Using a pulsed deflector for extraction of pulsed beams from the TRIUMF cyclotron
In the normal mode of operation, the TRIUMF cyclotron accelerates H/sup -/ ions to produce 500 MeV proton beams of 160 /spl mu/A with 4 nsec pulses separated by 43 nsec. A proposed experiment (/spl mu//spl rarr/e conversion) requires a 500 MeV beam with 100-200 nsec pulses separated by 1-2 /spl mu/ sec with an average intensity of 200 /spl mu/A. Two methods have been investigated to achieve this time structure. Both incorporate a pulsed electric deflector and take advantage of extraction by stripping. In the first case, a deflector with a thin septum deflects radially up to six accumulated turns onto a stripping foil in one turn. In the second, a pair of vertically deflecting plates are pulsed at a frequency to excite a coherent vertical growth, and the particles are eventually intercepted by a stripping foil. Under certain conditions extraction occurs in almost perfect synchronism with the driving pulse. Both methods will be described in detail and results of computer simulations will be presented.
Design for a FET based 1 MHz, 10 kV pulse generator
A pulse generator consisting of a coaxial cable and a high voltage modulator, incorporating two stacks of field-effect transistor (FET) switches operating in "push-pull" mode, has been designed and built. The modulator generates a continuous, unipolar, pulse train at a fundamental frequency of 1 MHz and a magnitude of 10 kV. The rise and fall times of the pulses are less than 39 ns. The two stacks each utilize 14 FETS, which are individually rated at 1 kV. The design incorporates a low-loss coaxial cable on which pulses are stored. Extensive PSpice simulations have been carried out to evaluate various design options. Subsequent measurements on the prototype pulse generator confirm the PSpice predictions.
How to do a p-descent on an elliptic curve
In this paper, we describe an algorithm that reduces the computation of the (full) p-Selmer group of an elliptic curve E over a number field to standard number field computations such as determining the (p-torsion of) the S-class group and a basis of the S-units modulo pth powers for a suitable set S of primes. In particular, we give a result reducing this set S of 'bad primes' to a very small set, which in many cases only contains the primes above p. As of today, this provides a feasible algorithm for performing a full 3-descent on an elliptic curve over Q, but the range of our algorithm will certainly be enlarged by future improvements in computational algebraic number theory. When the Galois module structure of E[p] is favorable, simplifications are possible and p-descents for larger p are accessible even today. To demonstrate how the method works, several worked examples are included.