Contents Particle Accelerators 3 9.1 Van De Graaff Generator 4 9.2 The Cyclotron 7 9.3 The Cockcroft–Walton Machine 10 9.4 Betatron 12 9.5 Electron Synchrotron 15 9.6 Proton Synchrotron 18 9.7 Synchrocyclotron 19 9.8 Linear Accelerators (Linac) 21 Summary 23 Solved Problems 24 Exercises 27 Remember and Understand 31 Answers to Objective Questions 32 Particle 9 Accelerators LEARNING OBJECTIVES LO-1 To learn about the need of particle accelerators LO-2 To understand the potential and circular orbit of accelerators LO-3 To know about positive-charge accelerators such that Van de Graaff generator and cyclotron LO-4 To know about the Cockcroft–Walton machine as voltage multiplier LO-5 To understand the principle, construction, and working of betatron as an electron ac- celerator and to get an insight of focused magnetic field, Lorentz magnetic field, and Lorentz force while dealing with the accelerators LO-6 To understand the principle, construction, and working of electron synchrotron LO-7 To learn the principle, construction, and working of proton synchrotron LO-8 To understand the construction and working principle of linear accelerators (LINACS) LO-9 To know about the construction, working, and principle of synchrocyclotron KEYWORDS ■■ Van de Graaff generator ■■ Electron synchrotron ■■ Dees ■■ Cyclotron ■■ Synchro cyclotron ■■ Betatron condition ■■ Betatron ■■ LINAC ■■ Synchrotron ■■ Radio-frequency oscillator 9.1 Need of Particle Accelerators In previous chapters, we have studied about the phenomena of radioactivity. LO-1 In the process of radioactivity, a, b, and g -rays are emitted. These radioac- In this secti on, you will tive particles can be further used to disintegrate other atomic nuclei. For this learn about the need of purpose, the elementary particles need to be accelerated to suitable energies. parti cle accelerators. The particles are accelerated by suitable devices known as particle accelerators. 4 Modern Physics Particle accelerators are specially designed machines that are used to accelerate the elementary particles to desired energy range. Both heavier and lighter nuclei can be used to accelerate the particles. Protons, neu- trons, deuterons, electrons, etc., are accelerated using particle accelerators. In addition to these particles carbon, neon, oxygen, and beryllium, etc., are also accelerated. For high-energy particle physics, particle accelerators play an imperative role. This chapter deals with basic particle accelerators and their working principles. There are some requirements that should be satisfi ed for every particle accelerator. Every accelerator requires a suitable source of particles. The source of particle should have negligible energy spread, high effi ciency and exhibit rich output (well collimated). Usually, the particles sources include spark discharge sources, electron oscillation sources, hot and cold cathode sources, and magnetic ion sources. Once these ions are obtained, then they should be introduced to the defi ned accelerator using proper accelerating voltage. Once the particle enters the accelerator, then it is under electric/magnetic fi eld and tra- verses an orbit of radius r and velocity v. The particles are accelerated up to the desired energy. Subsequently, when the desired energy level for the particle is obtained, then the particles are extracted out of the accelerator. The accelerators can work on continu- ous or pulsed fi elds. The accelerators should have energy stability and coherence along with good beam intensity. The accelerator should exhibit good particle collimation. In some of the accelerators, the particles are accelerated using constant potential difference. To know more on how Such accelerators fall under the category of electrostatic accelerators, for example, Van Parti cle Accelerators work (simulati on de Graaff generator and Cockcroft–Walton machine. The electrostatic accelerators can video) please visit give an output of particles with 4–6 MeV energy. When particles form closed-path again htt p://www.youtube. and again, then they get accelerated. The accelerators that work on closed-path orbits com/watch?v=DYpN- BRnBH0 or scan the and yield high energy particles are known as cyclic accelerators, for example, cyclotron, above code betatron, and synchrotron. 