Angular momentum loss from quadrupole EM radiation

[Barnak]

I'm looking for the general formula for Angular Momentum radiated away from quadrupolar electromagnetic radiation. I searched the usual books (Jackson, Landau-Lifchitz, ...) and just found the usual dipolar contributions.

Using dimensional analysis and energy radiated away, I found this formula, but I need a confirmation that it's the right one.

\frac{dL_i}{dt} = - \frac{1}{90} \, \frac{1}{4 \pi \epsilon_0 c^5} \, \varepsilon_{ijk} \; \ddot{Q}_{jl} \; \dddot{Q}_{lk}.

Someone has a comment on this ? Any reference ?

 

[Barnak]

Nobody knows anything about electromagnetic radiation here ?

For reference, the energy radiated away from the quadrupole contribution is

\frac{dE}{dt} = -\: \frac{1}{180} \, \frac{1}{4 \pi \varepsilon_0 c^5} \; \dddot{Q}_{ij} \; \dddot{Q}_{ij}.

This is a standard well-known result.