Physics 862 Accelerator System Introduction to RF and

Alireza Nassiri Adjunct Professor of ECE Outline • Three lectures: • Lecture 1 – today o Introduction o Overview of RF power generation • Lecture 2 – Wednesday, November 7 o Power transport – part one • Lecture 3 – Wednesday, November 7 o Power transport – part two o Introduction to low-level rf and controls • Homework

A. Nassiri PHY 862 Accelerator Systems 2 Electromagnetic Spectrum • All the electromagnetic waves travel with the same velocity (i.e. 3 X 108 m/s) in the free space with different frequencies. The arrangement of electromagnetic radiations according to wavelength or the frequency is referred as electromagnetic spectrum. • As we know electromagnetic spectrum has no definite upper or lower limit and various regions of EM spectrum do not have sharply defined boundaries. • The electromagnetic spectrum types, their frequency, wavelength, source and applications have been outlined in the table below. As mentioned EM waves include electric wave, radio wave, microwave, infrared, visible light,ultra violet,X-rays,gamma rays and cosmic rays.

A. Nassiri PHY 862 Accelerator Systems 3 Electromagnetic Spectrum

EM Wave Type Frequency (Hz) Wavelength (m) Source Applications

Electric wave 50 to 60 5 x 106 to 6 x 106 Weak radiation from AC circuit Lighting

Radio wave 3 x 104 to 3 x 109 1 x 10-1 to 104 Oscillating circuits Radio communication, TV

Microwave 3 x108 to 3 x 1011 1 x 10-3 to 1 Oscillating current in special vacuum tubes, Radar, TV, Satellite communication, remote sensing. Gunn, IMPATT, Tunnel Infrared 1 x 1013 to 4 x 1014 7.5 x 10-7 to 3 x 10-5 Excitation of atoms and molecules Gives information on the structure of molecules and of external atomic electron shells, remote sensing. Visible light 4 x 1014 to 8 x 1014 3.75 x 10-7 to 7.5 x 10-7 Excitation of atoms and vacuum spark Gives information on the structure of molecules and of external atomic electron shells, remote sensing Ultra violet 8 x 1014 to 1 x 1016 3 x 10-8 to 3.75 x 10-7 Excitation of atoms and vacuum spark Gives information on the structure of molecules and of external atomic electron shells, remote sensing Bombardment of high atomic number X-rays therapy, industrial radiography, medical radiography, X-ray 1 x 1016 to 3 x 1019 1 x 10-10 to 3 x 10-8 target by electrons crystallography

Gamma Ray 3 x 1019 to 5 x 1020 6 x 10-15 to 1 x 10-10 Emitted by radioactive substances Gives information about the structure of atomic nuclei

Stars from Cosmic Ray > 1020 < 10-11 other galaxies

A. Nassiri PHY 862 Accelerator Systems 4 Introduction • RF transmitter for accelerating cavities

 Cavity tuning loop  Amplitude loop  Phase loop

RF Distribution Control System Four Components 1. RF Source 2. Power supply Pre- Power Master Oscillator LLRF 3. Transport (WG system) amp. 4. LLRF

• Power Supply • Modulator

Termination Load

RF source Accelerating Cavity

What is the Overall Efficiency? Later in the lecture.

A. Nassiri PHY 862 Accelerator Systems 5 Glossary of Terms as relates to RF • Frequency range o are dominant and used above 300 MHz o Other devices such as IOT, Diacrode, and SSA below 300 MHz • Peak power o Is related to energy gain in an accelerator as well as the overall length of a given accelerator system. High peak power typically results in arcing within the accelerating structures. • Average power o Is defined as the product of peak power and DF in pulsed systems o For CW systems, the output power is equal to the average power. . Define the amount of heat produced by the system • Gain o Defines by rf drive. Klystrons, in general, have a high gain ~50 dB ( i.e. less drive power). IOTs are low gain devices- ~20 dB ( i.e., more drive power). • Phase Stability o is a voltage driven device and the rf phase is stable if the voltage is stable.

