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RF System I & II ... System I & II S. Rimjaem Chiang Mai University (CMU) SLRI - CERN ASEAN...
Transcript of RF System I & II ... System I & II S. Rimjaem Chiang Mai University (CMU) SLRI - CERN ASEAN...
RF System I & II
S. Rimjaem
Chiang Mai University (CMU)
SLRI - CERN ASEAN Accelerator School 2017
August 28 - September 1, 2017
SLRI, Nakhon Ratchasima, Thailand
Outline
2S. Rimjaem RF System, SLRI – CERN ASEAN Accelerator School 2017
RF system I:
➢RF acceleration
➢Typical RF system
➢RF sources
RF system II:
➢RF transportation
➢Waveguides
➢RF cavity
➢RF coupling to cavity
Electrostatic acceleration
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Consider positive charge q is accelerated with potential V.
➢ It gains a kinetic energy of
➢ In this case, the accelerating voltage is limited for a few MV.
.kE qV
[Wille, Klaus. The Physics of Particle Accelerators: An Introduction. Oxford University Press, 2000.]
Time-varying electric field acceleration
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By switching the charge on the plates in phase with the particle motion,
the particle always sees an acceleration.
➢ In this case, we only need to hold the voltage between the two plates
not the full accelerating voltage of the accelerator.
E E E
v
v
Radiofrequency (RF) waves
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[Courtesy: E. Montesinos, RF powering, CAS 2015, Vösendorf, Austria]
➢ Frequency range: 10 MHz - 30 GHz
➢ Accelerating gradient: 1 - 100 MV/m
Acceleration in an RF gap
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Instead of two electric plates, we apply a radiofrequency (RF) field to a
gap between two drift tubes. Then, the particle gains kinetic energy of
0 cos ( )kE q E ds qE t ds
/2
00
/2
cos ( / )
L
k
L
qVE s v ds qV T
L
0
sin( / 2 )
/ 2
kE L vT
qV L v
Transit time factor
0 0 /E V L Consider constant
Two RF cavities acceleration
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Consider a series of 2 gaps and replace static fields by time-varying
periodic fields. Then, the particle exposes to the wave at certain selected
points and times. There are 2 types of acceleration:
➢ -mode acceleration:
➢ 0-mode or 2-mode acceleration:
Multi RF cavities acceleration: Wideröe linacs
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Synchronicity condition:vT
2 2
rf rf
il
-mode acceleration
[Courtesy: G. Hoffstaetter, “Accelerator Physics, U.S. Particle Accelerator School, June 2010]
Proposed by Ising in 1925 & built by Wideröe in 1928.
Drift tube linacs (DTL): Alvarez linacs
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Synchronicity condition: vTi rf rfl
0-mode or 2-mode acceleration
[Courtesy: G. Hoffstaetter, U.S. Particle Accelerator School, June 2010; E. Jensen, CERN Accelerator School, Divonne 2009 ]
Alvarez linac was developed in 1947.
RF cavities for acceleration
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Electron linacs
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➢ Development of the first electron linac by Ginzton, Hansen, Kennedy in 1948
at Stanford University.
➢ 3GHz Travelling-wave structures with iris loaded.
- Magnetron of 1 MW was firstly developed.
- High-power klystron of 8 MW was developed in 1946 – 1949.
Present linac structures
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Two principal types of RF linacs:
➢ Travelling wave structures:
disk loaded waveguides
➢ Standing wave structures:
resonant cavities
Cavity linacs
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These devices store large amounts of energy at a specific frequency
allowing low power sources to reach high fields.
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How to couple the RF power
to the accelerator?
RF
Source
RF
AcceleratorsRF Power
To be continue …..
Typical RF system
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4 primary components in high level RF system :
– Modulators: convert line AC → pulsed DC for klystrons
– RF amplifier e.g. klystrons: convert DC → RF at given frequency
– RF distribution: transport RF power → accelerating structures
– Accelerating structures: transfer RF power → beam
Typical RF system
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RF accelerator: Transformer principle
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An RF accelerator is a large vacuum transformer. It converts a high current, low voltage signal into a low current, high voltage signal.
➢ The RF amplifier converts the energy in the high current beam to RF.
➢ The RF cavity converts the RF energy to beam energy.
RF power source classification
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Vacuum Tubes
Grid
Tubes
Triodes
Tetrodes
Pentodes
Diacrodes
Linear Beam Tubes
Klystrons
Travelling Wave Tubes
(TWT)
Gyrotrons
Inductive Output Tube
(IOT)
Crossed-field Tubes
Magnetrons
Transistors
Bipolar Junction Transistor (BJT)
Field Effect Transistor (FET)
Junction Gate FET (JFET)
Metal Oxide Semiconductor FET
(MOSFET)
power MOSFET
Vertically Diffused Metal Oxide
Semiconductor (VDMOS)
Laterally Diffused Metal Oxide
Semiconductor (LDMOS)
General principles of RF system
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Grid tubes: vacuum tube principle
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➢ RF vacuum tubes operate using high current (A - MA) low voltage (50kV-
500kV) electron beams.
