Isochronous Field Research Articles

Comparative Analysis of Methods for Isochronous Magnetic-Field Calculation

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Accurate magnetic fields are needed for defining the operation of a multipurpose cyclotron as well as for designing other parts of the machine, as an input parameter. The quality of an isochronous magnetic field is evaluated by the closeness of the obtained ion gyration frequency to its required value. The commonly used method of isochronous field calculation for sector focused cyclotrons was Gordon's procedure. The incorporation of the gyration frequency criterion in isochronous field calculation has grown with the increase of the computer speed. We suggest a highly accurate method for the isochronous magnetic field calculation based on the gyration frequency adjustment. </para>

Permanent Magnet System for PET Cyclotron

The recent paper is devoted to design, manufacturing and testing the permanent magnet system to be used for Positron Emission Tomography (PET) cyclotron. The using permanent magnet material instead of copper coils allows essential electric power savings during PET cyclotron operation, though it comes to some increasing construction cost. The main problem why until now permanent magnets were not used for PET cyclotron magnet system is huge magnetic force, making cyclotron assembling/disassembling and isochronous magnetic field adjustment very difficult. For presented magnet system that problem is solved by applying rotating system providing the magnetic field switch-off (reduction to practically zero level inside working aperture). It makes assembling and adjustment easy at force free conditions. The main parameters of permanent magnet system are as follows: the average field is 1.4 T, pole radius is 375 mm and weight is 900 kg. As it shown in paper the magnetic properties of constructed permanent magnet system does satisfy to specification for magnet system of typical 10 MeV cyclotron for PET radioisotope production.

Bifurcation of critical periods from the rigid quadratic isochronous vector field

This paper is concerned with the study of the number of critical periods of perturbed isochronous centers. More concretely, if X 0 is a vector field having an isochronous center of period T 0 at the point p and X ϵ is an analytic perturbation of X 0 such that the point p is a center for X ϵ then, for a suitable parameterization ξ of the periodic orbits surrounding p, their periods can be written as T ( ξ , ϵ ) = T 0 + T 1 ( ξ ) ϵ + T 2 ( ξ ) ϵ 2 + ⋯ . Firstly we give formulas for the first functions T l ( ξ ) that can be used for quite general vector fields. Afterwards we apply them to study how many critical periods appear when we perturb the rigid quadratic isochronous center x ˙ = − y + x y , y ˙ = x + y 2 inside the class of centers of the quadratic systems or of polynomial vector fields of a fixed degree.

Focusing limit of a cyclotron: Axial betatron instability against beam dynamics approach

In an isochronous relativistic cyclotron, axial defocusing of a beam caused by the radial growth of the isochronous magnetic field is compensated by the azimuthal field gradient introduced by sectors. The focusing capabilities of sectors set the maximum ion energy obtainable from the machine. Usually, the focusing limit of a machine is determined by using the criterion for axial beam instability evolving from the equations of betatron oscillations. The obtained value of the focusing limit is approximate because the equations of betatron oscillations it originates from are approximate as well. The accurate value of the focusing limit is obtained by simulating accelerated beam dynamics in the extraction region. It is shown that the focusing limit of a cyclotron resulting from the two methods could differ for more than 9%. The suggested third method for focusing limit computation relies on the beam dynamics simulation along the critical equilibrium orbit rather than the acceleration orbit and thus it is less time consuming although equally accurate.

Trim coil system design of a superconducting ring cyclotron

The trim coil system of a superconducting ring cyclotron currently under design at RIKEN is composed of five sets of superconducting and twenty sets of normal-conducting coils. A major correction for isochronization of the magnetic field is accomplished by the superconducting coils, and a fine correction by the normal-conducting coils. For an optimal design of the system, a numerical procedure was developed to generate isochronous fields for design nuclei and consequently current settings on the main and trim coils, employing an iteration of a least-squares fitting to minimize orbital frequency errors. The main and normal-conducting coils can also be used to correct unwanted harmonic fields with sector dependent and/or radially localized excitations. The correction schemes were conceived for presumed error fields, alignment tolerances being estimated based upon beam optics requirements. On the other hand, a new trim coil design was envisaged, which comprises only superconducting trim coils. The subcoils in the present five-set design can be independently excited to replace the normal-conducting coils. This option may be more economical, but complications on the superconducting coil system raise a reliability concern.

