RF System I & II ... System I & II S. Rimjaem Chiang Mai University (CMU) SLRI - CERN ASEAN Accelerator School 2017 August 28 - September 1, 2017 SLRI, Nakhon Ratchasima, Thailand

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


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


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


[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


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


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


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


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


Electron linacs


➢ 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


Two principal types of RF linacs:

➢ Travelling wave structures:

disk loaded waveguides

➢ Standing wave structures:

resonant cavities

Cavity linacs


These devices store large amounts of energy at a specific frequency

allowing low power sources to reach high fields.


How to couple the RF power

to the accelerator?

RF

Source

RF

AcceleratorsRF Power

To be continue …..

Typical RF system


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


RF accelerator: Transformer principle


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


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


Grid tubes: vacuum tube principle


➢ 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


➢ 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


➢ 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


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


A diacrode is a sort of two sided tetrode that doubles the power.

Linear beam tubes: klystron


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


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


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


[www2.slac.stanford.edu/vvc/accelerators/klystron.html]

CERN LHC, TH 2167 klystron

330 kW @ 400 MHz

Linear beam tubes: Inductive output tube (IOT)


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


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


➢ 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


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)


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


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


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


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


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


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


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


Decompose Maxwell’s equations into longitudinal and transverse

components.

Gradient operator:

Wave equations (Helmholtz equation):

Guided Propagation


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


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


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


Rectangular waveguide


We get the frequency as

TM01 mode


Some standard waveguide dimensions


Waveguides of different sizes


RF power coupling to the cavity


[Wille, Klaus. The Physics of Particle Accelerators: An Introduction. Oxford: Oxford University Press, 2000.]

Circular Waveguide


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


Pillbox Cavities


➢ 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


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


➢ 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


➢ 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


Cavity design: shape optimization


Practical standing wave cavity


Resonant cavity to equivalent circuit (1)


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]



➢ 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



➢ 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


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


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


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


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!)


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


➢ 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


➢ 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


RF Transportation to travelling wave structures


RF Transportation to Standing wave structures


Circulator

Example of RF system: RF-gun and electron linac


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


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

Documents

RF System I & II ... System I & II S. Rimjaem Chiang Mai University (CMU) SLRI - CERN ASEAN Accelerator School 2017 August 28 - September 1, 2017 SLRI, Nakhon Ratchasima, Thailand