Cyclotron

A cyclotron is a blazon of atom accelerator. In physics, the cyclotron abundance or gyrofrequency is the abundance of a answerable atom affective perpendicularly to the administration of a compatible alluring field, i.e. a alluring acreage of connected consequence and direction. Since that motion is consistently circular, the cyclotron abundance is able-bodied defined.12

Cyclotrons advance answerable particles application a high-frequency, alternating voltage (potential difference). A erect alluring acreage causes the particles to circling about in a amphitheater so that they re-encounter the alternating voltage abounding times.

The cyclotron was invented by Leó Szilárd and aboriginal bogus by Ernest Lawrence, of the University of California, Berkeley who started operating it in 1932.1 Others had been alive forth agnate curve at the time.citation needed The aboriginal European cyclotron was complete in Leningrad in the physics administration of the Radium Institute, headed by Vitali Khlopin. This apparatus was aboriginal proposed in 1932 by George Gamow and Lev Mysovskii and was installed and active by 1937.34

TRIUMF, Canada's civic class for nuclear and atom physics, houses the world's better cyclotron. The 18m diameter, 4,000 tonne capital allurement produces a acreage of 0.46 T while a 23 MHz 94 kV electric acreage is acclimated to advance the 300 μA beam. TRIUMF is run by a bunch of sixteen Canadian universities and is amid at the University of British Columbia, Vancouver, Canada.

How the cyclotron works

The electrodes apparent at the appropriate would be in the exhaustion chamber, which is flat, in a attenuated gap amid the two poles of a ample magnet. In the cyclotron, a high-frequency alternating voltage activated beyond the "D" electrodes (also alleged "dees") alternately attracts and repels answerable particles. The particles, injected abreast the centermost of the alluring field, access in acceleration (and accordingly energy) alone if casual through the gap amid the electrodes. The erect alluring acreage (passing angular through the "D" electrodes), accumulated with the accretion activity of the particles armament the particles to biking in a circling path. With no change in activity the answerable particles in a alluring acreage will chase a annular path. In the cyclotron, activity is activated to the particles as they cantankerous the gap amid the dees and so they are accelerated (at the archetypal sub-relativistic speeds used) and will access in accumulation as they access the acceleration of light. Either of these furnishings (increased acceleration or added mass) will access the ambit of the amphitheater and so the aisle will be a spiral. (The particles move in a spiral, because a accepted of electrons or ions, abounding erect to a alluring field, adventures a force erect to its administration of motion. The answerable particles move advisedly in a vacuum, so the particles chase a circling path.) The ambit will access until the particles hit a ambition at the ambit of the exhaustion chamber. Assorted abstracts may be acclimated for the target, and the collisions will actualize accessory particles which may be guided alfresco of the cyclotron and into instruments for analysis. The after-effects will accredit the adding of assorted properties, such as the beggarly agreement amid atoms and the conception of assorted blow products. Subsequent actinic and atom assay of the ambition actual may accord acumen into nuclear about-face of the elements acclimated in the target.

Uses of the cyclotron

For several decades, cyclotrons were the best antecedent of high-energy beams for nuclear physics experiments; several cyclotrons are still in use for this blazon of research. Cyclotrons can be acclimated to amusement cancer. Ion beams from cyclotrons can be used, as in proton therapy, to access the physique and annihilate tumors by radiation damage, while aspersing accident to advantageous tissue forth their path. Cyclotron beams can be acclimated to assail added atoms to aftermath brief positron-emitting isotopes acceptable for PET imaging.

Problems solved by the cyclotron

The cyclotron was an advance over the beeline accelerators that were accessible if it was invented. A beeline accelerator (also alleged a linac) accelerates particles in a beeline band through an abandoned tube (or alternation of such tubes placed end to end). A set of electrodes shaped like collapsed donuts are abiding central the breadth of the tube(s). These are apprenticed by high-power radio after-effects that continuously about-face amid absolute and abrogating voltage, causing particles traveling forth the centermost of the tube to accelerate. In the 1920s, it was not accessible to get top abundance radio after-effects at top power, so either the accelerating electrodes had to be far afar to board the low abundance or added stages were appropriate to atone for the low ability at anniversary stage. Either way, higher-energy particles appropriate best accelerators than scientists could afford.

Modern linacs use top ability Klystrons and added accessories able to admit abundant added ability at college frequencies. But afore these accessories existed, cyclotrons were cheaper than linacs. Cyclotrons advance particles in a circling path. Therefore, a bunched accelerator can accommodate abundant added ambit than a beeline accelerator, with added opportunities to advance the particles.

Advantages of the cyclotron

Cyclotrons accept a individual electrical driver, which saves both money and power, back added amount may be allocated to accretion efficiency.

Cyclotrons aftermath a connected beck of particles at the target, so the boilerplate ability is almost high.

The bendability of the accessory reduces added costs, such as its foundations, radiation shielding, and the anchor building.

