# ZVS circuit to generate high DC voltage

I'm trying to design a high DC voltage generator to create a voltage differential between the upper and the lower part of a cloud chamber I'm building. I'm trying to use a ZVS circuit to amplify an input voltage of 12V and then further amplifying it using a transformer. I'm following the circuit shown in this video (https://www.youtube.com/watch?v=iHkKTGYc6aA&ab_channel=GreatScott%21, minute 8:30 and on) using same components. Now, what I need is really a DC output, whereas the output I get is AC (8-10kV, I assume): working with ZVS circuit is pretty new to me, hence I would like to ask if there was a method to rectify output current cheeply, without using high voltage bridge rectifier and capacitor after the transformer.

Nonetheless, there is no other way I've already tried searching for such components. My reasoning was the following. The input current of the circuit, as it is shown in the video, is about 400mA. Then, the current flowing through the primary of the transformer should have an RMS value of about 600mA. Since the power ideally is conserved, across the transformer, the output RMS current should be of I2 = (V1 / V2) * I1 = 0.8mA. Thus, I would need 4 diodes which can handle at least 10kV of reverse voltage and 0.8mA. I calculated the capacitance for the ripple capacitor using the formula C = I / (2 f Vpp) where V_pp is the peak to peak voltage of the ripple. The frequency of the ZVS circuit is about 42kHz. Setting Vpp = 1V, the capacitor should mesure C=10nF and should handle 10kV at least (which is a very difficult to find). Is this reasoning correct?

This is the circuit schematic from the video: 