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Nuclear Engineering Department , Alexandria University
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Cyclotron
Cyclotron is a type of circular accelerators. The term circular accelerator refers to any machine in which beams describe a closed orbit. All circular accelerators have a vertical magnetic field to bend particle trajectories and one or more gaps coupled to inductively isolated cavities to accelerate particles.
Beam orbits are often not true circles; for instance, large synchrotrons are composed of alternating straight and circular sections.
The main characteristic of resonant circular accelerators is synchronization between oscillating acceleration fields and the revolution frequency of particles.
Particle recirculation is a major advantage of resonant circular accelerators. In a circular machine, particles pass through the same acceleration gap many times (102 to greater than 108).
High kinetic energy can be achieved with relatively low gap voltage. One criterion to compare circular and linear accelerators for high-energy applications is the energy gain per length of the machine; the cost of many accelerator components is linearly proportional to the length of the beam line.
The gradient is considerably higher for accelerators with superconducting magnets. This figure of merit has not been approached in either conventional or collective linear accelerators.
What is a cyclotron?
A cyclotron is an accelerator for charged particles. In our case, it accelerates one of the four lightest nuclei, H, D, 3He or 4He, to energies from 5 MeV to 45 MeV depending on the settings.
The operating principle is illustrated below.
The ions (charged particles) are injected by an ion-source near the center of the machine. They immediately start going in circular orbits in a magnetic field inside the cyclotron, according to the formula:
F = qv x B (1)
where F is the force vector, q is the charge, v is the velocity vector and B is the magnetic flux density vector.
Most of their orbit, the particles move within a hollow D-shaped metal electrode, called a "D" (or "dee"). Here they only experience the magnetic field, as they are screened from any electric field inside the cyclotron by what is known as Faraday Cage Effect. Only when the particles move in the small gap between the dees, they are influenced by an electric field applied from one dee to the other. We will then get an acceleration of the particles, according to:
F = qE (2)
where E is the electric field vector.
Of course, there will only be acceleration if the electric force has the same direction as the velocity. Therefore, the electric field must change its direction while the particles are screened inside the dees
This means that the electric field has to oscillate with a frequency corresponding to the particles' revolution frequency.
If this condition is met, and we assume that the magnetic force is equal to the centripetal force of the circular movement, we get the cyclotron equation:
r = mv/qB (3)
where r is the radius of the particle orbit.
As we can see from this, the particles will increase their energy (velocity) proportional to the radius of their orbit, until they after typically a few hundred orbits reach the energy desired. They can then be extracted by a new electric field combined with a magnetic field, and be transported through a beam tube to the point where they are to be used to initiate nuclear reactions.
The observant reader will notice that (3) above requires the mass m to be constant for v to be directly proportional to r. Relativistically, the mass is not constant, but increases with v. This is highly relavant in our context, since for instance 35 MeV protons have a velocity of about 0.3 c.
Physically, the cyclotron weighs about 60 tons, and is located inside an inner vault with walls and doors of about 2 m concrete, to shield the surroundings from the nuclear radiation which is present when the machine runs. Fortunately, most of this radiation has a half-life of only seconds to minutes, so there are no long-term waste disposal problems.
Types of cyclotrons
A cyclotron has constant magnetic field magnitude and constant rf frequency. Beam energy is limited by relativistic effects, which destroy synchronization between particle orbits and rf fields.
Therefore, the cyclotron is useful only for ion acceleration. The virtue of cyclotrons is that they generate a continuous train of beam micropulses. Cyclotrons are characterized by large-area magnetic fields to confine ions from zero energy to the output energy.
1. Uniform-Field Cyclotron
The uniform-field cyclotron has considerable historic significance. It was the first accelerator to generate multi-MeV particle beams for nuclear physics research.
The vertical field is uniform in azimuth. The field magnitude is almost constant in the radial direction, with small positive field index for vertical focusing. Resonant acceleration in the uniform-field cyclotron depends on the constancy of the non-relativistic gyrofrequency.
The energy limit for light ion beams is about 15-20 MeV, determined by relativistic mass increase and the decrease of magnetic field with radius. There is no synchronous phase in a uniform-field cyclotron.
2. Azimuthally-Varying-Field (AVF) Cyclotron
The AVF cyclotron is a major improvement over the uniform-field cyclotron. Variations are added to the confining magnetic field by attaching wedge-shaped inserts at periodic azimuthal positions of the magnet poles.
The extra horizontal-field components enhance vertical focusing. It is possible to tolerate an average negative-field index so that the bending field increases with radius. With proper choice of focusing elements and field index variation, the magnetic field variation balances the relativistic mass increase, resulting in a constant-revolution frequency.
