Can electromagnetic wave cause a charged particle to move with constant velocity? I'm reading through Kleppner and Kolenkow's Introduction to Mechanics (2nd ed), and in it, they go through the example of an electron subject to an oscillating electric field (example 1.11). The example and the math is straightforward, but at the end of the explanation, they say:
Here is the problem statement:
The ionosphere is a region of electrically neutral gas, composed of positively charged ions and negatively charged electrons, that surrounds the Earth at a height of approximately 200 km (120 mi). If a radio wave passes through the ionosphere, its electric ﬁeld accelerates the charged particles. Because the electric ﬁeld oscillates in time, the charged particles tend to jiggle back and forth. The problem is to ﬁnd the motion of an electron of charge−e and mass m which is initially at rest, and which is suddenly subjected to an electric ﬁeld E = $E_0$ sinωt (ω is the frequency of oscillation in radians/second).
And the evaluation portion (the italicized one) writes:
RESULT: The electron is initially at rest, $x_0$ = $v_0$ = 0, so we have x(t) = ($a_0$/ω) t − ($a_0$/$ω^2$) (sinωt). 
The result is interesting: the second term oscillates and corresponds to the jiggling motion of the electron that we predicted. The ﬁrst term, however, corresponds to motion with uniform velocity, so in addition to the jiggling motion the electron starts to drift away. Can you see why?
I'm not sure I'm able to see why, as they say. I understand that the drift comes as a result of the integration step. If you double integrate a sine, you have a constant term that then becomes the drift term, but I'm not seeing an "aha" explanation as they seem to suggest. I feel like I'm missing an insight that they are referring to. Am I?
 A: 
The ﬁrst term, however, corresponds to motion with uniform velocity, so in addition to the jiggling motion the electron starts to drift away. Can you see why?

It's all to do with velocity.
The particle initially moves away with a positive force on it until the force has completed half it's cycle and then the force becomes negative.
But by the time the force becomes negative the electron has already acquired a forward momentum which will not be reversed during the negative cycle !
All the negative part of the force cycle can do is slow it down, but it will always have a positive velocity until right at the end of the complete cycle, when velocity becomes zero again (at which point we start another cycle and repeat this process).
So averaged over every complete cycle it always has a non-negative velocity and on average this moves it forward and is the reason for that linear term in the displacement equation.
A: The net displacement of the electron will be due to the resultant of the two terms in the equation. The net effect of the two terms in the displacement equation (first linear term and the second oscillating term) is only oscillating.
So the electron only jiggles about the original place and there would not be ant net drifting.
A: Just a minor point. If the velocity was constant, there would be a frame in which it was at rest. If you want a truly constant velocity, that would correspond to a temperature of $0$ K. That isn't possible. If nothing else, thermal motion of the moving charges that set up the field will prevent you from setting up an ideal field. However nothing prevents you from getting close.
Aside from that, as Stephen G says, the field you are thinking of leaves the charge oscillating. On the face of it, nothing prevents the amplitude of the oscillations from being $0$. But if nothing else does, thermal motion will. This doesn't mean thermal motion of a single charge trapped in the field. The charge had thermal motion when it entered the field.
If you reduce thermal motion far enough, the fields confine the charge. The uncertainty principle limits how small you can make the momentum of a confined charge.