A. Nassiri PHY 862 Accelerator Systems 6 Glossary of Terms as relates to RF

• Decibel (dB) o 푑퐵푚=10 퐿표푔10 ("PmW") o 푑퐵=10 퐿표푔10 (푃1/푃2) o 푑퐵=20 퐿표푔10 (푉1/푉2) o 푑퐵푉=20 퐿표푔10 ("VVrms") o 푑퐵µ푉=20 퐿표푔10 (푉µ푉푟푚푠) o 푑퐵푐=10 퐿표푔10 (푃푐푎푟푟푖푒푟/푃푠푖푔푛푎푙) • dBm, W (푥푑퐵푚/10) 푥푑퐵푚 = 10 퐿표푔10 PmW 푃푚푊 = 10

0 dBm = 1 mW 30 dBm = 1 W 60 dBm = 1 kW 90 dBm = 1 MW

A. Nassiri PHY 862 Accelerator Systems 7 Glossary of Terms as relates to RF

(푥 /10) 푥푑퐵=10 퐿표푔10 (푃/푃푟푒푓) ↔ 푃∕푃푟푒푓=10 푑퐵

A. Nassiri PHY 862 Accelerator Systems 8 RF Power Sources • Two principal classes of microwave vacuum devices are in common use today: o Linear-beam tubes o Crossed-field tubes Linear Beam Devices

Klystrons Hybrid O-type TWT

Multi- cavity Two - cavity Twystron Helix Helix Ring-bar BWO TWT

Reflex Laddertron Coupled cavity TWT

A. Nassiri PHY 862 Accelerator Systems 9 Linear Beam Devices

• In a linear-beam tube, as the name implies, the electron beam and the circuit elements with which it interacts are arranged linearly. • In such a device, a voltage applied to an anode accelerates electrons drawn from a cathode, creating a beam of kinetic energy. • Power supply potential energy is converted to kinetic energy in the electron beam as it travels to- ward the microwave circuit. • A portion of this kinetic energy is transferred to micro-wave energy as RF waves slow down the electrons. The remaining beam energy is either dissipated as heat or returned to the power supply at the collector. • Because electrons will repel one another, there usually is an applied magnetic focusing field to maintain the beam during the interaction process.

A. Nassiri PHY 862 Accelerator Systems 10 Cross-Field Devices • The magnetron is the pioneering device of the family of crossed-field tubes. • Although the physical appearance differs from that of linear-beam tubes, which are usually circular in format, the major difference is in the interaction physics that requires a magnetic field at right angles to the applied electric field. • Whereas the linear-beam tube sometimes requires a magnetic field to maintain the beam, the crossed-field tube always requires a magnetic focusing field.

Crossed-field devices

Distributed emission Injected beam tube

MBWO Magnetron Crossed-field amplifier Carcinotron

Voltage tunable Crossed field amplifier magnetron

A. Nassiri PHY 862 Accelerator Systems 11 Commercial RF Sources

Tetrodes & Diacrodes available from industry 10000

peak < 1 1000 ms

100 Power per kW single tube Power 10 0 100 200 300 400 500 Frequency MHz A. Nassiri PHY 862 Accelerator Systems 12 Amplifier Class Class A Class B Class C Operative curve Operative curve Operative curve Output Signal Output Signal Less than 180⁰ Unsused Output Unsused area Signal area

Input Input Input Signal Signal Signal

C Efficiency Amplifier Class Description AB B A 100% Class-A Full cycle 360⁰ of conduction 75% 50% Class-AB More than 180⁰ of conduction 25% 0% Class-B Half cycle 180⁰ of conduction A AB B C Class-C Less than 180⁰ of conduction

360⁰ 270⁰ 180⁰ 90⁰ 0⁰ 2π 3π/4 π Conduction Angle 0 A. Nassiri PHY 862 Accelerator Systems 13 Grid Vacuum Tubes • The physical construction of a causes the output power and available gain to decrease with increasing frequency. The principal limitations faced by grid-based devices include the following: o Physical size. Ideally, the RF voltages between electrodes should be uniform, but this condition cannot be realized unless the major electrode dimensions are significantly less than 1/4 wavelength at the operating frequency. This restriction presents no problems at VHF, but as the operating frequency increases into the microwave range, severe restrictions are placed on the physical size of individual tube elements. o Electron transit time. Inter electrode spacing, principally between the grid and the cathode, must be scaled inversely with frequency to avoid problems associated with electron transit time. Possible adverse conditions include: 1) excessive loading of the drive source, 2) reduction in power gain, 3) back-heating of the cathode as a result of electron bombardment, and 4) reduced conversion efficiency. o Voltage standoff. High-power tubes operate at high voltages. This presents significant problems for microwave vacuum tubes. For example, at 1 GHz the grid-cathode spacing must not exceed a few mils. This places restrictions on the operating voltages that may be applied to the individual elements. o Circulating currents. Substantial RF currents may develop as a result of the inherent inter electrode capacitances and stray inductances/capacitances of the device. Significant heating of the grid, connecting leads, and vacuum seals may result. o Heat dissipation. Because the elements of a microwave grid tube must be kept small, power dissipation is limited.

