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Transcript
Radio frequency usage/applications Dr S. T. Boogert (accelerator physicist) John Adams Institute at Royal Holloway [email protected] Royal Holloway : PH4450 University College London 19th February 2009 Outline • Introduction • • • Electromagnetism (revision) Energy from field to beam Electromagnetic spectrum (extension) • Generation of RF for acceleration • • • Synchrotron/storage ring Klystrons RF accelerating cavities • Use of beam generated RF for diagnostics • Beam position monitor systems Outline • Introduction • • • Electromagnetism (revision) Energy from field to beam Electromagnetic spectrum (extension) • Generation of RF for acceleration • • • Synchrotron/storage ring Klystrons RF accelerating cavities • Use of beam generated RF for diagnostics • Beam position monitor systems Electromagnetism • Maxwell’s equations (MEs) in free-space (accelerator vacuum) • Lorentz force on a charge in magnetic and electric fields: Energy transfer • Change in energy due to electromagnetic field • Acceleration is adding energy to a particle via electric and magnetic fields • What about the inverse? From particles to electric and magnetic fields Solving for W • Energy of particle • Easy to solve for position and velocity • First need electric and magnetic fields, hence solve Maxwell’s equations Boundary conditions for Maxwell • There can be no electric field parallel to a conducting surface. • Surface must be at same potential so field lines much be normal to the surface Electromagnetic waves • Maxwell’s equations predict electromagnetic waves • Free space solution to MEs • Boundaries still allow propagating and standing oscillating solutions for the electric and magnetic fields • • Transmission lines, waveguides Standing electromagnetic waves • Although not in free space can still describe by frequency and amplitude • Need to look at electromagnetic waves, not in free space Electromagnetic waves • Solve Maxwell’s equations • No currents • curl each side • use ME3 • wave eqn! Solutions of traveling wave type Electromagnetic spectrum • Familiar with x, gamma, UV, optical, IR.... microwaves Outline • Introduction • • • Electromagnetism (revision) Energy from field to beam Electromagnetic spectrum (extension) • Generation of RF for acceleration • • • Synchrotron/storage ring Klystrons RF accelerating cavities • Use of beam generated RF for diagnostics • Beam position monitor systems Acceleration/longitudinal dynamics • Acceleration from Dr. Karataev’s lectures •Voltage change per turn •Synchronicity •Need to choose RF frequency and voltage Pillbox cavity (1) • What does an accelerating cavity look like? • Parallel plates? • Solve Maxwell’s equations for a cylinder (apply boundary conditions) Remembering Off you go! Pill box cavity (2) • Cavity models labelled by three integers m,n,v • Solve Maxwells equations in cylindrical coords •J m(x) is a Bessel function of order m kmna is the nth zero of Jm(x) Accelerating cavity as resonator • Imagine injecting some EM into a cavity at t=0 • Does the energy stay there for ever? signal less loss FT higher loss Accelerating cavity as resonator • Damped harmonic oscillator • Define “quality factor” • Energy stored compared to energy loss per cycle • Need to keep adding energy into accelerating cavity • Losses (what are the losses?) Cavity parameters • Cavity frequency • harmonic number, number of bunches in machine • • Energy loss per turn (storage ring) • • Length of time between injecting RF energy into cavity • Voltage Energy gain per tern (synchrotron) • Quality factor What is the quality factor of a superconducting cavity? • Lets look at a real example Accelerating cavities • Reality more complex than simple cylinder • • • • Need beam input and output ports Need to get RF into cavity Need to extract Higher order modes Tuning (i.e changing frequency) • Review some real systems at accelerators • Technical systems much more complicated in reality • Lets take a look at a real system in terms of what we have learned Accelerator Test Facility • Test accelerator for the Linear collider • My research interest! • KEK Tsukuba, Japan • • • • • Linac 1.54 GeV Frequency 714 MHz Harmonic number 330 Q ~ 22100 Loaded Q? ATF design report ATF Damping ring cavity ATF design report ATF Damping ring cavity ATF Cavity mode structure Klystrons (producing RF) • Need to generate RF power • • High powers are required Pulsed and continuous operation • Linear accelerator, precisely control amplitude, frequency and phase of RF. Example of Klystrons ATF Damping ring 714 CW Klystron Australia n Light source Klystron Outline • Introduction • • • Electromagnetism (revision) Energy from field to beam Electromagnetic spectrum (extension) • Generation of RF for acceleration • • • Synchrotron/storage ring Klystrons RF accelerating cavities • Use of beam generated RF for diagnostics • Beam position monitor systems Cavity beam position monitors • Beam position monitors are essential for stable accelerator operation • • Invert the acceleration Couple power out of the charged particle beam! • Choose a pillbox mode where the TM mode excitation is dependent on where the beam goes through the cavity • Cavity Beam Position Monitors (BPMs) Cavity BPM theory • Beam transit excites both • • • Calculate W! lowest order mode (monopole, lowest frequency) second order mode (dipole, higher frequency) Example system • Cavity with waveguide s on beam line • Use dipole mode • Filter out monopole • f = 5.5 GHz • Q~500 RF signal processing • Mix and filter cavity output signal • Reduce whole waveform to just amplitude and phase information Cavity BPM results • C-band cavity from ATF2 extraction line • Predicted resolution 50nm!!!!! • Cylindrical cavity with slot waveguide couplers • Move the BPM and look at the output • Data taken on Tuesday Summary • Simple introduction from first principles (Maxwell’s equations) to RF cavity design considerations • Can start designing acceleration systems (well almost) • Complexity is mainly in solving for the complex electric and magnetic field configurations • Complex task, computationally difficult (i.e interesting!) • Technically challenging • Accelerators need 100s of these things (accelerating cavities, BPMs etc) References & further reading • http://www.wikipedia.org (diagrams and EM spectrum) • Particle Accelerator Physics, H. Wiedemann, ISBN 3-540-00672-9 • Handbook of Accelerator Physics and Engineering, A. W. Chao & M. Tigner, ISBN 9810235005 • Electricity and Magnetism, W. J. Duffin, ISBN 007-084111-X • Microwave engineering, D. M. Pozar, ISBN 0471-17096-8 Ph.D opportunities @ JAI • We are actively working on developing new systems and novel new devices for accelerators all over the world (Japan-KEK, Germany-DESY, US-SLAC, Switzerland-CERN) •Interested students please contact me at Royal Holloway! •[email protected]