Edwin M. McMillan

Violation of the Reciprocity Theorem in Linear Passive Electromechanical Systems

A simple energy argument is used to show that the theorem of reciprocity is not necessarily valid for linear passive electromechanical systems. It is found that in the case of crystal or electrostatic transducers the theorem is satisfied, while in the case of magnetic or electrodynamic transducers it is satisfied in magnitude but not in sign. It is further shown that by combining the two types of transducers, systems can be constructed that violate reciprocity in magnitude.

SOME THOUGHTS ON STABILITY IN NONLINEAR PERIODIC FOCUSING SYSTEMS

A brief discussion is given of the long-term stability of particle motions through periodic focusing structures containing lumped nonlinear elements. A method is presented whereby one can specify the nonlinear elements in such a way as to generate a variety of structures in which the motion has long-term stability.

A history of the synchrotron

Speaking not as a historian but from a personal point of view, I would like to tell the story of the origin of the synchrotron as I saw it. The beginning, for me, was in the spring of 1945, when I was on the staff at Los Alamos, the wartime atomic‐bomb laboratory. The Trinity test was in preparation, and I was already thinking about what to do on my return to Berkeley—from which I was on leave—after the war ended. I had spent a great deal of time and effort before the war on the design and operation of cyclotrons, I had a reasonably good understanding of the limits on the particle energies attainable by cyclotrons, and it seemed like a worthy goal to find ways to exceed these limits. The cyclotron, as you know, is a resonance accelerator; it pushes particles to high energies by the repeated application of a moderate voltage, which must be applied at the proper instant each time the particle comes around in its circular orbit.

Part II, History of the cyclotron

As Dr. Livingston has told you, our activities overlapped by a few months, so that between, us we can give a continuous story of cyclotron development as carried out at Berkeley under the guidance of Professor Lawrence. My start in his laboratory was in April of 1934, but I was around Berkeley before that working in Le Conte Hall on a molecular beam problem. Therefore, I have two kinds of early memories of the Radiation Laboratory at that time. One is as a place that I visited occasionally before I was working there; the other is as a place where I came to work, which I remember better, although it still seems like a very long time ago. The whole way of working was rather different from what it is in most laboratories today. We did practically everything ourselves. We had no professional engineers, so we had to design our own apparatus; we made sketches for the shop, and did much of our own machine work; we took all of our own data, did all our own calculations, and wrote all our own papers. Things are no...

FOCUSING IN LINEAR ACCELERATORS

UCRLO80 TWO-WEEK L O A N COPY This is a Library Circulating For a personal retention Copy which may be borrowed for two weeks. copy, call Tech. Info. Division, Ext. 5545 RADIATION LABORATORY

Multipoles in cylindrical coordinates

Solutions of Laplaces equation for azimuthally symmetrical potentials in cylindrical coordinates are found which can be correlated with two-dimensional multipoles in planes theta = const. Formulas are presented by which the coefficients for linear combinations of these solutions can be calculated to describe fields whose values are known along given axial or radial lines. (NL)

Notes on Quadrupole Focusing

~adiatka Uboratory Berkeley, California Contract Noo W-4405-tng-48 NOTES ON QUABRUPOLE FOCUSXkSG Edurin M e M c Millan February 9 , 1956 w Printed for the U, S. Aaornic Energy Commission