Lorentz force is the force a magnetic field exerts on moving electric charge, acting at right angles to both the motion and the field — and, summed over every charge in a current-carrying conductor, the mechanical load a magnet's structure has to carry.
For a single charge the force is qv × B, the cross product that also adds an electric term qE in the full expression. For a wire it reduces to a form an engineer can use directly: a conductor carrying current I over a length L in field B feels a force I L × B, perpendicular to both. The same force that curves a charged particle onto a 📝gyroradius in a confined 📝plasma therefore also pushes on the coils producing the field. In a magnet the load is self-inflicted: each turn sits in the field its neighbors make, so a solenoid is pulled outward in hoop tension, and the 📝toroidal field coil set of a 📝Tokamak is squeezed inward toward the machine axis by a large centering force while the 📝poloidal field twists each coil out of its own plane.
The scaling is what makes this the governing constraint at high field. Force density goes as current density times field, and the equivalent magnetic pressure goes as B²/2μ₀ — about 160 megapascals at 20 📝tesla, a stress comparable to the yield strength of structural steel and nearly three times what a 12-tesla magnet must survive. Raising the field to shrink a machine buys 📝fusion power density at the price of structure, which is why the characteristic D profile of a toroidal field coil is chosen as the curve along which those forces resolve into pure tension, and why 📝REBCO conductor is jacketed, soldered, and impregnated rather than merely wound: the ceramic film loses 📝critical current under strain, so the structure must take the load before the 📝superconductor does.