Is my amp "High Current"?

Nsgarch, itm is the speaker that 'decides' what it needs to produce sound, not the amplifier.
The electroststic speaker's membrane moves in concert with the alternating Voltage with which it is charged, just as you said. And, as you said, not much energy (watts) is used during that action. Not much more energy is necessary to produce the high frequencies (in fact less is usually necessary due to the low volume of those frequencies)in spite of the lowered impedence, thus no real need for 'high current' capability. The biggest problem for the amp on electrostatics is ringing or oscillation due to the highly capacitive nature of the load, not current draw.

Inpep, it's OK to think of it this way I suppose:

it is the speaker that 'decides' what it needs to produce sound, not the amplifier.

so long as it's understood that what is meant by "decides" is whether the speaker presents an electromagnetic load to the amp, or an electostatic load to the amp. If the load is electomagnetic, the amp will be required to supply voltage, but at a more or less constant current. If it's electrostatic, the amp will be required to provide current but at a more or less constant voltage.

So lets say you have a 40W tube amp, and that at 40 watts output, you're getting the product of 10A x 4V (= 40W) Now lets say you have 100W ss amp and that at 100 watts output you're getting the product of 10A x 10V (= 100W).

So both amps can deliver 10A. But the tube amp can deliver 10A at 40W output, while the ss amp delivers 10A at 100W output. If you need big voltage to provide power to drive an electomagnetic load like a big woofer, the high output ss amp makes more sense because it delivers 10V at it's max. 100W output. The toobie only delivers 4V at its max. 40W output. But if you're driving an electrostatic load, then the tube amp makes more sense because you can get the same current at less than half the power output of the ss amp. And you're gonna say, "So what, you're still driving the stat with 40W instead of 100W, so it won't be as loud as with the SS amp." However, that's not true if you're delivering the same high current (not voltage) the stat needs to generate strong electrostatic attraction/repulsion. In fact it is this property of tube amps which leads to the (erroneous) statement, which you may have heard, that "Tube watts are more powerful than SS watts." This is of course bullpuckey. I just depends what kind of watts your speaker "decides" it needs ;-)

Nsgarch, if a speaker needs big voltage (say 40 v) to drive it to a certain level then that is what it needs, and the subsequent power that it needs will follow if the amp can supply the current. The tube amp will give it that voltage (40V) and what ever current is necessary up to its power limits. If the speaker needs 40V and 100watts to produce that certain level, then the amp will supply the 2.5 amps x 40 Volts quite easily. The 40V requirement and 100watts requirement are fixed by the speaker. The amp can't decide that, because it can't produce 40V but can supply 25V at 4 amps thus 100watts, it will do that. As long as the voltage demand and power demand are within the tube amp's specifications, the voltage will not be be dragged down by the load. This not the case with SS, unless it is capable of increasing its amps into lower loads in order to make up for the increased power demand. That is why dynamic speakers are considered more 'current' driven.
At any rate, as you have said there is not much current involved in electrostatics, therefore it is varying Voltage that drives them. Electrodynamics, due to the varying current demands along with the varying voltage driving them, are more current driven. This the opposite to what you have contended.

Inpep, you still appear to misunderstand the the terms voltage, power and current, and more important, how they relate to each other. If you will spend some time with this site:
http://www.allaboutcircuits.com/vol_1/index.html
until these relationships are second nature, you will understand what I am trying to say.

Speakers (with voice coils, and primarily woofers) need power (watts) if it takes work to move them (power = voltage x current.) BUT, they need those watts (power) to come primarily from a larger reservoir of voltage since voltage drops as power is consumed. An ESL needs power too, but from a reservoir of current. As the frequency rises and the impedance drops, yes, they need power too, but they are going to draw current out of those watts to maintain the strength of the static charge on the membrane. They don't need volts for that!

All amplifiers supply BOTH increasing voltage AND current as the volume (input signal to the amp) is increased. The maximum output of the amp (in watts) is a product of its max. voltage times its max. current, and those two can be in ANY proportion. But with tube amps, current is usually in larger proportion to voltage than in ss amps where it's the reverse. I just don't know how to say it any more clearly.
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Nsgarch, this discussion is getting nowhere precisely for the reason that you think that my understanding of power etc. is faulty, when in fact I can say the same for your understanding.
I guess my fault is in trying to explain in layman's terms what the relationship is among power, potential and current.
let's leave it at that.
One lat note, though. I am not the only person who pointed out that your understanding was reversed.
respectfully, Bob p.