Drift velocity and current at different cross sections in the tube during photoelectric effect

In photoelectric effect if we look at two different cross sections inside the tube at saturation current. Then the average drift velocity will be different as the electrons are accelerated by external battery.

So does this mean average current is different at different cross sections. According to me it (current) should remain the same at both cross section. But average drift speed is different. So by $$I=neAv_d$$ Either n should be different at different cross sections or i should be different. But if n is different is there any explanation why does electron density change.

Note:- I am assuming cross sectional area constant through the tube

• @ATHARVA Imagine a bunch of cars moving at $1$m/s, at $10$ m intervals. First car crosses the start line and accelerates. Second car crosses the start line $10$ sec later and accelerates, etc. The cars will be crossing the finish every $10$ seconds, but the distance between them will be greater, since their speeds are greater. So the cars move faster, with lower density, but we still have one car crossing the start line and finish line every $10$ seconds. – V.F. Sep 19 '18 at 19:23