radio frequency usage/applications dr s. t. boogert (accelerator physicist) john adams institute at...
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Radio frequency usage/applications
Dr S. T. Boogert (accelerator physicist)John Adams Institute at Royal Holloway
Royal Holloway : PH4450
University College London19th 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
• Jm(x) is a Bessel function of order m kmna is the nth zero
of Jm(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 loss higher loss
signal FT
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 ~ 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 KlystronsATF
Damping ring
714 CW Klystron
Australian 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 waveguides 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 0-07-084111-X
• Microwave engineering, D. M. Pozar, ISBN 0-471-17096-8
• Accelerator Test Facility http://atf.kek.jp
• Cavity Beam Position Monitors, R. Lorenz, DESY-Zeuthen
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!