Reply To: extracting energy out off the plasma soup

[Francisl]

You have to consider the direction of the magnetic field. An alpha particle beam passing lengthwise through the center of a solenoid is equivalent to an electric conductor running lengthwise through the center of a solenoid. The lines of the magnetic field surrounding the conductor run parallel to the windings of the solenoid. Each layer of windings in the solenoid are exposed to the same intensity of the magnetic field from one end of the coil to the other. There is no driving force to create a voltage difference and current flow.
If you turn the solenoid perpendicular to the direction of the particle beam then you get a difference in the magnetic field from one end of the coil to the other end and that would cause a voltage difference and a current flow. The coils have to be designed to take into account the high speed pulses of the particle beam. Many such coils could surround the particle beam.
Here is a link to a Rogowski coil.
I think other variants would work too since this is a pulsed current. You just have to keep in mind the direction and intensity of the magnetic field as it changes with time.