An investigation is made of the non-relativistic motion of a charged particle (in a plasma) in an external rotating electromagnetic field of the form: Hx = H0 cos (ωy/c) cos ωt, Hy = H0 cos (ωx/c) sin ωt, Hz = constant, Ex = Ey = 0, Ez = H0 [sin (ωx/c) cos ωt + sin (ωy/c) sin ωt], with ωx/c ≪ 1 and ωy/c ≪ 1. If the condition −1 < (eHz/mcω) < −1 + (eH0/mcω)2 is satisfied, then the particle moves away from the Z-axis. The particle energy is ∼H02e22/(mc2k) in °K where is the average distance from the Z-axis.The motion of the plasma is then investigated taking into account its proper electromagnetic field. The following transport equation is used: nm + v ∇⋅v = nq (E + v × H/c) − ∇ψ − nm∇φ + p. The assumptions are: a plasma consisting of equal populations of electrons and deuterons with density ∼1015/cm3, ω ≤ 1010/sec, H0 ∼ 103 G, ν ≤ 0.1 c. At t = 0 it is assumed that T = 106 °K and ν = 0 and that the derivatives of the plasma density with respect to the space variables are negligible compared to other terms of the transport equation. An expansion in powers of ν/c is used. Zeroth, first and second order approximations are calculated using the Laplace transformation. Up to the second order of approximation, the field causes neither a durable change in plasma density nor a charge separation.Oscillations of four different frequencies appear in the plasma. At a definite frequency of the rotating field there appears a resonance phenomenon in which the amplitude of oscillation increases linearly with t. At resonance the mean energy per ion (in °K) transferred directly to the ionic part of the plasma increases with time as follows: (1/192 π2) (e2m/c4M4k) (H04Hz2/n02) t2. This means, for example, that in an axial field of 104G and a rotating field of amplitude 103G, the time necessary to provide energy corresponding to 108 °K (disregarding losses) is ∼0.3 sec.