Система аксиальной инжекции циклотрона У-400 М тема автореферата и диссертации по физике, 01.04.20 ВАК РФ

JOINT INSTITUTE FOR NUCLEAR RESEARCH

MOHAMED NASHAT MOHAMED EL-SHAZLY

¡IK 621.384.633.5

AXIAL INJECTION SYSTEM FOR THE U-400M CYCLOTRON

Supervisor: D.Sc. R. Ts. Oganessian

SPECIALTY: 01.04.20 - CHARGED PARTICLE BEAM PHYSICS AND ACCELERATOR TECHNOLOGY

Ph.D. THESIS

7/

DUBNA, 1999.

INTRODUCTION...........................................................................................................................................3

Cyclotrons................................................................................................................................................3

Ion Sources................................................................................................................................................5

Neutral Beam Injection............................................................................................................................6

Median plane ion injection.......................................................................................................................7

Helical axial injection.............................................................................................................................8

Axial Injection systems............................................................................................................................8

Fundamentals of beam transport............................................................................................................9

The U-400M Cyclotron...........................................................................................................................14

Motivation of This study........................................................................................................................17

Outline of Thesis.....................................................................................................................................17

CHAPTER 1..................................................................................................................................................19

BEAM TRANSMISSION LINE AND THE OPTICAL ELEMENTS........................................................19

The main concept.....................................................................................................................................19

The beam line...........................................................................................................................................20

Coil Design...............................................................................................................................................33

Solenoid lens...........................................................................................................................................35

Charge Analysis of the BEAM and the bending magnet.....................................................................39

Solenoids..................................................................................................................................................47

The Fringing magnetic field...................................................................................................................50

Steering magnet......................................................................................................................................52

Buncher....................................................................................................................................................56

CHAPTER 2..................................................................................................................................................65

AN INVESTIGATION OF THE PRESSURE DISTRIBUTION AND THE TRANSMISSION FACTOR DUE TO THE CHARGE EXCHANGE CROSS SECTION IN THE AXIAL INJECTION SYSTEM OF THE U-400M CYCLOTRON.......................................................................................................................65

Introduction............................................................................................................................................65

Pressure distribution..............................................................................................................................66

Program versions....................................................................................................................................78

Vacuum system........................................................................................................................................80

Transmission factor................................................................................................................................85

Results.....................................................................................................................................................90

CHAPTER 3..................................................................................................................................................92

INFLECTOR AND CENTRAL REGION...................................................................................................92

Inflector Types.......................................................................................................................................92

The Electrostatic Mirror........................................................................................................................93

Spiral Inflector......................................................................................................................................93

The Hyperboloid Inflector......................................................................................................................93

The Parabolic Inflector..........................................................................................................................94

The inflector of the .axial injection system.........................................................................................94

The central region..................................................................................................................................97

ACKNOWLEDGEMENTS........................................................................................................................105

REFERENCES............................................................................................................................................106

INTRODUCTION...........................................................................................................................................3

Cyclotrons................................................................................................................................................3

Ion Sources................................................................................................................................................5

Neutral Beam Injection............................................................................................................................6

Median plane ion injection.......................................................................................................................7

Helical axial injection.............................................................................................................................8

Axial Injection systems............................................................................................................................8

Fundamentals of beam transport............................................................................................................9

TheU-400M Cyclotron...........................................................................................................................14

Motivation of This study........................................................................................................................17

Outline of Thesis.....................................................................................................................................17

CHAPTER 1..................................................................................................................................................19

BEAM TRANSMISSION LINE AND THE OPTICAL ELEMENTS........................................................19

The main concept.....................................................................................................................................19

The beam line...........................................................................................................................................20

Coil Design...............................................................................................................................................33

Solenoid lens...........................................................................................................................................35

Charge Analysis of the BEAM and the bending magnet.....................................................................39

Solenoids..................................................................................................................................................47

The Fringing magnetic field...................................................................................................................50

Steering magnet......................................................................................................................................52

Buncher....................................................................................................................................................56

CHAPTER 2..................................................................................................................................................65

AN INVESTIGATION OF THE PRESSURE DISTRIBUTION AND THE TRANSMISSION FACTOR DUE TO THE CHARGE EXCHANGE CROSS SECTION IN THE AXIAL INJECTION SYSTEM OF

THE U-400M CYCLOTRON.......................................................................................................................65

Introduction............................................................................................................................................65

Pressure distribution..............................................................................................................................66

Program versions....................................................................................................................................78

Vacuum system........................................................................................................................................80

Transmission factor................................................................................................................................85

Results.....................................................................................................................................................90

CHAPTER 3.....................................................................................................................................:............92

INFLECTOR AND CENTRAL REGION...................................................................................................92

Inflector Types.......................................................................................................................................92

The Electrostatic Mirror........................................................................................................................93

