8.2 - Particle Accelerators And Detectors Flashcards
How do we investigate the internal substructure of particles like nucleons
Scientists collide them with other particles at very high speeds (very high energies).
What are nucleons
Protons and neutrons
Why must high energy particles be collided compared to lower energies
It is necessary to use high energy particles because at lower energies the particles just bounce off each other, keeping their internal structure secret 🤫🤫
If we can collide particles together hard enough, they will break up, revealing their structure. In most cases, additional particles are created from the energy of the collision.
What’s the challenge for accelerating particles
The challenge for scientists has been to accelerate particles to high enough speeds. Charged particles can be accelerated in straight lines using electric fields, and their direction changed along a curved path by a magnetic field.
What is a linac accelerator also known as
A linear particle accelerator
Tell me about linear accelerators briefly
One of the simplest ways to produce energy high enough for these particle collisions is to accelerate a beam of charged particles along a straight path.
However, this is limited by the maximum achievable potential difference. In order to overcome this problem, the particles are accelerated in stages. They are repeatedly accelerated through the maximum p.d, making the particle energies very high.
Explain how linear accelerators work
If the particles to be accelerated by the linear accelerator are electrons, they are generated by an electrostatic machine and then introduced into the accelerator. Once inside the cylinder, the electrons move In a straight line, as the electrode is equally attracting in all directions. The alternating voltage supply is made to change as the electrons reach the middle of a drift tube, so it becomes negative. This repels the electrons out of the end of that tube and towards the next, and then accelerated towards the next. This carries on until the electrons reach the end of the line, at which point they emerge to collide with a target.
In linac accelerators, why must drift tubes be made longer and longer as the particle is accelerated
In order to keep accelerating particles that are moving faster and faster, the acceleration (drift) tubes must be made longer and longer as the particles travel through each successive one at a higher speed, whilst the time between potential difference flips is fixed as the alternating voltage has a uniform frequency of a few gigahertz.
What’s the limit on the use of linear accelerators
The limit on the use of this kind of accelerator is how long you can afford to build it, remembering that the whole thing must be in a VACUUM so that particles do not collide with air atoms, and it must be perfectly straight.
Was Einstein right? Tell me about relativistic speeds
One of Einstein’s claims in his theory of special relativity is that nothing can accelerate beyond the speed of light. This means that particles in accelerators must be faced with a problem when they are already travelling close to the speed of light and then pass through a p.d. which should accelerate them beyond it.
However, it was demonstrated that at very high speeds, particles deviate from the equation 1/2mv^2 = qv, and do indeed never accelerate beyond the speed of light. It can be shown that whilst the kinetic energy and momentum of particles can continue to increase without limit, their speed does not. This can only happen if the mass of a particle seemingly increase with speed.
This apparent mass increase becomes significant at speeds approaching light speed - known as ‘relativistic speeds’
Look at diagrams and graph on page 95 please
Idk how to explain on here?
Page 95
Why do we accelerate particles in circles
As scientists struggled to produce ever longer linear accelerators, they sought to coil their accelerators up into a circle so that the particles could be accelerated in an electric field repeatedly in a smaller space. To do this, we use the fact that charged particles moving across a magnetic field will feel a centripetal force, and so will move in a circular path. We can work out the radius of this circular path, and use it to construct a circular accelerator of the right dimensions.
How can field lines be shown to be moving out of a page
Drawing a dot
How can we show field lines as going into the page
Drawing a cross
How can we derive the equation:
r = p/Bq
We have previously seen the equation for the force on a charged particle moving across a magnetic field, F = Bqv
The force acts at right angles to the velocity, v, meaning that the particle will follow a circular path. Recall that the equation for the centripetal force on anything moving in a circle is: F = mv^2/r
We can equate these two expressions. Dividing out the velocity from each size and rearranging to find an expression for the radius of a circle gives:
r = p/Bq
What does the equation r = p/Bq mean?
This means that for a given magnetic field, the radius of the path of a charged particle is proportional to its momentum. At slow speeds, the radius is proportional to velocity (or the square root of kinetic energy), but as these experiments generally send particles at speeds approaching the speed of light, relativistic effects need to be accounted for. In particular, at these very high speeds the particles mass appears to increase, which would also alter its momentum. The overall result is that a particle increasing in speed would travel along an outwardly spiralling path.
What is a cyclotron and how does it work
Ernest Lawrence developed the first cyclotron, a circular accelerator which could give protons about one MeV of energy.
In a cyclotron, there are two D-shaped electrodes (or dees), and the particles are accelerated in the electric field in the gap between them. Whilst inside the dees, the particle will travel along a semicircular path under the influence of the magnetic field, before being accelerated across the gap again, then another semicircle, another acceleration across the gap, and so on. As each acceleration increases the momentum of the particle, the radius of its path within the dees increases, and so it steadily spirals outwards as it emerges from an exit hole and hits the target placed in a bombardment chamber in its path.
It’s alternating current, so as it leaves one electrode/Dee the current switches polarity so charged particle is repelled from one to the other Dee and then travels around etc. Inside the cyclotron is a vacuum.
Why does the p.d need to switch direction
In order to maintain the accelerations at exactly the correct moment, the p.d. needs to switch direction exactly when the particle exits from one Dee to move across the gap between them. This means the voltage supply has to follow a square wave pattern where it flips polarity instantaneously.
The frequency of these polarity switches only depends on the particle being used and the strength of the magnetic field applied.
How can we work out the frequency needed for a cyclotron
The frequency of these polarity switches only depends on the particle being used and the strength of the magnetic field applied.
f = 1/T
T = 2pi x r/v
During on complete period of the alternating voltage the particle will pass through both dees, thus completing a full circle at that radius.
However: r = mv/Bq
So, T = 2pi x mv/Bqv
So by dividing by velocity, and since f = 1/T
F = Bq/2pi x m
Thus the frequency needed is independent of the radius, meaning that a constant frequency can be used and the particle will complete each semicircle through a Dee in the same time. That is until the speed becomes so fast that mass changes through relativistic effects.
