Radio frequency usage/applications Dr S. T. Boogert (accelerator physicist) John Adams Institute at Royal Holloway 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

Voltage change per turn Synchronicity Need to choose RF frequency and voltage Acceleration/longitudinal dynamics Acceleration from Dr. Karataev’s lectures

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 k mn a is the n th zero of J m (x) Imagine like solutions for wavefunction of Hydrogen atom (n,l,m) Hermite polynomials, Laguerre polynomials and spherical harmonics

Accelerating cavity as resonator Imagine injecting some EM into a cavity at t=0 Does the energy stay there for ever? less losshigher loss signalFT

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 Voltage Energy loss per turn (storage ring) Energy gain per tern (synchrotron) Quality factor Length of time between injecting RF energy into cavity 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 ~ 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 (diagrams and EM spectrum)/ Particle Accelerator Physics, H. Wiedemann, ISBN Handbook of Accelerator Physics and Engineering, A. W. Chao & M. Tigner, ISBN Electricity and Magnetism, W. J. Duffin, ISBN X Microwave engineering, D. M. Pozar, ISBN Accelerator Test Facility Cavity Beam Position Monitors, R. Lorenz, DESY-Zeuthen

Ph.D 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!