Other Accelerators

Question 1

what was the solution to being able to accelerate a charged particle indefinitely, without the limit of space

Answer 1

build a circular accelerator

Question 2

why does a circular accelerator allow for a particle to be indefinitely accelerated

Answer 2

the particles could be accelerated in an electric field repeatedly in circles

Question 3

why do the particles move in a circular path

Answer 3

• 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

Question 4

what symbols are used to show the magnetic field is going into or out of the page

Answer 4

• a cross means its into the page

- a dot means its out of the page

Question 5

what is the equation for the force a charged particle feels in a magnetic field

Answer 5

F = BQv

Question 6

what is the equation for centripetal force

Answer 6

F = mv^2 / r

Question 7

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

Answer 7

• the force the charged particle feels in the magnetic field is equal to the centripetal force it feels
• BQv = mv^2 / r

Question 8

how do you rearrange that equation to show that r = p / Bq

Answer 8

• r = mv^2 / Bqv (divide by v)
• r = mv / Bq
• p = mv (momentum equation)
• r = p / Bq

Question 9

when the charged particle is approaching relativistic speeds, how would the radius / motion change

Answer 9

the particle would begin travelling in an outwardly spiralling path

Question 10

why does the particle begin travelling in an outwardly spiralling path

Answer 10

• 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

Question 11

what is the name of the first circular accelerator

Answer 11

the cyclotron

Question 12

what was the main thing a cyclotron could do

Answer 12

• accelerate protons

- to give them 1 MeV of energy

Question 13

what is the basic setup of a cyclotron

Answer 13

• 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

Question 14

where specifically is the particle accelerated in this setup

Answer 14

in the gap between the dees

Question 15

what is accelerating the particle when its in the gap

Answer 15

the electric field formed by the alternating pd supply

Question 16

how is the particle accelerated around the cyclotron generally

Answer 16

• 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

Question 17

when this process keeps repeating itself, how does the motion of the particle change and why

Answer 17

• 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

Question 18

what is the goal of accelerating a particle in a cyclotron anyway

Answer 18

• 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

Question 19

what needs to happen with the pd in order for this acceleration to work

Answer 19

• it needs to be switching direction

- exactly when the particle exits from one dee

Question 20

why does the pd need to switch in this manner

Answer 20

• 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

Question 21

what kind of wave pattern does the pd supply need to follow when its polarity flips and why

Answer 21

• a square wave pattern

- so the switch is instantaneous

Question 22

what two things does the frequency of the polarity switches depend on

Answer 22

• the particle being used

- the strength of the magnetic field applied

Question 23

what does the time period equal in this accelerator, in terms of r and v

Answer 23

T = 2 pi r / v

Question 24

what is the equation for the frequency of the pd supply , in terms of B, q and m

Answer 24

f = Bq / 2pi m

Question 25

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

Answer 25

• no
• the speed could be so large that the mass changes through relativistic effects
• therefore changing the frequency required

Question 26

what does the equation for frequency change to when relativistic effects are taken into account

Answer 26

f = (Bq / 2pi m(0)) * root of (1 - (v^2/c^2))

Question 27

what is m(o)

Answer 27

the particles initial / rest mass

Question 28

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

Answer 28

the synchrocyclotron

Question 29

what is a synchrotron

Answer 29

• a particle accelerator with a single ring as its path

- so can only accelerate particles in a fixed circular path

Question 30

how does a synchrotron work with only having one set path for the particles to accelerate around

Answer 30

• 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

Question 31

what would be the response by the synchrotron if the momentum of the particles increased and why

Answer 31

• 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