Accelerator Basics Abhishek Rai IUAC School on Accelerator Science and Technology May 7-18, 2018
Some basics Charge on an electron(e) = 1.6 10-19 Coulomb (1 unit of charge) 1 Atomic mass unit (amu) = 1.66 10-27 Kgs. Energy gained by an electron across 1 volt of potential difference 1eV= 1.6 10-19 X 1V= 1.6 10-19 Joule 1keV=10 3 ev 1MeV=10 6 ev 1GeV=10 9 ev
Some basics E
Some basics An electron is projected horizontally into a uniform electric field produced by two charged plates. The electron undergoes a downward acceleration (opposite E), and its motion is parabolic while it is between the plates.
Some basics Sign of q matters!!
Some basics Since the force is perpendicular to the velocity, the charged particle experiences an acceleration that is perpendicular to the velocity. The magnitude of the velocity does not change, but the direction of the velocity does producing circular motion. Circle Paths: v is perpendicular to B (uniform); Helical Paths: v has a component parallel to B. v v v cos v sin
Some basics The magnetic force does NO work on the particle. Can magnetic fields be used for particle acceleration??
Some basics Betatron Ñ L B E. dl. ds t s Faraday s Law of induction Ñ L D H. dl J. ds t S s Ñ D ds. v Ñ S v dv B. ds 0 Ampere s Law Gauss s Law for electricity Gauss s Law for magnetism D E B H J E
Some basics E B t Faraday s Law of induction D H J t Ampere s Law. D v Gauss s Law for electricity Gauss s Law for magnetism D E B H J E Equation of continuity
Some basics SI Units J Amp/ metre 2 D Coulomb/metre 2 H Amps/metre B Tesla Weber/metre 2 E Volt/metre Farad/metre Henry/metre Siemen/metre
Some basics In free space: =0 J=0 also =0 2 2 E H o 2 E 2 t 2 H o 2 t H y E x E H Maxwell s equations lead to the three-dimensional wave equation to describe the propagation of E and H fields Plane sinusoidal waves are a solution to the 3D wave equation These waves have only transverse E and H components Ez, Hz=0 E and H in phase and orthogonal
Some basics Boundary conditions at the surface of a conductor (large ) n E n H n. D n. B 1 1 1 1 0 J 0 s s
Some basics EM waves in a closed hollow conducting cylinder TM 010 modes suitable for particle acceleration 2.405r E z E0J 0( ) exp( it) b E0 2.405r B i J1( ) exp( it) c b 2.405c b m = no. of full period variations of the field components along n= no. of zeros along of Ez along r p= no. of half period variations of the field components along z
Some basics EM waves in a closed hollow conducting cylinder TM 010 modes suitable for particle acceleration Ez H
What is a Particle Accelerator? A particle accelerator is a device that uses electromagnetic fields to propel electrically charged particles to high speeds and to contain them The picture shows an early particle accelerator from 1937. This accelerator was used in the development of the first atomic bomb. It currently resides at the National Science Museum, London.
Why do we need Particle accelerators Particle accelerators are like microscopes that help physicists probe in to the subatomic world. They have led to the discovery of the fundamental building blocks of matter = h / p, Early accelerator developments were driven by the quest for higher and higher particle energies, which in turn was driven by developments in nuclear physics (through the 1960s) and then elementary particle physics (1960s-onward)
Why do we need Particle accelerators De Broglie s equation : l h/p Patricle with a higher momentum has smaller l. = h / p, Resolving power 1/ l
Living cell : an optical microscope which receives scattered photons of visible light. Sub-micron objects: electron microscopes where electrons, accelerated typically to a few hundred kilovolts, are used to hit the objects and scatter from them. Quarks and leptons : can be sensed down to distances of 10-18 meters by means of particles from giant accelerators.
Why do we need Particle accelerators For example if an electron is required to have a de Broglie wavelength comparable to the size of the nucleon, it must have a kinetic energy of ~1,200 MeV (for an electron energy above 10 MeV, kinetic energy is proportional to momentum). This energy is several thousands times higher than the typical = energy of electrons used in electron microscopes. h / p,
Why do we need Particle accelerators Energetic beams from particle accelerators are also used for: Understanding the structure and dynamics of materials and their properties (physics, chemistry, biology, = medicine) h Sterilization / p, Medical treatment of tumours and cancers Ion Implantation to modify the surface of materials
Why do we need Particle accelerators There is active, ongoing work to utilize particle accelerators for Transmutation of nuclear waste = h Generating power more safely / in subcritical nuclear reactors p,
Why do we need Particle accelerators
Particle accelerators Timeline 1896 J.J. Thomson Cathode Ray Tube 1920 H.Greinacher Concept of Cascade Generator 1924 T.Ising Idea of linac with drift tubes 1929 Rolf Wideröe 1st Linear Accelerator 50 kev Na, K ions 1929 E.O. Lawrence Principle of Cyclic Accelerator 1931 M.S. Livingston 1st Cyclotron 4.5 Ø 80 kev, Protons 2nd Cyclotron 11 Ø 1 MeV 1931 Van de Graaff 1st electrostatic accelerator 800kV 1932 Cockcroft & Walton p + 7 Li 2a at 800 kev 1935 W.H. Bennett Tandem accelerator 1938 L.H. Thomas AVF Cyclotron 1940 Donald Kerst Betatron accelerator 1941 Touschek and Wideroe Concept of a particle storage ring 1943 Oliphant Concept of synchrotron 1947 Ginzton Electron Linear accelerator = h / p,
Particle accelerators Timeline 1947 L.Alvarez Drift tube Linear Accelerator 1949 E.McMillan 320 MeV electron Synchrocyclotron 1954 R.R. Wilson et. al. First strong-focusing synchrotron at Cornell 1957 O'Neill & Panofsky Concept of Electron Collider 1960 First electron-positron collider ADA at Frascati 1970 Kapchinsky & Tepliakov Concept of Radio Frequency Quadrupole 1972 First proton-proton collider: ISR at CERN 1980 First RFQ accelerator operational at LANL 1981 First proton-antiproton collider: SPS at CERN = h / p,
Particle accelerators Early History = h / p, Ernest Lawrence received the Nobel Prize in 1939 "for the invention and development of the cyclotron and for results obtained with it, especially with regard to artificial radioactive elements." The first successful cyclotron, the 4.5-inch model built by Lawrence and Livingston.
