Particle Accelerators

Question 1

What is the main purpose of a particle accelerator?

Answer 1

To accelerate charged particles to high energies and collide them to study fundamental particles and forces.

Question 2

How do accelerators help us to study particles?

Answer 2

The more energy particles have the shorted their De Broglie wavelength lambda = h/p
Hence the greater detail in which they can be investigated

Question 3

Why do we need high energy particles?

Answer 3

To enable particles of the same charge to get close to each other.

Question 4

What happens when high energy particles collide?

Answer 4

Energy is redistributed and the higher the energy the more available to produce new particles

Question 5

What are the two main components required in a particle accelerator?

Answer 5

Electric fields to accelerate particles and magnetic fields to steer/focus them.

Question 6

What is relativistic momentum?

Answer 6

p = m_0 gamma beta c

where gamma = lorentz factor
beta = v/c

Question 7

What is the Relativistic energy?

Answer 7

E = m_0 gamma c^2

where gamma = lorentz factor

Question 8

Energy momentum relation?

Answer 8

E^2 = p^2 c^2 + m_0 ^2 c^4

Question 9

What is energy momentum relation for highly relativistic particles?

Answer 9

E ~= pc

Question 10

Relativistic KE

Answer 10

T = m_0 c^2 (gamma - 1)

where gamma = lorentz factor

Question 11

Why are magnetic fields used in accelerators?

Answer 11

Because magnetic fields change the direction of charged particles without changing their speed.

Question 12

Why are electric fields used in accelerators?

Answer 12

Because electric fields change the energy (speed) of charged particles.

Question 13

What is the Lorentz force law for a charged particle?

Answer 13

F = q(E + v × B), where E is electric field and B is magnetic field.

Question 14

For a single particle with no radiation losses motion in EM field is described by..

Answer 14

Lorentz force

Question 15

If E = 0 and B is perpendicular to V then we get…

Answer 15

circular motion

Question 16

Relativistic centripetal force is given by

Answer 16

F = pv/r

p = m_0 v gamma
where r is radius of orbit

Question 17

In a uniform magnetic field, what path does a charged particle follow?

Answer 17

A circular path due to the magnetic force acting as a centripetal force.

Question 18

What determines the radius of curvature of a charged particle in a magnetic field?

Answer 18

The particle’s momentum, charge, and the magnetic field strength.
r = p/qB

Question 19

What is the time orbit and frequency of a particle in a uniform, constant magnetic field, orbit radius r?

Answer 19

T = 2 pi r/v = 2 pi p/(vqB) = 2 pi mi/ (qB)

f = 1/T = qB/(2 pi m)

Question 20

Why do higher-energy particles require larger accelerator rings?

Answer 20

Because higher momentum particles have larger radii of curvature in a given magnetic field.

Question 21

What is the problem with accelerating a particle through electric fields

Answer 21

It requires a large potential difference, voltage breakdown which limits the energy to MeV

Question 22

What is a linear accelerator (linac)?

Answer 22

An accelerator that speeds up particles in a straight line using a series of electrodes with oscillating electric fields.

Question 23

Advantages of LINAC

Answer 23

No expensive magnetics needed
no energy lost from synchrotron radiation

Question 24

Disadvantages of LINAC

Answer 24

Requires many structures and voltage breakdown is still an issue
Large energy requires long accelerator

Question 25

What is a cyclotron? And how does it work?

Answer 25

A circular accelerator that uses a constant magnetic field and alternating electric field (applied across two semi circular dee's) to accelerate particles in a spiral path. Particle is accelerated in the gap between the dee's. After crossing the gap the polarity is reversed.

Question 26

Time taken and frequency of orbit in cyclotron?

Answer 26

T = 2 pi r/v = 2 pi p/(vqB) = 2 pi mi/ (qB) f = 1/T = qB/(2 pi m)

Question 27

What do we need to specify about a cyclotron electric field?

Answer 27

Constant frequency

Question 28

Why does a classical cyclotron fail at very high energies?

Answer 28

Particle spirals to larger radii r = p/qB gain in orbit length needs to be exactly compensated by gain in velocity to maintain const. freq

Question 29

What leads to maximum cyclotron energy?

Answer 29

Particles getting larger orbits and velocities, would be preferable for particles to orbit at a constant radius

Question 30

What is maximum cyclotron non-relativistic energy and velocity?

Answer 30

Non relativistic energies KE max = q^2 B^2 R^2 / (2m) Max velocity = qBR/m

Question 31

Cyclotron at relativistic energies

Answer 31

Mass increases and hence orbital frequency changes (which we don't want)

Question 32

What is a synchrotron?

Answer 32

A circular accelerator in which the magnetic field strength and electric field frequency are varied to keep particles in a stable orbit as they gain energy.

Question 33

Frequency of a synchrotron to maintain synchronisation

Answer 33

f = qB/2 pi m = qB c^2 / (2 pi m c^2) = =qbc^2/(2 pi sqrt(q^2r^2B^2c^2 +m_0^2 c^4)) using relativistic energy

Question 34

What is the advantage of a synchrotron over a cyclotron?

Answer 34

It accounts for relativistic effects and can accelerate particles to much higher energies.

Question 35

What is the main problem of a synchrotron

Answer 35

Energy losses due to radiation

Question 36

Why are colliders preferred over fixed-target experiments at high energies?

Answer 36

Because colliders use energy more efficiently

Question 37

What is the issue with colliding beam accelerators and how is it resolved?

Answer 37

Beam density is small resulting in few collisions Resolved by storing accelerator pulses in storage rings.

Question 38

What happens when high-energy particles collide?

Answer 38

Their kinetic energy can be converted into mass, producing new particles according to E = mc^2.