An AVF cyclotron with this property is called an isochronous cyclotron. An additional advantage of AVF cyclotrons is that the stronger vertical focusing allows higher beam intensity. AVF machines have supplanted the uniform-field cyclotron, even in low-energy applications.
3. Separated-Sector Cyclotron
The separated-sector cyclotron is a special case of the AVF cyclotron. The azimuthal field variation results from splitting the bending magnet into a number of sectors.
The advantages of the separated sector cyclotron are modular magnet construction and the ability to locate rf Cyclotrons and Synchrotronsfeeds and acceleration gaps between the sectors.
The design of separated-sector cyclotrons is complicated by the fact that particles cannot be accelerated from low energy.
This feature can be used to advantage; beams with lower emittance (better coherence) are achieved if an independent accelerator is used for low-energy acceleration.
4. Spiral Cyclotron
The pole inserts in a spiral cyclotron have spiral boundaries. Spiral shaping is used in both standard AVF and separated-sector machines. In a spiral cyclotron, ion orbits have an inclination at the boundaries of high-field regions.
Vertical confinement is enhanced by edge focusing. The combined effects of edge focusing and defocusing lead to an additional vertical confinement force.
5. Superconducting Cyclotron
Superconducting cyclotrons have shaped iron magnet poles that utilize the focusing techniques outlined above. The magnetizing force is supplied by superconducting coils, which consume little power.
Superconducting cyclotrons are typically compact machines because they are operated at high fields, well above the saturation level of the iron poles. In this situation, all the magnetic
dipoles in the poles are aligned; the net fields can be predicted accurately.
When particle accelerators, in particular cyclotrons, were first developed during the period 1929 - 1935 research and application in nuclear sciences has gained a quantum jump.
The first artificially produced radio-isotope became available. Use of nuclear techniques in medicine and other branches of pure and applied sciences started.
This necessitates ever increasing development of different types of panicle accelerators.
With the development of nuclear fission reactors in 1942 both neutrons and charged particles contributed equally well to the fear and welfare of the human race.
Concerning cyclotrons, these simple reliable and important machines undergo development starting from 1930 till now. In this lecture we outline their types, parameters, distribution and utilization.
The Classical Cyclotrons:
The idea of gaining energy by repeated use of a single small accelerating electric field was first propose by E.O. Lawrence in 1929. The accelerated charged panicles are constrained by a magnetic field to move in circular orbits so that they repeatedly return to the electric field.
The first cyclotron-as the machine was called - was built in 1931 at the University of California in Berkeley by E.O. Lawrence and M.S. Livingstone. In 1932 a beam of protons of 1 MeV energy was obtained.
In its simplest form the cyclotron consists of two hollow metal electrodes called the dees (from their shape) placed in an evacuated chamber. The chamber with dees inside is placed in a roughly uniform electric field as shown in Figure below.
Simplified Construction of a Two-Dee Cyclotron
A radio frequency oscillator is connected to the dees each of which is made alternatively positive and negative and thus generating an oscillating electric field in the gap between them. Charged panicles are produced by an ion source located centrally between the dees.
A particle with mass m and charge q will be projected from the ion source with velocity v in a direction perpendicular to the magnetic lines of force.
The particle will be forced to move in approximately circular orbits inside the dees and across the gap between them. Under favorable conditions the charged particle may gain energy at each gap crossing.
The radius of the orbit in a magnetic field of flux density B is given by the equation:
Mv2 / r = q v B
From which
r = m*v / )q*B) (1 )
And
v = q B r / m (2)
The time required for one orbit is:
T= 2
r / v = 2r m / )q B (3)
It is fundamental to the operation of the cyclotron that T is independent of speed and radius and is the same for all particles of the same mass to charge ratio (m/q). Particles that cross the dee gap at such an instant that the potential difference is capable of their acceleration will continue to be accelerated by all subsequent gap crossings provided q/m does not change and that the cyclotron is operated at a constant radio frequency (f = 1 /T) and magnetic field.
The radius of accelerated particles orbit, being a function of their speed, will increase with time so that the panicles will follow a spiral path from the ion source to the edge of the dee where they are pulled out as an external beam by means of an electrostatic or magnetic deflector. As shown in Figure below.
If R is the radius of the dee structure the maximum energy attained is;
E= 0.5 m v2 = 0.5 m (q*B*R/m)2=(q2/2m)*B2*R2 (4)
Or E
(B2 R2) for a given kind of
particles
Since B is limited by the properties of iron to 2 tesla, then E a R2 and higher energies can only be reached by increasing R and hence the size of the magnet. It is known that, while revolving with instantaneous radius in a cyclotron, particles have horizontal stability. In the vicinity of stable radius ro, vertical stability cannot be maintained unless B is decreasing slightly with radius r according to the expression.
B=Bo*(ro/r)*n (5)
where n is the magnetic field index, 0<n<l and particularly 0 < n < 0.2 to give field decrease of a four percent (n ~ 0.03 - 0.05), Fig. (3).
