Single particle behavior in plasmas Page: 20 of 31
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-8-
which will appear many times at this college, we can write down the
result of applying this method to eliminating the gyrorotation from the
equations of motion of a charged particle (3.1). These are the well
known drift-equations: (Morozov and Soloviev, 1966).
= v + ( g x ) + m x (6.e)-9 + x 78 (3.13)
t e6 2eB
de a t " e + me2 a8
dt dt 28 at
dt
where the energy of the realivistic particle is a = moc3/(C 2 - ve2 + n!)1/2
or, for a non-relativistic particle k _ (_2 . "y). .. .trae tnat,-to
tnis order, the perpendicular velocity is determined by the constant af
the motion, the adiabatic invariant %n. When V xi = 0 the magnetic drifts
are of the same form and we get
dl + f)
t= v + Gf ( l x + (e VB8)(2v + v.) (3.14)
8 2eB
One essential assumption in the derivation was that E < v B/c. If we
allow for a large drift-velocity, vE 2 c the equations are modified
to
- +(U-')- x B + B x aB (3.15)
c = E v+v+rE4), v. +'E
The second term in (3.15) is the drift due to the inertial effect of the
large electric drift. These drift equations are very useful in determining -
the dynamics of a plasma on time scales long compared with the cyclotron
period. Jn some cases the drift equations themselves will deSCribe a still
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McNamara, B. Single particle behavior in plasmas, report, March 10, 1977; Livermore, California. (https://gateway.okhistory.org/ark:/67531/metadc1055867/m1/20/?q=%22~1~1~1%22~1: accessed July 16, 2024), The Gateway to Oklahoma History, https://gateway.okhistory.org; crediting UNT Libraries Government Documents Department.