Влияние краевых поле й на бетатронные колебания в ускорите ле с разрезным магнитом II

. .

---

The influence of fringing on betatron oscillations in an accelerator with a sectioned magnet II

The influence of stray fields at the edges of pole pieces on the deformation of equilibrium trajectory and betatron oscillations is studied. A new definition of the effective length of segments for the approximative solution is given.

     

БЕТАТРОННЫЕ КОЛЕБАН ИЯ В УСКОРИТЕЛЕ С ОБЩИМ ПО ЛЕМ II

, , . , I. . . , .

---

Betatron oscillations in an accelerator with a general field. II

In the second part of the theory of an accelerator with a generalized field the author solves the dynamics of particles in a stationary approximation (without acceleration). The trajectories of the particles in the neigbourhood of the equilibrium orbit are related to it as betatron oscillations. An analysis of betatron oscillations includes the region of stability determined by means of Routh-Hurwitz criterion, damping, resonance effects and field perturbations. A general matrix method is presented permiting the inclusion of all the focusing structures used in accelerators.

     

Спектралъный метод о пределения изотопно го состава свинца. Частъ II

, . , [1]. 1–4 mg PbJ₂, . (c. m. c.) PbI 4058 Å. , , - , 5–7%. 3–4% –183 °C. , . 10% . , .     

Влияние давления на а бсорбцию галогенидо в серебра. Часть II

AgBr, Agcl AgI — 160°C. AgBr AgCl . AgI .     

Nuclear β-decay. II

A general expression for the beta-decay transition amplitude is evaluated, using the decomposition of the nuclear current matrix element into beta-decay form factors as obtained in the previous paper. For the electron radial wave functions the finite nuclear size is taken into account. Formulas for the spectrum shape factor and the polarisation are calculated.     

Constrained quantisation and θ-angles II

Certain aspects of the quantisation of 2D Yang-Mills theory are analysed with a new constrained quantisation technique, which quantises classical symplectic reduction. To apply this new method, it is necessary to take the gauge group as a Hilbert Lie group, and use the Wiener measure on a certain completion of the gauge group. The physical Hilbert space, the Hamiltonian and the Wilson loop observables for 2D Yang-Mills with a semisimple compact structure group are explicitly constructed using this technique. A new theory of θ-angle, not particular to 2D, emerges naturally. An interesting relation between Fock space coherent states and heat kernels on compact Lie groups is also found. All computations are explicit and simple in the sense that all results originate from the fundamental properties of Wiener measure. An example of SO(3) Yang-Mills is given. The possibility and difficulties of generalising our computations to higher dimensions by utilising the Levy measure (which generalises the Wiener measure) is briefly discussed.     

К ТЕОРИИ СПОНТАННОЙ Н АМАГНИЧЕННОСТИ ТОНКИХ СЛОЕВ. II. ЧАСТЬ)

- , . - . - - . , . 1956 .     

Aesthetic fields—Null theory II

We have again studied a null theory within the complex aesthetic field theory. This time we required that the spatially inverted origin point data represent the imaginary part of the complex origin point data. This was not the case in our previous studies of the null aesthetic field theory. However, this procedure did not lead to effects not previously observed as far as we could tell. Adding an additional term to the origin point data that presented the null character of the theory also did not lead to new effects. We also investigated a real null theory that led to constant fields. This theory was then made complex by a procedure discussed in the early part of the paper. We found that the resulting complex theory remained trivial nevertheless. Again, we found that it was not necessary for the theory to be null to find confluence type solutions.