Introduction to accelerator and their applications: Exercize 2 Gabriele Chiodini - INFN Lecce - May 2015

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Introduction to accelerator and their applications: Exercize 2 Gabriele Chiodini - INFN Lecce - May 2015

PhD lessons in Physics for Università del Salento 2015 (20 hours, 4 CFD)

Question 1

In a straight section of a synchrotron the beam size grows along the orbit. Why?

• The beta function grows along the orbit and therefore also the size of the beam because the emittance is constant.

• The particles move away from the orbit because falling down due to the gravity.

Question 2

A synchrotron consists of arcs with dipoles and straight sections without magnets. Which of the following statements are true?

• It can not work because the particles along the straight sections are not focused.

• It can not work because the dispersion along the arcs are not compensated by quadrupoles.

• It can work but with a very weak beam intensity.

Question 3

A beam of large section requires magnets with large opening.

This involves:

• Low magnetic fields

• Greater dispersion

• Beam instability Question 4

What is the ideal orbit?

• The particle orbit without betatron oscillations.

• The orbit of the particles not touching the pipe vacuum walls.

• The orbit of the particles closest to the pipe vacuum walls.

Question 5

In a small accelerator the dipoles focusing is strong.

• Yes, but only in the horizontal direction.

• No, they defocusing in the vertical direction.

• No, the focusing is weak.

Question 6

Is a single quadrupole focusing?

• Yes, it focuses strongly in one direction and weakly in the other.

• No, you need to use a second quadrupole rotated by 90 degrees to have a net focusing.

• Yes, it is focusing strongly.

Question 7

A synchrotron consists of eight arcs and eight straight sections.

The 8 arches are composed of 3 cells each one consisting of a quadrupole+dipole+quadrupole. The 8 straight sections are composed of 3 cells each one consisting of two quadrupoles.

Which of the following sentences is correct?

• The beta function along the ring has periodicity 8.

• The beta function along the ring has periodicity 3.

• The beta function along the ring has periodicity 8/3.

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Introduction to accelerator and their applications: Exercize 2 Gabriele Chiodini - INFN Lecce - May 2015

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Question 8

A beam is generated by a source with large angular dispersion but with very small cross section. What you need to do in this case if you want to get high intensity?

• Add just after the source a doublet of quadrupole to focus in both orthogonal directions (FODO cell) at the output source.

• Add just after the source a very long and narrow tube to reduce the beam divergence.

• Add just after the source a dipole to bend the beam in the acceptance of the accelerator vacuum tube.

Question 9

Where the beta function is and high?

• In dipoles.

• In focussing quadrupoles.

• In defocussing quadrupoles.

Question 10

What does a high beta function involve?

• Large beam radius.

• Passage of a single particle far away from the ideal orbit.

• Low beam emittance.

Question 11

A good source must have:

• Small emittance.

• Reduced beam section.

• Reduced beam divergence.

Question 12

Which are the horizontal and vertical TUNES that make the beam more stable?

• Qx = 1, Qy = 2

• Qx = 1/10, Qy = 3/2

• Qx = 15/10, Qy = 20/15 Question 13

• Which are the horizontal and vertical TUNES a cyclotron in uniform and vertical magnetic field?

• Qx=1, Qy = 0

• Qx=1, Qy = 1

• Qx=0, Qy = 1 Question 14

What study the transverse dynamic?

• the verticle motion of the particle and in the direction of the particle curvature

• the particle velocity dispersion

• the conditions of phase stability

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Introduction to accelerator and their applications: Exercize 2 Gabriele Chiodini - INFN Lecce - May 2015

Question 15

The longitudinal dynamics on which principle is based?

• Phase space conservation in a conservative dynamic system.

• Closed orbits around the ring.

• Phase stability principle Question 16

What is the ideal orbit ?

• The particle orbit without betatron and synchrotron oscillations.

• The particle orbit not touching vacuum tube walls.

• The particle orbit satisfying the synchronisation condition with the radio frequency and without betatron and synchrotron oscillations.

Question 17

Why the condition of synchronisation with the radio-frequency does not involve loss of the beam?

• The synchrony condition is satisfied for a harmonic numbers h different from q/p, where q and p are integers, so it doesn’t occur resonance between the radio-frequency and the longitudinal motion.

• The synchrony condition determines an acceleration of the beam along the vacuum tube and therefore an increase of longitudinal speed and the particle remains far from the walls of the vacuum tube because it doesn’t undergo a transverse motion.

• The synchrony condition determines an acceleration of the beam along the vacuum tube and therefore an increase of longitudinal speed. The particle remains far from the walls of the vacuum tube if the current of the dipoles is increased proportionally.

Question 18

When a beam of protons is accelerated at the maximum of the energy what to do with the radio-frequency cavities?

• Turn off the radio-frequency cavities.

• Keep the radio-frequency cavities turned on as during the acceleration phase.

• Keep the radio-frequency cavities turned on but reduce the amplitude and fix the phase to zero in order to keep tight the proton packets.

Question 19

When a beam of electrons is accelerated at the maximum of the energy agrees what to do with the radio-frequency cavities?

• Turn off the radio-frequency cavities

• Keep the radio-frequency cavities turned on as during the acceleration phase.

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Introduction to accelerator and their applications: Exercize 2 Gabriele Chiodini - INFN Lecce - May 2015

• Keep the radio-frequency cavities turned on and set the amplitude and the phase compensate for the loss of energy due to synchrotron light emission.

Question 20

The longitudinal emittance leads to a dispersion of the moment and can generate instabilities of the beam unless:

• the dipoles have a small scattering function,

• the quadrupoles have a strong normalized gradient k,

• sextuple magnets are present to reduce strongly then quadrupole chromaticity.

Question 21

The longitudinal emittance leads to dispersion of the moment and to an increase of the effective beam size:

• Only along the horizontal direction where the particles are curved by the dipoles.

• In both transverse directions in correspondence of the quadrupoles.

• In both transverse directions in correspondence of the sextuples.

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Question 22

What is the function of dispersion?

• a solution of the transverse motion equation

• a solution of the transverse motion equation for a particle with transverse momentum p + dp = 2p

• the percentage change in size of the beam with respect to the ideal beam

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Exercise 1

The emittance of the proton beam injected in the SPS (SuperProtonSyncroton) is equal to 2π xmm x mrad.

a. Calculate the radius of the beam at a focusing quadrupole with beta equal to 108 m.

b. Calculate the divergence of the beam at a defocusing quadrupole with beta equal to 18 m.

c. The moment of the proton at the injection is equal to 10GeV/c and after the acceleration is equal to 400 GeV/c. Calculate the radius of the beam after acceleration.

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Exercise 2

A synchrotron has an effective length of 1000 m and accelerates protons of 1 GeV up to 10 GeV. If the harmonic number is equal to 100 which is the value of the RF frequency at the beginning and at the end of the acceleration cycle?

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