Two-Cavity Klystron Amplifier Virtual Laboratory

01 Learning Objectives

Velocity Modulation

Understand how the input cavity modulates electron beam velocity based on RF signal amplitude.

Electron Bunching

Analyze the formation of electron bunches in the drift space due to velocity differences.

Power & Gain

Measure output power and calculate power gain as functions of beam voltage and input power.

02 Theoretical Background

Operating Principle

The two-cavity klystron is a velocity-modulated amplifier. The electron beam emitted from the cathode passes through:

1 Buncher Cavity: Input RF signal creates alternating fields that accelerate/decelerate electrons (velocity modulation).
2 Drift Space: Faster electrons catch up to slower ones, forming bunches (density modulation).
3 Catcher Cavity: Bunched beam induces current, delivering amplified RF power to load.

Key Equations

DC Electron Velocity:

v₀ = 0.593 × 10⁶ × √V₀ [m/s]

Bunching Parameter:

X = (π × M × V₁ × L) / (v₀ × d)

where M = beam coupling coefficient, L = drift length

Output Power:

P_out = 2 × I₀ × V₀ × J₁(X) × M

J₁ = Bessel function of first kind

Schematic Diagram

Buncher Gap Velocity modulation occurs here. Electrons are accelerated or decelerated based on RF phase.

Catcher Gap Energy extraction occurs here. Bunched beam induces current in output cavity.

03 Interactive Simulation

Parameters

Beam Voltage (V₀) 400 V

300V 600V

Input RF Power (P_in) 10 mW

1mW 50mW

Drift Length (L) 2.5 cm

1cm 5cm

Beam Current (I₀) 25 mA

Results

Electron Velocity 11.86 × 10⁶ m/s

Bunching Param (X) 1.84

Output Power 245 mW

Power Gain 13.9 dB

Efficiency 2.45%

Electron Bunching Animation

Distance along beam axis →

Fast e⁻

Slow e⁻

Cathode Buncher Drift Space Catcher Collector

Output Power vs. Beam Voltage

Power Gain vs. Input Power

Applegate Diagram (Velocity vs. Distance)

Shows electron trajectories forming bunches at specific drift distances

04 Experimental Procedure

Experiment 1: Beam Voltage vs. Output Power

Determine the optimum beam voltage for maximum power transfer

Steps:

Set Input Power to 10 mW and Drift Length to 2.5 cm
Vary Beam Voltage from 300V to 600V in steps of 50V
Record Output Power and calculate Power Gain at each step
Plot Output Power vs. Beam Voltage curve
Identify the voltage at which maximum bunching occurs (J₁(X) maximum)

Expected Observation:

Output power varies periodically with voltage due to changing transit angle. Maximum power occurs when bunching parameter X ≈ 1.84 (first maximum of J₁(X)).

X = (ω × L) / (2 × v₀) × (V₁/V₀)

Experiment 2: Input Power vs. Gain (Linearity)

Analyze the small-signal gain characteristics

Steps:

Set Beam Voltage to 400V (optimal from Exp. 1)
Vary Input Power from 1 mW to 50 mW
Calculate Power Gain (dB) at each input level
Identify the linear region and saturation point
Calculate 1dB compression point

Analysis:

At low input powers, gain remains constant (linear region). As input increases, gain decreases (saturation) due to over-bunching and Bessel function rolloff.

Experiment 3: Drift Length Optimization

Study the effect of drift space on bunching efficiency

Fix Beam Voltage at 400V and Input Power at 10 mW
Vary Drift Length from 1 cm to 5 cm
Observe the Applegate diagram changes
Record the drift length for optimum bunching at the catcher cavity

05 Lab Report Guidelines

Required Contents

Aim and theoretical background of velocity modulation
Tabulated data for all three experiments with calculated values
Graphs: P_out vs V₀, Gain vs P_in, Efficiency vs Beam Voltage
Applegate diagram sketch showing bunching formation
Calculation of electronic efficiency and beam coupling coefficient

Key Questions for Discussion

Q1: Why does output power vary periodically with beam voltage?

Consider the transit angle and Bessel function dependence.

Q2: What limits the maximum theoretical efficiency?

Hint: Maximum value of J₁(X) is 0.582 at X=1.84.

Q3: How does drift length affect the operating frequency?

Consider the relationship between bunching time and RF period.