A. Nassiri PHY 862 Accelerator Systems 14 Tetrode • Vacuum tube based on intensity modulation of a electron beam • Typical parameters: • Frequency: accelerator applications up 300 to 400MHz • Finite electron drift time limits the achievable gain at higher frequencies • Limiter gain of ~15 dB mean that thigh power tetrode need 2-3 stage of amplification, which drives up the cost and results in complicated amplifier systems.

Grounded Grid

Grounded Cathode

A. Nassiri PHY 862 Accelerator Systems 15 Planar • The envelope is made of ceramic, with metal members penetrating the ceramic to provide for connection points. The metal members are shaped either as disks or as disks with cylindrical projections. • The cathode is typically oxide-coated and indirectly heated. The key design objective for a cathode is high emission density and long tube life. Low-temperature emitters are preferred because high cathode temperatures typically result in more evaporation and shorter life. • The grid of the planar triode is perhaps the greatest design challenge for tube manufacturers. Close spacing of small-sized elements is needed, at tight tolerances. Good thermal stability also is required, because the grid is subjected to heating from currents in the element itself, plus heating from the cathode and bombardment of electrons from the cathode. • The anode, usually made of copper, conducts the heat of electron bombardment to an external heat sink. Most planar are air- cooled. • Planar triodes designed for operation at 1 GHz and above are used in a variety of circuits. The grounded-grid configuration is most common. The plate resonant circuit is cavity-based, using waveguide, coaxial line, or stripline. Electrically, the operation of the planar triode is much more complicated at microwave frequencies than at low frequencies. A. Nassiri PHY 862 Accelerator Systems 16 Diacrode • The Diacrode (Thales) is a promising adaptation of the high-power UHF tetrode. The operating principle of the Diacrode is basically the same as that of the tetrode. The anode current is modulated by an RF drive voltage applied between the cathode and the power grid. The main difference is in the position of the active zones of the tube in the resonant coaxial circuits, resulting in improved reactive current distribution in the electrodes of the device. Double the • The main difference is in the position of output power the active zones of the tubes in the at a given resonant coaxial circuits, resulting in frequency improved reactive current distributing in the tube’s electrodes. Double the frequency at The tetrode is located at the end of 1/4, theoretically at the given output current node side. power. The Diacrode is located at the middle of the 1/2 and thus the current node and the voltage anti-node are situated at the center of the cathode/ and screen grid/anode space.

A. Nassiri PHY 862 Accelerator Systems 17 IOT • Inductive Output Tube (IOT) Klystrode • IOT developed for accelerators [Thales, CPI]:80 kW CW at 470 –760 MHz o High efficiency (70%) operation in class B o Intrinsic low gain ( 20– 25 dB) ⇒Pin= 1 Kw . Less gain than klystrons but higher than . No need for a long drift space ( like klystrons) • More compact and cost efficient o IOTs ( and all gridded tubes) are limited in their frequency reach by the distance of the control grid from the cathode. As a tetrode As a klystron o The RF period has to be smaller than the time of flight from cathode to this grid. . Frequency of IOTs is limited to ~ 1.3 GHz . The max. power of a single beam IOTs is limited to ~100 kW. o Less Amplitude/Phase sensitivity to HV ripples o Compact, external cavity ⇒easy to handle o Low unit power ⇒power combiners • 1.3 GHz for cw XFEL linacs and ERLs o 16 to 20 kW CW, efficiency 55 to 65% ( CPI, E2V, Thales) CERN SPS TH795 IOT transmitters. Two transmitters (4 tubes) deliver 18 A. Nassiri PHY 862 Accelerator Systems 480 kW at 801 MHz. MB-IOT • ESS doing R&D on Multi-Beam IOT o Alternative to klystrons • Two prototypes o 1.3 MW @704 MHz up to 3.5 ms pulse

A. Nassiri PHY 862 Accelerator Systems 19 Klystron • Principle of klystrons was published by Oskar and Agnessa Heil (Germany) in 1935. • During the same time, W. W. Hansen at Stanford was investigating “ a scheme for producing high- voltage electrons” for use in X-ray spectroscopy. In the process, he invented the microwave cavity , “ Rhumbatron.” • Working with Hansen Varian brothers (Russell and Sigurd) developed klystron

Beam Beam Electron Continuous Bunched arrives at arrives at gun beam beam Collector 1st cavity 2nd cavity

