Other Accelerators Flashcards
what was the solution to being able to accelerate a charged particle indefinitely, without the limit of space
build a circular accelerator
why does a circular accelerator allow for a particle to be indefinitely accelerated
the particles could be accelerated in an electric field repeatedly in circles
why do the particles move in a circular path
- theres a magnetic field present within the accelerator
- referring back to FLHR, a charged particle moving across a magnetic field will experience a centripetal force towards the tip of the thumb
- causing it to move in a circular path
what symbols are used to show the magnetic field is going into or out of the page
- a cross means its into the page
- a dot means its out of the page
what is the equation for the force a charged particle feels in a magnetic field
F = BQv
what is the equation for centripetal force
F = mv^2 / r
if the force exerted on the charged particle in the magnetic field is what is causing it to travel in a circular path, what is the relationship between those two equations
- the force the charged particle feels in the magnetic field is equal to the centripetal force it feels
- BQv = mv^2 / r
how do you rearrange that equation to show that r = p / Bq
- r = mv^2 / Bqv (divide by v)
- r = mv / Bq
- p = mv (momentum equation)
- r = p / Bq
when the charged particle is approaching relativistic speeds, how would the radius / motion change
the particle would begin travelling in an outwardly spiralling path
why does the particle begin travelling in an outwardly spiralling path
- as it approaches those speeds, its velocity and mass are increasing
- this disrupts the directly proportional relationship between velocity and radius that would normally be maintained at lower speeds
- resulting in a more exponential increase in radius for a given B and q
what is the name of the first circular accelerator
the cyclotron
what was the main thing a cyclotron could do
- accelerate protons
- to give them 1 MeV of energy
what is the basic setup of a cyclotron
- there are two D-shaped electrodes (dees) facing each other, creating a thing gap between them
- both electrodes are connected to an alternating pd supply
- they are surrounded with a south pole above them and a north pole below them
where specifically is the particle accelerated in this setup
in the gap between the dees
what is accelerating the particle when its in the gap
the electric field formed by the alternating pd supply
how is the particle accelerated around the cyclotron generally
- the particle will be experiencing a force on it due to the magnetic field produced by the magnets
- when inside one of the dees, it will travel in a semicircular path
- it will exit on dee, be accelerated through the electric field in the gap and enter the other dee
- following the same semicircular path again
when this process keeps repeating itself, how does the motion of the particle change and why
- the velocity of the particle keeps increasing due to it constantly being accelerated
- this increases its momentum overtime
- resulting in the radius of its path increasing in a spiralling manner
what is the goal of accelerating a particle in a cyclotron anyway
- the goal is to accelerate the particle until it emerges from an exit hole
- hitting the target placed in a bombardment chamber in its path
what needs to happen with the pd in order for this acceleration to work
- it needs to be switching direction
- exactly when the particle exits from one dee
why does the pd need to switch in this manner
- the particle needs to be repelled from the dee its in
- meaning it would also be attracted to the other dee
- when it leaves the repelling dee and enters the attracting one, the pd needs to switch so its repelled from the dee its in now
- which allows the accelerating process to repeat itself
what kind of wave pattern does the pd supply need to follow when its polarity flips and why
- a square wave pattern
- so the switch is instantaneous
what two things does the frequency of the polarity switches depend on
- the particle being used
- the strength of the magnetic field applied
what does the time period equal in this accelerator, in terms of r and v
T = 2 pi r / v
what is the equation for the frequency of the pd supply , in terms of B, q and m
f = Bq / 2pi m
does the equation for frequency mean that a constant frequency can be used for a particle to complete each semicircle through the dee in the same time, all times
- no
- the speed could be so large that the mass changes through relativistic effects
- therefore changing the frequency required
what does the equation for frequency change to when relativistic effects are taken into account
f = (Bq / 2pi m(0)) * root of (1 - (v^2/c^2))
what is m(o)
the particles initial / rest mass
as the frequency of the applied accelerating potential difference now depends on the velocity of the particles, a cyclotron would need clever circuitry to produce accurately timed polarity switches,what is the name of the new particle accelerator that could successfully generate high particle beams while meeting these requirements
the synchrocyclotron
what is a synchrotron
- a particle accelerator with a single ring as its path
- so can only accelerate particles in a fixed circular path
how does a synchrotron work with only having one set path for the particles to accelerate around
- by varying the strength of its magnetic field using an electromagnet
- this allows for the radius of the particles beams path to be kept constant
what would be the response by the synchrotron if the momentum of the particles increased and why
- its magnetic field strength would increase
- F = mv^2 / r
- an increase in momentum counteracted by an increase in force allows r to remain constant
