Cyclotron ( Concept and Operation ) -1

THE HISTORY of linear accelerators dates back to 1924 when G.Isingproposeda structure comprised of sequentially pulsed drift tubes, where particles would be accelerated in the gaps between them . In 1928, R. Wider?e proposed applying RF voltage between successive drifttubes ,which was successfully tested .In1931,D.H.SloanandE.O.Lawrence made improvements to Wider?e’s accelerator while M. Stanley Livingston worked on a “cyclic” accelerator which later became the ?rst RF accelerator, cyclotron and

These early developments laid the groundwork for higher frequencies and higher RF power systems for particle accelerators. Major breakthroughs in the development of RF accelerating happened at the end of World War II, when RF power sources in mega-watts (MW) ranges at frequencies of hundreds of mega-hertz (MHz) were developed mainly for radars.

The foundation for modern microwave technology was established by W.W.Hansenat Stanford University in 1937, while working on the concept of resonant cavities .Hansen, along with Russell and Sigurd Varian (the Varian brothers) invented the klystron, a high-frequency ampli?er for generations of microwaves, at Stanford University .We should empha size that post World War II transformation of high-frequency RF devices into a mature technology for a wide range of applications including accelerators was mainly based on the war effort toward radar device development , speci?cally the development of high-power radar devices related to the work on high-power magnetron oscillators which were conducted at Birminghamin theUnited Kingdom during early part of 1940’s.

 Basic Principles

Magnetic filed is towards the slide If Magnetic field and Charge of the particle remain constant, then if Velocity or Mass increases the radius increases

If Mass and Velocity remain constant, then if Magnetic field or Charge increases the radius decreases

If Mass remain constant then if Charge or Magnetic Field increases rotational frequency of the particle increases

If Charge and Magnetic field remain constant then if Mass increases the rotational frequency of the particle decrease

The cyclotron was one of the earliest types of particle accelerators, and is still used as the first stage of some large multi-stage particle accelerators. It makes use of the magnetic force on a moving charge to bend moving charges into a semicircular path between accelerations by an applied electric field. The applied electric field accelerates electrons between the "dees" of the magnetic field region. The field is reversed at the cyclotron frequency to accelerate the electrons back across the gap

When the cyclotron principle is used to accelerate electrons, it has been historically called a betatron. The cyclotron principle as applied to electrons is illustrated below.

When the cyclotron principle is used to accelerate electrons, it has been historically called a betatron. The cyclotron principle as applied to electrons is illustrated below.

Cyclotron Frequency

A moving charge in a cyclotron will move in a circular path under the influence of a constant magnetic field. If the time to complete one orbit is calculated:

it is found that the period is independent of the radius. Therefore if a square wave is applied at angular frequency qB/m, the charge will spiral outward, increasing in speed.

When a square wave of angular frequency

is applied between the two sides of the magnetic poles, the charge will be boosted again at just the right time to accelerate it across the gap. Thus the constant cyclotron frequency can continue to accelerate the charge .

Classical Cyclotron

• Flat top Pole faces unable to do vertical focusing except near the end of pole faces where the field lines are bent
• A very gradual curvature in the vertical directions (upward for upper pole piece and downward for the lower pole piece helps vertical weak-focusing
• Negative radial field gradient creates a serious limitation about the maximum energy of the particle 
• This is contrary to the requirement :-

? As the particle velocity increases its mass increases due to relativistic effect as seen by the magnetic field

? The particle frequency decreases and the particle no longer remains synchronized with the alternating voltage

How the Cyclotron Works 

A cyclotron consists of two D-shaped regions known as dees. In each dee, there is a magnetic ?eld perpendicular to the plane of the page. In the gap separating the dees, there is a uniform electric ? eld pointing from one dee to the other. When a charge is released from rest in the gap it is accelerated by the electric ? eld and carried into one of the dees. The magnetic ? eld in the dee causes the charge to follow a half-circle that carries it back to the gap. W hile the charge is in the dee the electric ? eld in the gap is reversed, so the charge is once again accelerated across the gap.

