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Beam Coupling Coefficient in Two Cavity Klystron Formula

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Beam Coupling Coefficient is a measure of the interaction between an electron beam and an electromagnetic wave in a resonant cavity. Check FAQs

β i = \frac{\sin (\frac{θ g}{2})}{\frac{θ g}{2}}

β_i - Beam Coupling Coefficient?θ_g - Average Transient Angle?

Beam Coupling Coefficient in Two Cavity Klystron Example

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Here is how the Beam Coupling Coefficient in Two Cavity Klystron equation looks like with Values.

Here is how the Beam Coupling Coefficient in Two Cavity Klystron equation looks like with Units.

Here is how the Beam Coupling Coefficient in Two Cavity Klystron equation looks like.

0.0326 = \frac{\sin (\frac{30.38}{2})}{\frac{30.38}{2}}

0.0326 = \frac{\sin (\frac{30.38rad}{2})}{\frac{30.38rad}{2}}

0.0326 = \frac{\sin (\frac{30.38}{2})}{\frac{30.38}{2}}

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Beam Coupling Coefficient in Two Cavity Klystron Solution

Follow our step by step solution on how to calculate Beam Coupling Coefficient in Two Cavity Klystron?

FIRST Step Consider the formula

β i = \frac{\sin (\frac{θ g}{2})}{\frac{θ g}{2}}

Next Step Substitute values of Variables

∴

β i = \frac{\sin (\frac{30.38rad}{2})}{\frac{30.38rad}{2}}

Next Step Prepare to Evaluate

∴

β i = \frac{\sin (\frac{30.38}{2})}{\frac{30.38}{2}}

Next Step Evaluate

∴

β i = 0.0325945749394359

LAST Step Rounding Answer

∴

β i = 0.0326

Beam Coupling Coefficient in Two Cavity Klystron Formula Elements

Variables

Functions

Beam Coupling Coefficient

Beam Coupling Coefficient is a measure of the interaction between an electron beam and an electromagnetic wave in a resonant cavity.

Symbol: β_i

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Beam Coupling Coefficient

Average Transient Angle

Average transient angle is Stability of Paralleled Synchronous and Virtual Synchronous Generators in Islanded Microgrids.

Symbol: θ_g

Measurement: AngleUnit: rad

Note: Value can be positive or negative.

Formulas to find Average Transient Angle

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.

Syntax: sin(Angle)

Other formulas in Klystron Cavity category

Go Induced Current in Catcher Cavity

I 2 = I t0 \cdot β i

Go Buncher Cavity Gap

d = τ \cdot E vo

Go Induced Current in Walls of Catcher Cavity

I 2 = β i \cdot I o

Go Phase Constant of Fundamental Mode Field

β o = \frac{2 \cdot π \cdot M}{L \cdot N}

How to Evaluate Beam Coupling Coefficient in Two Cavity Klystron?

Beam Coupling Coefficient in Two Cavity Klystron evaluator uses Beam Coupling Coefficient = sin(Average Transient Angle/2)/(Average Transient Angle/2) to evaluate the Beam Coupling Coefficient, The Beam Coupling Coefficient in Two Cavity Klystron formula is defined as the degree to which the electrons undergo the process of velocity modulation. It is quite similar to the modulation index which determines the degree to which the carrier is modulated with respect to the message signal. Beam Coupling Coefficient is denoted by β_i symbol.

How to evaluate Beam Coupling Coefficient in Two Cavity Klystron using this online evaluator? To use this online evaluator for Beam Coupling Coefficient in Two Cavity Klystron, enter Average Transient Angle (θ_g) and hit the calculate button.

FAQs on Beam Coupling Coefficient in Two Cavity Klystron

What is the formula to find Beam Coupling Coefficient in Two Cavity Klystron?

The formula of Beam Coupling Coefficient in Two Cavity Klystron is expressed as Beam Coupling Coefficient = sin(Average Transient Angle/2)/(Average Transient Angle/2). Here is an example- 0.032595 = sin(30.38/2)/(30.38/2).

How to calculate Beam Coupling Coefficient in Two Cavity Klystron?

With Average Transient Angle (θ_g) we can find Beam Coupling Coefficient in Two Cavity Klystron using the formula - Beam Coupling Coefficient = sin(Average Transient Angle/2)/(Average Transient Angle/2). This formula also uses Sine (sin) function(s).

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