Vacuum dissociation at acceleration of H −, D − beams on the AIC-144 S cyclotron

At present, the modification projects of the operating isochronous cyclotrons (IC) are a matter of interest because of the necessity to produce beams of higher intensity and energy for application in medicine and radioisotope production. The advantage of H −, D − acceleration in IC is very well known. But there are restrictions such as ion dissociation which limits the beam intensity. In this connection the problems concerned with dissociation of H −, D − ions were considered in order to define the acceleration conditions in terms of the AIC-144 S vacuum condition influence on it at an isochronous magnetic field of 1.85T. In this paper particular emphasis is given to the acceleration phase shift effect on the H −, D − ion losses. Some results and methods presented with reference to the AIC-144 S are given. The paper is the second part of the previously reported one (Schwabe, 1996).

Magnetic dissociation conditions of acceleration of H−, D− beams on the AIC-144 S cyclotron

Abstract The advantage of H − , D − acceleration in isochronous cyclotrons (IC) due to high efficiency of their extraction by stripping methods is very well known. The problem of H − , D − magnetic dissociation is not so drastic as regards the particle acceleration up to 45 MeV/nucl. However, lately high interest in increasing the proton and deuteron energy on IC is observed. This situation seems to be caused by using these machines in many medical and technical applications. Since new IC-projects for higher acceleration energy are being designed now, it is useful to consider the problems connected with dissociation conditions for H − , D − ions accelerated in the higher energy range at isochronous magnetic field up to 1.85 T. Some results and methods, by which the acceleration conditions in terms of magnetic dissociation may be determined, are given in this paper.

Mathematical modelling of the ion motion in the isochronous magnetic and radio frequency electric fields

The results of mathematical modelling of the ion motion show the possibility of the phase focusation of the ions with utilization of the radial force. This force is realized with a radial component of electric field. The beam monochromatization is analyzed simultaneously.

Beam phase measurement system for the K130 cyclotron in Jyväskylä

A phase measurement system for Jyväskylä new K = 130 heavy ion cyclotron has been designed and realized. The phase measurement is done using a set of capacitive probes to detect phase information from the internal ion beam. This data is vital for tuning purposes to obtain an isochronous magnetic field and to maximize the ion beam intensity.

Magnetic field control and orbit studies for H − acceleration in a 65 MeV cyclotron

The results of the mapping of the isochronous magnetic field for the Medicyc cyclotron are presented. The validity of the developed nonlinear methods for the magnetic field control is established, and certain results of detailed orbit studies for H − acceleration up to 65 MeV in this machine are given.

Zero degree neutron time-of-flight facility at RCNP

An outline of the 0° neutron time-of-flight facility at RCNP is briefly described. A technique has been developed for obtaining a narrow beam burst width by detuning the isochronous cyclotron magnetic field. An overall subnanosecond time resolution has been achieved for 50–80 MeV proton beams. Applications have been made to polarization transfer experiments for the (p, n) reaction at 0°.

Magnetic Field and Beam Dynamics Calculations for SUSE

The SuSe magnet system is designed using the program GFUN3D. A small version of this program was connected to a general fit program by means of which the current in the main and trim coils was determined for a given isochronous mean field B?(r). For beam dynamics calculations with the code GOC accurate fields (?B?/B? ? 1%) were used which were obtained by means of the program GFUN400 where the unique part of the magnet iron is subdivided into 400 elements at maximum. Several coil systems have been investigated. In an alternative design all coils have straigth sections which are easier to manufacture than coils with negative curvature. The main coils have a largest radial extension of 3.08 m. There are 22 correcting coils inside each main coil.

Study of Beam Parameters of 240-CM Isochronous Cyclotron

For two years beam parameter investigations have been carried out at the Kiev cyclotron for the extraction process and the beam transport system. The data obtained show that high quality beam is obtained with 0.1% accelerating voltage stabilization and shape selection of the isochronous magnetic field which limits phase shift to ±5°. The system for radial beam phase selection provides control of bunch phase duration within 5°-25°. In this case the radial oscillation amplitude does not exceed 2-3 mm and extraction efficiency from the cyclotron is about 70%. The measured beam emittance at the accelerator output is 20 mm-mrad. for vertical motion and 28 mm-mrad. for horizontal motion. Energy spread in the extracted beam is less than the energy gain per turn and is about 0.3%. The complete beam transport system is in use and provides beam without losses to any of six experimental rooms.