Spiral Inflector......................................................................................................................................93

The Hyperboloid Inflector......................................................................................................................93

The Parabolic Inflector..........................................................................................................................94

The inflector of the axial injection system.........................................................................................94

The central region..................................................................................................................................97

ACKNOWLEDGEMENTS........................................................................................................................105

REFERENCES............................................................................................................................................106

INTRODUCTION

Cyclotrons

The development of nuclear physics lead to the construction of many huge machines that enabled us to achieve more developed and complicated investigation in the field. The types of cyclic charged particle accelerators played a significant role in the development of the experimental set-up possibilities in the nuclear research. The cyclotron is one of these machines. Cyclotrons were subjected to many stages of improvement. The whole process of the cyclotron improvement can be summarised in five stages. The first stage began in 1929 when conceived the idea of non-relativistic isochronous cyclotron. The first cyclotron was built in 1931 at the university of California in Berkeley-USA by E.O. Lowrence and M.S. Livingstone. This kind of the cyclotron was capable of accelerating high current beam to non-relativistic energies (v/c ~ 0.1 or a kinetic energy of about 12 MeV for protons).

The U-300 heavy ion accelerator is a cyclotron of a classical type. It is designed for acceleration of heave ions from B to Zn to the energies of about 5 up to 10 MeV/nucleon. The cyclotron was started m 1960 at the Laboratory of Nuclear Reactions of the Joint Institute for Nuclear Research (Dubna, USSR). The accelerator was designed and built at the enterprises of the USSR. The U-300 cyclotron is equipped with a powerful pulsed cyclotron source of an arc type with a heated cathode.

The second stage was required when, the quest for a solution to reach a higher energies was strongly stimulated. The development of the relativistic frequency modulated (FM) synchrocyclotron has began when two proposals was independently published by V. Veksler [1] and E.M. McMillan [2]. These cyclotrons do have a radially decreasing magnetic field in order to enhance axial focusing, but in order to reach relativistic energies the frequency has to be lowered while the particles are accelerated. The ~T 84-inch" synchrocyclotron in

Berkeley was the first one to be built, again by E.O. Lawrence [3]. The highest beam energy from a frequency modulated cyclotron was achieved in Gatchma (St. Petersburg Russia). These machines can accelerate beam to relativistic energy of 1 GeV for protons; however they have a low duty cycle and the current produced are much smaller than those in an isochronous cyclotron.

The cyclotron went through a third stage of evolution when Thomas suggested that axial stability could be obtained if the magnetic field had an azimuthal variation but it was not taken up at that time [4]. It was not until the early 1950s that liis work received experimental verification. In 1957 the first AVF cyclotron in Delft (The Netherlands) produced a beam. With the discovery of the sector focusing principle, it became possible to construct isochronous cyclotron high duty cycle, high current cyclotron operating at relativistic energy.

At the Laboratory of the Nuclear Reaction has become a traditional one and has received further development. In 1968 m Dubna, a new ion accelerator -isochronous cyclotron with the pole diameter of 2 m (U-200) was built. The U-200 cyclotron is the first isochronous cyclotron that accelerates heavy ions in the USSR. On the U-200 cyclotron a wide range of ions from helium up to Argon can be accelerated. A high level of the average magnet field (20 kG) made it possible to accelerate ions on this, cyclotron up to the energy of 5-16 MeV/nucleon [5].

One of the greatest improvement in the operation of the AVF cyclotrons over the last decades has been the use of the external ion source, especially for the acceleration of heavy ions (ECR) [6,7], negative ions [8,9] and polarised ions, as shown in this chapter further.

The fourth stage in cyclotron design from sector-shaped pole shims to separated-sector magnets, as proposed by H.A. Willax [10], was just a logical expansion of the AVF principle. The free space between separated sectors or magnets allows the installation of powerful an efficient high RF cavities or resonators instead of Dees squeezed in between the magnet poles. This gives

considerably higher acceleration voltage which results in good turn separation. The beam can easily be extracted with little beam loss, which is a mandatory condition for high beam intensity cyclotrons.

With the development of superconductivity the question had to come up whether superconductivity would to make a contribution to cyclotrons and the answer was the fifth stage. The first was built by H.G. Blosser [11] at the National Superconducting Cyclotron Laboratory in East Lansing (USA) producing beam in 1982. It is a K=500 superconducting cyclotron.

Ion Sources.

A hot filament ion source was placed within the first cyclotron. Sources of polarised protons, deuterons and high charge state ions are too large to fit inside a cyclotron. In the unrestricted exterior space very large and powerful ion sources can be built; it is only necessary to inject the ion beams into the cyclotron in such a way that particles will be accelerated just as through they come from an internal source. The ECR ion sources have become the most frequently used as external heavy ion source for cyclotrons. The Grenoble group developed the first high charge state ECR source in 1974. The mam advantages of an external source are listed below:-

1. With an external source differential pumping may be used between the source and the median plane of the cyclotron. This improves the vacuum of the central region and the beam loss will be decreased consequently.

