What is Poynting Flux?

今天又重读了BZ77，想弄清楚BZ过程产生的Poynting喷流到底是什么。看到摘要有这样一句话：
1） When a rotating BH is threaded by magnetic field lines supported by external currents flowing in an equatorial disc, and electric potential difference(电势差) will be induced. If the strength is large enough, the vacuum is unstable to a cascade(喷流) production of electron-positron paris and a surrounding force-free magnetosphere will be established.

读Komissarov的"Electrodynamics of BH magnetoshperes" astro-ph/0402403有下面的文字：
1） to get better insights into the properties of the plasma filled magnetospheres of BH.

It is generally accepted that the magnetospheres of BH are filled with perfectly conducting e^+ ~ e^- plasma (BZ77).
这些说明：磁球是充满由正负电子对组成的等离子体的；

2） Contray to what is expected in the Membrane paradigm, the energy and angular momentum are not only along the magnetic field lines penetrating the event horizon but along all field lines penetrating the ergoshpere.
说明：磁力线是穿过黑洞视界面的；

3） The electrodynamic mechanism together with the horizon theory (the event horzon could be treated as a rotating conducting surface with surface charges, surface currents, and a finite surface resistivity) now widely accepted by the astrophyics community. In great contrast to this mainstream (主流) trend, Punsly and Coroniti and later Punsly completely rejected (拒绝) both these theories. They argued that the event horizon cannot be regarded as a unipolar inductor because it is causally diconnected from the outgoing wind. Indeed, both the fast and the Alfven waves generated at the event horizon can propagate only inwards and cannot effect the events in the outer space.
注：Punsly和Coroniti是很反对BZ77的；


看了astro-ph/0302468终于找到一丝线索：
Though usually thought of as a property of vacuum waves, the Poynting flux
S = cE × B/4π is a more generally useful quantity. In ideal MHD1, the electric
field is E = v × B/c, where v is the fluid velocity. The Poynting flux is thus
S = v⊥B^2/4π, where v⊥ is the velocity component perpendicular to the field
lines.
Thus the Poynting flux in ideal MHD can be seen as a magnetic energy
carried by the flow. However, it is also clear that it is not just the magnetic
energy density B^2/8π that is being carried, since that accounts for only half of
the Poynting flux. The other half can be accounted for by interpreting S as the
flux of magnetic enthalpy, wm = Um + Pm, where Um and Pm are the magnetic
energy density and the magnetic pressure, both equal to B^2/8π. This is similar
to ordinary hydrodynamic flow, where the thermodynamic energy flux is given
by the flux of enthalpy w = U +P, instead of just the flux of thermal energy U.
This distinction between enthalpy- and energy fluxes plays a crucial role in the
following, where we discuss the acceleration of the flow.
(1We assume ideal MHD here. It turns out that for typical GRB parameters (energy, mass flux)
ample charge carriers are present to maintain ideal MHD conditions (E ≪ B in the fluid frame)
out to distances several orders of magnitude larger than the photosphere. One also verifies that
the charge density which generically accompanies relativistic MHD flows only has fluctuating
components, associated with the reconnection process. The charge density associated with the
net azimuthal field that carries the magnetic energy flux vanishes.)

关于磁能耗散 （Dissipation of magnetic energy）
Through instabilities and reconnection, the magnetic energy in the flow can be
converted into kinetic energy of the plasma or into fast particles, and from there
into heat or radiation. The effects of this dissipation depend on how fast it takes
place. If the dissipation is very fast so that it takes place close to the central
engine, the magnetic energy flux is converted into a dense pair plasma, which
then expands creating a classical fireball. The main use of the magnetic field
in this case is to transfer rotational energy of the central engine to the outside,
into the low-baryon environment needed for a gamma-ray burst.
If the dissipation is sufficiently slow, on the other hand, most of the magnetic
energy flux can dissipate outside the photosphere of the flow. The dissipation
then takes place in an optically thin environment. Instead of thermalizing, the
fast particle populations produced by the reconnection process then radiate their
energy as synchrotron emission in the magnetic field of the outflow.
At the same time, dissipation of magnetic energy reduces the total pres-
sure and thus creates an pressure gradient that accelerates the flow outward.
In this way, a magnetic central engine can provide both the acceleration of the
flow and the dissipation outside the photosphere needed for efficient prompt ra-
diation. Finally, under just the same conditions, the magnetic field outside the
photosphere is large enough (10^7-10^8 G) for the most likely radiation mecha-
nism, synchrotron emission, to be very efficient. Hence three crucial ingredients
for prompt GRB emission are the natural result of magnetic dissipation in a
magnetically powered GRB outflow.