1. Angular momentum conservation: 1
Azimuthal component x R gives torque balance:
Couple exerted by Lorentz
force on unit volume
Angular momentum
transported by flow

2. Angular momentum conservation: 2
Equation of motion becomes:
constant

3. Net angular momentum flux
Integrate azimuthal equation of motion to get:
Constant of integration on each
field-streamline. L is the
net angular momentum per
unit mass carried in the plasma
motion and the magnetic stresses
Wind carries angular momentum away from star.
Lorentz force transmits torque to stellar surface.
Star spins down.

4. The story so far:
Induction 1
Mass continuity 2 3
Torque balance

5. The Alfvénic point Use (1) - 0/R2 (3) to eliminate B: Substitute:
to get:
u is singular at Alfvenic point up=uA unless:

6. Weber-Davis radial-field model
Radial field lines close to star (“split monopole”).
Spherical Alfvénic surface, radius rA.
Isotropic mass loss.
Angular momentum flux across area ds is:
Mass flux
Net specific angular
momentum transported
along field line anchored
at latitude 
Area of surface element ds
=4/3

7. Net spindown torque on star
Density at Alfven radius:
Net torque on star:
Radial or
dipole field
For thermal driving, uA~ 2 to 3 cs, indep. of .
For linear dynamo law, B0 ~ .
If stellar moment of inertia is constant:

8. General braking laws
Asymptotically:
Hence for p = 3,
cf. Skumanich.