t - Time elapsed

v - Speed of the positive charge

F
Things to Notice
Electric Field

The bottom graph illustrates the second derivative ($\frac{d^2 x'}{dt^2}$) of the apparent position of the charge ($x'(t)$). The radiated electric field measured by a distant observer is proportional to $-\frac{d^2 x'}{dt^2}$. That is why the electric field vectors point in the opposite direction to the acceleration curve does. The electric field is only correct if we are far away from the charge.

Electric Field Pulses

Look at the electric field vectors when $v$ is very high. Instead of a smooth wave, the radiation is concentrated into intense pulses separated by periods of near silence. This beaming effect is a hallmark of synchrotron radiation.

Why the Direction Change in the Spikes?

Try changing $v$ to around $0.75c$. You can see that the acceleration curve (in light blue) spikes downwards at equal intervals, so the electric field there has large pulses upwards. But if you increase $v$ even more, to around $0.85c$, you'll notice that the massive downwards spikes are way steeper, and now next to them, there are large upwards spikes too.

To understand why this is, we have to go on a bit of a tangent. The charge moves in a circle, which means at the end of each cycle it goes back to its original position; therefore, its motion is periodic. Because of that, $v' = \frac{dx'}{dt}$ also has to be the same at the start and end of each cycle. We can write this as $$v'(T) = v'(0),$$ where $T$ is the period of the circular motion. For seemingly no logical reason, we will now integrate the second derivative $a' = \frac{dv'}{dt}$ over one period, from $0$ to $T$. With the help of the fundamental theorem of calculus, we can evaluate the integral: $$\int_{0}^{T}a'(t)dt = v'(T) - v'(0) = 0,$$ because $v'(T) = v'(0)$ from above. This means the area under the acceleration curve across each cycle must be zero.

With this knowledge, we found a mathematical reason for the upwards spikes: if a downwards spike has a large "negative" area under it, we must compensate for that with a large amount of positive area, hence the upwards spikes. But if you increase $v$ even more, you'll see the downwards spikes disappearing from the plot. This is just a visual bug; actually, they are there, and they are massive, but too narrow to be drawn (aliasing problems). Because the upwards spikes are smaller and wider, they are still drawn, as are the electric field vectors under them. But if there were way more arrows, the massive upwards spike in the electric field would still be visible.