Repeller Voltage Calculator

Repeller Voltage Formula:

\[ V_r = \sqrt{\frac{8 \cdot \omega^2 \cdot L_{ds}^2 \cdot V_o}{\left(2\pi M - \frac{\pi}{2}\right)^2 \cdot \frac{m_e}{e}}} - V_o \]

Angular Frequency (ω):

rad/s

Drift Space Length (L_ds):

Small Beam Voltage (V_o):

Number of Oscillation (M):

Repeller Voltage (V_r):

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1. What is Repeller Voltage?

Repeller Voltage refers to the voltage applied to a repeller electrode in a vacuum tube. The repeller voltage is typically negative with respect to the cathode voltage and is used to control electron beam behavior in electronic devices.

2. How Does the Calculator Work?

The calculator uses the Repeller Voltage formula:

\[ V_r = \sqrt{\frac{8 \cdot \omega^2 \cdot L_{ds}^2 \cdot V_o}{\left(2\pi M - \frac{\pi}{2}\right)^2 \cdot \frac{m_e}{e}}} - V_o \]

Where:

\( V_r \) — Repeller Voltage (V)
\( \omega \) — Angular Frequency (rad/s)
\( L_{ds} \) — Drift Space Length (m)
\( V_o \) — Small Beam Voltage (V)
\( M \) — Number of Oscillation
\( m_e \) — Mass of electron (9.10938356×10^-31 kg)
\( e \) — Charge of electron (1.60217662×10^-19 C)

Explanation: This formula calculates the repeller voltage required for specific electron beam behavior based on angular frequency, drift space length, beam voltage, and number of oscillations.

3. Importance of Repeller Voltage Calculation

Details: Accurate repeller voltage calculation is crucial for proper operation of vacuum tubes, electron beam devices, and particle accelerators. It ensures optimal electron beam control and device performance.

4. Using the Calculator

Tips: Enter angular frequency in rad/s, drift space length in meters, small beam voltage in volts, and number of oscillation as a positive integer. All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a repeller electrode used for?
A: A repeller electrode is used in vacuum tubes to repel electrons back toward the cathode, controlling electron flow and beam behavior in electronic devices.

Q2: Why is the repeller voltage typically negative?
A: The repeller voltage is negative relative to the cathode to create a repelling electric field that pushes electrons back, controlling their movement in the device.

Q3: What applications use repeller voltage calculations?
A: This calculation is used in klystrons, traveling wave tubes, particle accelerators, and other electron beam devices where precise beam control is required.

Q4: How does angular frequency affect repeller voltage?
A: Higher angular frequencies generally require higher repeller voltages to maintain proper electron beam synchronization and oscillation patterns.

Q5: What are typical values for repeller voltage?
A: Repeller voltage values vary widely depending on the specific device and application, ranging from a few volts to several thousand volts in different electronic systems.