PPPL-4155 is available in <a href="PPPL-4155.pdf">pdf</a> format (304 KB).

<p>
<b>An Exact Magnetic Moment Invariant of Charged Particle Gyromotion</b>
</p>

<p>
<b>Authors:</b> Hong Qin and Ronald C. Davidson
</p>

<p>
<b>Date of PPPL Report:</b> March 2006
</p>

<p>
<b>Submitted to:</b> Physical Review Letters</p>


<p>

For the motion of a charged particle in a uniform, time-dependent axial magnetic field &Beta;(t)e<sub>z</sub>, it is shown that there is an exact magnetic moment invariant of the particle dynamics M, to which the adiabatic magnetic moment invariant &mu; = mv<sup>2</sup><sub>&perp;</sub>/2B is asymptotic when the time-scale of the magnetic field variation is much slower than the gyro-period. The connection between the exact invariant M and the adiabatic invariant &mu; enables us to characterize in detail the robustness of the adiabatic magnetic moment invariant &mu;.







</p>