➢ They rely on the RF input to bunch the beam. As the beam has much
more power than the RF, it can induce a much higher power at an output
stage.
➢ These devices act very much like a transistor when small AC voltages can
control a much higher DC voltage, converting it to AC.
Diodes electron guns
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➢ When a cathode is heated, electrons are given sufficient energy to
leave the surface.
➢ When a high enough voltage is applied, electrons will travel across
the voltage gap.
➢ A current is then measured on the anode.
Triode electron guns
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➢ A grid can be inserted into a diode to control the voltage on the
cathode surface.
➢ An RF voltage can be applied to the grid to produce bunches of
electrons.
Triodes and Tetrodes
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The most basic types of RF amplifiers are triodes and tetrodes. A tetrode has a
2nd grid to screen the control grid from the anode to avoid feedback.
➢ They are operated by using the grid to bunch the beam and then the beam is
collected at the anode, where the potential fluctuates with the electron beam
and hence providing an AC voltage.
➢ They usually have low frequency e.g. 200 MHz.
➢ Low gain and low efficiency.
Diacrodes
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A diacrode is a sort of two sided tetrode that doubles the power.
Linear beam tubes: klystron
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Velocity modulation in klystron converts
the kinetic energy of electrons into RF
power.
➢ Vacuum tube
➢ Electron gun produces electron beam.
- Thermionic cathode
- Anode
➢ Drift space
- Electrons travel with constant speed.
➢ Collector
- High power RF wave
Klystrons: Cavity resonators
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RF input cavity (Buncher) modulates
electrons’ velocities and causes
bunching of electrons
- Some electrons are accelerated
- Some have constant velocities
- Some are decelerated
RF output cavity (Catcher)
- Resonating at the same
frequency as the input cavity
- At the place with the numerous
number of electrons, kinetic
energies of electrons are
converted into voltage and
extracted out off the cavity.
Buncher
Catcher
Klystrons: Additional bunching cavities
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Additional bunching cavities
- Resonate with the pre-
bunched
electrons beam
- Generate an additional
accelerating/decelerating field
- Better bunching
- Gain 10 dB per cavity
Focusing magnets
- To maintain the e- beam as
expected and where expected
Example of klystrons
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[www2.slac.stanford.edu/vvc/accelerators/klystron.html]
CERN LHC, TH 2167 klystron
330 kW @ 400 MHz
Linear beam tubes: Inductive output tube (IOT)
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IOT density modulation converts the
kinetic energy into RF power.
➢ Vacuum tube
➢ Triode input
- Thermionic cathode
- Grid modulates electron emission
➢ Klystron output
- Anode accelerates electron buckets
- Short drift tube & magnets
- Catcher cavity
- Collector
Example of IOT
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CERN SPS, TH 795 IOT, Trolley (single amplifier), and transmitter (combination of amplifiers)
Two transmitters of four tubes delivering 2 x 240 kW @ 801 MHz, into operation since 2014
[Courtesy: E. Montesinos, RF powering, CAS, Accelerators for Medical Applications, Vösendorf, Austria, 2015.]
Magnetrons
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➢ Magnetrons are normally used for small industrial or hospital linacs.
➢ It works by having an electron cloud rotate around a coaxial cathode due to
interaction of electrons in crossed electric and magnetic fields.
➢ They are cheap and fairly efficient and can reach powers of 5 MW pulsed or
30 kW CW at 3 GHz (100 kW at lower frequencies).
➢ Phase stability is not good enough for large accelerators.
Transistors for RF power
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In a push-pull circuit, the RF signal is
applied to two devices
- One devices is active on the positive voltage
and off during the negative voltage.
- The other device works in the opposite
manner.
- So that the two devices conduct half the time,
the full RF signal is then amplified.
NXP Semiconductors AN11325
2-way Doherty amplifier with BLF888A
Examples of solid state power amplifier (SSPA)
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ESRF four 150 kW @ 352 MHz
solid state amplifiers (2012)SOLEIL 45 kW @ 352 MHz
solid state amplifier towers (2004 & 2007)
Choices of device frequency & RF power source
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Frequencies of RF tend to correspond to integer wavelengths in mm and
inches and try to avoid frequencies used in broadcast and communication.
