High-order harmonic generation
"Simple man's model"

Free electron motion, electron released at phase ϕ of driving field

d2 x/ d2 = - (e/m) E0 Cos[ω t + ϕ]
integrate to get velocity: 
vx[t] = - (e/m ω) E0 Sin[ω t + ϕ] + v0x = - v0 Sin[ω t + ϕ] + v0x
with v0 = (e/m ω) E0, which is the maximum amplitude of the velocity

integrate again to get position
x[t] = (e/m (ω^2)) E0 Cos[ω t + ϕ] + v0x t + x0x = x0 Cos[ω t + ϕ] + v0x t + x0x
with x0 = (e/m (ω^2)) E0, which is the max amplitude of oscillation

Apply initial conditions: 
vx[0] = 0 = - v0 Sin[ϕ] + v0x
v0x = v0 Sin[ϕ]
x[0] = 0 = x0 Cos[ϕ] + x0x
x0x = -x0 Cos[ϕ]

calculations: 
vary the phase of electron release and look at the change in trajectory
some phases (e.g. 17deg) will give a fast returning electron
It would be very straightforward to extend this to include some y-dependence to the electric field - this ellipticity will make the electron miss the ion

The next step to extend this is to find the time of recollision, then evaluate the electron KE at that time. 

Then plot that vs initial phase.

x0  :=  ((e E0)/(m (ω^2)));
v0  :=  ((e E0)/(m ω));
x0x[ϕ_]  :=  - 
            x0 Cos[ϕ];
v0x[ϕ_]  :=  v0 Sin[ϕ];
x[t_, ϕ_] = 
        x0 Cos[ω t]  +  v0x[ϕ] t  +  
          x0x[ϕ];
vx[t_, ϕ_] = -v0 Sin[ω t]  +  
          v0x[ϕ];

m = 1; e = 1; ω = 1; E0 = 1;
Up0 = 
        (e^2) (E0^2)/(4 m (ω^2));
ϕ0  =  17;    
Print["position vs. time"];
Plot[x[t, ϕ0 Degree], {t, 0, 10}];
Print["velocity vs. time"];
Plot[
        vx[t, ϕ0 Degree], {t, 0, 10}];
Print["KE/Up ratio vs. time"];
Plot[m vx[t, ϕ0 Degree]^2/2/Up0, {t, 0, 10}, 
        PlotRange -> All];