The Motion of Electrons Between Coaxial Cylinde Under the Influence of Current Along the Axis

Current from a large electrically heated filament to a coaxial cylindrical anode, limited by the circular magnetic field.---(1) Motion of the electrons. Richardson has shown that if the filament current is sufficiently large (or the plate voltage too small), its magnetic field should prevent electrons reaching the anode. The equation for the critical plate voltage is here derived in a simpler and more general form which holds for any degree of space charge. Electrons leaving the filament are deflected in the direction of the electron current in the wire and describe paths which are found, by approximate integration of the equations of motion, to be somewhat elongated cycloids. The dimensions of the paths are calculated for typical cases. No electrons reach the anode unless the plate voltage is above ${V}_{c}=2(\frac{e}{m}){I}^{2}{[log(\frac{R}{{r}_{0}})]}^{2}$ (neglecting small terms which involve the initial velocities). The effect of space charge is to elongate the cycloidal paths, but in practical cases the effect is small. The effect of superposing an axial magnetic field $H$ is to add to ${V}_{c}$ the critical potential $V_{c}^{}{}_{}{}^{\ensuremath{'}}=\frac{1}{8}(\frac{e}{m}){H}^{2}{R}^{2}$ due to the field $H$ alone. This conclusion that the circular and axial magnetic fields act independently was fully verified experimentally. (2) Plate current as a function of voltage. Results for tubes with tungsten filaments 3/4 mm and 2.5 mm in diameter are given. The steep part of the curve points in each case to the theoretical critical voltage, but there is a foot extending to lower voltages, due to reflection and scattering of electrons. This foot is much less with a small anode (2.5 cm diam.) than with one four times the diameter. The reflection effect was directly proved with a special tube which enabled the current to various sections of the anode to be measured independently. If at a steep part of the curve an alternating plate voltage is superposed, the effective alternating current resistance is only about 35 ohms for a tube with 2.5 cm anode. (3) Plate current as a function of filament current. If the voltage is kept constant at a high enough value, and the filament current slowly increased, emission begins at a certain temperature and increases rapidly (temperature limited) and then decreases sharply to zero (magnetically limited). With a 2.5 mm filament in a 10 cm anode, for instance, for 800 volts potential the plate current is zero except for the range 130 to 200 amp., while for 1000 volts, it is zero except between 130 and 225 amp. With an alternating filament current the plate current is suppressed except during the part of each cycle when the instantaneous filament current is below the critical maximum. Thus the tube gives an intermittent unidirectional current of twice the frequency of the filament current. In a tube with filament 1 cm in diam. carrying 1600 amp. and anode 4.6 cm in diam. at 3100 volts, a plate current (space charge limited) of 45 amp. was completely controlled by the magnetic field of the filament current.Experiments with Pring tube containing filament and metal disk.---The explanation offered by Langmuir in 1913 that the decrease of electron emission with improvement in vacuum observed by Pring and Parker was due to charge on the glass walls, is verified.