Assume to have a relativistic electron beam. First of all, can the beam treated as an electron plasma? If yes, how its plasma frequency can be calculated? This electron beam has specified characteristics (total current, relativistic factor gamma) and it is confined under an external magnetic field.
Can anyone calculates the electron beam plasma frequency using the classical formula which involves the plasma density? And if yes, how in this case the electron number density can be calculated?
Any references will be appreciated.
Dear Dimitrios,
The electron beam can be considered as a plasma , if it satisfies the properties of a plasma like quasi-neutrality. Which happens when the ion or electron beam is space charge compensated, particularly under low energy beam transport. In this case one can calculate plasma density by classical formula.
In your case the beam is relativistic and i don't think it can be regarded as a plasma .
You can read the literature on plasma lens in intense beam transport .
So, a relativistic beam in a vacuum tube (that is what I'm interested in) cannot be considered as plasma in any case. I can't understand the reason for this no-consideration if the beam is relativistic.
What are you trying to do? Neglecting the B-field, the plasma frequency is essentially /screening length, where refers to the mean **RANDOM MOTION ** speed
It is related to screening effects
So sure you can calculate a plasma frequency. What are you going to use it for will determine whether you use it correctly or not.
you know the relativistic factor so calculate the velocity (usuali the beam are considered like no vel. spread....you need the size of the beam and that's it
Dear Dimitrios,
It is not simple. The classical formula for determination of plasma frequency from plasma components are complicated. If you have beam with compensation of space charge, potentially you can take concentration of electrons in your beam. The reason is simple: you use electron beam for ionization of gas and kinetic of production of ion determines by cross section of ionization of electrons with your kinetic energy for electron beam. But, when you created plasma and you have compensation of space charge of beam, you can point, that you have concentration of ions relative same with concentration of electrons, You can calculate plasma frequency based on concentration of electrons in yours beams. Good luck!! Let me know final results of your experiments? I have questions: Why do want to know plasma frequency? What is current of your electron beam and what is relativistkii factor of your electron beam or what is kinetic energy of yours electron beam. The Bennet's condition gives correction on the compensation of space charge from relativistkiii factor ( gamma= 1+ Energy of beam/ rest energy of electron beam = 0,510 MeV=510 KeV). We made a lot of experiments with transport of beam across plasma channels for compensation of space charge of electron beam and my opinion, that if you study propagation of electron beam in plasma, much better to make plasma in the dielectric pipe and make injection of beam to channel with plasma. Efficiency of propagation is high in compare with creation of plasma by electron beam ionization. The ionization processes are not simple and are not stable in time. Again, good luck.
Thank you for all the answers. As I can see the problem is rather complicated and depends on each situation
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