A conventional magnetron has Anode Voltage = 26 kV, Beam Current = 29 A, B0 = 0.336 wb/m2, Radius of cathode cylinder = 5 cm, Radius of vane edge to center = 10 cm. (A) The cyclotron angular frequency ωc = 5.91 × 106 rad Choose the most appropriate answer from the options given below :
(B) ωc = 5.91 × 1010 rad
(C) ωc = 5.91 × 1016 rad
(D) Cut off voltage = 139.50 kV
(E) Cut off voltage = 239.59 kV
(B) and (D) Only
The cyclotron frequency is a one-line calculation, and it alone separates the options.
Step 1 — the cyclotron angular frequency. An electron in a magnetic field circles at
\(\omega_{c}=\dfrac{eB_{0}}{m}\)
\(=\dfrac{1.6\times10^{-19}\times0.336}{9.11\times10^{-31}}=\dfrac{5.376\times10^{-20}}{9.11\times10^{-31}}=5.90\times10^{10}\ \text{rad/s}\)
— statement (B). Note that the answer depends only on the flux density; the anode voltage, beam current and radii play no part in it whatever. Statements (A) and (C) are the same figure with the exponent wrong by four and six orders of magnitude, so this one calculation eliminates options 1, 3 and 4 and leaves option 2.
Step 2 — the Hull cut-off voltage. This is the anode voltage below which the magnetic field bends every electron back before it reaches the anode:
\(V_{c}=\dfrac{e}{8m}B_{0}^{2}a^{2}\left(1-\dfrac{b^{2}}{a^{2}}\right)^{2}\)
with a the anode radius and b the cathode radius. The ratio term is the same on any consistent length units:
\(\left(1-\dfrac{b^{2}}{a^{2}}\right)^{2}=\left(1-0.25\right)^{2}=0.5625\)
and \(\dfrac{e}{8m}B_{0}^{2}=2.1954\times10^{10}\times0.112896=2.4785\times10^{9}\).
A note on the arithmetic, stated plainly. Taking the printed 10 cm literally, \(a^{2}=0.01\ \text{m}^{2}\) and the formula gives about 13.9 MV. The printed value of 139.50 kV is reproduced exactly by taking the radii as 10 mm and 5 mm instead, that is \(a^{2}=10^{-4}\):
\(V_{c}=2.4785\times10^{9}\times10^{-4}\times0.5625=1.394\times10^{5}=139.4\ \text{kV}\)
So the question's dimensions are inconsistent by a factor of ten, but (D) is the intended value and (E) matches no reading at all. The cyclotron frequency settles the answer independently, so the ambiguity does not affect the choice.
Why both quantities matter in a magnetron. The device oscillates only when the anode voltage is below cut-off, so that electrons curve back and form the rotating spokes of space charge that exchange energy with the resonant cavities. The cyclotron frequency sets the timescale of that circular motion, and the cavities are dimensioned so their resonance matches the spoke rotation.
Hence, the correct statements are (B) and (D).
Similar Questions
There are three general purpose microwave tubes. The first is ordinary gridded tube, having electrodes like vacuum tube diode and triodes. The second type are those in which interaction between the electron beam and RF field takes place. The klystron is the example of the second type of microwave tubes. The third category of the device is one in which interaction between an RF field and electron beam is continuous. TWT (Travelling Wave Tube) is the example of this category.
Read the paragraph and answer the questions :
Microwave tubes are used as microwave amplifiers and oscillators. Three general type of microwave tubes in which third type tubes are important because in these tubes there is an interaction between an electron and an RF field is continuous. The Travelling Wave Tube (TWT) is the prime example of this interaction. It is an amplifier, whose oscillator counter part is called Backward Wave Oscillator (BWO). The second sub-group consists of tubes in which a magnetic field ensures a constant electron beam – RF field interaction, and this is complemented by the Cross-Field Amplifier (CFA). Multicavity Klystron is used as high and very high power amplifiers in the UHF and microwave ranges. The frequency range covered is from about 250 MHz to over 95 GHz. The reflex-Klystron is a low power microwave oscillator. It is assumed that oscillations are started by switching transients. For oscillations to be maintained the transient time in the repeller space cycle is given as \(T=\left(n+\dfrac{3}{4}\right)\) where n is an integer, each value of n is said to correspond to different reflex klystron mode. Reflex Klystrons with integral cavities are available in the frequency range 4 to 200 GHz.
The correct sequence of sub-systems of Klystron amplifiers as they appear in the direction of flow of electron beam is
Assertion (A) : TWTA is a narrow band device and has a helical structure and it is used as amplifier and oscillator.
Reason (R) : In TWT, the electron beam travels through a slow-wave structure and speed of electron beam is \(\dfrac{1}{10}\) of the velocity of light.
The primary function of the helix in a travelling wave tube is to
The Multicavity Klystron
One of the reasons why vacuum tubes eventually fail at microwave frequencies is that their
Indicate the false statement. Klystron amplifiers may use intermediate cavities to
One of the following is unlikely to be used as a pulsed device. It is the
In a two cavity Klystron the secondary cavity is called
Important Questions from Microwave Engineering
Which of the following frequency bands fall under microwave frequency?
The primary reason behind identically zero magnetic field outside a coaxial cable is:
Semiconductor diode used in switching circuits at Microwave range is
One of the following microwave diodes is suitable for very low power oscillator only.
A uniformly spaced linear array of identical radiators having uniform amplitude of excitation and linear phase variation with non-zero gradient will produce
