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 acceleration 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.
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 acceleration 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.
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