Separated Orbit Research Articles

Specification and ω-chaos in non-compact systems

In this paper, we demonstrate conditions under which a Lindelöf dynamical system exhibits ω-chaos. In particular, if a system exhibits a generalized version of the specification property and has at least three points with mutually separated orbit closures, then the system exhibits dense ω-chaos.

Orbit correction in an orbit separated cyclotron

The orbit separated proton cyclotron (OSC) described in [1] differs in concept from that of a separated orbit cyclotron (SOC) [2]. Synchronous acceleration in an OSC is based on harmonic number jumps and orbit length adjustments via reverse bending. Four-turn acceleration in the OSC enables it to have four times fewer cryogenic-cavity systems than in a superconducting linac of the same high beam power and energy range.Initial OSC studies identified a progressive distortion of the spiral beam orbits by the off-axis, transverse deflecting fields in its accelerating cavities. Compensation of the effects of these fields involves the repeated use of a cavity field map, in a 3-D linac tracking code, to determine the modified arc bends required for the OSC ring. Subsequent tracking studies confirm the compensation scheme and show low emittance growth in acceleration.

A new accelerator option for driving a sub-critical reactor

A linac and two cyclotrons, of a new type, are considered as a proton driver for an ADSR sub-critical reactor. The cyclotrons use reverse bending, for orbit length adjustments, and harmonic number jumps to achieve a synchronous acceleration. This is a different basis from that of a separated orbit cyclotron (SOC) where accelerating fields must vary over the cavity apertures in a defined manner to maintain synchronism. The new ring is called an orbit separated cyclotron (OSC) as it has the shape of an irregular SOC. An OSC design example is presented, with a six-cell superconducting cavity in each of the eight ring periods. Acceleration, over four turns, of a 10mA (cw) proton beam from 0.5 to 1.0GeV relates to input and output beam powers of 5 and 10MW, respectively. A key design issue is the unusual, spiral magnet system, with all 32 superperiods requiring different combined function magnet designs. One main advantage of an OSC ring over a linac stage is the four times fewer cryogenic and cavity systems, due to the use of the four turn acceleration.

Orbit spaces of Small Tori

Consider an algebraic torus of small dimension acting on an open subset of ℂn, or more generally on a quasiaffine variety such that a separated orbit space exists. We discuss under which conditions this orbit space is quasiprojective. One of our counterexamples provides a toric variety with enough effective invariant Cartier divisors that is not embeddable into a smooth toric variety.

First Beam Accelerated in the TRITRON Superconducting Separated Orbit Cyclotron

First Beam Accelerated in the TRITRON Superconducting Separated Orbit Cyclotron

Computer simulation of electromagnetic fields in the Tritron cavities

The Tritron, a superconducting separated orbit cyclotron, is under construction at Münich. The six superconducting cavities operate in the fundamental mode at 170 MHz. The higher order modes were investigated numerically by means of a three-dimensional computer code ISFEL3D. Computed results are given in comparison with some measured results.

The superconducting accelerating cavities for the Tritron

Abstract The Tritron is a separated orbit cyclotron with superconducting magnets and rf-cavities. The six cavities operate at 170 MHz. They are designed to have a small field enhancement factor. The cavities are fabricated by electroplating copper onto fibreglass shells. The copper is electroplated with PbSn as superconductor. Test results for the first two cavities are given. The values for the accelerating voltage and the quality factor Q lie above the design values for the Tritron accelerator. The highest gap field reached was 10.6 MV/m.

Superconducting cyclotrons

Superconducting cyclotrons with compact geometry and solenoidal coils are operating since several years, indicating the successful introduction of superconductivity in cyclotron design. Some of these facilities use or will use tandems as injectors, some operate as stand-alone machines. The technical problems of this concept are caused mainly by the compactness, which is the attractive feature of the design of course. In order to achieve specific energies above ∼ 300 MeV/u separated sector cyclotrons with superconducting magnets are still under consideration. Technical difficulties are related to the large stored magnetic field energy, to the strong electromagnetic forces and to the non-circular shape of the coils. A rather small separated orbit cyclotron with superconducting channel magnets and superconducting cavities is under construction in Munich. This type of cyclotron offers unique focusing properties at relaxed injection and extraction conditions. The large number of individual controllable channel magnets gives some flexibility. On the other hand it demands a high degree of reliability of many complex components, requiering simple solutions wherever possible. The present status of the Tritron-project is given in detail.

The Superconducting Separated Orbit Cyclotron Tritron

At the Munich 13 MV-Tandem Laboratory the TRITRON is under development, which will be the prototype of a superconducting separated orbit cyclotron for acceleration of heavy ions with 0.04 < i 0.14 and 0.1 0.3. It consists of 12 flat, superconducting sector magnets with 20 neighbouring channels for the spiral-orbit (rin = 70 cm, re, = 150 cm). Due to the individual magnetic channels the transversal and longitudinal focusing properties are as in synchrotrons. The constant turn separation of Ar = 4 cm requires a maximum accelerating voltage of 3 MV per turn, which will be provided by 6 superconducting cavities positioned in each second field free sector gap (see contribution of L. Dietl). Due to the longitudinal focusing the RFfrequency (-170 MHz) may be a high harmonic (h 2 20) of the revolution frequency. Thus the frequency range for acceleration of ions with different revolution frequency can be kept small (+3 %). The magnets as well as the cavities are contained in the same cavity.