A. Nassiri PHY 862 Accelerator Systems 20 RF and Microwave

• Both RF and Microwave are used to represent frequency ranges in the electromagnetic spectrum. Both are used for many similar as well as different applications. RF is the short form for '' signal. • RF (Radio Frequency) o EM spectrum has been classified into eight regions based on radiation intensity. The major divisions are into radio spectrum and optical spectrum. Radio spectrum covers radio waves, and terahertz radiations. Optical spectrum covers infrared, visible, ultra violet, X-rays and gamma radiations. Radio waves range from 3 KHz to 300 GHz. Hence RF. starts from much lower than the microwave starting range. o In radio waves antenna wavelength varies from hundreds of meters to about 1 millimeter. • Microwave o The term "micro" means very small. It is basically millionth part of a unit. The term Microwave is used to identify EM waves above 1GHz in frequency because of short physical wavelength of these frequencies. Microwaves are basically radio frequency(RF) waves. However there is difference between RF and microwave as far as operating range and applications are concerned. Microwaves range starts from 300MHz to 300GHz. o Most of the microwave applications range up to 100 GHz. Following are the unique features of the microwaves: • High antenna gain and directivity • Large Bandwidth • It travels by LOS(Line Of Sight) • In 1-10GHz range Microwaves noise level is very low and hence very low signal can also be easily detected at receiver • Microwaves penetrate ionosphere with less attenuation as well as less distortion.

A. Nassiri PHY 862 Accelerator Systems 21 Difference between RF and Microwave

• The terms RF and Microwave are interchangeably used by engineers across the globe, there is slight distinction between them. The same have been highlighted in the page. • Although there is ambiguity in starting range of microwave, in general it starts from 1GHz and span till 1 Tera-Hertz. Hence corresponding wavelengths range from 30cm to 0.3mm.

Specifications RF Microwave Frequency range(Hz) 3 x 105 to 3 x 1011 3 x 108 to 3 x 1011 Wavelength 103 to 10-3 meters 1 to 10-3 meters Mobile,AM/FM radio, radar, satellite and space Applications television communication

A. Nassiri PHY 862 Accelerator Systems 22 Properties of Microwaves

1. Microwave is an electromagnetic radiation of short wavelength. 2. They can reflect by conducting surfaces just like optical waves since they travel in straight line. 3. Microwave currents flow through a thin outer layer of an ordinary cable. 4. Microwaves are easily attenuated within short distances. 5. They are not reflected by ionosphere

A. Nassiri PHY 862 Accelerator Systems 23 Advantages and Limitations

• Increased bandwidth availability o Microwaves have large bandwidths compared to the common bands like short waves (SW), ultrahigh frequency (UHF) waves, etc. o For example, the microwaves extending from  = 1 cm -  = 10 cm (i.e) from 30,000 MHz – 3000 MHz, this region has a bandwidth of 27,000 MHz. • Improved directive properties o The second advantage of microwaves is their ability to use high gain directive antennas, any EM wave can be focused in a specified direction (Just as the focusing of light rays with lenses or reflectors) • Fading effect and reliability o Fading effect due to the variation in the transmission medium is more effective at low frequency. o Due to the Line of Sight (LOS) propagation and high frequencies, there is less fading effect and hence microwave communication is more reliable. • Power requirements o Transmitter / receiver power requirements are pretty low at microwave frequencies compared to that at short wave band.

A. Nassiri PHY 862 Accelerator Systems 24 Advantages and Limitations

• Transparency property o Microwave frequency band ranging from 300 MHz – 10 GHz are capable of freely propagating through the atmosphere. o The presence of such a transparent window in a microwave band facilitates the study of microwave radiation from the sun and stars in radio astronomical research of space. • Applications o Scientific – Accelerators o Telecommunication: Intercontinental Telephone and TV, space communication (Earth – to – space and space – to – Earth), telemetry communication link for railways etc. o Radars: detect aircraft, track / guide supersonic missiles, observe and track weather patterns, air traffic control (ATC), burglar alarms, garage door openers, police speed detectors etc.

A. Nassiri PHY 862 Accelerator Systems 25 Applications • Scientific – Accelerators • Telecommunication: Intercontinental Telephone and TV, space communication (Earth – to – space and space – to – Earth), telemetry communication link for railways etc. • Radars: detect aircraft, track / guide supersonic missiles, observe and track weather patterns, air traffic control (ATC), burglar alarms, garage door openers, police speed detectors etc. • Commercial and industrial o Microwave oven o Drying machines – textile, food and paper industry for drying clothes, potato chips, printed matters etc. o Food process industry – Precooling / cooking, pasteurization / sterility, hat frozen / refrigerated precooled meats, roasting of food grains / beans. o Rubber industry / plastics / chemical / forest product industries o Mining / public works, breaking rocks, tunnel boring, drying / breaking up concrete, breaking up coal seams, curing of cement. o Drying inks / drying textiles, drying / sterilizing grains, drying / sterilizing pharmaceuticals, leather, tobacco, power transmission. o Biomedical Applications ( diagnostic / therapeutic ) – diathermy for localized superficial heating, deep electromagnetic heating for treatment of cancer, hyperthermia ( local, regional or whole body for cancer therapy).

