Phase Constant of Fundamental Mode Field Solution

STEP 0: Pre-Calculation Summary
Formula Used
Phase Constant for N-cavities = (2*pi*Number of Oscillation)/(Mean Distance Between the Cavities*Number of Resonant Cavities)
βo = (2*pi*M)/(L*N)
This formula uses 1 Constants, 4 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Phase Constant for N-cavities - Phase Constant for N-cavities is the constant phase in total present.
Number of Oscillation - Number of Oscillation refers to the occurrence of the oscillation.
Mean Distance Between the Cavities - (Measured in Meter) - Mean distance between the cavities is defined as the average distance between the cavity of the resonator.
Number of Resonant Cavities - Number of resonant cavities is defined as structure that supports standing waves at particular resonant frequencies, and can be used in various electromagnetic devices.
STEP 1: Convert Input(s) to Base Unit
Number of Oscillation: 4 --> No Conversion Required
Mean Distance Between the Cavities: 261.7 Millimeter --> 0.2617 Meter (Check conversion here)
Number of Resonant Cavities: 16 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
βo = (2*pi*M)/(L*N) --> (2*pi*4)/(0.2617*16)
Evaluating ... ...
βo = 6.00227866562819
STEP 3: Convert Result to Output's Unit
6.00227866562819 --> No Conversion Required
FINAL ANSWER
6.00227866562819 6.002279 <-- Phase Constant for N-cavities
(Calculation completed in 00.004 seconds)

Credits

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Bipin Tripathi Kumaon Institute of Technology (BTKIT), Dwarahat
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14 Klystron Cavity Calculators

Average Microwave Voltage in Buncher Gap
Go Average Microwave Voltage = Input Signal Amplitude*Beam Coupling Coefficient*sin(Angular Frequency*Entering Time+(Average Transient Angle/2))
Maximum Input Voltage in Two Cavity Klystron
Go Maximum Input Voltage in Two Cavity Klystron = (2*Reflex Klystron Voltage*Bunching Parameter)/(Beam Coupling Coefficient*Average Transient Angle)
Average Distance between Cavities
Go Mean Distance Between the Cavities = (2*pi*Number of Oscillation)/(Phase Constant for N-cavities*Number of Resonant Cavities)
Phase Constant of Fundamental Mode Field
Go Phase Constant for N-cavities = (2*pi*Number of Oscillation)/(Mean Distance Between the Cavities*Number of Resonant Cavities)
Magnitude of Microwave Signal at Input Cavity
Go Magnitude of Microwave Signal = (2*Cathode Buncher Voltage*Bunching Parameter)/(Beam Coupling Coefficient*Angular Variation)
Velocity Modulation of Electrons in Klystron Cavity
Go Velocity Modulation = sqrt((2*[Charge-e]*High DC Voltage)/[Mass-e])
Conductance of Resonator
Go Conductance of Cavity = (Capacitance at Vane Tips*Angular Frequency)/Unloaded Q-factor
Beam Coupling Coefficient in Two Cavity Klystron
Go Beam Coupling Coefficient = sin(Average Transient Angle/2)/(Average Transient Angle/2)
Number of Resonant Cavities
Go Number of Resonant Cavities = (2*pi*Number of Oscillation)/Phase Shift in Magnetron
Induced Current in Catcher Cavity
Go Induced Catcher Current = Current Arriving at Catcher Cavity Gap*Beam Coupling Coefficient
Buncher Cavity Gap
Go Buncher Cavity Gap = Average Transit Time*Electron Uniform Velocity
Induced Current in Walls of Catcher Cavity
Go Induced Catcher Current = Beam Coupling Coefficient*Direct Current
Average Transit Angle
Go Average Transient Angle = Angular Frequency*Average Transit Time
Average Transit Time
Go Average Transit Time = Buncher Cavity Gap/Velocity Modulation

Phase Constant of Fundamental Mode Field Formula

Phase Constant for N-cavities = (2*pi*Number of Oscillation)/(Mean Distance Between the Cavities*Number of Resonant Cavities)
βo = (2*pi*M)/(L*N)

What is Resonant Cavity?

A conducting surface enclosing a space in which an oscillating electromagnetic field can be maintained, the dimensions of the cavity determine the resonant frequency of the oscillation.

How to Calculate Phase Constant of Fundamental Mode Field?

Phase Constant of Fundamental Mode Field calculator uses Phase Constant for N-cavities = (2*pi*Number of Oscillation)/(Mean Distance Between the Cavities*Number of Resonant Cavities) to calculate the Phase Constant for N-cavities, Phase Constant of Fundamental Mode Field refers to the phase shift experienced by the electric field of the mode as it propagates through a transmission line or waveguide. Phase Constant for N-cavities is denoted by βo symbol.

How to calculate Phase Constant of Fundamental Mode Field using this online calculator? To use this online calculator for Phase Constant of Fundamental Mode Field, enter Number of Oscillation (M), Mean Distance Between the Cavities (L) & Number of Resonant Cavities (N) and hit the calculate button. Here is how the Phase Constant of Fundamental Mode Field calculation can be explained with given input values -> 6.002279 = (2*pi*4)/(0.2617*16).

FAQ

What is Phase Constant of Fundamental Mode Field?
Phase Constant of Fundamental Mode Field refers to the phase shift experienced by the electric field of the mode as it propagates through a transmission line or waveguide and is represented as βo = (2*pi*M)/(L*N) or Phase Constant for N-cavities = (2*pi*Number of Oscillation)/(Mean Distance Between the Cavities*Number of Resonant Cavities). Number of Oscillation refers to the occurrence of the oscillation, Mean distance between the cavities is defined as the average distance between the cavity of the resonator & Number of resonant cavities is defined as structure that supports standing waves at particular resonant frequencies, and can be used in various electromagnetic devices.
How to calculate Phase Constant of Fundamental Mode Field?
Phase Constant of Fundamental Mode Field refers to the phase shift experienced by the electric field of the mode as it propagates through a transmission line or waveguide is calculated using Phase Constant for N-cavities = (2*pi*Number of Oscillation)/(Mean Distance Between the Cavities*Number of Resonant Cavities). To calculate Phase Constant of Fundamental Mode Field, you need Number of Oscillation (M), Mean Distance Between the Cavities (L) & Number of Resonant Cavities (N). With our tool, you need to enter the respective value for Number of Oscillation, Mean Distance Between the Cavities & Number of Resonant Cavities and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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