Average Distance between Cavities Calculator

✖Number of Oscillation refers to the occurrence of the oscillation.ⓘ Number of Oscillation [M]			+10% -10%
✖Phase Constant for N-cavities is the constant phase in total present.ⓘ Phase Constant for N-cavities [β_o]			+10% -10%
✖Number of resonant cavities is defined as structure that supports standing waves at particular resonant frequencies, and can be used in various electromagnetic devices.ⓘ Number of Resonant Cavities [N]			+10% -10%

✖Mean distance between the cavities is defined as the average distance between the cavity of the resonator.ⓘ Average Distance between Cavities [L]

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Formula

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Average Distance between Cavities

Formula

`"L" = (2*pi*"M")/("β"_{"o"}*"N") `

Example

`"261.7994mm"=(2*pi*"4")/("6"*"16") `

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Average Distance between Cavities Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mean Distance Between the Cavities = (2*pi*Number of Oscillation)/(Phase Constant for N-cavities*Number of Resonant Cavities)
L = (2*pi*M)/(β_o*N)
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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 Oscillation - Number of Oscillation refers to the occurrence of the oscillation.
Phase Constant for N-cavities - Phase Constant for N-cavities is the constant phase in total present.
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
Phase Constant for N-cavities: 6 --> No Conversion Required
Number of Resonant Cavities: 16 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L = (2*pi*M)/(β_o*N) --> (2*pi*4)/(6*16)

Evaluating ... ...

L = 0.261799387799149

STEP 3: Convert Result to Output's Unit

0.261799387799149 Meter -->261.799387799149 Millimeter (Check conversion here)

FINAL ANSWER

261.799387799149 ≈ 261.7994 Millimeter <-- Mean Distance Between the Cavities

(Calculation completed in 00.004 seconds)

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Created by Shobhit Dimri

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

Average Distance between Cavities Formula

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

Average Distance between Cavities calculator uses Mean Distance Between the Cavities = (2*pi*Number of Oscillation)/(Phase Constant for N-cavities*Number of Resonant Cavities) to calculate the Mean Distance Between the Cavities, The Average Distance between Cavities formula is defined as the average distance between the cavity of the resonator. Mean Distance Between the Cavities is denoted by L symbol.

How to calculate Average Distance between Cavities using this online calculator? To use this online calculator for Average Distance between Cavities, enter Number of Oscillation (M), Phase Constant for N-cavities (β_o) & Number of Resonant Cavities (N) and hit the calculate button. Here is how the Average Distance between Cavities calculation can be explained with given input values -> 261799.4 = (2*pi*4)/(6*16) .

FAQ

What is Average Distance between Cavities?

The Average Distance between Cavities formula is defined as the average distance between the cavity of the resonator and is represented as L = (2*pi*M)/(β_o*N) or Mean Distance Between the Cavities = (2*pi*Number of Oscillation)/(Phase Constant for N-cavities*Number of Resonant Cavities). Number of Oscillation refers to the occurrence of the oscillation, Phase Constant for N-cavities is the constant phase in total present & 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 Average Distance between Cavities?

The Average Distance between Cavities formula is defined as the average distance between the cavity of the resonator is calculated using Mean Distance Between the Cavities = (2*pi*Number of Oscillation)/(Phase Constant for N-cavities*Number of Resonant Cavities). To calculate Average Distance between Cavities, you need Number of Oscillation (M), Phase Constant for N-cavities (β_o) & Number of Resonant Cavities (N). With our tool, you need to enter the respective value for Number of Oscillation, Phase Constant for N-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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