I want to regulate the input current into an ultrasound transducer (40 kHz, 50W). The signal is being generated by PCB. I read that regular potentiometers are usually employed up to a power of 1 Watt. I have found potentiometers that could be used, but they seem a bit bulky and expensive (ca. 80 EUR). Is there an alternative to a standard potentiometer to regulate the current up to 50W?
Don't try to scale down the 50 W signal coming out of the driver. Instead, control the driver circuit to produce a lower amplitude signal.
This is the same concept as a volume control for audio. There isn't some big fat pot between the power amp output and each speaker. Instead, the volume control adjusts the amplitude of the low power signal going into the amplifier.
Show the power driver, and how it is controlled. From that we can probably recommend ways to cause it to make less power. Without those details, there is little to say.
You could use a MOSFET as a Voltage Controlled Resistor, as long as you use a large heat sink and perhaps a fan.
Piezo devices are dielectric resonators and as such the current is proportion to voltage and frequency.
If you want to regulate the power, the most convenient way is to have a voltage controlled Vcc to the driver which can be done with a low power pot to an adjustable SMPS or LDO in the feedback ratio.