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TRANSCRIPT
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Lecture 3 Introduction
Moses Chung | Basics of RF Systems 2
• In general, charged particles are focused and bent by use of magnets, and accelerated by use of electromagnetic waves in cavities.
• DC acceleration is limited by high-voltage sparking and breakdown. It is very difficult to produce DC voltages more than a few million volts.
• RF accelerators bypass this limitation by applying a harmonic time-varying electric field to the beam, which is localized into bunches, such that the bunches always arrive when the field has the correct polarity (phase) for acceleration.
• The beam is accelerated within electromagnetic-cavity structures, in which a particular electromagnetic mode is excited from a high-frequency external power source.
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Moses Chung | Basics of RF Systems 3
DC Acceleration
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Moses Chung | Basics of RF Systems 4
RF Acceleration
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History: Not Yet a Cavity
Moses Chung | Basics of RF Systems 5
• Time-varying electric field is applied through transmission lines. The electrical
charges are actually travelling from one tube to the next by passing through the RF generator.
• The RF phase changes by 180º (π-mode), while the particles travel from one tube to the next.
• When using low frequencies, the length of the drift tubes becomes prohibitive for high-energy particles.
• When using high frequencies, the drift tubes would act more like antennas and radiate energy instead of using it for acceleration.
Wideröe
+ + + - - + + - -
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History: Tube Inside a Cavity
6
• The RF power is inductively coupled through a transformer consisting of a one turn primary inserted through the wall of the resonant tank containing the drift tubes.
• While the electric fields point in the “wrong direction” the particles are shielded by the drift tubes.
• The RF phases are same (0-mode), while the particles travel from one tube to the next.
Alvarez
Moses Chung | Basics of RF Systems
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Conditions for RF Acceleration
Moses Chung | Basics of RF Systems 7
• The wave must have an electric field component along the direction of particle motion.
– This condition is not satisfied by EM waves in free space, but can be satisfied by a transverse magnetic (TM) wave propagating in a uniform waveguide.
• For a sustained energy transfer and an efficient particle acceleration, the phase velocity of the wave must be closely matched to the beam velocity.
– This condition is not satisfied for a uniform waveguide, because the phase velocity 𝑣𝑝𝑝 > 𝑐.
– In periodically-loaded waveguide, reflections from the loading elements reduce the phase velocity.
• The distance between accelerating gaps (𝑙) is proportional to particle velocity.
– Here, we neglect the increase in 𝛽 inside the waveguide structure.
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Moses Chung | Basics of RF Systems 8
Block Diagram of RF Accelerator
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Moses Chung | Basics of RF Systems 9
Circuit Diagram of RF Accelerator
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Moses Chung | Basics of RF Systems 10
Real Pictures of RF Accelerator
~78%
~95%
LLRF
Wall Plug
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Moses Chung | Basics of RF Systems 11
Building Blocks of RF Systems
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Moses Chung | Basics of RF Systems 12
Hertz (Hz)
Heinrich Rudolf Hertz
IEEE Band
Frequency Range Origin of Name Wavelength in free
space (centimeters)
L 1 to 2 GHz L for "long" wave. 30.0 to 15.0
S 2 to 4 GHz S for "short" wave 15 to 7.5
C 4 to 8 GHz C for "compromise" between S and X band. 7.5 to 3.8
X 8 to 12 GHz Used in WW II for fire control, X for cross (as in crosshair). 3.8 to 2.5
Ku 12 to 18 GHz Ku for "kurz-under". 2.5 to 1.7
K 18 to 26 GHz German "kurz" means short, yet another reference to short wavelength. 1.7 to 1.1
Ka 26 to 40 GHz Ka for "kurz-above". 1.1 to 0.75
V 40 to 75 GHz V for "very" high frequency band (not to be confused with VHF). 0.75 to 0.40
W 75 to 110 GHz W follows V in the alphabet. 0.40 to 0.27
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decibel (dB)
Moses Chung | Basics of RF Systems 13
• Means of expressing large values via a logarithmic ratio.
• In RF and microwave systems, typical power and voltage ratios are expressed in dB.
• Sometimes, reference power is normalized to 1 mW.
• Attenuation is
Alexander Graham Bell
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Moses Chung | Basics of RF Systems 14
Connectors
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CW Power Sources
Moses Chung | Basics of RF Systems 15
• The two main categories are solid-state devices and vacuum tubes.
IOT: Inductive Output Tube SSPA: Solid State Power Amplifier
Class B PA: 50% of the input signal is used
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Pulsed Power Sources
Moses Chung | Basics of RF Systems 16
• Klystrons (>350 MHz) for electron linacs and modern proton linacs. RF distribution via waveguides.
• RF tube (<400 MHz) or solid state amplifiers for proton and heavy ion linacs. RF distribution via coaxial lines.
