Thesis (Ph. D.)--University of Chicago, 1939. / Lithoprinted. "Private edition, distributed by the University of Chicago libraries, Chicago, Illinois." Includes bibliographical references.

Thesis (M.S. in Electrical Engineering)--University of California, Berkeley, Jan. 1958. / "UCRL [i.e. University of California Radiation Laboratory]-8033."

This thesis is considered with the problem of the electrostatic inflection of an axially directed ion beam into the magnetic median plane at the center of a cyclotron. The analysis is applied to the case of the TRIUMF 500 MeV H cyclotron, where the beam from the ion source has an energy of 300 keV and the central magnetic field is approximately 3.0 kG. The properties of several inflector designs are briefly considered, and it is shown that the spiral inflector is most flexible, because it has two free parameters which may be varied to optimize the position and velocity of the ion beam at the entrance to the cyclotron injection gap. This type of inflector was therefore singled out for more detailed study. The first order optical properties of a spiral inflector operating in the presence of a homogeneous magnetic field were calculated using an analytic method similar to the one used by Belmont and Pabot. It was found that the accuracy of their calculation could be improved considerably by including an additional first order term in their electric field approximation. The origin of this additional term is studied in detail. Numerical results are presented for a typical spiral inflector design. The electric potential distribution inside a spiral inflector was calculated by solving Laplace's equation numerically in three dimensions. Trajectories were then numerically integrated through this potential distribution in the presence of a homogeneous magnetic field. The results obtained in these calculations were found to be in good agreement with the previous results obtained using the analytic approach. The characteristics of a spiral inflector operating in the presence of a non-homogeneous magnetic field similar to the one in the TRIUMF cyclotron is proposed. The optical properties of the proposed TRIUMF design have been calculated assuming an idealized electric field distribution within the body of the inflector. The spiral inflector has been constructed with the aid of a numerically controlled milling machine for cutting the electrode surfaces. A description is given of the milling procedure and of the computer program which was used to control the movement of the tool head. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Thesis (M.S.)--University of Michigan, 1962.

The lifetime of the negative hydrogen ion in an electric field is of crucial importance for the design and performance of negative ion sector-focussed cyclotrons. The v x B force of the ion moving with a velocity v in a magnetic field B acts like an electric field which removes an electron from the ion. In previous calculations of the dissociation rate, a simple one-electron picture, in which the escaping electron moves in the field of a neutral H atom and tunnels through the barrier formed by the combination of the electric potential and the potential well of the neutral atom was used. We improve the best potential previously chosen by requiring the one-electron state of the second electron to be properly bound with the ionization energy of the H ̄ ion in the absence of the external field. The methods of nuclear reaction theory are then applied in an accurate calculation of the width. The disagreement between the calculated mean lifetime and the experimental values indicates this simple picture of the H ̄ ion is inadequate and the correlations between the two electrons are important. Therefore these are included by using an accurate two electron variational wavefunction. The form of the single particle state from which one of the electrons is removed is then defined unambiguously and a spectroscopic factor results which includes the two electron aspects of the problem. The calculated mean lifetime is then found to agree with the experimental values to within the accuracy of the two sets of results. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The complex dispersion relation which describes transverse plasma waves propagating in a cold gyrotropic ambient plasma parallel to the background magnetic field as they interact with charged particle streams is derived by solving the linearized collisionless Boltzmann equation simultaneously with Maxwell's equations using the Fourier-Laplace transform method. The wave frequency is allowed to be complex with a positive imaginary part corresponding to a growing instability. The real and imaginary parts of the dispersion relation yield two separate equations. Under several assumptions, the equations can be simplified to yield an expression for the imaginary part of the frequency (the growth rate) and an equation relating the real wave frequency and the wave number. The theory is then applied to the magnetosphere by choosing a dipole model for the earth's magnetic field and a suitable distribution function for the particles. The specific case of waves of the ion-resonance mode interacting with mono-energetic, contra-streaming protons is considered in detail, and the results of this calculation are used in explaining hydro-magnetic (hm) emissions. In particular, it is suggested that the high frequency cutoff is a result of the pitch angle distribution of the particle stream. Computer calculations are done in order to display the general results of the theory. Specifically, when low energy protons (10 - 20 kev), trapped on a field line with an L value of 5.6 are considered, it is found that the region of instability occurs near the geomagnetic equator, and that the growth rate is a sharply peaked function of the frequency. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