A. Nassiri PHY 862 Accelerator Systems 26 Performance Parameters of Different RF Sources

F. Gerigk, CERN, IPAC2018

A. Nassiri PHY 862 Accelerator Systems 27 RF Sources Efficiency Summary

RF source type Gain Maximum Rise time Pulse Repetition Maximum Efficiency High Frequency output length rate range output at voltage range power range power CW working needs pulsed point

[dB] [kW] [µs] [ms] [Hz] [kW] [%] [kV] [MHz] Tetrode 14-16 4000 ns 1500 70 10 – 25 30 – 400 Almost whatever Diacrode 14-16 3000 ns requested 2000 70 20 – 30 30 – 400 IOT 20-23 130 ns (depends on HVPS 85 70 36 – 38 ? – 1300 design) MB-IOT 20-23 1300 ns 150 (tbc?) 70 50 704

Courtesy of E. Montesinos, CERN

A. Nassiri PHY 862 Accelerator Systems 28 PRFin ≃ 1 to 5 % PRFout (Gain is usually Overall Efficiency of RF System high)

ηRF/DC ≃ 65 % (including overhead)

η PAC/PDC ≃ 95 % to 98 %

Amplifier cooler ≃ 15 % PRFout Amplifier Building Cooler Cooler Building cooler ≃ 30 % PRFout 퐎퐯퐞퐫퐚퐥퐥 퐞퐟퐟퐢퐜퐢퐞퐧퐜퐲 Heat out 퐏 = 퐑퐅퐨퐮퐭 RF power in RF power out 퐏퐑퐅퐢퐧 + 퐏 퐀퐂퐢퐧 + 퐏 퐜퐨퐨퐥퐞퐫퐬 Amp DUT (Device Under Test) 퐏 ≃ 퐑퐅퐨퐮퐭 퐏 (ퟎ. ퟎퟓ + ퟏ. ퟔퟐ + ퟎ. ퟒퟓ) DC power in 푹푭풐풖풕 AC power in AC/DC ≃ ퟒퟓ %

푶풗풆풓풂풍풍 풆풇풇풊풄풊풆풏풄풚 푷 ≃ 푹푭풐풖풕 ≃ 45 % 푷푨푪풊풏+푷푹푭풊풏 +푷풄풐풐풍풆풓풔

A. Nassiri PHY 862 Accelerator Systems 29 RF Power Distribution • Consider a simple high power rf layout:

RF power source Circulator DUT (Cavity) Klystron, etc. Driver Amplifier Outer conductor Inner conductor Size Outer Inner Outer Inner Coaxial line Waveguide Waveguide diameter diameter diameter diameter 7/8" 22.2 mm 20 mm 8.7 mm 7.4 mm 1 5/8" 41.3 mm 38.8 mm 16.9 mm 15.0 mm 3 1/8" 79.4 mm 76.9 mm 33.4 mm 31.3 mm 4 1/2" 106 mm 103 mm 44.8 mm 42.8 mm 6 1/8" 155.6 mm 151.9 mm 66.0 mm 64.0 mm Coaxial Lines Load (Termination)

Coaxial cables are often with PTFE foam to keep concentricity Flexible lines have spacer helicoidally 60 퐷 placed all along the line Rigid lines are made of Z = ln c ε 푑 two rigid tubes 푟 maintained concentric with supports A. Nassiri PHY 862 Accelerator Systems 30 Rectangular Waveguide

• Waveguides are usable over certain frequency ranges o For very lower frequencies the waveguide dimensions become impractically large o For very high frequencies the dimensions become impractically small & the manufacturing tolerance becomes a significant portion of the waveguide size

λ λ푔 = Wavelength λ 1−( )2 2푎 c Cut-off frequency dominant mode fc = 2푎 b c a Cut-off frequency next higher mode f c2 = 4푎

Usable frequency range 1.3 fc to 0.9 fc2

Waveguide name Recommended Cutoff frequency Cutoff frequency Inner dimensions of frequency band of lowest order of next waveguide opening of operation (GHz) mode (GHz) mode (GHz) (inch) EIA RCSC IEC