➢ RF cavities: 200, 267, 352, 400, 508, 650, 704 MHz
➢ RF guns and RF linacs: 1.3, 2.856, 3, 3.7, 3.9, 5.6, 9.3, 11.424, 11.994 GHz
Outline
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RF system I:
➢RF acceleration
➢Typical RF system
➢RF sources
RF system II:
➢RF transportation
➢Waveguides
➢RF cavity
➢RF coupling to cavity
RF power transportation
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Purpose: Transmission of RF power of several kW up to several MW
at frequencies from the MHz to GHz range.
Requirements: low loss, high efficiency, low reflections, high reliability,
adjustment of phase and amplitude ability, ….
There are 2 types of RF couplers:
➢ Waveguide type: NC SW cavity, NC TW structure, SC SW cavity
➢ Coaxial type: NC SW cavity, SC SW cavity
RF Coupling to Cavity
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Cavities have to be powered to replace the losses in the walls and to
provide the power delivered to the beam.
Aperture or slot (EM-coupling) Antenna (E-coupling) Loop (B-coupling)
Waveguide / Coaxial Couplers
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Parameter Waveguide Coaxial
Dimensions larger smaller
Power handling capacity higher lower
Attenuation lower higher
Vacuum / pumping speed better worst
Variable coupling difficult easier
Colling better worst
Notes:
➢ Waveguide type is preferred at high
frequencies & high gradient structures.
➢ Coaxial type is preferred at low frequencies.
[D. Alesini, Power Coupling, CAS, Ebeltoft, Denmark, June 2010]
Maxwell equations and waveguides
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In a waveguide system, solutions of Maxwell’s equations that are
propagating along the guiding direction and are confined in the guiding
structure can be assumed to have the form:
𝛽 is the propagation wavenumber
along the guide direction.
Guided Propagation
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Decompose Maxwell’s equations into longitudinal and transverse
components.
Gradient operator:
Wave equations (Helmholtz equation):
Guided Propagation
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Depending on whether both, one or none of the longitudinal components
are zero, solutions are classified as transverse electric and magnetic
(TEM), transverse electric (TE), transverse magnetic (TM), or hybrid:
➢ TEM, TE and TM waves exist in power transportation systems.
➢ In hollow waveguides only TE and TM modes are present.
➢ These are characterized by indices nm, according to the number of
half waves in the x and y direction of the waveguides
Rectangular waveguide: TE10 and TEn0 modes
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For transverse electric (TE) modes the longitudinal component of the
electric field is 0.
The simplest and dominant propagation mode is the TE10 mode and
depends only on the x-coordinate. The Helmholtz equation reduces to:
Rectangular waveguide
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Applying boundary conditions, we get the corresponding cutoff frequency
and wavelength as
The boundary conditions require:
Magnetic and electric fields become
Electric field distributions of TEnm and TMnm modes
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Rectangular waveguide
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We get the frequency as
TM01 mode
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Some standard waveguide dimensions
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Waveguides of different sizes
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RF power coupling to the cavity
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[Wille, Klaus. The Physics of Particle Accelerators: An Introduction. Oxford: Oxford University Press, 2000.]
Circular Waveguide
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Similar to the rectangular waveguide, many modes exist in circular
waveguides. These modes are indexed with two numbers: the first for
the azimuthal, the second for the radial ‘number of half-waves’.
a is the radius of the circular waveguide
𝑞𝑛𝑚 is the m-th zero of the derivatives of Bessel function of order n.
𝑝𝑛𝑚 is the m-th zero of Bessel function of order n.
Circular Waveguide: Electric field distributions
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Pillbox Cavities
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➢ If we place metal walls at each end of the waveguide we create a cavity.
➢ The waves are reflected at both walls creating a standing wave.
➢ If we superimpose a number of plane waves by reflection inside a cavities surface we can get cancellation of E|| and BT at the cavity walls.
➢ The boundary conditions must also be met on these walls.
➢ These are met at discrete frequencies only when there is an integer number of half wavelengths in all directions.
011 22
22
zk
rrr
rr
im
tm erkJA )(1
Wave equation in cylindrical coordinates
Solution to the wave equation
TM010 Pillbox cavity
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Bessel functionsm = number of full wave variations around theta
n = number of half wave variations along the diameter
P = number of half wave variations along the length
0 0
0 1
0
2.405
0
0
2.405
0
0
i t
z
z
r
i t
r
rE E J e
R
H
H
i rH E J e
Z R
E
E
2 2.405c
c
kR
Cavity quality factor
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➢ An important definition is the cavity Q factor, given by
where U is the stored energy given by,
➢ The Q factor is 2 times the number of rf cycles it takes to dissipate the energy stored in the cavity.
➢ The Q factor determines the maximum energy the cavity can fill to with a given input power.
cP
UQ
0
dVHU 2
02
1
0
0
expt
U UQ
The beam tube makes the field modes more complicated
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➢ Peak electric field is no longer on axis
➢ Resonant frequency is more sensitive to cavity
dimensions. Thus, mechanical tuning &
detuning are needed.