9.2 Van De Graaff Generator Van de Graaff developed an electrostatic accelerator in 1881, which could LO-2 accelerate particles up to energy 10 MeV. In this secti on, you will know about positi ve- 1. Principle charge accelerators (i) It is based on the principle that sharp pointed surfaces have large charge such that Van de Graaff densities, that is, generator and cyclotron q along with their s = 2 • principle 4pr • constructi on For sharp points, r → 0, and hence theoretically the charge density →∞. • working (ii) If small conducting charged shell of radius r1, is located inside a charged and conducting shell of radius r2, then the charge q1 will move from shell A to shell B if both the shells are connected to each other (with key K) (Figure 9.1). Hence, the charge tends to move to outer the surface of spherical shell and does not reside inside the conductor. This leads to increase of the potential of outer surface. Particle Accelerators 5 q2 r2 r1 q1 K A B Figure 9.1 Demonstration of charge on hollow conductor. In actual practice the maximum potential on the outer shell does not go infinite because their is electric breakdown of air which surrounds the shell. 2. Construction Two combs C1 and C2 are provided with sharp point ends (Figure 9.2). C1 is maintained at 52− 0 kV w.r.t. ground. S is large hollow sphere that is mounted on two pillars D1 and D2. There are two frictionless pulleys P1 and P2 over which a well-insulated belt (B) passes over. C1 is spray comb and C2 is collector comb. There + + S + + + + Ion source + + C2 + P2 + + I − + + + + + W + + B D1 D2 + + + + + + C + 1 + P1 HT + M T Figure 9.2 Schematic sketch of Van de Graaff generator. 6 Modern Physics is discharge tube I which contains positive ions to be accelerated so that they can hit the target (T). The discharge tube is made up of porcelain glass. The discharge tube is highly evacuated in order to avoid any discharge inside the tube. The whole appa- ratus is inside gas tight steel chamber W. Their could be methane, freon ()CCl22F , air, or nitrogen inside the chamber. 3. Working Electric motor M makes a well-insulated belt B rotate over two pulleys P1 and P2. Metallic comb C1 (Spray comb) is charged to high positive potential. Due to corona discharge action on its sharp points, the spray comb C1 gives its positive charge to belt. The moving belt carries the charge to collector comb C2. Due to induction, “-ve” charge appears on the pointed ends of the comb and in turn “+ve” charge builds up at the base of the C2 comb. This charge gets transferred to the outer shell S. As the belt moves continuously, hence the charge on outer shell gets accumulated, which is turn raises the potential of outer shell as follows: If q is charge accumulated over a spherical shell of radius “r”, then potential (V) is q V = 4peor While the charge continues to increase on the spherical shell, the ionization leakage also increases. Hence, the leakage is prevented by steel tank W. The charged particles inside the discharge tube T are at high poten- tial. They get accelerated downward and hit the target after coming out of discharge tube. Mathematical analysis can be given as follows: Capacity C for spherical shell = 4peor if r is the radius of spherical shell. Hence, potential q V = (1) C Rate at which potential is build up on the shell is given by the following equation: dV 1 dq i == (2) dt C dt C i is charging current that is usually composed of many components as follows: ii=+ii++i (3) plsc ip = current due to positive ion source il = leakage current along the discharge tube is = is the current due to stray/secondary electrons that strike the wall ic = current due to breakdown condition as a result of excess potential at surfaces. It is also known as corona current. If the “S” is made negative, then electrons can also be accelerated. These days, particles up to “20 MeV” energy can be produced using Van de Graaff generator. Particle Accelerators 7 Robert Jemison Van de Graaff earned his Bachelor of Science and Master of Science in 1922 and 1923, respectively, from the University of Alabama. Van-de Graaff was awarded PhD in 1928 form Queen’s College, Oxford where he was a Rhodes fellow. It was Oxford where he fi rst conceived the idea of high-volt- age generator. He was infl uenced by Rutherford’s challenge to pro- duce highly accelerated particles for nuclear disintegrations. He returned to United States in 1929, where he constructed the fi rst working model of the generator while work- ing as a National Research Fellow at Princeton University under the supervision of Karl Taylor Compton. Compton also worked on electrostatic VAN DE GRAAFF (LEFT SIDE) generator as designed by Lord Kelvin. But this electrostatic generator dripped charged water; hence, he thought of exceeding electric fi eld in order to overcome the gravity. He worked as a research associate at the Massachusetts Institute of Technology, where he continued his work on accelerating the charged particles. During World War II, he was appointed as the Director of MIT’s high-voltage For a demo video of radiographic project. He was the chief of physics of High Voltage Engineering Van de Graaf accelera- Corporation after the war. tor please visit htt p://www.youtube. The sphere of Van de Graaff generator holds considerable amount of charge com/watch?v=XIxw before arc discharge occurs.