A cyclotron with slightly falling magnetic field and operating at fixed frequency is known as the classical cyclotron.
The Relativity Effect:
In a classical cyclotron, as a particle is accelerated its speed increases. At relativistic speeds (V ~ c, the speed of light) the mass of a particle is related to its rest mass by the relation:
m=mo/ (1- V2 /C2 )0.5
The mass therefore increases during acceleration. Thus at v = 0.8c we have m = 1.67 mo and at v = 0.9c, we have m = 2.29 mo.
From Eq. (3) we see that the revolution period T also increases and the particle gradually gets out of phase with the high frequency potential at the dees. The particle may no longer be accelerated.
In order to compensate for this effect we may:
(a) Keep B unaltered and reduce the oscillator frequency f as required.
(b) Keep f fixed and increase B as required
In classical cyclotrons the maximum
attainable particle energy is severely limited by relativistic mass
increase as well as mechanical engineering difficulties and expense. The
maximum particle energy from a classical cyclotron is limited to the range
20-25 MeV for protons and 40-50 MeV for alpha-particles, attainable
currents of the accelerated particles are 100-1000
A.
The Synchrocyclotron:
In 1945 a method was devised independently by V.I. Veksler and E.M. McMillan to overcome the relativistic limit.
In this method the magnetic field dependence on radius, required to preserve particles vertical stability, is maintained while the high frequency on the dees is decreased in a manner to compensate for the increase in particles revolution period.
This is carried out by a rotating variable capacitor giving the required frequency variation. Rotations up to 1500-3000 RPM may be needed. Particles or ions can then be accelerated to very high energies and the cyclotron becomes a synchrocyclotron.
Particle orbit in synchrocyclotron is so stable that even after several hundred thousand revolutions the particles still cross the gap at the correct position. The energy added at each turn need only be a few keV and the construction of the dee system is greatly simplified.
One of the dees is replaced by an earthed shield called the dummy dee. The dummy dee serves to concentrate the lines of force across the gap, and avoids the difficulty which arises in feeding the r.f. supply to the two dees whose dimensions are comparable with the wave length of the oscillator. As shown in Figure below.
In the synchrocyclotron the accelerated beam is pulsed being in synchronization with frequency change (modulation).
The rate of pulse repetition is ~ 100 sec'1 with pulse duration ~ 100 [isec. The average beam intensity is 0.1 -1, [lA and the maximum proton energy is ~ 0.8 GeV.
The AVF Cyclotron:
In this type of cyclotrons the magnetic field B is allowed to increase with radius by just the amount needed to compensate for the relativistic increase of mass.
The tine of revolution T remains constant and thereby the oscillator frequency f. The constancy of f requires that B changes according to the law,
B=Bo(l+W/Eo) (7)
where W = mov2/2 is the kinetic energy.
Eo = moc2 is the rest mass energy.
Bo is the magnetic flux density at r = 0 and B is the flux density at r.
For the acceleration of protons (Eo = 938 MeV) to W = 60MeV, the B field must increase by ~ 6.4%.
The increase in B with r is usually accomplished by means of circular coils placed on the surface of the poles of the magnet.
The destroyed vertical stability is restored employing the idea of I.H. Thomas who showed theoretically in 1938 that vertical stability could be maintained if the magnetic field is allowed to vary according to the expression,
B=Bo(l-
*r*cos 
+B*r2) (8)
Such expression allows both radial (r) and
angular (azimuthal,) dependence. Correct choice of parameters
and 
in expression (8) may yield field dependence with
radius similar to (7). Under (7) the frequency f remains constant over the
whole energy range. The azimuthal dependence given by the component r cos allows for vertical stability of the revolving
particles.
The azimuthal variation of
could be obtained by adding radial "hills" to the pole
tips as shown in Fig. (5). The field between the hills (valleys) is larger
(smaller) than the averaged field . The panicle orbits are no longer circular. They
move inside and outside the circular orbit that would be given by the
azimuthally averaged field and enter and leave boundary between the
sectors (hills or valleys) non-normally.
The curvature of the field lines at sector boundaries, combined with the non-normal motion is responsible for the vertical stability.
A cyclotron in which the field is varied azimuthally is called the azimuthally varying field (AVF) cyclotron. From the point of view of vertical stability it is also a sector focused cyclotron, and taking in consideration that the revolution period and hence the frequency of the oscillator is constant and does not depend on panicle energy, the cyclotron is termed as isochronous cyclotron.
