This is a diagram of the exterior of a electrostatic propulsion system. I fully aim to prove that this is not only possible but, the cleanest means of reaching space. The whole propulsion system is dependent on a few factors. How many watts the Cathode can actually handle, how many watts it takes to beat the speed of sound, and how much the entire system weighs.
The first priority is to determine how many volts, and how many watts are required to lift one gram. We go to this link at NASA. Why, because, they have an electrostatic levitator, and step one in this process would be replace the droplet of molten metal and weighing a battery operated circuit against a counter weight. It's pretty obvious that NASA's Levitation system works using a process similar to the magnetic levitation devices and kits that you often see on the internet. NASAs device controls the voltage, and current between the two plates as opposed to controlling the magnetizing current through a coil Example. The lasers are doing the job of the sensors in NASA's example, and the computer is doing the job of the operational amplifier by controlling the output of a high voltage supply.
This would mean building your own small scale test circuit to rectify a high voltage, between 10kV and 40kV then measure the difference apparent weight between a counterweight and the circuit. You would design the circuit in a plastic model making use of styrene as a the dielectric hull, a series of diodes in a voltage doubler rectifier to make the cathode negative, and keep the anode positive. Finding the actual thrust would require balancing the circuit against a counterweight at an equal distance from the fulcrum of the lever. Placing a scale under the counterweight, or using successively smaller counterweights in place of the original while the circuit is on. In the diagram it is positioned to lift itself, and will push the counterweight side of the balance beam down. At this point only the number we are interested in is the gram/watt ratio. This would give us, how many grams per Watt, or Watts required to lift one gram based on the output of any given circuits actual output. This is only true if you know where all the power in the circuit is being used. Some will go to biasing the oscillator, and some will be lost as a result of resistance, and impedances that are present as a result of power conversion. That means that part of the draw on the battery is divided up into biasing of the oscillator, pre-amplifier, and finally the AC to DC conversion required for lift. Now, if you built the Chaotic Resonant Circuit the measured output of the final stage would be the number of watts used by the cathode, if you know the impedance of air, or measure current from the output between the voltage doubler negative output connection to the proposed cathode mounted on the model from the inside. Operating the circuit with two 9V batteries in place of a split regulated power supply, and a counterweight of equal proportions.