WR2300 WG0.0 R3 0.32 — 0.45 0.257 0.513 23.000 × 11.500 WR1150 WG3 R8 0.63 — 0.97 0.513 1.026 11.500 × 5.750 WR340 WG9A R26 2.20 — 3.30 1.736 3.471 3.400 × 1.700 WR75 WG17 R120 10.00 — 15.00 7.869 15.737 0.750 × 0.375 WR10 WG27 R900 75.00 — 110.00 59.015 118.03 0.100 × 0.050 WR3 WG32 R2600 220.00 — 330.00 173.571 347.143 0.0340 × 0.0170

A. Nassiri PHY 862 Accelerator Systems 31 Reflection

• Reflection occurs when there is impedance mismatch between the device under test ( e.g., cavity) and the line. • SWR is a measure of this impedance mismatch where a incident wave is partially reflected when the TL in not terminated in resistance equal to its characteristic impedance Source • The reflection coefficient,  is defined as Zc

푉푟 Г = Line = Zc 푉푓 • Boundary conditions: o  = -1 short circuit , full negative reflection o Vr  = 0 perfectly matched, no reflection Vf o  = 1 open circuit, full positive reflection

 Zd Zd Zc

A. Nassiri PHY 862 Accelerator Systems 32 Reflection • Forward and reflected waves are in phase

푉푚푎푥 = 푉푓 + 푉푟 Source Zc = 푉푓 + Г푉푓 = 1 + Г 푉푓 Line = Zc Full reflection: 푉푚푎푥 = 2 푉푓 • When the waves are 180 out of phase 푉푚푖푛 = 푉푓 − 푉푟 = 푉푓 − Г푉푓 = 1 − Г 푉푓 Full reflection: 푉푚푎푥 = 0

V Vf 푉푚푎푥 1 + Г r V푆푊푅 = = 푉푚푖푛 1 − Г Zd

A. Nassiri PHY 862 Accelerator Systems 33 Reflection

• In case of a full reflection Vmax = 2 Vf (Pmax equivalent to 4 Pf)

Pf • One needs to protect the RF power Pr amplifiers if Pr > Prmax o Not always possible or may not be desirable since it may impact operation Swift protection if Pr

A. Nassiri PHY 862 Accelerator Systems 34 Circulator • Protect from this reflected power o passive non-reciprocal three-port device o signal entering any port is transmitted only to the next port in rotation

• The best place to insert it is close to the reflection source

o Lines between circulator and DUT will see 4xPf if fully reflected.

o A load for Pf is needed on port 3 to absorb Pr Vf Vf

Vr

Vr

Load

A. Nassiri PHY 862 Accelerator Systems 35 Circulator

• Even in case of full reflection Vmax = 2 Vf (Pmax equivalent to 4 Pf) o RF power amplifiers will not see reflected power and will not be affected

o Lines between circulator and DUT MUST at least be designed for 4 Pf

o Loads must be designed for Pf 4Pf Pf

Pf

Load

36 A. Nassiri PHY 862 Accelerator Systems Limitations of Microwave Tubes • Performance is limited by a number of factors including: o Heat dissipation o Voltage breakdown o Output window failure o Multipactor discharge • The RF structures and the windows of microwave tubes generally scale inversely with frequency. • The maximum CW or average power that can be handled by a particular type of tube depends upon the maximum temperature that the internal surfaces can be allowed to reach. • This temperature is independent of the frequency, so the power that can be dissipated varies inversely with the frequency. • can handle a higher power of the same frequency than klystrons because they have simpler structures and, if operated in a higher order mode, their structures are larger for a given frequency. • The power is also limited by the power that can be generated by an and formed into a beam. The beam diameter scales inversely with frequency and the beam current density is determined by the maximum attainable magnetic focusing field. • Since the field is independent of frequency the beam current scales inversely with the square of the frequency A. Nassiri PHY 862 Accelerator Systems 37 Limitations of Microwave Tubes • The beam voltage is related to the current by the gun perveance 푰 which typically in the ൗ푽ퟏ.ퟓ range of 1.0 to 2.0 for power tubes. • The maximum gun voltage is limited by the breakdown field in the gun and therefore varies inversely with frequency for constant perveance. • The maximum power obtainable from a tube is  푓−2.5 푡표 −3.0 depending on the assumptions made. • The efficiencies of tubes tend to fall with increasing frequency. This is partly because the RF losses increase with frequency and partly because of the design compromises that must be made at higher frequencies. • The maximum power obtainable from a pulsed tube is often determined by the power-handling capability of the output window. The output window of an external cavity klystron is in the form of a cylinder within the cavity and close to the output gap. This arrangement is limited to powers of about 70 kW. At higher power levels integral cavities are used and the power is brought out through waveguide or coaxial line windows. • Very high power klystrons commonly have two windows in parallel to handle the full output power. • Windows can be destroyed by excessive reflected power, by arcs in the output waveguide, by X-ray bombardment, and by the multipactor discharges described in the next Section. The basic cause of failure is overheating and it is usual to monitor the window temperature and to provide reverse power and waveguide and cavity arc detectors. A. Nassiri PHY 862 Accelerator Systems 38 Power Handling – Coaxial Line • The coaxial transmission line supports a TEM mode which has no cut-off frequency, that is, coax can be used down to d.c. This mode, in which the electric field is radial and the magnetic field azimuthal, has phase velocity and characteristic impedance given by

