. The Bell System technical journal . because the radius of the rolling circle, its angularfrequency of rotation, and the velocity of its center, for the epicycloid,all approximate those for the cycloid of the plane case. These approxima-tions improve with increasing ratio of cathode to anode radii. Severalelectron orbits in a DC cylindrical magnetron are shown in Fig. 4 for severalmagnetic fields. 176 BELL SYSTEM TECHNICAL JOURNAL It is clear from this simplified picture of the orbits in a DC cylindricalmagnetron without space charge, that, at a given electric field, an electronorbit for a su
. The Bell System technical journal . because the radius of the rolling circle, its angularfrequency of rotation, and the velocity of its center, for the epicycloid,all approximate those for the cycloid of the plane case. These approxima-tions improve with increasing ratio of cathode to anode radii. Severalelectron orbits in a DC cylindrical magnetron are shown in Fig. 4 for severalmagnetic fields. 176 BELL SYSTEM TECHNICAL JOURNAL It is clear from this simplified picture of the orbits in a DC cylindricalmagnetron without space charge, that, at a given electric field, an electronorbit for a sufficiently strong magnetic field may miss the anode completelyand return to the cathode. The critical magnetic field at which this is justpossible is called the cut-off value, Be. For a given voltage between cathodeand anode, as the magnetic field is increased, the current normally passedby the device falls rather abruptly at 5c. A current versus magnetic fieldcurve, together with electron orbits corresponding to four regions of the. Fig. 4.—Electron paths in a cylindrical DC magnetron at several magnetic fields aboveand below the cut-off value, Be. The electrons are assumed to be emitted from the cathodewith zero initial velocity. curve, are shown in Fig. 5. For the case of parallel plane electrodes, thecut-off relation between the critical anode potential, Fc, and magnetic , and the electrode separation, d, for the parallel plane case, is obtainedby equating the electrode separation to the diameter of the rolling , d = \d)BV 2 -t -f 1-, from which F. = eBtd2m MAGNETRON AS GENERATOR 01 CENTIMETER WAVES 177 For the cylindrical case, the relation may be shown to be (8) -■■•-ff--(;;)■]■ in terms of cathode and anode radii, r< and fa- 2. Types of Magnetron Oscillators Definitions: The DC magnetron may be converted into an oscillator,suitable for the generation of centimeter waves, by introducing RF fields intothe anode-cathode region. This may
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