ECE 662

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ECE 662

• Introduction to
• High-Power
• Microwave Sources
• and Electron Beams
• March 10-24, 2005

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Peak-Power vs Average Power Domains for Microwave
Productionref High Power Microwave Sources and
Technologies, ed. Barker and Schamiloglu
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Power vs Frequency for solid-state and Vacuum
Electronics Microwave devices
Ref The Microwave Engineering Handbook (vol. 1)
ed. Smith ( 1993)
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Dominant Vacuum and solid-state power Source
Technologies Ref Applications of high-Power
Microwaves, ed. Gaponov-Grekhov and Granatstein
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Historical Evolution of Microwave Tubes Ref Gran
atstein High-Power Microwave Sources (1987)
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Results of Microwave generation experiments using
intense relativistic electron beams peak power
vs. wavelengthRef Applications of high-Power
Microwaves, ed. Gaponov-Grekhov and Granatstein
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Components to Generate High-Power Electromagnetic
Radiation
Rf
Diagnostics
Electron Sources
Wave-Particle Interactions
Accelerator
Beam Transport
Stability Vacuum Magnets Cooling Control systems
Marx generators Modulators Transmission
Lines Switching High Vacuum Thermionic Emission
Linear accelerators
Output Wave Structure
Beam Collection
Applications
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Another View of Energy Conversion - Rf System
DC Power P0(V0), ?P
Electron Kinetic Energy, KEB(eV0,IB, ?B)
PIN
Input DC
Diode Kinetic Energy (DC)
PRfin
Rf Structure Waveguide Cavity
Rf Power Generated at f(Tf)
PRf out
Rf Circuit
Conversion to Rf
PRf out ?B/Rf?D/B PIN and Tfltlt ?B
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Wave Particle Interaction

• Parametric Devices
• Klystrons, Free-electron Lasers
• Slow-Wave devices
• Magnetrons, Cerenkov Masers, backward wave
  oscillators
• Fast Wave Devices
• Cyclotron Resonant Masers (Gyrotrons)
• Plasma Devices
• Virtual Cathode Oscillators, Beam-Plasma
  Interactions Orbitrons

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Beam Sources

• Hot Cathode
• voltage Pulse applied across Cathode-Anode Gap
  and electrons are emitted from a hot
  (approximately 1000oC) cathode (Tungsten).
• electrons are accelerated in the gap to full
  energy
• temperature and space-charge limited operation
• Pulsed - DC
• moderated high power, high repetition rate
• period approx. 1 - 10 microsec. (many pulses/sec)
• voltage approximately 10 - 500 kV
• current approx. 1-200 A (Power approx. lt100 MW)

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Energy Exchange 1

• Interaction between 2 conceptual entities
• Normal electromagnetic modes of waveguides and
  cavities
• natural modes of oscillation of electron beams
• the two exist independently except at certain
  values of f (or ?) for which there is an exchange
  of energy resonantly.
• Waveguides act as ducts for propagating microwave
  radiation

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Energy Exchange - 2

• Waveguides of constant cross-section and long
  (end-effects neglected) then
• z (axial) dependence is exp (jkzz) where kz
  2?/? axial wavenumber, and ? wavelength along
  the axis of the waveguide.
• time dependence is exp (j?t), where ? 2?f
• ? and kz are related to one another by a
  so-called dispersion relation

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Electron Beam Spreading
Many microwave tubes use small-diameter electron
beams with high axial charge density. Such a
beam generates a radial field, which in the
absence of other fields causes the beam to spread.
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Electron Beam Spreading
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Beam Spreading w/o Neutralization
Without neutralization, the radial motion of the
outer edge of the beam as a result of the radial
electric field is described by the following
equation
If vz is constant this equation may be solved to
produce the universal beam spreading curve. The
beam will have a nearly uniform density across
its cross section.
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The Universal Beam Spreading Curve
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A Uniform Axial Magnetic Field Leading to a
Brillouin Flow
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Beams Space-Charge Waves and TWTs

• Energy Exchange
• Beam Spreading Brillouin Flow
• Relativistic Velocities
• Planar Diode (Space Charge Limited Condition
• Plasma Electron Cyclotron Frequencies
• Fast and Slow Space-Charge Waves
• Traveling Wave Tubes (TWT)

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For high-power microwave devices the voltages
typically are large in excess of tens and even
hundreds of kilovolts. Consequently, the question
arises about the need to consider relativistic
velocities.
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The Planar Diode

• Four Distinct Emission Conditions
• Cathode at x0 (V0), Anode at xd (VVa)
• Cathode is cold-electrons emitted at negligible
  rate

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The Planar Diode

• Temperature-Limited operation
• Raise cathode temperature ?small current flows,
  but every electron reaches the anode. So cathode
  temperature controls the current collected by the
  anode. Change in anode potential has little
  effect on current reaching the anode.

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The Planar Diode

• Onset of Space-Charge-Limited operation
• Raise cathode temperature further, such that
  there exists a sufficient number of electrons
  outside cathode to make the field at the cathode
  zero.

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The Planar Diode

• Space-Charge-Limited operation
• Raise cathode temperature further, the potential
  outside the cathode is depressed below the
  cathode potential. Electrons must have
  sufficient energy to overcome the depression to
  reach the anode.
• Current is now independent of temperature.

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The Planar Diode

• Treat the case of the onset of Space Charge
  Limited case.

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The Planar Diode
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The Planar Diode
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The Planar Diode

• Another form for the potential
• Curve shown earlier for space charge limited case

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The Planar Diode

• Typically, electron gun several ?pers
• without focusing, beam spreads
• apply strong axial magnetic field B0 to confine
  the flow.
• A confined flow of electrons is typically
  characterized by plasma cyclotron frequencies

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Plasma Frequency or Space Charge Oscillations
Consider a uniform electron gas of density, n or
charge density, ?. Let a one-dimensional
perturbation of the electrons occur so
that electrons at position x are displaced a
small amount x1. Now the local density changes
by
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Plasma Frequency or Space Charge Oscillations
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Electron Cyclotron Frequency