Abstract
This study analyzes the performance of a coaxialwaveguide gyrotron backwardwave oscillator (gyroBWO) operating at the fundamental harmonic by considering mode competition, which may be attributed to higherorder axial modes and competing transverse modes. In the coaxial waveguide with a short length and uniform cross section, the threshold currents of the higherorder axial modes are substantially higher than the operating current. Additionally, when the beam voltage or the magnetic field is adjusted, the oscillation that neighbors the minimum startoscillation current of a transverse mode has a positive field profile, and is excited near the cutoff frequency. As a result, the distributed wall losses at the downstream end of the interaction structure effectively damp the positive field, and raise significantly the minimum startoscillation currents of the competing transverse modes. This study also investigates how the parameters, including lossy section length, outer wall resistivity, inner wall resistivity, and ratio of the outer radius to the inner radius, affect the startoscillation currents of the competing transverse modes in order to obtain stable operation conditions in the frequency tuning range. As is forecasted, when using a 15 A electron beam, the Kaband coaxial gyroBWO produces an output power of 137 kW and 3 dB bandwidth of 4.2% by magnetic tuning and an output power of 145 kW and 3dB bandwidth of 2.0% by beam voltage tuning.
The authors would like to thank the National Science Council of the Republic of China, Taiwan for financially supporting this research under Contract Nos. NSC 952221E346002 and NSC 992221E346003.
Professor Y. S. Yeh is thanked for his valuable discussions. Ted Knoy is appreciated for his editorial assistance.
I. INTRODUCTION
II. NUMERICAL METHOD AND SIMULATION MODEL
III. NUMERICAL RESULTS
IV. CONCLUSIONS
Key Topics
 Magnetic fields
 20.0
 Copper
 8.0
 Cyclotron resonances
 8.0
 Electrical resistivity
 7.0
 Gyrotrons
 5.0
Figures
(a) Projection of electron orbit (circle) on the crosssectional plane of the waveguide in the presence of a uniform magnetic field. Point O is the center of the coaxial waveguide. and are the inner and outer radii of the coaxial waveguide, respectively. Point A is the guiding center of the gyrating electron. Point B is the instantaneous position of the electron. and are the guidingcenter radius and the Larmor radius, respectively. (b) Schematic drawings of the coaxial gyroBWO with distributed wall losses.
(a) Projection of electron orbit (circle) on the crosssectional plane of the waveguide in the presence of a uniform magnetic field. Point O is the center of the coaxial waveguide. and are the inner and outer radii of the coaxial waveguide, respectively. Point A is the guiding center of the gyrating electron. Point B is the instantaneous position of the electron. and are the guidingcenter radius and the Larmor radius, respectively. (b) Schematic drawings of the coaxial gyroBWO with distributed wall losses.
diagram of the fundamental harmonic gyroBWO operating in the coaxialwaveguide mode (dotted point). The parabolas represent the transverse waveguide modes and the oblique lines denote the beamwave resonance lines. Parameters used are , velocity ratio , and . The radius ratio and the outer radius of the coaxial waveguide are 2.2 and 0.4258 cm, respectively.
diagram of the fundamental harmonic gyroBWO operating in the coaxialwaveguide mode (dotted point). The parabolas represent the transverse waveguide modes and the oblique lines denote the beamwave resonance lines. Parameters used are , velocity ratio , and . The radius ratio and the outer radius of the coaxial waveguide are 2.2 and 0.4258 cm, respectively.
Axial profiles of field amplitude (solid line), phase angle (dotted line), and beam energy deposition rate (dashed line) for the first three axial modes of at their startoscillation currents . Parameters used are , , , , , , and .
Axial profiles of field amplitude (solid line), phase angle (dotted line), and beam energy deposition rate (dashed line) for the first three axial modes of at their startoscillation currents . Parameters used are , , , , , , and .
Dependence of coupling strength on normalized guidingcenter radius for the transverse modes that (a) corotate and (b) counterrotate with the electrons.
Dependence of coupling strength on normalized guidingcenter radius for the transverse modes that (a) corotate and (b) counterrotate with the electrons.
Startoscillation currents (solid line) and transit angles (dashed line) of the first three axial modes of the mode vs (a) magnetic field and (b) beam voltage . Parameters used are in (a), in (b), , , , , and .
Startoscillation currents (solid line) and transit angles (dashed line) of the first three axial modes of the mode vs (a) magnetic field and (b) beam voltage . Parameters used are in (a), in (b), , , , , and .
Startoscillation currents of the transverse modes vs (a) magnetic field and (b) beam voltage . Parameters used are the same as those in Fig. 5.
Startoscillation currents of the transverse modes vs (a) magnetic field and (b) beam voltage . Parameters used are the same as those in Fig. 5.
Startoscillation currents of the competing transverse modes vs (a) the inner wall resistivity and (b) the outer wall resistivity of the lossy section, where and are normalized to the resistivity of copper . Parameters used are in (a), in (b), , , , , , , , and , where is the grazing magnetic field of the respective mode.
Startoscillation currents of the competing transverse modes vs (a) the inner wall resistivity and (b) the outer wall resistivity of the lossy section, where and are normalized to the resistivity of copper . Parameters used are in (a), in (b), , , , , , , , and , where is the grazing magnetic field of the respective mode.
Startoscillation currents of the competing transverse modes vs the lossy section length in two cases: (a) the inner wall resistivity and (b) the outer wall resistivity . The other parameters are the same as those in Fig. 7.
Startoscillation currents of the competing transverse modes vs the lossy section length in two cases: (a) the inner wall resistivity and (b) the outer wall resistivity . The other parameters are the same as those in Fig. 7.
Startoscillation currents of the transverse modes vs (a) magnetic field and (b) beam voltage . The solid curves and the dashed curves represent cases of light losses and heavy losses, respectively. Although the other parameters are the same as those in Fig. 5, , , and for the case of heavy losses.
Startoscillation currents of the transverse modes vs (a) magnetic field and (b) beam voltage . The solid curves and the dashed curves represent cases of light losses and heavy losses, respectively. Although the other parameters are the same as those in Fig. 5, , , and for the case of heavy losses.
(a) Profile of the distributed losses. [(b)–(d)] Axial field profiles of the competing mode at , , and , where . The dashed curves and the solid curves represent cases with and without heavy losses, respectively. Parameters used are , , , , , , , , for the case of light losses, and for the case of heavy losses.
(a) Profile of the distributed losses. [(b)–(d)] Axial field profiles of the competing mode at , , and , where . The dashed curves and the solid curves represent cases with and without heavy losses, respectively. Parameters used are , , , , , , , , for the case of light losses, and for the case of heavy losses.
Startoscillation currents of the competing transverse modes vs (a) magnetic field and (b) beam voltage for (solid line) and (dashed line). Parameters used are in (a), in (b), , , , , and . for ; for .
Startoscillation currents of the competing transverse modes vs (a) magnetic field and (b) beam voltage for (solid line) and (dashed line). Parameters used are in (a), in (b), , , , , and . for ; for .
Calculated output power and oscillation frequency vs (a) magnetic field and (b) beam voltage . Parameters used are in (a), in (b), , , , , , , , and .
Calculated output power and oscillation frequency vs (a) magnetic field and (b) beam voltage . Parameters used are in (a), in (b), , , , , , , , and .
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