Not sure if I’m interpreting this right, but here’s what I got for the light position:
fps = 1/thisComp.frameDuration;
t = Math.floor(fps*time)/fps;
cur_frame = time*fps;
lambda = cur_frame%1*30;
x= 100*Math.exp(-(t-5)*(t-5)*lambda)*Math.cos(10*t);
y = 100*Math.exp(-(t-5)*(t-5)*lambda)*Math.sin(10*t);
z = 20*t;
[x,y,z]
With 30000 particles per second and a particle life of one frame, I get something that looks like this (a still from early in the animation). This shape unfurls along time.

Kalleheikki Kannisto
Senior Graphic Designer