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N = q 2 B 2 R 2 4 m q V


K max = 2 q N V

Clearly, the numbers of revolutions is inversely proportional to the potential difference applied in the gap. On the other hand, maximum energy of the particle is directly proportional to the product “NV”. Combining two facts, we find that energy of the particle is indeed independent of the applied voltage in the gap.

Limitations of cyclotron

We have already noted two limitations of cyclotron as accelerator. One limitation is that it can not accelerate neutral particle. Second limitation is that lighter elementary particles like electrons or positrons can not be accelerated and requires important changes or modifications of the device. In addition to these, there are two other important limitations as described here.

Relativistic effect

The relativistic effect becomes significant enough to be neglected when particle achieve 10 % of the speed of light. The energy corresponding to this speed for a proton is about 5MeV. Initially, the small relativistic effect is accommodated by an standard cyclotron, but it begins to fail to accelerate charged particle at higher energy level of 50 MeV or so.

At higher speed, the mass of the particle increases in accordance with following equation :

m = m 0 1 v 2 c 2

where mo is rest mass and c is the speed of light in vacuum. The particle becomes heavier at higher speed. Putting this in the expression of frequency, we have :

ν = q B 1 v 2 c 2 2 π m 0 ν = ν 0 1 v 2 c 2

where ν 0 is classical frequency. Clearly, the frequency of revolution decreases with increasing velocity whereas frequency of applied electrical oscillator is fixed. The particle, therefore, gets out of step with the alternating electrical field. As a result, speed of the particle does not increase beyond a certain value.

High energy particle

The cyclotron is also limited by the mere requirement of magnet size as radius of Dees increases with increasing speed of the particle being accelerated. Let us calculate speed corresponding of a 100 GeV particle in a magnetic field of 1 T. The radius of revolution is related to kinetic energy :

K max = q 2 B 2 R 2 2 m R = 2 m K max q 2 B 2

The given kinetic energy is :

K max = 100 X 10 9 e V = 10 11 X 1.6 X 10 - 19 = 1.6 X 10 - 8 J

Now, putting values assuming particle to be a proton,

R = 2 X 1.66 X 10 - 27 X 1.6 X 10 - 8 1.6 X 10 - 19 2 X 1 R = 0.144 X 10 2 = 14.4 m

We can imagine how costly it would be to create magnet of such an extent. For higher energy, the required radius could be in kilometers.

Synchrocyclotron and synchrotron

The synchrocyclotron is a device that addresses the limitation due to relativistic effect. The frequency of oscillator is reduced gradually in order to maintain the resonance with the spiral motion of charged particle. Note that magnetic field remains constant as in the case of cyclotron.

In synchrotron as against synchrocyclotron, both magnetic field and electric field are variable. It aims to address both the limitations due to relativistic effect as well as due to the requirement of large cross section of magnets. The particle is accelerated along a fixed large circular path inside a torus shaped tunnel. The magnetic field here bends the particle, where as electric field changes speed. Clearly, the requirement of a large cross section of magnet is converted into multiple bending magnets along a large radius fixed circular path.

Questions & Answers

how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
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what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Electricity and magnetism. OpenStax CNX. Oct 20, 2009 Download for free at http://cnx.org/content/col10909/1.13
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