The behaviour of ion orbits in the magnetic and electric fields at the centre of a cyclotron is studied in detail. The objective is to optimize the phase acceptance and beam quality for a 500 MeV H¯ isochronous cyclotron. Since accurate electric fields are necessary for orbit calculations, a numerical method for calculating these fields is examined in detail. The method is suitable for complicated electrode shapes and converges rapidly, yielding potentials in three dimensions with average errors of less than 0.01%. The magnetic fields used in the orbit calculations are measured on model magnets. The axial motions are examined using a thick lens approximation for the accelerating gaps. A method is demonstrated for calculating the axial acceptance of the cyclotron as a function of RF phase. This method is used to evaluate the merits of various central geometries and injection energies. This method is also used to examine the effects of flat-topping the RF voltage by adding some third harmonic to the fundamental waveform. It is found that addition of the optimum amount of third harmonic increases the phase acceptance by about 20 deg. Finally, the effects of field bumps on the axial motions are investigated. To allow accurate radial motion calculations to high energy, an approximate formula is developed which yields accurate (<1%) values for the changes in orbit properties of an ion crossing a dee gap. The geometry of the orbit on the first turn is discussed in detail. The radial centring is studied by tracking ions from injection to 20 MeV, and a method is described for choosing the starting conditions of the beam so as to minimize the radial betatron amplitude over a desired phase range. The problems associated with using a three-fold symmetric magnetic field with a two-fold symmetric electric field are also discussed. Besides the well-known gap-crossing resonance, a previously ignored phase-oscillation effect is found to be important for cyclotrons operating on a high harmonic of the ion rotation frequency. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

This thesis presents some of the techniques used in designing the sector-focused magnet for the TRIUMF cyclotron. An empirical method is given for calculating the magnet pole tip shape required to contain a 500 MeV beam of H⁻ ions. The method is good only for small changes in the shape. In the test case, the generated pole tip had a spiral angle correct to within ±5 degrees, and a hill angle correct to ±1 degree. The average field was found to be isochronous to ±70 gauss. An empirical solution to the problem of finding the field inside the magnet air gap is also given. The magnetic field resulting from a given pole tip contour is calculated at a point on the median surface by finding the perpendicular distance from the point to the edge of the pole and comparing this to an experimentally measured curve of field against distance. Fields generated by this technique have their averages correct to within 70 gauss and flutter to within 8%. Again, previous knowledge of similar pole tips is assumed. The method and results of calculating the pole edge position tolerances for the latest model magnet are given. The field strengths inside the steel return yoke as obtained from a series of flux measurements are also presented. Finally, it is shown that a simple approximation to the magnetic circuit of the magnet predicts the coil induction required to an accuracy of only 25%. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

No description available.

This thesis discusses the design of a stable 150 KW 23MHz RF system for the TRIUMF CRM cyclotron. The required characteristics of this system are presented with emphasis on the amplitude and phase modulation constraints. The composition of an amplifier system satisfying the power, bandwidth and noise requirements is discussed. Both the initial and present PA designs are presented, as is the design of the driver amplifier. Also included is a discussion of the choice of tubes and RF circuits. The usefulness of feedback control in satisfying the RF stability requirements is shown. The conditions a stable feedback system must satisfy are also given. Two amplitude control systems (drive control and screen control) are designed using Bode techniques. A digital simulation of these systems using an electrical analogue is presented. Implementation and results are discussed. / Science, Faculty of / Physics and Astronomy, Department of / Graduate