Electronic – Why do resistors in parallel with each diode in a diode string prevent high voltage damage

The purpose of the resistors across the diodes is a balance the magnitude of the reverse voltage across each individual diode.

A quick way to estimate the resistor value is to check the diode datasheet for the maximum reverse current at the maximum voltage you will be applying across the diode. Then choose a resistor value that gives about 10 times that current, again at the maximum voltage across the diode.

You also need to ensure that the voltage rating of the resistor is adequate. That is: the maximum voltage across the resistor must be less than what the datasheet for the resistor says.

Because the diode curve is exponential when forward biased, a slight increase in voltage above the threshold voltage in a diode results in a relatively huge potential current change. R1 in your case is linear (since it's a resistor) so when you try and force a huge current through it because of the diode, the voltage on R1 correspondingly rises. This leaves little voltage left over for RL to get. In fact it will be "Vt+ a little bit". In this way, the diode doesn't perfectly clip the voltage to RL, but to a broad approximation does.

To a broad approximation this is the equation that would show clipping. In it, I'm ignoring current through RL because I'm assuming that it's negligible relative to the diode current at high voltages. n~1, VT~0.025 (thermal voltage), Is~1e-12. $$ V_{R_L} = V_{sin} - R1*I_s(e^\frac{V_D}{nV_T}-1) $$

https://en.wikipedia.org/wiki/Diode_modelling