Improvements to the Beam Properties of the TRIUMF Cyclotron

The behaviour of the internal H- and external proton beams has been considerably improved during the past year. Better steering near the centre has resulted in the internal vertical emittance being reduced to hTr mm-mrad, while the external beam emittances are now 37? mm-mrad vertically and 3? mm-mrad horizontally, for 90% of the beam. Digitization of probe data together with computer-aided trim coil tuning has enabled the beam to be centred vertically to within ±6 mm; this has been important in simplifying the simultaneous extraction of two beams at independently variable energies (183 to 520 MeV) and intensities (split-ratios from 1/1 to 1/5000). Beam losses in the cyclotron are <20%; direct evidence is presented for gas and electromagnetic stripping, and also for a loss of a few per cent by resonant processes. New techniques have been developed to measure the phase, and have enabled the phase excursions (?sin?) to be reduced from ± 0.7 to <± 0.2 below 400 MeV. At high energies the phase excursions reach ±0.4, as anticipated from the magnetic field survey. However, a method is proposed by which separated turns could still be achieved and the energy spread reduced to 0.1 MeV, just as in a perfectly isochronous field.

Semiautomatic system for measuring the induction of an isochronous cyclotron's magnetic field

Semiautomatic system for measuring the induction of an isochronous cyclotron's magnetic field

An instability in the numerical calculation of the isochronous field of an A.V.F. cyclotron

In the numerical calculation of the isochronous field of a cyclotron one can encounter an instability problem. This is due to the fact that the revolution frequency and the magnetic field are not exactly linearly coupled. A small variation in the frequency is connected with a small variation in the magnetic induction via an integral operator. The corrections in frequency and magnetic induction are functions of the radius. These functions can be given in a fourier expansion representation. Using this representation it can be shown that oscillations easily can arise at radii where the mean magnetic induction changes rapidly. Especially near the extraction region one can observe this phenomenon. The period of the oscillations equals roughly two times the oscillation amplitude of the equilibrium orbit.

Some Orbit Calculations for TRIUMF

This paper is a report of some studies made of orbit properties in the TRIUMF Cyclotron. We will describe a numerical technique for obtaining solutions of ill-conditioned linear equations, this has proved useful when trying to produce a desired field with 54 trim coil pairs using the method of least squares, and in calculating an isochronous field. We will also describe a phase dependent centring error which can distort the horizontal emittance of beams with positive phases, thus limiting the phase acceptance of a cyclotron; and tolerances for field imperfections imposed by certain resonances in TRIUMF will also be reported. These calculations are chiefly concerned with phenomena away from the immediate central region and consequently electric focusing forces have been ignored. Central region calculations that include electric fields will be reported elsewhere.

Isochronous Cyclotron with Axially-Symmetric Electric and Magnetic Fields

An electron model of an axially-symmetric isochronous cyclotron was constructed and the beam properties were investigated for the purpose of studying, experimentally, an accelerator using electric and magnetic fields in combination as a guide field. As a model cyclotron of those which accelerate proton beams up to ∼100 MeV, a maximum energy of electrons of 50 KeV (γ\\cong1.1) was chosen. The isochronous field of the cyclotron was composed of electric and magnetic fields–the electric field having a radial component and the magnetic field having an axial component on the median plane. The electric field was produced by concentrically devided electrodes set on the inside walls of the dees; the magnetic field was produced by using a pair of air-core coils. Electron beams were accelerated up to almost maximum energy. The behavior of the electron beam was in good agreement with computer calculations.

Design considerations for a separated turn isochronous cyclotron

The objective of this machine is the production of large proton currents at energies from 200 to 1000 MeV with clear turn separations so that 100% beam extraction is achieved. Each stage of the cyclotron consists of a “ring” of identical magnet sectors interpersed with an appropriate set of rf acceleration cavities. The beam is injected from a linac thereby eliminating the central region problems associated with present isochronous cyclotrons. As a result of the narrow magnet gaps, the machine has relatively strong axial focusing throughout. The orbital frequency is high enough so that the beam can be accomodated within the space charge limits. Additional small third harmonic cavities provide for a “flat-top” on the resultant voltage wave form thereby allowing a relatively large phase width in the accelerated beam. Conditions for achieving clear turn separation are analysed and found feasible. For a reasonable total number of turns, the isochronous field trimming requirements are quite tractable. Tentative design figures are presented and compared with the present Separated Orbit Cyclotron (SOC) designs.

Influence of Magnetic Elements on an Isochronous Cyclotron Field

One of the main advantages of using magnetic field measuring equipment supported external to the cyclotron magnet is the ability to map the field before and after installation of the extraction elements. Field measurements with extraction elements in place are usually precluded by the size of internally mounted field mapping equipment (e.g., a wheel). The magnetic field of the NRL-isochronous cyclotron was measured to full radius before installation of extraction elements. After installation the influence on the magnetic field of each extraction element energized separately was measured. These measurements were used to determine the perturbation of the extraction channel on the isochronous field. Ion orbit calculations were then used to determine necessary field corrections to accelerate ions to the extraction radius. These field corrections are translated to currents needed in each of the various coils via a least squares fitting program.