energy of the synchrotron at nominal energies of 1, 2, 3, 4, 5 and 6 GeV. These measurements show that the peak synchrotron energy is linear with peak synchrotron magnet current. Expressed in terms of the synchrotron magnet d.c. current (in terms of millivolts on the shunt), the result 62.73 mV/GeV was obtained. This result is accurate to better than ±0.2%. It was found that careful control of hysteresis and eddy current effects in the deflecting magnet were essential in obtaining reproducible magnetic field plots.

Instability of the drift-dissipative type, of a weakly ionized non-isothermal plasma in crossed electric and magnetic fields (Simon; Hoh) has been studied in the quasi-classical approximation for two cases: (a) Ω_eτ_e ≫ 1, Ω_iτ_i ≫ 1, (b) Ω_eτ_e ≫ 1, Ω_iτ_i ≪ 1. The increment and frequency of the instability of such a plasma against potential disturbances have been deduced in the linear approximation. Equations of strong turbulence evolved with the aid of Mikhailovskii's diagram method have been used in estimating the maximum value of the spectrum function of the electric field of oscillations and of the coefficient of turbulent diffusion. The concluding part of the paper presents a set of equations of strong turbulence in the dimensionless form suitable for computer analyses.

The coupling of waves in a region of varying density in a hot anisotropic electron plasma is studied theoretically. The influence of the width of the inhomogeneous region and of the angle between the propagation vector and the static magnetic field are investigated. The latter parameter is shown to be very important.

A slightly ionized, spatially homogenous gas is subjected to a weak constant electric field, and the relaxation of an arbitrary velocity distribution function for the electrons is studied. When the cross section for electron-molecule collisions decreases faster than 1/v² for large velocities there exists no stationary solution of the Boltzmann equation. The runaway rate for different collision cross sections is calculated. As a further application the runaway rate for electrons in n-InSb at helium temperatures is estimated.

The mechanism of build-up of radial oscillations of the electron beam in a high-current linear accelerator has been investigated. The calculation was based on an examination of the properties of hybrid non-symrnetric waves in a retarding accelerator structure and on a study of the excitation of these waves by the electron beam. The dynamics of the electrons in the field of the non-symmetric wave excited by the beam of particles was also studied. It is shown that the amplitude of the radial displacement away from the axis increases virtually exponentially as a function of the injectin time provided one neglects the damping of the field in the retarding structure. The effect of this damping on the dynamics of the radial motion of the particles is estimated.

A short review is presented of those plasma instabilities the development of which requires the presence of both a directed motion of the particles and a transverse inhomogeneity of their distribution function. The mechanism of the instabilities considered here arises from the effect of charge convection across the perturbing electric field and the main magnetic field. Since the wave vector of the unstable oscillations is directed almost perpendicularly to the magnetic field, ion motion plays an important part. As a result of interaction with these oscillations, the ions are able to acquire from the beam a large fraction of its energy. This possibly explains the experimentally discovered effect of strong heating of the ions when an electron beam with finite boundaries passes through a plasma.

A short description is given of the main features and principal parameters of the 30 MeV microtron injector now operating in the Neutron Physics Laboratory at JINR, Dubna. An electron current of 60 mA in the pulse is extracted and focused onto a distant target. A novel optical system for extracting, focusing and directing the electrons onto the target, as well as the low energy spread (0.3 per cent) and angular divergence of the beam, provide 100 per cent utilization of the electrons in the final (30th) orbit.

An analysis has been made of the fundamental properties of non-linear focusing taking the simple example of non-linear focusing in a symmetric magnetic field of the fifth degree. The dimensions of the first stability region with regard to small non-linear z-oscillations are determined. The influence of r-z-resonances was studied and also the maintenance of stability when allowing for adiabatic damping with the help of external or mutual r- and z-phase stabilization. It was found that mutual phase stabilization arises in the region of a r-z-resonance.

A numerical and partly analytical study of these effects has been made.

A description is given of the procedure used in adjusting a synchrotron with external single-turn injection and single-turn extraction of electrons. The electromagnet is of special design.

Radial-phase self-oscillations in high-current storage rings are discussed and the conditions for stability are derived for the case of an accelerating system with arbitrary frequency characteristics. A study is made of the interaction of the beam with the accelerating system and with other components of the vacuum vessel at harmonics of the bunch revolution frequency. Results are given of an experimental investigation of the self-excitation of phase oscillations in the storage rings of the Institute of Nuclear Physics of the Siberian section of the U.S.S.R. Academy of Sciences.

Results are presented of an experimental study of the interaction between colliding beams in storage rings.

A study has been made of the effect of the electromagnetic field of an `oncoming' bunch on the betatron oscillations of the particles in a `small' bunch. Effects due to the non-linearity of the transverse part of the oncoming bunch are considered.

A short description is given of the system which controls the electron beam parameters in the electron-electron storage machine VEP-1. The methods being applied to observe and monitor the beam parameters are discussed.

Experimental data are presented on the influence of a helical l = 3 magnetic field on the discharge development, the magnitude of the conductivity and the stabilization of the position of the plasma column. Values of T_e = 20-30 eV and T_i = 10 eV, corresponding to a conductivity of the order of 10¹⁵ e.s.u. were obtained. It is shown that the helical field improves the conditions for the discharge development and the plasma heating. The plasma containment time is unchanged on the application of helical fields.

A general survey is given of magnetic configurations with minimum B, possessing helical symmetry. An approximate analytical expression is derived for the volume per unit flux V'(Φ) in the neighbourhood of the helical magnetic axis. Exact formulae for V' (Φ) and the mean rotational transform angle ι = 2πχ' (Φ) are expressed as single integrals. On the basis of numerical computation of these integrals, graphs of V' (Φ) and χ'(Φ) up to the separatrix of the magnetic surfaces are constructed.

The interaction has been studied experimentally between the microwave fields (ω = 2 × 10¹⁰ sec^-1) of a volume resonator and a dense plasma (n ≈ 10¹³-10¹⁴ cm^-3) in a constant magnetic field. Under the action of the r.f. pressure, a paramagnetic current is formed in the plasma causing an increase in the static magnetic field inside the plasma which is in good agreement with the calculated dependence.

For ω_H/ω = 0.5 an electron parametric resonance is found which results in a sharp increase of the plasma pressure p₀ up to β = 8πp₀/H₀² ≈ 0.2.

The possibility is considered of increasing the efficiency of injecting fast hydrogen atoms into a magnetic trap, by the following methods.

1. Increasing the population of the upper levels (n ≈ 10) in a beam of fast hydrogen ions by irradiating them with quanta which are resonant with a chosen n₁l₁ → n₂l₂ transition, for example 2s → 10p. The dependence is found of the population of the n₂l₂ level on the radiation density and the transit time of the atoms in the radiation field. An estimate of the power of the light source required is made on the basis of the data obtained.

2. Photo-ionization of the hydrogen atoms directly in the active region of the trap. On the basis of the calculated dependence of the magnitude of the photo-ionization cross section of the H-atom on the wavelength of the radiation, an estimate is made of the power of the light flux needed for effective ionization of the atoms.

The results are described of measurements of the magnitude of the transverse plasma energy in a Tokamak machine, from a diamagnetic signal. It is shown that, for conditions in which the discharge current axis coincides within the limits of experimental error with the axis of the discharge vessel, the electron temperature measured by this method agrees with that calculated from the conductivity. A difference is observed only when the discharge is heated at low initial hydrogen pressures and the current axis is displaced towards the inside wall of the vessel.