The cycle continues with the magnetic ? eld in the dees continually bringing the charge back to the gap. Every time the charge crosses the gap it picks up speed. This causes the half-circles in the dees to increase in radius, and eventually the charge emerges from the cyclotron at high speed. T  he electrodes would be in the vacuum chamber, which is ? at, in a narrow gap between the two poles of a large magnet. In the cyclotron, a highfrequency alternating voltage applied across the “D” electrodes (also called “dees”) alternately attracts and repels charged particles.

The particles, injected near the center of the magnetic ? eld, increase in speed (and therefore energy) only when passing through the gap between the electrodes. The perpendicular magnetic ? eld (passing vertically through the “D” electrodes), combined with the increasing energy of the particles, forces the particles to travel in a spiral path. With no change in energy, the charged particles in a magnetic ? eld will follow a circular path. In the cyclotron, energy is applied to the particles as they cross the gap between the dees and so they are accelerated (at the typical sub- relativistic speeds used) and will increase in mass as they approach the speed of light. Either of these effects (increased velocity or increased mass) will increase the radius of the circle and so the path will be a spiral.

(The particles move in a spiral, because a current of electrons or ions, ? owing perpendicular to a magnetic ? eld, experiences a force perpendicular to its direction of motion. The charged particles move freely in a vacuum so the particles follow a spiral path). The radius will increase until the particles hit a target at the perimeter of the vacuum chamber. Various materials may be used for the target, and the collisions will create secondary particles which may be guided outside of the cyclotron and into instruments for analysis. The results will enable the calculation of various properties, such as the mean spacing between atoms and the creation of various collision products. Sub sequent chemical and particle analysis of the target material may give insight into nuclear transmutation of the elements used in the target

 Components:

1. RF resonator and dees

2. Magnet Iron

3. Cryostat for superconducting coils

Radio Frequency System for Cyclotron , Resonators are effectively quarter wave transmission line type resonators short circuited at one end and open circuit at the Dee-end ,Very high (infinite in case of loss less line) voltage is generated at the open end due to multiple reflection from both end Very high current flows in the short-circuit end

Power is fed in between the short and the open by capacitive Coupling or Inductive Coupling , Maximum Voltage obtainable depends on the how much power is fed and how much is the heat dissipation acceptable by the resonator subject to no sparking

In Box type Resonator Physical length is much less than the electrical quarter wave length e.g. in K 130 Cyclotron

In Coaxial Resonator Physical length is same as electrical quarter wave

Order of Dee Voltage: 30 KV to 100 KV 

Order of Anode Voltage: 10 to 20 KV and Amplifiers work in Class AB mode

Injection into Cyclotrons

The acceleration of heavy ions or polarized ions requires ion sources of larger dimensions that could not be confined in the central region of the cyclotron. This calls for external injection systems injecting ions either radially or axially. It is also needed when a cyclotron works as a booster accelerator for another cyclotron or a linear accelerator. Radial injection is used mostly in separated sector cyclotrons where there is plenty of space available to house large inflector and/or stripper. Most compact cyclotrons utilize versatile external ion source together with an external injection system injecting the ions axially. A typical layout of an external injection system 

The beam from Electron Cyclotron Resonance (ECR) ion source is extracted using a high voltage electrode (usually 10–20 keV). The extracted heavy ion beam from the source is transported to an analyzing magnet where the required charge state of the ion is selected. The analyzed beam is then transported to the buncher, which converts the dc beam from ECR ion source into bunched beam for proper RF matching. This bunched beam is guided to the inflector in the central region, which bends the beam by 900 into the median plane and places the beam on the orbit for acceleration.