2. If an external source is used, a bunching system can be placed between the ion source and the central region to increase the intensity of the accelerated ions.

3. If a polarised beam have to be accelerated, a polarised source must be used. These sources are too large and must be shielded from stray magnetic field

then, the unique method is to locate the ion source away from the cyclotron magnet.

4. All ions with wrong charge to mass ratio are removed before acceleration so, the space charge effect will be less and the sputtering of the central region components.

The mam disadvantages of an external source is that:-

1. It requires an injection system which cost additional money.

2. In an injection system there is excessive beam loss due to charge exchange with the residual gases.

Before beginning these studies, we shall briefly review some of the work being done on the cyclotron injection system.

Neutral Beam Injection

One of the idea in designing an injection system for use with an external

source is to inject neutral particles which may be ionised by means of stripping foil or an electric arc once they have reached the centre.

The first published proposal for neutral hydrogen injection was made by Keller at CERN [12]. Keller's group proposed to inject neutral beam from a polarised source in the cyclotron median plane. The atoms were ionised m the centre by electron bombardment. The group tested tliis method with a 4.5 MeV model cyclotron.

More recently, neutral thermal ion injection has been used at Saclay to accelerate the beam of 0.5 nA of polarised protons to an energy of 22 MeV. The current were at least a factor of ten below the currents which could be obtained using an external source combined with an external ionizer. A thermal ion neutral

beam injection system has also been used with the Lyon 28 MeV synchrocyclotron; however, the injected current is again quite low [13]. This method has the advantage that it does not lomse residual gas. Another advantage is that the beam can be focused after the ion source, before the neutralisation. A neutral beam injection scheme using 30 keV hydrogen atoms has also been investigated by Pils at Dubna [14].

Median plane ion injection

This type of mjection has been usually used in the separated sector cyclotrons.

In median plane injection systems a beam of ions is injected mto the cyclotron by travelling along the radial path of the beam from the outer edge of the cyclotron. Once the beam has reached the centre of the cyclotron, steering inflectors are used to centre the beam for injection.

One particularly simple form of radial injection is the trochoidal method used by Lebedev Institute m Moscow [15]. In this injection system the ions loop mward by travelling along a hill-valley interface, and focusing of the incoming beam is achieved by means of the hill-valley gradient. Using this method approximately 20% of the injected beam has been accelerated in a small 300 keV cyclotron. An alternative median plane mjection system has been used for injection of polarised protons at Sacaly [16,17]. Here the effect of the magnetic field were compensated by placing electrostatic deflectors along the path of the incoming ions. Electrostatic quadrupoles were installed along the mjection path to provide focusing. Also, median plane mjection was installed for the 580 MeV SIN cyclotron and for the 200 MeV Indiana University cyclotron, both of which have separated sector magnets. Both of these cyclotrons are operated in conjunction with small injector cyclotrons and the injection energies are 70 MeV and 15 MeV respectively.

Helical axial injection

A concept for injection of high energy beams into a very high field cyclotron

has been presented by Hudson [18]. In the helical injection system, the incoming beam is in a plane parallel to the median plane. Using the long solenoid coil, the beam is deflected into a helical path, transported to the median plane and inflected into an accelerated orbit as shown in Fig.l. The field along the axis is about twice the median plane field.

Fig. 1 The helical axial injection.

Axial Injection systems

In Axial injection systems the beam is injected through an axial hole in the

magnet yoke. Once the beam has reached the median plane, it is bent through 90 degree by means of an mflector. This method was first developed by Powel for use on the Birmingham ragial ridge cyclotron [19]. Since then many groups have worked on the problem of axial mjection. The hardware for these injection systems differs in the type of focusing elements and inflector used.

The focusing elements between the ion source and the inflector have been eitiier electrostatic quadrupoles, magnetic quadrupoles, einzel lenses, or solenoids. Most of the axial injection systems which are currently m operation have been designed to work with relatively low injection energies in the 10 to 25 keV range, and as a result the space charge forces along the injection line have been very important. The first axial injection system for the heavy ions in the USSR has been designed and installed in the Flerov Laboratory of Nuclear Reaction. It has installed to inject the highly charged heavy ions to the U-200 cyclotron. The mam components of the axial injection system of the U-200 cyclotron is shown in Fig. 2.

Fundamentals of beam transport

A beam consists of a group of many particles with neighbouring trajectories.

