Average Microwave Voltage in Buncher Gap Calculator

✖Input Signal Amplitude is the maximum amplitude or peak value of the input signal, which is usually a sinusoidal signal, and is measured in units of volts or decibels relative to a reference level.ⓘ Input Signal Amplitude [V_in]			+10% -10%
✖Beam Coupling Coefficient is a measure of the interaction between an electron beam and an electromagnetic wave in a resonant cavity.ⓘ Beam Coupling Coefficient [β_i]			+10% -10%
✖Angular Frequency of a steadily recurring phenomenon expressed in radians per second.ⓘ Angular Frequency [ω]			+10% -10%
✖Entering Time refers to the instant at which an electron enters into the cavity.ⓘ Entering Time [t₀]			+10% -10%
✖Average transient angle is Stability of Paralleled Synchronous and Virtual Synchronous Generators in Islanded Microgrids.ⓘ Average Transient Angle [θ_g]			+10% -10%

✖Average microwave voltage is the average volt that the microwave uses.ⓘ Average Microwave Voltage in Buncher Gap [V_avg]

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Formula

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Average Microwave Voltage in Buncher Gap

Formula

`"V"_{"avg"} = "V"_{"in"}*"β"_{"i"}*sin("ω"*"t"_{"0"}+("θ"_{"g"}/2))`

Example

`"14.70728V"="50V"*"0.836"*sin("7.9e8rad/s"*"0.005s"+("30.38rad"/2))`

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Average Microwave Voltage in Buncher Gap Solution

STEP 0: Pre-Calculation Summary

Formula Used

Average Microwave Voltage = Input Signal Amplitude*Beam Coupling Coefficient*sin(Angular Frequency*Entering Time+(Average Transient Angle/2))
V_avg = V_in*β_i*sin(ω*t₀+(θ_g/2))
This formula uses 1 Functions, 6 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)

Variables Used

Average Microwave Voltage - (Measured in Volt) - Average microwave voltage is the average volt that the microwave uses.
Input Signal Amplitude - (Measured in Volt) - Input Signal Amplitude is the maximum amplitude or peak value of the input signal, which is usually a sinusoidal signal, and is measured in units of volts or decibels relative to a reference level.
Beam Coupling Coefficient - Beam Coupling Coefficient is a measure of the interaction between an electron beam and an electromagnetic wave in a resonant cavity.
Angular Frequency - (Measured in Radian per Second) - Angular Frequency of a steadily recurring phenomenon expressed in radians per second.
Entering Time - (Measured in Second) - Entering Time refers to the instant at which an electron enters into the cavity.
Average Transient Angle - (Measured in Radian) - Average transient angle is Stability of Paralleled Synchronous and Virtual Synchronous Generators in Islanded Microgrids.

STEP 1: Convert Input(s) to Base Unit

Input Signal Amplitude: 50 Volt --> 50 Volt No Conversion Required
Beam Coupling Coefficient: 0.836 --> No Conversion Required
Angular Frequency: 790000000 Radian per Second --> 790000000 Radian per Second No Conversion Required
Entering Time: 0.005 Second --> 0.005 Second No Conversion Required
Average Transient Angle: 30.38 Radian --> 30.38 Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_avg = V_in*β_i*sin(ω*t₀+(θ_g/2)) --> 50*0.836*sin(790000000*0.005+(30.38/2))

Evaluating ... ...

V_avg = 14.7072773033651

STEP 3: Convert Result to Output's Unit

14.7072773033651 Volt --> No Conversion Required

FINAL ANSWER

14.7072773033651 ≈ 14.70728 Volt <-- Average Microwave Voltage

(Calculation completed in 00.004 seconds)

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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

Average Microwave Voltage in Buncher Gap Formula

Average Microwave Voltage = Input Signal Amplitude*Beam Coupling Coefficient*sin(Angular Frequency*Entering Time+(Average Transient Angle/2))
V_avg = V_in*β_i*sin(ω*t₀+(θ_g/2))

What is Buncher Cavity Gap?

A buncher is an RF accelerator followed by a drift space. Its purpose is to bunch the dc ion source beam into suitable bunches for acceleration in a linac. The voltage in a simple buncher is a sine wave at the linac frequency.

How to Calculate Average Microwave Voltage in Buncher Gap?

Average Microwave Voltage in Buncher Gap calculator uses Average Microwave Voltage = Input Signal Amplitude*Beam Coupling Coefficient*sin(Angular Frequency*Entering Time+(Average Transient Angle/2)) to calculate the Average Microwave Voltage, The Average Microwave Voltage in Buncher Gap formula is defined as a periodic waveform whether it is a sine wave, square wave, or triangular waveform is defined as the quotient of the area under the waveform with respect to time. Average Microwave Voltage is denoted by V_avg symbol.

How to calculate Average Microwave Voltage in Buncher Gap using this online calculator? To use this online calculator for Average Microwave Voltage in Buncher Gap, enter Input Signal Amplitude (V_in), Beam Coupling Coefficient (β_i), Angular Frequency (ω), Entering Time (t₀) & Average Transient Angle (θ_g) and hit the calculate button. Here is how the Average Microwave Voltage in Buncher Gap calculation can be explained with given input values -> 14.70728 = 50*0.836*sin(790000000*0.005+(30.38/2)).

FAQ

What is Average Microwave Voltage in Buncher Gap?

The Average Microwave Voltage in Buncher Gap formula is defined as a periodic waveform whether it is a sine wave, square wave, or triangular waveform is defined as the quotient of the area under the waveform with respect to time and is represented as V_avg = V_in*β_i*sin(ω*t₀+(θ_g/2)) or Average Microwave Voltage = Input Signal Amplitude*Beam Coupling Coefficient*sin(Angular Frequency*Entering Time+(Average Transient Angle/2)). Input Signal Amplitude is the maximum amplitude or peak value of the input signal, which is usually a sinusoidal signal, and is measured in units of volts or decibels relative to a reference level, Beam Coupling Coefficient is a measure of the interaction between an electron beam and an electromagnetic wave in a resonant cavity, Angular Frequency of a steadily recurring phenomenon expressed in radians per second, Entering Time refers to the instant at which an electron enters into the cavity & Average transient angle is Stability of Paralleled Synchronous and Virtual Synchronous Generators in Islanded Microgrids.

How to calculate Average Microwave Voltage in Buncher Gap?

The Average Microwave Voltage in Buncher Gap formula is defined as a periodic waveform whether it is a sine wave, square wave, or triangular waveform is defined as the quotient of the area under the waveform with respect to time is calculated using Average Microwave Voltage = Input Signal Amplitude*Beam Coupling Coefficient*sin(Angular Frequency*Entering Time+(Average Transient Angle/2)). To calculate Average Microwave Voltage in Buncher Gap, you need Input Signal Amplitude (V_in), Beam Coupling Coefficient (β_i), Angular Frequency (ω), Entering Time (t₀) & Average Transient Angle (θ_g). With our tool, you need to enter the respective value for Input Signal Amplitude, Beam Coupling Coefficient, Angular Frequency, Entering Time & Average Transient Angle 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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