Velocity Drifts of proton-muon gas

[QuarkDecay]

When do we use the equations of curvature drift ( ΔΒ⊥Β) V_∇B= ±1/2u_⊥r_L (B x ∇B)/B² and the general V_F= c/q (F x B)/B²?

For particles like muons and protons, do they need different equations to calculate a gas' drift velocity, when the gas is made of protons or muons instead of electrons?

Am I wrong if I think that since protons or Atoms like He can be considered non relativistic particles, we consider that the gravity is the one responsible for their drift, therefore they need the V_F one, meanwhile muons' mass is too small to use the V_F, so we need the V_∇B one?

 

[LightHero]

The equations of curvature drift (ΔΒ⊥Β) V∇B= ±1/2u⊥rL (B x ∇B)/B2 and the general VF= c/q (F x B)/B2 are used to calculate the drift velocity of charged particles in a magnetic field. The equation used depends on the energy of the particles. For non-relativistic particles such as protons and helium atoms, the VF equation can be used. For relativistic particles, such as muons, the V∇B equation should be used instead.