Lead Alloys for Superconducting Cavities

For the superconducting separated orbit cyclotron Tritron six large, wedge shaped cavities for simultaneous acceleration of 19 parallel ions beams are needed. The indirectly cooled superconducting cavities with frequencies of ~170 MHz ± 3 % will be made of copper electroplated with lead alloy. With PbSn and PbBi as superconductor stable surfaces without chemical polishing can be obtained. The results of measurements on a 500 MHz test cavity (PbSn) are reported.

Point-group selection rules for ΔS=2 multiplicity change: Application to catalysis and organo-transition metal reaction

Electron spin–spin and second-order spin-orbit interaction operators are expanded as products of irreducible representations of symmetry point groups (Oh, Td, D5d, D6d, and C4v). From the transformation of the separated orbit and of the spin part, the selection rules for off-diagonal matrix elements may be deduced by taking direct products of the ‘‘initial’’ and ‘‘final’’ states. The special ΔMl selection rule for the orbital part of spin–spin interaction after expansion is also discussed. Emphasis is given to the ΔS=2 change connected by these operators. Possible examples of ΔS=2 change in d4, d5, and d6 configurations under the above mentioned point groups are given. As illustrations of the selection rules, the matrix elements for ΔS=2 and ΔMs=2 for these configurations are evaluated in the decoupled representation and given in terms of common parameters. The relevance of these multiplicity change to catalysis and reaction of organo-transition metal complexes is briefly alluded to.

Experimental Research of the Closed Orbit Expansion Effect in the Strong Focusing Cyclotron

The theoretical and experimental study of beam extraction method using the closed orbit expansion effect is described. The steep slope of the magnetic field variation magnitude is used to change the momentum compaction factor for the limit radial area. The orbit separation is found by computing the dynamical equations, since the behaviour of the betatron oscillation frequencies and the beam phase are investigated in this radial region. The experimental study of the effect is carried out with the ring cyclotron electron model, which is a strong focusing eight sector isochronous cyclotron. Calculated orbit separation in the extraction area is about 2+4 cm. The magnet system which is to obtain the proper gradient of the magnetic field variation and the magnet measurements results are described. The measured value of the orbit separation equals 4 cm. At the same time the space between two orbits without current (free of particles) is about 2 cm and the full current on the separated orbit is equal to that before separation. The theoretically predicted beam phase shift is found to be equal to 30+40°. The obtained results confirm the possibility of the 100% beam extraction from the accelerator with space magnetic field variation.

A Multi-Orbit Recirculation System for a Superconducting Linear Accelerator - The Recyclotron

The energy available from a superconducting linear electron accelerator (SCA) may be increased many times by means of an economical multi-orbit recirculation system, which preserves the most desirable characteristics of the SCA: good energy resolution (~10-4), high current and unity duty cycle. Furthermore, these properties of the SCA and its excellent emittance considerably simplify the design of the transport system and minimize aperture requirements. In order to maintain energy resolution each orbit of the recirculation system must be isochronous with respect to all phase space variables and beams must be reinjected into the linac precisely at the correct phase. These conditions have been achieved in a compact separated orbit design which uses multi-channel uniform field bending magnets. It is suggested that such a device be called a recyclotron. At HEPL a prototype 4 orbit recirculation system is being planned as part of the SCA program. Cost estimates for machines of this type have been made and show considerable advantage over other types of accelerator, especially at very high energies. The configuration also shows promise as an intermediate energy, high current accelerator, which could provide a source for a medical pion therapy facility.

A Sector Magnet for a 10-50 MeV Soc

A full-scale prototype magnet sector of a 12-sector, 10-50 MeV separated orbit cyclotron has been built and tested. Eleven pairs of alternating-gradient pole tips are mounted on a yoke structure which provides a common magnetic return path. The pole tips are all excited by a single pair of coils which surround the pole tip mounting bases at the upper and lower yoke faces. The pole tips combine both the negative- and positive-gradient sections in a single unit; the magnetic field gradients are about 800 gauss/in. The pole tips are 4.5 in. wide and have a mean gap of 1.75 in. They were machined by the numeric controlled milling process. Special edge contours were developed to achieve a useful radial aperture of 3 inches. Experience with the prototype magnet demonstrates that magnets for separated orbit cyclotrons present no special difficulty in design, construction, or alignment.

The Oak Ridge Separated Orbit Cyclotron Project; Progress and Status, January 1966

The Oak Ridge Separated Orbit Cyclotron Project; Progress and Status, January 1966