Predicting Lorentz force fluid particle trajectories

MagnetoBLI

I am trying to understand how the Lorentz force affects bulk fluid motion when I have an applied electric field (y-axis), applied magnetic field (x-axis) and bulk fluid velocity (z-axis), all orthogonal to each other.

I understand that if the fluid was at rest, an electrostatic force would generate a velocity in the y-axis, which would also generate a Lorentz force/velocity in the z-axis and form the cyclotron effect.

However, when the bulk fluid velocity in the z-axis exists, I presume this flow cannot be considered a moving charge (as both ions and electrons are travelling) and therefore the only moving charge is associated with the electric field. Instead a dynamo effect would take place such that the momentum force of the z-axis fluid flow would generate a current in the negative y-axis (should be negative in the image) and this current would in turn produce a force in the z-axis, thus accelerating the bulk fluid motion. Therefore the net effect would be to increase the radius of the cyclotron affect in the z-axis. Is this correct?

Could you tell me where the magnetic and electric field vectors should be to produce a force perpendicular to the bulk fluid motion (right schematic in the attachment)?

Any comments are much appreciated.

Cheers.

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