We can therefore represent the beam as a volume in an abstract six-dimensional 'phase space' whose co-ordinates are positions and momenta. In general the shape of the beam envelop will change as a function of time, but the six-dimensional volume itself is usually governed by Liouville's theorem. This theorem states that under the action of the forces which can be derived from a Hamiltonian, the motion of a group of particles is such that the local density of representative points in the appropriate phase space remains everywhere constant. This is equivalent to requiring that the volume occupied be a beam m phase space remains constant. Liouville's theorem is applicable whenever a group of ions moves under the influence of external electric and/or magnetic fields provided no ions are lost from the beam.

ISM

Fig. 2 The axial injection system of the U-200 cyclotron.

Although the most general phase space is a six-dimensional hypervolume whose co-ordinates are position and momenta components m three different

directions, when there is no coupling between different directions, we need only consider the behaviour of two-dimensional projections of the hypervolume. Under this circumstances, Liouville's theorem requires that the area of the two-dimensional projections must remain constant. This is quite common occurrence in beam transport system, and the area of the two-dimensional projection is known as the beam emittance. For the sake of convenience, these projections are usually assumed to be either ellipses or parallelograms. In this thesis, we shall work exclusively with ellipses.

The determination of beam behaviour in a transport system can be divided into two parts. First is the determination of the 'central trajectory'; the path of some representative particle in the group, usually one at the centroid of the phase space volume, second is the determination of the motion of the other particles relative to the central trajectory, i.e. the change m the shape of the phase space volume as a function of time.

If the particle in the beam carry a charge q and have a mass m, their equation of motion is

(i)

mr=q(rxg + £)

Where is the electric field, g is the magnetic field, ^ is the position

vector and the dots indicate differentiation with respect to time. This equation solved for the initial conditions of the centroid of the phase space volume yields the central trajectory rc{t). For other trajectories we write

-»->-» (2) r(t)= rc(0 + Ar(0

Using this expression we can expand eq 1.1 in terms of Usually, all of the trajectories within a beam will lie close enough to the central ray trajectory

that we need only keep first-order terms m Ar- This is the linear approximation, and we may use it to write out solutions for Ar in the matrix form.

Ax' ~ Ax

AP X AP

Ay A P = R(t') Ay A P y

Az Az

AP_ i-t' AP_

Where Ax, 4>',and Az are three components of /^y ^^ and APare the tree components of , R{t) is known as a transfer matrix, and it six by

six whose component are time dependent. R{t) operates on a column vector

—»

consisting of components of A/* and evaluated at time t=0 and generates a

column vector containing the components of A r and A/4 at some different time t — t'. The transfer matrix may be calculated by solving the linearized equations of motion for six linearly independent states of initial conditions.

One method for tracing a phase space volume through a beam transport system is to start with a large number of points on the surface of the phase space volume and follow their progress through the beam transport system. This obviously requires a great deal of computational labour, and shortcuts have been developed [20,21]. The transport matrix formalism described by K.L. Brown assumes that the phase space volume is contained in a six-dimensional hyper-ellipsoid. Such an ellipsoid may easily be tracked through a series of linear algebra.

A somewhat similar method has been described by K.G. Steffen [22] for the case of a two dimensional phase space. This transformation is used for the vertical space charge calculations.

The basic assumption is that all forces are linear or can be linearized. If the six coordinates of a particle are known at some location Si along a transport system, then at s2, the coordinates can be calculated by a single matrix multiplication. That is,

x(s2) = fofa) (4)

where xfs) is a 6x1 column vector of the coordinates at location s, and R is a 6x6 matrix whose elements depend on the transport elements between s[ and s., and on the size of the beam (for computing space-charge forces) in this interval. The jR-matrix is referred to as the transfer matrix between locations and si. Transfer matrices representing particle transport over long distances are determined by a sequence of matrix multiplication of transfer matrices representmg particle transport over smaller intervals that comprise the total transport distance.

If the transfer matrix between si and si is known, and if the beam matrix at ¿T is known, then the beam matrix at si is calculated by the following equation:

g(S2) = R^R7

where R1 denotes the transpose of R. The dynamics calculations are done by a sequence of transformations as specified above. Starting with an initial cr-matrix, a transfer matrix is constructed from the external forces for a small transport interval and a new cr-matrix is calculated. This process is repeated until the beam has been followed through the specified elements

The U-400M Cyclotron

The heavy ion cyclotron U-400M at the Flerov Laboratory of Nuclear

Reactions is built basing on the magnet of the magnet of the U-300 cyclotron. The U-400M compact cyclotron is designed for the acceleration of ions from He to U with the energies ranging from 20 up to 100 MeV/nucleon. Its construction was staited in 1989. In May 1991 the first internal beam of 4Hel+ with the energy of 30 MeV/n and the intensity of 1014 pps on the U-400M with the PIG ion source [23,24] has been obtained [25]. The characteristics of the U-400M cyclotron are presented in Table 1

The parameters of the internal beams produced with the PIG io