Reply To: Proliferation?

[Joseph Chikva]

You are absolutely right worrying about two-stream instability. That is issue of given Concept.
But this type of instability is more critical for electron-electron streams interaction and less for electron-ion or ion-ion.

Applications of the two-stream instability to plasma heating involve high-power-density relativistic beams. We have found that the growth of the two-stream instability depends on changes in the axial velocity of beam particles. Because a relativistic beam travels near the speed of light variations of kinetic energy cause only small changes of axial velocity. Therefore, bunching takes place slowly for a relativistic beam.

Stanley Humphries, Jr., Charged Particle Beams, Originally published in1990 by John Wiley and Sons
Also:

Instability of relativistic electron beam with strong magnetic field Zhijing Liu, H. L. Berk and Xiantu He

http://www.springerlink.com/content/q61nq245w64h35p5/

Annotation

Stability criteria for a weak relativistic beam-plasma interaction in a strong magnetic field are found. Two beam modes occur,ω≈k zC andω≈k zC-ωc. The dispersion equation of electrostatic two-stream is exactly solved with analytical method.

Also:

Two-stream instability in the presence of longitudinal magnetic field, El-Labany, S. K.; El-Hanbaly, A. M.

http://adsabs.harvard.edu/abs/1989Ap&SS.153…75E

Abstract

A multiple scales perturbation theory has been applied to investigate the nonlinear behavior of beam-plasma system near a marginally stable state in the presence of longitudinal magnetic field. The perturbation method leads to a nonlinear Schroedinger equation for the finite amplitude. The coefficients of this equation show that only if the beam is compressed isothermally can there exist a range of wavenumbers for which stabilization might occur. The stable region increases with the applied magnetic field.

Commonly, strong longitudinal mag field, high relativistic factors, absence of electron-electron streams interaction and some consultations with very skilled experts allow me to be sure on this type of instability too.

In a given sample I have kinetic energy difference equal to 150keV, but center-of-mass collision energy is equal only to 30keV. Yes, this will create transverse momentums depending on impact parameter the value of which is probabilistic. But scattered particle will return back to the axis then oscillating around that. During oscillation only part of radial (transverse) momentums will be transferred to electron gas. Electron oscillations will be damped thanks to Bremsstrahlung. And certain thermal equilibrium will occur.

Mentioning your pressure estimation 4.7*10^8 Pa except number density you should also know temperature as well. And you do not. At least I did not say yet. Recall that Ohmic heating of plasma is more effective at low collision energies and less effective at high. And we initially will have high collision energy that should then be kept comparatively constant thanks to externally applied electric field.
We will have 444’000 Amperes of circulated current and combined beam’s diameter about 5mm. Before calculating of kinetic pressure can we calculate mag field yet? And its pressure?