*Astron. Astrophys. 326, 1277-1284 (1997)*
## On collimation of the outflows in force-free magnetospheres
**
I. Okamoto
**
Division of Theoretical Astrophysics, National
Astronomical Observatory, Mitaka, Tokyo, 181 Japan
*Received 29 August 1996 / Accepted 9 June 1997*
**Abstract**
It is pointed out that "an indeterminacy" claimed to exist in the
*pulsar equation* (Sulkanen & Lovelace 1990) or a "free"
function (Appl &
Camenzind 1993a,b) can be
uniquely related to the stream function at the boundary of the
force-free region to the load region at infinity (Michel 1973b:
Okamoto 1974). The form of is given by
from the plasma conditions at infinity, where
is the angular velocity of field lines. This
relation can be interpreted as indicating Ohm's law for the return
current from the equatorial region to the polar region on the 'sphere
at infinity' with finite resistivity Ohm,
thereby ensuring the current closure. The field structure tends to be
asymptotically conical, toward the 'sphere at infinity' and fields
fill all the space there. It is argued that force-free models for
purely cylindrical jets cannot self-consistently conserve electric
current. The role of the plasma conditions in the black hole equation
is mentioned as well.
**Key words:** MHD
ISM: jets and
outflows
galaxies: jets
Black hole
physics
pulsars: general
*Send offprint requests to:* I. Okamoto (okamoto@nao.ac.jp)
### Contents
© European Southern Observatory (ESO) 1997
Online publication: April 8, 1998
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