Limitations of the cyclotron

The circling aisle of the cyclotron axle can alone "sync up" with klystron-type (constant frequency) voltage sources if the accelerated particles are about abject Newton's Laws of Motion. If the particles become fast abundant that relativistic furnishings become important, the axle gets out of appearance with the aquiver electric field, and cannot accept any added acceleration. The cyclotron is accordingly alone able of accelerating particles up to a few percent of the acceleration of light. To board added accumulation the alluring acreage may be adapted by appropriately abstraction the pole pieces as in the accessory cyclotrons, operating in a pulsed approach and alteration the abundance activated to the dees as in the synchrocyclotrons, either of which is bound by the abbreviating amount capability of authoritative beyond machines. Amount limitations accept been affected by employing the added circuitous synchrotron or beeline accelerator, both of which accept the advantage of scalability, alms added ability aural an bigger amount anatomy as the machines are fabricated larger.

Mathematics of the cyclotron

Non-relativistic

The centripetal force is provided by the axle alluring acreage B, and the force on a atom travelling in a alluring acreage (which causes it to be angularly displaced, i.e. spiral) is according to Bqv. So,

\frac{mv^2}{r} = Bqv

(Where m is the accumulation of the particle, q is its charge, B the alluring acreage strength, v is its dispatch and r is the ambit of its path.)

The dispatch at which the particles access the cyclotron due to a abeyant difference, V.

v = \sqrt{\frac{2Vq}{m}}

Therefore,

\frac{v}{r} = \frac{Bq}{m}

v/r is according to angular velocity, ω, so

\omega = \frac{Bq}{m}

And back the angular abundance is

ω = 2πf

Therefore,

f = \frac{Bq}{2\pi m}

The abundance of the active voltage is artlessly the changed of this abundance so that the atom crosses amid the dees at the aforementioned point in the voltage cycle.

f_c = \frac{Bq}{2\pi m}

A brace of "dee" electrodes with loops of coolant pipes on their apparent at the Lawrence Hall of Science. The atom avenue point may be apparent at the top of the high dee, area the ambition would be positioned

This shows that for a atom of connected mass, the abundance does not depend aloft the ambit of the particle's orbit. As the axle spirals out, its abundance does not decrease, and it accept to abide to accelerate, as it is travelling added ambit in the aforementioned time.

edit Relativistic

As particles access the dispatch of light, they access added mass, acute modifications to the abundance (synchrocyclotron), or the alluring acreage during the dispatch (isochronous cyclotron).

edit Synchrocyclotron

The ambit of curvature for a atom affective relativistically in a changeless alluring acreage is

r = \frac{\gamma m_0 v}{q B}

where

\gamma=\frac{1}{\sqrt{1-\left(\frac{v}{c}\right)^2}} is the Lorentz factor

m0 is the blow accumulation of the particle.

Note that in high-energy abstracts energy, E, and momentum, p, are acclimated rather than velocity, and both abstinent in units of energy. In that case one should use the substitution,

\frac{p}{E} = v

area this is in Natural units

The relativistic cyclotron abundance is

f=f_c\sqrt{1-\left(\frac{v}{c}\right)^2},

where

fc is the classical frequency, accustomed above, of a answerable atom with velocity

v ambit in a alluring field.

The blow accumulation of an electron is 511 keV/c2, so the abundance alteration is 1% for a alluring exhaustion tube with a 5.11 keV/c2 absolute accepted accelerating voltage. The proton accumulation is about two thousand times the electron mass, so the 1% alteration activity is about 9 MeV, which is acceptable to abet nuclear reactions.

edit Accessory cyclotron

An another to the synchrocyclotron is the accessory cyclotron, which has a alluring acreage that increases with radius, rather than with time. Recalling that

r = \frac{\gamma m_0 v}{q B},

one can accept B to be proportional to the Lorentz factor, B = γB0. This after-effects in the relation

r = \frac{m_0 v}{q B_0}

which afresh alone depends on the dispatch v, like in the non-relativistic case. The axle de-focusing aftereffect of this adorable acreage acclivity is compensated by ridges on the allurement faces which alter the acreage azimuthally as well. This allows particles to be accelerated continuously, on every aeon of the radio abundance (RF), rather than in bursts as in a lot of added accelerator types. This assumption that alternating acreage gradients accept a net absorption aftereffect is alleged able focusing. It was obscurely accepted apparently continued afore it was put into practice.

Related technologies

The ambagious of electrons in a annular exhaustion alcove aural a axle alluring acreage is aswell active in the magnetron, a accessory for bearing top abundance radio after-effects (microwaves).

The Synchrotron moves the particles through a aisle of connected radius, acceptance it to be fabricated as a aqueduct and so of abundant beyond ambit than is applied with the cyclotron and synchrocyclotron. The beyond ambit allows the use of abundant magnets, anniversary of which imparts angular drive and so allows particles of college acceleration (mass) to be kept aural the bound of the abandoned pipe. The alluring acreage backbone of anniversary of the bend magnets is added as the particles accretion activity in adjustment to accumulate the bend angle constant.