Download Generation of RF for acceleration

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]