Plasma Frequency Calculator

✖DC Electron Charge Density refers to the measure of the density of free electrons in a material or a medium in a steady state or DC (direct current) condition.ⓘ DC Electron Charge Density [ρ_o]

+10%

-10%

✖Plasma frequency is the frequency at which the response of a plasma is dominated by the motion of free electrons, rather than by the slower motion of ions or other species in the plasma.ⓘ Plasma Frequency [f_p]

⎘ Copy

👎

Formula

✖

Plasma Frequency

Formula

`"f"_{"p"} = sqrt(("[Charge-e]"*"ρ"_{"o"})/("[Mass-e]"*"[Permitivity-vacuum]"))`

Example

`"1.4E^6rad/s"=sqrt(("[Charge-e]"*"10e-11C/m³")/("[Mass-e]"*"[Permitivity-vacuum]"))`

Calculator

LaTeX

Reset

👍

Download Microwave Tubes and Circuits Formula PDF

Plasma Frequency Solution

STEP 0: Pre-Calculation Summary

Formula Used

Plasma Frequency = sqrt(([Charge-e]*DC Electron Charge Density)/([Mass-e]*[Permitivity-vacuum]))
f_p = sqrt(([Charge-e]*ρ_o)/([Mass-e]*[Permitivity-vacuum]))
This formula uses 3 Constants, 1 Functions, 2 Variables

Constants Used

[Permitivity-vacuum] - Permittivity of vacuum Value Taken As 8.85E-12
[Charge-e] - Charge of electron Value Taken As 1.60217662E-19
[Mass-e] - Mass of electron Value Taken As 9.10938356E-31

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Plasma Frequency - (Measured in Radian per Second) - Plasma frequency is the frequency at which the response of a plasma is dominated by the motion of free electrons, rather than by the slower motion of ions or other species in the plasma.
DC Electron Charge Density - (Measured in Coulomb per Cubic Meter) - DC Electron Charge Density refers to the measure of the density of free electrons in a material or a medium in a steady state or DC (direct current) condition.

STEP 1: Convert Input(s) to Base Unit

DC Electron Charge Density: 1E-10 Coulomb per Cubic Meter --> 1E-10 Coulomb per Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f_p = sqrt(([Charge-e]*ρ_o)/([Mass-e]*[Permitivity-vacuum])) --> sqrt(([Charge-e]*1E-10)/([Mass-e]*[Permitivity-vacuum]))

Evaluating ... ...

f_p = 1409740.13822234

STEP 3: Convert Result to Output's Unit

1409740.13822234 Radian per Second --> No Conversion Required

FINAL ANSWER

1409740.13822234 ≈ 1.4E+6 Radian per Second <-- Plasma Frequency

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Electronics » Microwave Theory » Microwave Tubes and Circuits » Beam Tube » Plasma Frequency

Credits

Created by Shobhit Dimri

Bipin Tripathi Kumaon Institute of Technology (BTKIT), Dwarahat

Shobhit Dimri has created this Calculator and 900+ more calculators!

Verified by Urvi Rathod

Vishwakarma Government Engineering College (VGEC), Ahmedabad

Urvi Rathod has verified this Calculator and 1900+ more calculators!

< 20 Beam Tube Calculators

Microwave Voltage in Buncher Gap

Go Microwave Voltage in the Buncher Gap = (Amplitude of Signal/(Angular Frequency of Microwave Voltage*Average Transit Time))*(cos(Angular Frequency of Microwave Voltage*Entering Time)-cos(Resonant Angular Frequency+(Angular Frequency of Microwave Voltage*Buncher Gap Distance)/Velocity of Electron))

RF Output Power

Go RF Output Power = RF Input Power*exp(-2*RF Attenuation Constant*RF Circuit Length)+int((RF Power Generated/RF Circuit Length)*exp(-2*RF Attenuation Constant*(RF Circuit Length-x)),x,0,RF Circuit Length)

Repeller Voltage

Go Repeller Voltage = sqrt((8*Angular Frequency^2*Drift Space Length^2*Small Beam Voltage)/((2*pi*Number of Oscillation)-(pi/2))^2*([Mass-e]/[Charge-e]))-Small Beam Voltage

Total Depletion for WDM System

Go Total Depletion for a WDM System = sum(x,2,Number of Channels,Raman Gain Coefficient*Channel Power*Effective Length/Effective Area)