➢ Beam tubes add length w/o acceleration.
➢ Beam induced voltages ~ a-3 and leads to
Instabilities.
Cavity design: shape optimization
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Cavity design: shape optimization
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Practical standing wave cavity
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Resonant cavity to equivalent circuit (1)
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For simplicity, consider TM010 pill-box
cavity
➢ The electric field is contained between
2 metal plates. Capacitor
➢ The surface current circulates around
the outside of the cavity and induces
the magnetic field. Inductor
[G. Burt, Introduction to RF for Accelerators, Lancaster University]
Resonant cavity to equivalent circuit (2)
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➢ If the cavity has a finite conductivity,
the surface current will flow in the skin
depth causing ohmic heating and
power loss.
➢ In this model we assume the voltage
across the resistor is the cavity
voltage. Cavity shunt impedance
1
LC
2
2
cc
VP
R
2
2
cCVU
Resonant cavity to equivalent circuit (3)
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➢ Simple equivalent circuit can be used to calculate the cavity
parameters, which are
0
c
U CQ R
P L
2
0
1
2
cVR L
Q U C C
0cV V T
RF coupling to cavity: equivalent circuit
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The RF source is represented by an ideal current source in parallel to an
impedance Z0.
➢ The RF power is coupled from the source to the cavity via a coupler, which is
represented as an n:1 turn transformer.
[G. Burt, Introduction to RF for Accelerators, Lancaster University]
External Q factor
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ext
ext
UQ
P
➢ When an external RF is coupled to the cavity, we have to consider the loss from
the couplers. Thus, an external Q is defined as
Pext is the power lost through the coupler when the RF sources are turned off.
➢ A loaded Q factor (QL), which is the real Q of the cavity, is
0
1 1 1
L extQ Q Q
L
tot
UQ
P
0ext
c ext
P Q
P Q
RF coupling measurement & scattering parameters
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The most common RF coupling measurement is the S-parameters using e.g.
S-parameter network analyzer.
Trans:FWD
Trans:REV
11S
21S
12S
22SRefl:FWD
(Port 1)
Refl:REV
(Port 2)
Sab = Va / Vb = ratio of the voltage measured at the measurement port “a” to
the voltage at the input port “b”.
RF cavity responses
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RF reflections from the cavity are minimised and the transmission is maximized at
the resonant frequency.
➢ If the coupler’s impedance is matched to the cavity, the reflections will go to
zero and 100% of the power will get into the cavity when it is in steady state.
Thus, the cavity is filled.
11
1
1
ext
ext
S
0ext
ext
Q
Q
Cavity filling at steady state (No beam!)
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When the cavity is in steady state, the stored energy in the cavity is constant U=U0.
The cavity’s energy is maximum when β=1.
0 00
00 2
, ,
4
1
f
f c r
c c ext
f
PU QQ P P P
P P Q
P QU
2
1
1r fP P
Beam loading
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➢ In addition to ohmic losses in the cavity and the coupling system, we must
also consider the power extracted from the cavity by the beam.
➢ The beam draws a power the cavity as
where q is the bunch charge and f is the repetition rate.
➢ This means that the cavity requires different powers without beam or with
lower/higher beam currents.
b c bP V I bI q f
f c b rP P P P
Coupling with beam loading
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➢ The RF source will not see any difference between the power dissipated in the
cavity walls and the power extracted by the beam. Thus, a new Q factor with
beam is
➢ This means that the impedance will change and the system needs more power.
➢ Thus, we aim for =1 with beam and have some reflections when cavity is filled
without beam.
bc
cbPP
UQ
cbeb
e
Q
Q
0 2
4
1
eb f cb
eb
P QU
Equivalent Circuit of the Whole System
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RF Transportation to travelling wave structures
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RF Transportation to Standing wave structures
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Circulator
Example of RF system: RF-gun and electron linac
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RFF (-62.3dB)
RFR (-63.0 dB)
Directional Coupler
RFF (-81.6 dB)
RFR (-80.8 dB)
Directional
Coupler
Circulator Hybrid
Directional Coupler
Linac
RF-Gun
Modulator + PFN
Modulator + PFN
Oscillator
Phase Shifter
Amplifier 1
Klystron
1
Amplifier 2
Klystron
2
Major references
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1) G. Burt, Introduction to RF for Accelerators, Lancaster University.
2) E. Montesinos, RF powering, CAS, Accelerators for Medical
Applications, Vösendorf, Austria, 2015.
3) S. Choroba, RF Power Transportation, CERN School on RF for
Accelerators, 8-17 June 2010, Ebeltoft, Danmark.
Q & A