• Coaxial transmission lines for high-power transmission are commonly available in 50  and 75  characteristic impedances, the former representing a compromise between breakdown field strength and power handling capacity, and the latter being selected for minimum attenuation. The ratio b/a is fixed by the characteristic impedance of the line at 2.3 for the 50 line and 3.49 for the 75  line. Propagation on a coaxial line is as exp j(t −z) where = + j • The loss parameter is given by a b

A. Nassiri PHY 862 Accelerator Systems 39 Power Handling – Coaxial Line • The average power carried on a coaxial line depends on the peak electric field

• As a reference, the breakdown electric field strength in dry air at standard pressure and temperature is 3 MV/m. • Higher-order modes (TE and TM modes) can propagate in coax at higher frequencies, and one wants to avoid these modes because mode conversion from TEM to TE or TM modes represents a source of power loss. The cut off wavenumber for the mode with the lowest cut off frequency, the TE11 mode, is approximately given by

A. Nassiri PHY 862 Accelerator Systems 40 Coaxial Line – A numerical Example • Let us consider a 500 MHz power system using a rigid, air-filled, 75 aluminum 14 inch outer diameter outer conductor transmission line. The radii of the outer and inner conductors are then a = 51 mm and 7 b = 178 mm. Neglecting higher order waveguide mode effects and cu= 5.8× 10 mhos/m and Al = 7 −1 −3 3.5 × 10 mhos/m, so that the surface resistances are 푅푎= 휎푐푢훿푐푢 =5.8 × 10  per square and −1 −3 푅푏= 휎퐴퐿훿퐴퐿 =7.5 × 10  per square. The attenuation constant is:

• The power handling capacity ( w/o any corrections) is

• The cut-off wavenumber is:

A. Nassiri PHY 862 Accelerator Systems 41 Coaxial Line – A numerical Example

• Thus we would not want to use this particular coaxial line much above 400 MHz, for example. Raising the TE11 cut-off frequency to 550 MHz for the same characteristic impedance would require a = 41 mm and b=142 mm will yield . and a maximum average power of 155 MW.

A. Nassiri PHY 862 Accelerator Systems 42 Standard Waveguide Characteristics

WG designation Dimensions TE10 mode Cut-off frq. (MHz) Cut-off (inches) operating range wavelength (cm) WR2300 23.0  11.5 320 – 490 256 116.84 WR2100 21.0  10.5 350 – 530 281 106.68 WR1800 18.0  9.0 410 – 625 328 91.44 WR1500 15.0  7.5 490 – 750 393 76.20 WR1150 11.5  5.75 640 – 960 513 58.42 WR975 9.75  4.875 750 – 1120 605 49.53 WR770 7.7 3.85 960 – 1450 766 39.12 WR650 6.50  3.25 1200 – 1700 908 33.02

A. Nassiri PHY 862 Accelerator Systems 43 Standard Waveguide Characteristics

Attenuation constant for a 14 inch coaxial line and WR1800 WG.

A. Nassiri PHY 862 Accelerator Systems 44 Standard Waveguide Characteristics

Attenuation constant vs frequency for standard WGs.