Particle accelerators Early History = h / p, John Cockcroft, Ernest Rutherford, and E.T.S. Walton. Cockcroft and Walton were awarded the Nobel prize in 1951. Cockcroft-Walton accelerator installation at the Cavendish Laboratory in Cambridge, Massachusetts.
Particle accelerators Early History Robert Van de Graaff = h / p, Van de Graaff generator.
How acceleration is achieved DC Accelerator Electrostatic field These accelerators use a static, DC, potential difference between two conductors to impart a kinetic energy = h They Include / Cockcroft- Walton generators p, Van de Graf generators Tandems Highest voltages achieved are ~ 25 MV Difficult to establish and maintain a static DC field of 20+ MV
How acceleration is achieved DC Accelerator Electrostatic field = h / p, Van de graf and Tandem accelerators Cockroft-Walton generator
How acceleration is achieved Cyclic Accelerator Linear Accelerator Repeated application of RF Voltage = h / p, Use one or a small no. of radio frequency (RF) accelerating cavities and make use of repeated passage through them. Approach used in cyclotrons and synchrotrons Use many accelerating cavities through which particle beam passes only once. These are linear accelerators (LINACS)
Cyclotron The ions make multiple passes through the gap between the accelerating electrodes by an external magnetic field. The bending radius in the magnetic field r = mv/qb The time to complete one orbit T = 2pr/v = 2pm/qB independent of v! For synchronous operation, r.f. period should match the cyclotron frequency. = h / p, Fixed Frequency Cyclotron
Cyclotron Acceleration in a cyclotron is possible as long as relativistic effects are negligibly small, i.e. only for small speeds, at relativistic speeds, the mass of the particle is no longer constant and: m=m 0 / 1 - (v/c) 2 and T = 2pr/v = 2pm/qB (T increases with = m) As a result particles are no longer h in resonance with accelerating frequency. / For acceleration, need to change p, magnetic field B or accelerating frequency f or both. Isochronous cyclotron Synchrocyclotron Synchrotron
Linear Accelerators The Principle : Rolf Widroe In Linear accelerators the charged particle receives several small energy kicks in acceleration gaps between drift tubes that are powered by a radio frequency voltage source. The length of the drift tubes is so adjusted that the time taken by the particle to traverse a drift tube is integral multiple of half RF period. The Drift tube length is thus particle velocity dependent and increases with particle energy. L L=v/2f
Linear Accelerators The Principle : Alvarez The Widroe structure becomes inefficient at high frequencies due to dissipation of electromagnetic energy. Alvarez structure is enclosed in a metallic tank to form a resonant cavity. Unlike the Widroe structure the drift tubes are passive structures and the accelerating field arises from the electromagnetic radiation flooding the tank. L=v/f L Very high particle energies can be achieved through multiple acceleration. SLAC : 50 GeV electrons ILC : 250 GeV electrons
How acceleration is achieved Betatron Magnetic induction. Changing Magnetic Field induces an electric field. Accelerates electrons and hence the name. = h / p, Principal elements: A pulsed magnetic circuit to accelerate electrons by inductive fields. An air gap to force magnetic field into the beam transport region. Electrons Follow circular path in the bending field Shaped magnetic field for focusing
DC Accelerators Cockroft and Walton generator(1932) Few MV A C1 C C (0, 2v) C3 C3 E B C2 = h / p, D1 D2 D3 D4 D 4v C4 F Ripple in an 'n' stage circuit I 1 2 3 n I V... V n( n 1) 2F C n C n1 C n2 C1 4FC
DC Accelerators First artificial nuclear reaction using protons accelerated from a CW generator p + 7 Li 2a at 800 kev = h Limited to low voltages / ~few MV p, These accelerators are used as injectors to many other accelerators.
DC Accelerators Van de Graff Accelerator Few MV Terminal charged to high voltage ~ MV by bringing electric charge on an insulated belt which gets transferred to the terminal: V = Q/C = h Ions accelerated to an energy E / = qv by an uniform electric field gradient. p, Terminal voltage controlled by adjusting charging/discharging current. To minimize high voltage breakdown, enclosed in a pressure tank filled with insulating gas.
DC Accelerators Van de Graff Accelerator High Pressure tank High voltage terminal Insulating support Equipotential Ring Charging System Voltage measurement Voltage control Ion source Accelerator tube Analyzer magnet = h / p,