ECE 662

1. ECE 662 Introduction to High-Power Microwave Sources and Electron Beams March 10-24, 2005

3. Peak-Power vs Average Power Domains for Microwave Productionref: High Power Microwave Sources and Technologies, ed. Barker and Schamiloglu

4. Power vs Frequency for solid-state and Vacuum Electronics Microwave devices Ref: The Microwave Engineering Handbook (vol. 1) ed. Smith ( 1993)

5. Dominant Vacuum and solid-state power Source TechnologiesRef: Applications of high-Power Microwaves, ed. Gaponov-Grekhov and Granatstein

6. Historical Evolution of Microwave Tubes Ref: Granatstein High-Power Microwave Sources (1987)

7. Results of Microwave generation experiments using intense relativistic electron beams; peak power vs. wavelengthRef: Applications of high-Power Microwaves, ed. Gaponov-Grekhov and Granatstein

8. 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

9. 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/BPIN and Tf<< B

10. 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

11. 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. <100 MW)

12. 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

13. 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:

15. 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.

16. Electron Beam Spreading

17. 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 besolved to produce the universal beam spreading curve. The beam will have a nearly uniform density across its cross section.

18. The Universal Beam Spreading Curve

19. A Uniform Axial Magnetic Field Leading to a Brillouin Flow

20. 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)

21. 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.

22. The Planar Diode • Four Distinct Emission Conditions • Cathode at x=0 (V=0), Anode at x=d (V=Va) • Cathode is cold-electrons emitted at negligible rate

23. 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.

24. 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.

25. 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.

26. The Planar Diode • Treat the case of the onset of “Space Charge Limited” case.

27. The Planar Diode

28. The Planar Diode

29. The Planar Diode • Another form for the potential • Curve shown earlier for space charge limited case

30. 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

31. 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:

32. Plasma Frequency or Space Charge Oscillations

33. Electron Cyclotron Frequency