2003 I 2
From QED
The radial electric field may be found by Poisson's equation:
Since :
The radial force balance is:
Using Vθ = ωrr, , , and the result from part a:
Writing this in standard quadratic form:
The quadratic formula gives:
Rearranging:
Using ωc = eB0 / mc, :
The maximum density that can be confined is where the ωr becomes imaginary. Looking at eq. 2, this occurs at:
Plugging in for everything:
Solving for :
For this value of .
The self-electric field energy is:
Dividing by :
The rotational kinetic energy is:
Dividing by :
This page was recovered in October 2009 from the Plasmagicians page on Generals_2003_I_2 dated 00:50, 7 May 2007.