Azimuthally Varying Field (AVF) {AVF Accelerators }

The AVF class of fixed-field accelerators contains two families – the AVF cyclotrons and the FFAGs 

Advantages of fixed magnetic field:

?Higher duty factor – up to 100%

?Higher time-averaged beam current

?Simpler and inexpensive power supplies

?No eddy-current effects, no cyclical stressing of coils Principle disadvantage: particle beam moves radially – large aperture magnet, vacuum and radio-frequency systems Over-arching trend towards designs with increasing momentum compaction – narrower apertures, but longer orbits.

AVF Accelerators – past, present and future Introduction The AVF class of fixed-field accelerators contains two families – the AVF cyclotrons and the FFAGs α=(dp/p)/(dL/L) – Livingood definition of compaction α ≈ 1 for Lawrence cyclotron; α→ ∞ for Johnstone FFAG

Separated sector cyclotron (SSC):

SSC is also an AVF isochronous cyclotron where magnet sectors are separated by empty (zero field) valleys. The powerful RF accelerating structures are situated in the valleys between the magnets. This feature helps to make the magnet gaps quite small and thus improves the vertical focusing properties. It also enables to use high injection energy. The injection is usually from another accelerator. The radial separation between the orbits is sufficiently large which leads to almost loss less extraction. These unique features enable SSC to accelerate high beam current. Example: Ring Cyclotron at PSI, Switzerland, which delivers highest output beam power (2mA, 590 MeV) and is used for the production of pions and spallation neutrons.

Extraction from the Cyclotron

After acceleration to maximum energy, particles must somehow be pulled out of their orbits to form an external beam for utilization by experimentalists. The device used for this purpose is known as deflector. It consists of a channel formed by two electrodes across which an electrostatic field directed outwards (for positive ions) is maintained. As the particle advances in the channel, magnetic field gets progressively weaker and thus the channel width increases. The basic equation that holds at each point in the channel for central trajectory is:

where, E is the electric field in the channel and ρ is the radius of curvature of the channel at the point of consideration. In addition to an electrostatic deflector, magnetic shielding i.e. a magnetic channel is also used to reduce the fringe field. A properly designed magnetic channel helps in the extraction process and also provides radial focusing to the beam. The combination of electrostatic deflector and magnetic channel gives high extraction efficiency particularly at high beam energy. 

In many cyclotrons, designed to accelerate only protons, negative hydrogen ions ( ? H ) are accelerated. At a chosen radius in the acceleration chamber a thin foil (usually carbon) is inserted into the circulating beam. As a result, virtually all the ? H ions are converted into protons by stripping. The radius of curvature of the orbit is, therefore, reversed and all the protons bend out of the cyclotron magnet. By changing the radial position of the stripper foil one can also easily change the extraction energy. The extraction efficiency is ~99% or more. Unfortunately, it is not possible to simply increase the magnetic field in the cyclotron to achieve any desired extraction energy due to electromagnetic stripping forces, which tend to remove the outer electron bound only by .775eV and leaves a neutral hydrogen atom. For energies in the range of 20 MeV to 50 MeV, the compact ? H cyclotron is a far more economical choice for high intensity beam than a proton cyclotron. 

Transverse emittance:

It is a measure of the correlation between the position and divergence of the particles in the beam. Typical values of horizontal and vertical emittance of the extracted cyclotron beam are ~20 to 80 mm-mrad and vary from cyclotron to cyclotron. The brightness of the central part is intense and thus the emittance can be reduced using a collimator. The emittance of the beam emerging from an accelerator is usually limited by the space available for axial and radial oscillations during acceleration and sometimes by extraction system rather than the characteristics at the injection.

Energy resolution:

In an AVF cyclotron under normal operating conditions the beam has energy spread ?E/E ～ 0.5% (FWHM). The major contributing factor to this energy spread comes from the multi-turn extraction nature as a result of overlapping of orbits at the extraction radii. The energy resolution can be improved by using slits at the central region or an external analyzing magnet and slits in the beam line. 

To Be Continued .......

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