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Typical Klystron Operation
Moses Chung | Basics of RF Systems 17
• Decelerator: Amplify RF signals by converting the kinetic energy in a DC electron beam into radio frequency power. (velocity modulation bunching)
Cathode Collector
+ -
Modulator
Input Output
+ - + - + - + - Focusing
+ - Filament
Interlocks
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Typical Klystron Parameters
Moses Chung | Basics of RF Systems 18
• Power Gain 40-60 dB (104-106) • Power 103 to 107 Watts • Duty Cycle Continuous or Pulsed • Frequency Hundreds MHz to Tens GHz • Bandwidth 1% • Efficiency 50% • Cathode Volts 10’s to 100’s of kilovolts • Klystron Life 10,000-100,000 hours
Toshiba
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Typical Solid State Module
Moses Chung | Basics of RF Systems 19
• Solid state amplifiers are based on transistors instead of vacuum electron tubes as active device.
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Typical Solid State Parameters
Moses Chung | Basics of RF Systems 20
• Power Gain 20-70 dB (102-107) • Power 103 to 105 Watts • Duty Cycle Continuous or Pulsed • Frequency 1 MHz to 2 GHz • Bandwidth few % to decades % • Efficiency 10-50% • Supply Volts 20-50 volts DC • Life time 10,000-200,000 hours
Bruker
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Modulator
Moses Chung | Basics of RF Systems 21
• The modulators are locally and remotely controlled pulse generators that supply high-voltage pulses required for proper operation of high-power pulsed RF amplifiers.
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Pulse Forming
Moses Chung | Basics of RF Systems 22
Fast/High current switch
Fast/High current switch
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Moses Chung | Basics of RF Systems 23
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Power Transmission
Moses Chung | Basics of RF Systems 24
• Transmission lines transmit RF power from one point to another with minimum loss and external radiation of energy.
• Two common types: Rectangular waveguide type / Coaxial type
• Commonly used rectangular waveguides have an aspect ratio b/a of ~ 0.5.
Rigid line Hard line (Heliax)
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Moses Chung | Basics of RF Systems 25
6.50’’
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Moses Chung | Basics of RF Systems 26
• Coaxial cable is used for frequencies up to about 400 MHz and down to DC and waveguide at higher frequencies, where the loss is less than coaxial cable.
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Velocity of Propagation in a Coaxial Line
Moses Chung | Basics of RF Systems 27
• Typically, a coaxial cable will have a dielectric with relative dielectric constant 𝜖𝑟 between the inner and outer conductor, where 𝜖𝑟 = 1 for vacuum, and 𝜖𝑟 =2.29 for a typical polyethylene-insulated cable.
• For a polyethylene-insulated coaxial cable, the propagation velocity is roughly 2/3 the speed of light:
Ex] 1 nsec time delay in RG58 cable: ~ 19.8 cm
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Why 50 Ohms ?
Moses Chung | Basics of RF Systems 28
• The arithmetic mean between 30 ohms (best power handling) and 77 ohms (lowest loss) is 53.5, the geometric mean is 48 ohms. Thus the choice of 50 ohms is a compromise between power handling capability and signal loss per unit length, for air dielectric.
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Impedance Matching
Moses Chung | Basics of RF Systems 29
Radar works due to poor matching
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Moses Chung | Basics of RF Systems 30
Better matching (absorption) with the Stealth !
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Reflection Coefficient
Moses Chung | Basics of RF Systems 31
• Note that the generator has an internal impedance 𝑅. If 𝑅 = 𝑍0, the returning pulse is completely absorbed in the generator (Matched generator).
Short (𝑍𝐿 = 0)
Open (𝑍𝐿 → ∞)
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Moses Chung | Basics of RF Systems 32
RF Devices for Matching
Directional Coupler Three Stub Tuners
Waveguide Load
Circulator/Isolator
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LC Circuit to RF Cavity
Moses Chung | Basics of RF Systems 33
Beam
Shunt Impedance
Effectiveness of producing an axial voltage for a given power dissipated
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Methods of Coupling to Cavities
Moses Chung | Basics of RF Systems 34
• The coupling mechanism and the waveguide are represented by a transformer with a turns ratio of 1:n.
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Moses Chung | Basics of RF Systems 35
[Homework]
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Lecture 3 References
Moses Chung | Basics of RF Systems 36
• Basic Electromagnetism: – R. K. Wangsness, Electromagnetic Fields (Wiley, 1986) – J. D. Jackson, Classical Electrodynamics (Wiley, 1998)
• Beam and Accelerator Physics: – J. B. Rosenzweig, Fundamentals of Beam Physics (Oxford, 2003) – M. Conte and W. M. MacKay, An Introduction to the Physics of Particle Accelerators
(World Scientific, 2008) – T. P. Wangler, RF Linear Accelerators (Wiley, 2008)
• RF Technology:
– R. Pasquinelli and D. McGinnis, Microwave Measurements and Beam Instrumentation Lab. (USPAS, 2012)
– F. Gerigk, RF Basics I and II (CAS, 2013) – D. M. Pozar, Microwave Engineering (Wiley, 2012)
*Special thanks to USPAS director, Prof. William Barletta, who provides the USPAS lecture slides and allows me to reuse some of them for this lecture.