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Chapter The Synchrotron 1. Describe the design and operation of simple particle accelerators such as the cathode ray tube and including the application of 12 mv2 = eV for 8 electrons in an electron gun; Use given values of electron momentum in calculations relating to the radius of the trajectory of a low velocity electron to charge and magnetic field, r = mv/eB ; Model the force applied to an electron beam as F = evB in cases where the directions of v and B are perpendicular to each other and parallel to each other; Describe basic synchrotron design including electron linac, circular booster, storage ring, beamlines; Compare the characteristics of synchrotron radiation, including brightness, spectrum and divergence with the characteristics of electromagnetic radiation from other sources including lasers and X-ray tubes, in relation to applications; [3 marks] (2004 Sample Q1) X-rays are an important non-invasive diagnostic tool. Since their discovery, x-rays have had wide application in medicine and science. For most of this time, x-rays have been produced with small electron accelerators. In recent times, synchrotron radiation has emerged as a viable and superior alternative for the production of x-rays. Describe the characteristics of synchrotron radiation which make it superior to conventional xrays. 2. [3 marks] (2004 Sample Q3) A schematic diagram of a cathode ray oscilloscope (CRO) is shown below. It consists of an electron gun (filament) that boils off electrons into an evacuated space. The electrons are then accelerated to a positively charged anode. The anode contains a hole for the electrons to pass through. The electron has a charge of 1.6 × 10-19 C and a mass of 9.1 × 10-31 kg. Calculate the anode voltage (V) required to accelerate the electrons to a velocity of 5 × 107 m s-1. 3. [3 marks] (2004 Sample Q4) The figure below is a section of a typical linear accelerator (linac). The linac consists of an electron injector (gun) attached to a series of accelerating chambers. Electrons which emerge from the injector with kinetic energy of 120 keV are accelerated to very high energies, 300 MeV in this particular example. Briefly explain how the electrons in a linac are accelerated to these high energies. Make sure that you highlight in your answer what provides the high-potentials required for acceleration. 4. [2 marks] (2004 Sample Q5) The diagram below, is a prototype design for a high-energy electron synchrotron ring. A linac is used to accelerate the electrons which are then stored in the large ring. The storage ring is constructed from eight dipole bending magnets, each of magnetic field strength 1.5 T. Between each dipole magnet there is a straight section as indicated on the diagram. One of these sections contains a small RF power source. Pumps are used to maintain the ring under vacuum. Which one of the following statements (A – D) best describes why there is additional RF acceleration in the straight sections of a synchrotron ring? A. The vacuum is not completely zero and so electrons lose energy as they travel through the ring. B. The bending and focusing magnets consume energy. C. Electrons collide with each other and lose energy. D. Electrons lose energy because of synchrotron radiation. 5. [3 marks] (2004 Sample Q6) At each of the bending magnets, the electrons are bent through an arc of radius 10 m. Use this information, together with the characteristics of the magnet, to calculate the momentum of the electrons in the ring. 6. [4 marks] (2004 Pilot Q3) Identify two beneficial characteristics of the radiation produced by a synchrotron and explain why these characteristics are beneficial. 7. [2 marks] (2004 Pilot Q4) Each stage of a LINAC boosts the energy of an electron beam by the same amount. However, the physical lengths of the accelerating stages are different. Why is this the case? 8. [2 marks] (2004 Pilot Q5) A beam of 10 keV electrons enters a uniform magnetic field of strength 2.0T. Which one of the following best describes the path of an electron as it passes through the magnetic field above? A. the electron is deflected to the left B. the electron is deflected to the right C. the electron is deflected up D. the electron is deflected down. 9. [3 marks] (2004 Pilot Q6) Show that the velocity for 10 keV electrons is approximately 6 × 107 m s-1. (me = 9.1 × 10-31 kg) 10. [3 marks] (2004 Pilot Q7) Determine the radius of curvature of 10 keV electrons as they travel through a magnetic field of 2.0T. 11. [3 marks] (2005 Q1) In the sentences below, options are given within the brackets. Only one of the options will be correct. Circle the best option. In a synchrotron, the circulating electrons are produced in [an electron gun / a linac / a storage ring]. Ultimately the electrons are accelerated to a speed of approximately [50% / 90% / 99.99%] of the speed of light by [a linac / a storage ring / an undulator]. 12. [2 marks] (2005 Q2) One section of a storage ring is shown below. Electrons travelling through this section of the storage ring have a momentum of approximately 1.2 × 10-18 kg m s-1 and are bent through an arc of radius 7.7 m as shown. The charge on the electron is .1.6 × 10-19 C. Calculate the strength of the magnetic field required to keep the electrons on this arc. 13. [2 marks] Choose one of the following options to complete the sentence. Radiation generated by a synchrotron occurs because electrons A. have high energies. B. accelerate when they change direction. C. collide with other electrons. D. collide with residual air particles. (2005 Q6) 14. [2 marks] (2005 Q7) A typical cathode ray tube is shown below. It consists of an electron gun, a deflecting system and a fluorescent screen that emits light when struck by electrons. The electron gun consists of a filament that emits electrons with very small kinetic energy into an electric field created by a high voltage, V, applied between a pair of parallel plates. In a particular case the electrons emerge from the gun with an energy of 8.0 × 10-16 J. Charge on the electron: e = .1.6 × 10-19 C Calculate the voltage, V, between the plates, used to accelerate the electrons. 