Average Power Loss in Resonator

Go Average Power Loss in Resonator = (Surface Resistance of resonator/2)*(int(((Tangential Magnetic Intensity Peak Value)^2)*x,x,0,Radius of resonator))

Plasma Frequency

Go Plasma Frequency = sqrt(([Charge-e]*DC Electron Charge Density)/([Mass-e]*[Permitivity-vacuum]))

Total Energy Stored in Resonator

Go Total Energy Stored in Resonator = int((Permittivity of Medium/2*Electric Field Intensity^2)*x,x,0,Resonator Volume)

Skin Depth

Go Skin Depth = sqrt(Resistivity/(pi*Relative Permeability*Frequency))

Carrier Frequency in Spectral Line

Go Carrier Frequency = Spectral Line Frequency-Number of Samples*Repetition Frequency

Total Electron Beam Current Density

Go Total Electron Beam Current Density = -DC Beam Current Density+Instantaneous RF Beam Current Perturbation

Total Electron Velocity

Go Total Electron Velocity = DC Electron Velocity+Instantaneous Electron Velocity Perturbation

Total Charge Density

Go Total Charge Density = -DC Electron Charge Density+Instantaneous RF Charge Density

Power Obtained from DC Power Supply

Go DC Power Supply = Power Generated in Anode Circuit/Electronic Efficiency

Power Generated in Anode Circuit

Go Power Generated in Anode Circuit = DC Power Supply*Electronic Efficiency

Reduced Plasma Frequency

Go Reduced Plasma Frequency = Plasma Frequency*Space Charge Reduction Factor

Maximum Voltage Gain at Resonance

Go Maximum Voltage Gain at Resonance = Transconductance/Conductance

Return Loss

Go Return Loss = -20*log10(Reflection Coefficient)

Rectangular Microwave Pulse Peak Power

Go Pulse Peak Power = Average Power/Duty Cycle

AC Power Supplied by Beam Voltage

Go AC Power Supply = (Voltage*Current)/2

DC Power Supplied by Beam Voltage

Go DC Power Supply = Voltage*Current

Plasma Frequency Formula

Plasma Frequency = sqrt(([Charge-e]*DC Electron Charge Density)/([Mass-e]*[Permitivity-vacuum]))
f_p = sqrt(([Charge-e]*ρ_o)/([Mass-e]*[Permitivity-vacuum]))

What is Plasma Density?

The term Plasma Density refers to the concentration or count of ionized gas particles in a given volume.

How to Calculate Plasma Frequency?

Plasma Frequency calculator uses Plasma Frequency = sqrt(([Charge-e]*DC Electron Charge Density)/([Mass-e]*[Permitivity-vacuum])) to calculate the Plasma Frequency, The Plasma frequency formula is defined as the frequency at which the response of a plasma is dominated by the motion of free electrons, rather than by the slower motion of ions or other species in the plasma. Plasma Frequency is denoted by f_p symbol.

How to calculate Plasma Frequency using this online calculator? To use this online calculator for Plasma Frequency, enter DC Electron Charge Density (ρ_o) and hit the calculate button. Here is how the Plasma Frequency calculation can be explained with given input values -> 1.4E+6 = sqrt(([Charge-e]*1E-10)/([Mass-e]*[Permitivity-vacuum])).

FAQ

What is Plasma Frequency?

The Plasma frequency formula is defined as the frequency at which the response of a plasma is dominated by the motion of free electrons, rather than by the slower motion of ions or other species in the plasma and is represented as f_p = sqrt(([Charge-e]*ρ_o)/([Mass-e]*[Permitivity-vacuum])) or Plasma Frequency = sqrt(([Charge-e]*DC Electron Charge Density)/([Mass-e]*[Permitivity-vacuum])). DC Electron Charge Density refers to the measure of the density of free electrons in a material or a medium in a steady state or DC (direct current) condition.

How to calculate Plasma Frequency?

The Plasma frequency formula is defined as the frequency at which the response of a plasma is dominated by the motion of free electrons, rather than by the slower motion of ions or other species in the plasma is calculated using Plasma Frequency = sqrt(([Charge-e]*DC Electron Charge Density)/([Mass-e]*[Permitivity-vacuum])). To calculate Plasma Frequency, you need DC Electron Charge Density (ρ_o). With our tool, you need to enter the respective value for DC Electron Charge Density and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search