How to animate a vector field along a given curve with gganimate

Happy 2022, RStudio Community!

I want to animate a vector field along a given curve, using gganimate, so that at any given moment the current frame shows only the vector at the current position along the curve, but the entire curve is shown in every frame. I would really appreciate any help?

In the code chunk below, I almost created what I want but the curve loops back. Also, the curve looks very pixelated. There must be a way to turn this geom_function into a layer so that the entire curve is displayed in every frame, without looping back.

library(gganimate)
library(ggplot2)
data<- tibble(x = seq(0,20,by = 0.1), y = sqrt(x) , vx = 1, vy = 1)
p<-ggplot(data, aes(x,y)) +
  coord_fixed() +
  geom_function(fun=function(u) sqrt(u), xlim=c(0,20), col="gray") +
  geom_line() +
  geom_point() +
  geom_segment(aes(x = x, y = y, xend = x + vx, yend = y + vy), 
               arrow = arrow(angle = 30, length = unit(2, "mm"),
               ends = "last", type = "open"), col="blue")
p + transition_reveal(x)

test