15. [2 marks] (2005 Q8) After acceleration, the electrons enter the magnetic-deflecting system which consists of two pairs of mutually perpendicular magnetic-field coils (W and X), (Y and Z) aligned as shown above. The electrons are deflected downwards, as shown. Choose one of the following options to complete the sentence. The downward deflection can be achieved by the coils A. WX producing a magnetic field in direction W to X. B. WX producing a magnetic field in direction X to W. C. YZ producing a magnetic field in direction Y to Z. D. YZ producing a magnetic field in direction Z to Y. 16. [3 marks] (2006 Q1) A student is preparing a brief talk on the operation of the Australian Synchrotron Facility. In the speech below, options to complete each sentence are given within the brackets. Circle the correct option in each case. In the Australian synchrotron, a beam of electrons is accelerated to almost the speed of light by the [storage ring / linear accelerator / beam line]. The beam is then confined to a circular orbit by a series of [RF cavities / bending magnets / beam lines] separated by straight sections. As the beam is deflected, [monochromatic / longitudinal / electromagnetic] radiation, which is commonly called synchrotron light, is produced. 17. [4 marks] (2006 Q2) It is claimed that synchrotrons provide a superior source of X-rays compared to those produced by an X-ray tube. Explain two advantages of using a synchrotron as a source of X-rays rather than an X-ray tube. 18. [2 marks] (2006 Q3) In the Synchrotron Facility electrons are accelerated by several devices. Which one of the following statements (A - D below) best describes the order in which this acceleration occurs? A. linac electron gun booster ring B. electron gun linac booster ring C. linac booster ring electron gun D. electron gun booster ring linac 19. [2 marks] (2006 Q4) Electrons are circulated in the synchrotron ring when they have reached their maximum energy. To overcome energy loss in the circulating beam, additional energy is provided by RF acceleration in one of the straight sections of the ring. Which one of the following statements (A - D below) best describes the largest contribution to this energy loss? A. The vacuum is not completely zero and so electrons lose energy as they circulate through the ring. B. The bending and focusing magnets consume energy. C. Electrons collide with each other and lose energy. D. Electrons lose energy because of synchrotron radiation. 20. [3 marks] (2006 Q7) A simplified set-up for an electron gun is shown below. It contains a high-voltage source (HV). In normal operation, electrons emerge from the gun with energies of 5 keV. Calculate the velocity for electrons of energy 5 keV. (me = 9.11 × 10-31 kg) 21. [3 marks] (2006 Q8) As high-energy electrons pass through one of the bending magnets in the Australian Synchrotron Facility, they are bent through an arc of radius 7 m. The magnetic field strength is 1.7 T (Wb m-2). Use the information above to determine the momentum of the electrons. Include a unit in your answer. (Ignore any relativistic effects in your calculation.) 22. [3 marks] (2007 Q1) In the paragraph below, options to complete each sentence are given within the brackets. Circle the correct option in each case. The booster ring of a synchrotron [ gives the initial boost to stationary electrons / accelerates electrons from the linac / stores electrons until needed in a beam line ]. Synchrotron radiation emerges as the electrons in the storage ring [ pass from the storage ring into a beam line / travel around curved segments / travel at constant speed along straight segments ]. Energy lost by the electrons to synchrotron radiation is replenished by [ diverting the electrons through the booster ring / electric fields in the straight segments / the bending magnets in circular sections ]. 23. [2 marks] (2007 Q2) The figure below shows a simple electron gun used to inject electrons into the linac of a synchrotron. The accelerating voltage is 2000 V. Mass of electron = 9.11 × 10-31 kg Charge on electron = -1.60 × 10-19 C At what speed do the electrons emerge from the electron gun? (Ignore relativistic effects.) Use the following information to answer Questions 25 and 26. 24. [2 marks] (2007 Q3) A magnet called an injection magnet of magnetic field strength 1.2 × 10-4 T bends a pulse of electrons emitted from the linac so that they enter the circular booster ring as shown below. The electrons emerge from the linac with a speed of 5.0 × 106 m s-1. What is the magnitude of the radius of the trajectory of the electrons from the linac as they pass through the injection magnet? 25. [2 marks] (2007 Q4) In normal operation, the injection magnet switches on only for the brief instant necessary to direct the pulse of electrons into the circular booster ring. However, due to a malfunction, the magnet was still on after the pulse of electrons had completed one revolution of the circular booster ring. The electrons now pass through the magnet a second time. Which one of the following (A - D) would occur? A. The electrons would continue around the ring. B. The electrons would be deflected outwards from the ring. C. The electrons would be deflected inwards from the ring. D. The electrons would lose energy and continue around the circular booster ring at a lower speed. 26. [3 marks] (2007 Q5) In a synchrotron, an electron which is travelling at 2500 m s-1 moves from a linear region into a magnetic field of 0.50 T as shown below. What will be the magnitude and direction (into page, out of page, up page, down page) of the force on the electron? 27. [2 marks] (2007 Q6) In a typical synchrotron experiment to study a sample of material, which one of the following (A–D) passes along a beam line? A. a beam of energetic electrons B. a strong magnetic field C. a beam of electromagnetic radiation D. a beam of laser light