A. Nassiri PHY 862 Accelerator Systems 45 Rectangular Waveguide

• Standard rectangular waveguides have aspect ratios close to 2:1, but reduced-height waveguides are sometimes used for special purposes. The propagation constant in rectangular waveguide is given by

where the cut-off wavenumber kc = /a and the cut-off frequency fc = c/2a for the lowest mode of propagation. In this mode, the TE10 (or H10) mode, the electric field is normal to the broad wall and the magnetic field is parallel to the broad wall. Assuming that b = a/2 the attenuation constant is found to be

and the maximum power is

A. Nassiri PHY 862 Accelerator Systems 46 Rectangular Waveguide • Higher order waveguide modes are also a consideration in using rectangular waveguides. For the conventional choice of a 2 : 1 aspect ratio in the transverse dimensions, the first higher order mode is the TE20 mode (H20 mode), for which the cut-off frequency is just twice the cut-off frequency of the dominant TE10 mode (H10 mode). Common practice is to use a rectangular waveguide with a ±20% bandwidth about a center frequency which is 1.5 times the waveguide cut-off frequency. Roughly put, one operates in a band from approximately 1.25 fc to 1.90 fc. • In 200 MHz – 400 MHz, where one might want to choose either coaxial transmission line for its more compact size, or a waveguide for its lower attenuation, one must bear in mind both attenuation and power-handling capacity. • Consider the high-power transmission system before for a WR1800 WG made of Al with a = 18 inches, the attenuation constant is:

Max. power is

A. Nassiri PHY 862 Accelerator Systems 47 Rectangular Waveguide

• So operating at 500 MHz, choosing a waveguide over a coax is obvious. • In order to avoid higher order waveguide mode losses, the diameter of the coax must be reduced, leading to higher attenuation and lower power-handling capacity as shown above. For short distances of transmission, however, the higher losses of coaxial transmission lines may be acceptable.

A. Nassiri PHY 862 Accelerator Systems 48 Derivation of attenuation constant in coaxial line

• For a coaxial line with inner radius a and outer conductor radius b, the electric and magnetic fields of the dominant TEM mode are given by

where 0 is the characteristic impedance of free space. Corresponding to these field quantities one can calculate the integrated quantities of voltage and current

and

where the voltage and the current on the inner conductor are positive for positive E

A. Nassiri PHY 862 Accelerator Systems 49 Derivation of attenuation constant in coaxial line • Ration of V/I gives characteristic impedance of the coaxial line

• Poynting vector for this mode is

• Integrating over the cross sectional area of the line yields power flow:

A. Nassiri PHY 862 Accelerator Systems 50 Derivation of attenuation constant in coaxial line

• If the inner conductor is made of a material with conductivity a, and a is the skin depth, then Ra is −1 the surface resistance (a a ) of the inner conductor, so the power dissipated in this conductor in a length g = 2/b = 0 = c/f is

which is time-independent. So the power dissipated/length in the inner conductor is

A. Nassiri PHY 862 Accelerator Systems 51 Derivation of attenuation constant in coaxial line

• The outer conductor may be made of a material different from that of the inner conductor. For example, the inner conductor is most often made of copper, while the outer conductor may be made of aluminum to save weight (at a slight increase in attenuation per unit length). If the conductivity of the outer conductor is b, the power dissipated per unit length turns out to be:

• The attenuation constant (TEM mode) is given

A. Nassiri PHY 862 Accelerator Systems 52 Dominant mode in rectangular waveguide

• The fields of the H10 (TE10) mode in a rectangular waveguide [width a and height b (usually b = a/2)] are given by

where and

A. Nassiri PHY 862 Accelerator Systems 53 Dominant mode in rectangular waveguide • Poynting vector for this mode

A. Nassiri PHY 862 Accelerator Systems 54 Dominant mode in rectangular waveguide

• The power dissipated on one side wall in WG, g , is

A. Nassiri PHY 862 Accelerator Systems 55 Dominant mode in rectangular waveguide

• The power dissipated on top wall in WG of g , is

A. Nassiri PHY 862 Accelerator Systems 56 Dominant mode in rectangular waveguide

• The power dissipated in a length g (including top, bottom, and 2 sides) is

Thus the power dissipated per unit length is

For b=a/2

 1/, 푓  푓

A. Nassiri PHY 862 Accelerator Systems 57 Dominant mode in rectangular waveguide

• Note

o The contribution to the loss per unit length attributable to the transverse wall currents (arising from Hz) decreases with increasing frequency as −3/2

o The contribution from the longitudinal currents (arising from Hx) increases with increasing frequency as 1/2  ( for   c ). o This suggests that a mode inducing only transverse wall currents would have wall losses that decrease with increasing frequency. Such a mode is the H01 (TE01) mode in circular waveguide. o This mode has been the subject of considerable attention for many years for its potential for low-loss transmission. The fact that it is a higher order mode means that any imperfection in the waveguide will result in energy being converted from the desired H01 mode into other propagating modes, thus providing an energy loss mechanism other than Joule heating. • The attenuation constant is calculated ( for the case when b=a/2)

We used

A. Nassiri PHY 862 Accelerator Systems 58