Power formula for space navigation, MHD propulsion

[soliris]

TL;DR

Power = budi
Extended power formula for space navigation with MHD propulsion, considering that planet Earth owns such an engine..

Hello

Interested in MHD propulsion, I thought this power formula in watts, inspired by the Lorentz force, might be useful:
P = B.U.D.I,
where B = Tesla magnetic field, U = rotational speed, D = diameter of a rotating magnet, and I = intensity of the injected electric current.
The model used here, I admit, is that of planet Earth, which seems to possess such an internal engine!

What do you think?

 

[Baluncore]

While MHD may be important for ionic particles suspended in the atmosphere, the Earth's magnetic field is probably insufficient to keep a juggler's balls in the air.

What were you thinking of navigating through space ?
The Earth's magnetic field might be distorted by the object's mass.

 

[soliris]

Hehe, the juggler's balls..

You're absolutely right about the outer magnetosphere: the surface field is indeed minuscule (~50 microteslas). But it's different in the ferrous core, where the Earth's thermal and magnetic engine originates, isn't it?

Actually, I was thinking more about the Earth's depths, because my formula is inspired by geodynamo models in the liquid outer core, where Lorentz forces (F = I × L × B) coupled with convection currents generate the Earth's magnetic field. So, to answer your question about space navigation: no, I don't intend to use the Earth's field as a point of leverage! The Earth analogy simply came from the idea of a moving conducting fluid." under the influence of magnetic and electric forces.

I envision instead an MHD thruster carrying its own high-temperature superconducting magnet to generate a very intense local magnetic field (B).

(I previously subjected this formula to a rigorous dimensional analysis -taking U as the linear velocity at the rotor's extremities-. The product does indeed yield Watts. Obviously, this doesn't presuppose geometric coefficients (the π factors, the flux orientation, etc.) or Joule effect losses.

You mention the distortion of the field by the object's mass; regarding the formula P = B ⋅ U ⋅ D ⋅ I, if we apply it to a closed propulsion system (such as an MHD submarine or an autonomous space propulsion system with its own magnet), are you referring to a magnetic shielding effect or a specific magnetohydrodynamic interaction within the space plasma?