The AVF cyclotron produces beams with intensity and time structure of the classical machines but with design energies up to 580 MeV (for protons). Moreover, particles may be accelerated to any final energy (~ 900 MeV dictated by design and technical limitations) from very low up to the maximum, by changing the oscillator frequency, the average magnetic field and the radial increase in field (by changing the currents in the pole face coils)
Interdisciplinary Utilization of Cyclotrons:
During the last two decades throughout the world new application-oriented research and development projects have been initiated based on interdisciplinary utilization of accelerators, in particular Van De Graafs and cyclotrons. Among these accelerators AVF cyclotrons have the following advantages:
- Ability to accelerate light and heavy ions.
- Wide energy range and high current of accelerated particles.
Reliability and simplicity of operation.
Easy maintenance
- Compactness and moderate cost
- Low power consumption
- Safety
i) Basic research in nuclear and atomic physics:
Nuclear reaction structure and mechanisms' studies, life time measurements of excited states; level formation and decay scheme studies, nuclear reaction cross-section determination, investigation of charged particles ionization cross-section, ion-atom collision studies, etc.
ii) Production of short-lived cyclotron isotopes:
With an AVF cyclotron with Ep 20 MeV the following radioisotopes can be produced
11C, 13N, 15O, 18f, 24Na, 43K 48Cr 52Fe, 55Co, 56Mn, 62Zn, 67Ga , 77Br, 8lRb 111In ,123I, 127Xe 197Hg ,201TL and 203Pb.
All these isotopes are neutron deficient isotopes with half-lives in the minutes-hours range, they are preferred for many medical and biological applications. A short half-life is often required to avoid unnecessary irradiation of tissues. The first four isotopes are known as PET isotopes, they are used in positron emission tomography.
iii) Material science and solid state physics:
This includes radiation damage in metals and semiconductors, materials modification, study of wearing, ageing and corrosion processes, synthesis of thin films, etc.
iv) Use of nuclear analytical methods of analysis:
Trace element analysis with sensitivity up to 10-8 and sample weight as little as 0.1 mg are done by means of: PIXE particle induced x-ray emissions), PIGE (particle induced y -ray emission), BSA (back scattering analysis), CPAA (charged particle activation analysis, prompt), FNAA (fast neutron activation analysis), and other related techniques.
v) Fast neutron research and applications:
With high flux (1011 - 1012 n/s cm2) and average neutron energy in the range 3.7 - 9.0 MeV, the following fields of research and applications are covered: fast neutron reactions, production of neutron excessive isotopes, fast neutron therapy, production of radio mutations, fast neutron applications in material sciences, application of pulsed-neutron methods in geology and earth sciences, etc.
vi) Nuclear microbeam applications:
Scanning by spot-size (~ 2xl0-6m) ion beams, STIM (scanning transmission ion microscopy) imaging micro-electronic chip treatment and fabrication, microfilter production, etc.
vii) Nuclear data and services:
filling gaps in cross-section data in nuclear reactions induced by light and heavy ions on thin and thick targets, improving data on panicle (charged and neutral) induced radioactive decay, study of particle interaction with bulk media, establishing and mastering methods and techniques of radioisotope production and other
nuclear methods and techniques to be used in basic science and applications.
Factors to be considered in irradiation of targets in cyclotrons:
In irradiation targets by charged particles in the cyclotron the following factors have to be taken into consideration
1- Charged panicles interact with the material of the target and cause ionization of the target medium which can lead to ionic chemical reactions.
2- Charged particles passing through the target loss energy and cause heating of the target. Heat transferred through out the medium according to the thermal conductivity of the medium.
3- Charged panicles may undergo deflection and this lead to spreading of the beam.
4- Maximum yield of the specified nuclear reaction has to be estimated carefully.
5- Knowledge of the expected interfering reactions. These reactions will often produce unwanted impurities which must be removed.
6- Accurate measurements of the beam current is important in
7- estimating the expected yield from the target.
8- Saturation factor for the production procedure has to be determined by comparison of the half life of the produced radioisotope and the irradiation time.
9- lonization of the medium results in production of ions and electrons. The reactions of these ions are very important in prediction of the chemical form of the produced radioisotope. The form may change depending on the beam intensity and irradiation time as well as the nature of the target.
10- Hot atom reactions which occur between the highly energetic atoms and molecules of the target medium is important in determining the chemical form of the final isotopically labelled species.
11- Minimizing contaminants in the targets which can be lead to unwanted side-products.
12- The target temperature has to be measured during irradiation. The temperature will have an effect on the chemical form of the produced radioisotope. The temperature inside the target will vary depending on the irradiation conditions.
13- The heat created by the passage of the charged particles must be removed from the target medium in order to maintain thedensity of the target material at a reasonable level. The modes of heat transfer in any target are conduction, convection and radiation. The relative importance of these modes varies with material and irradiation conditions.
14- The target foil material must be able to withstand the pressure within the target at the temperatures expected to occur during bombardment and must be also inert chemically to the target medium.
