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Hi,
the major Probs regarding a DD-ESL-Amp are the high voltages needed, the reactive, strongly varying impedance of the ESL and the enormous power You need for sufficient bandwidth.
Because of the fallig impedance of a capacitor, You´ll need some current to drive the ESL at higher freqs, i.e a lot of wattage. Additionally the amp has to work stable with highly capacitive loads.
Using high efficiency panels like MLs that don´t need much voltage to sing is the first way to a solution.
Simple triode amps can do the job then -when You´ve got the right tube, i.e a KR845 running on 2kV plate voltage and Class A. A triode with an active load (current source) will be better, especially with regard to higher load currents and greater bandwidth and linearity and low output impedance. Feedbackless amplification with exceptional good sound and dynamics is then possible

Using a good panel You only need to equalize the phase cancellation which is easily done with an active filter and which doesn´t stress the amp because of the low load currents in that frequency range.
Nearly all other concepts work with pentodes (Class B, or AB) and rely on heavy feedback and compensation to get the thing linear (Beveridge, Acoustat, AudioExclusiv). The sound of these devices is relatively poor with regard to cost and is imo no way better than using a good but much cheaper and safer trannie.
One of the biggest probs is to find the right power devices (e.g running a 6HB5 or PL509 on 5kV can´t be good, when the tube is rated for 700V continous plate voltage, even when 7kV pulses are allowed!) If You´re using triodes for the power stages the driver stages will be quite demanding, but highvoltage FETs could do the job.
There are just a very few special highvoltage transistors around that aren´t intended for these applications, so in most cases tubes do the job, but not normal audio tubes. You won´t find 5kV, 500mA babes in the standard audio department.
Another prob is to get a good and clean power supply. Best thing is probably to get one from those highvoltage companies, who sell supplies up to several hundred kV and kW.
The whole beast will work and sound deliciously good but it´ll cost! It´ll be rather inefficient! It´ll heat up the listening room!
It can be a very dangerous part to work with!
But what the h...
Yeah
Calvin