From: bds@ipp-garching.mpg.de (Bruce Scott TOK )
Newsgroups: sci.physics.fusion,sci.physics.plasma
Subject: Re: Is an ion beam conductive?
Organization: Rechenzentrum der Max-Planck-Gesellschaft in Garching

Torin Walker (torin@torinet.com) wrote:

: In a toroidal magnetic confinement chamber, an energized plasma is
: conductive. Inside the plasma, ions travel in one direction, electrons
: in the other. Y'all know the theory...

: What can be said for ions only? If one has an ion stream configured
: in a ring, or loop, it is also conductive? (I would imagine so.)

Ions are still charged particles, and because of that they do feel an
electric force. The short answer is that unless you have an exotic
situation, in steady state the electric field parallel to the magnetic
field has to vanish (or if there is no magnetic field the electric field
has to completely vanish). In that sense, you can say the conductivity
is infinite.

With conductivity (or its inverse, resistivity, since we usually have
resistive dissipation in mind), we usually think of electrons, since
being less massive they carry most of the current if you look in the
center of momentum frame. It is mostly collisional friction against the
ions which causes resitive dissipation, but it is modified by the fact
that there are also electron-electron collisions.

In a two-component plasma resistivity is a process of momentum exchange
which acts to reduce the relative drift between the two species, that
is, to reduce the current. In a pure ion or pure electron plasma it is
quite different (and interesting). Since there is only one species,
there can be no change of the momentum solely as a result of collisions
between individual particles (each particle-particle pair in a collision
conserves momentum and energy during the collision), and therefore the
collisional process cannot lead to resistance. The conductivity in this
sense is therefore infinite, whether you are dealing with ions or
electrons -- there is only one species. There may be some subtleties I
am missing [1], but I would write the equation for momentum parallel to
the magnetic field (or in general if there is no magnetic field) as
this:

n_i M_i (d/dt) u = - grad p_i + n_i Z e E

neglecting viscosity, where p_i is the ion pressure, n_i is the ion
density, Z e is the charge on one ion, u is the ion fluid velocity, and
d/dt is the total derivative including advection by u. Since ion-ion
collisions do not change the net momentum, they may cause viscosity but
this cannot lead to any reduction of the current per se. If you turn
this around, into an equation for E, the electric field, you get

E = (1/n_i Z e) grad p_i + (M_i/Z e) (d/dt) u

and if as may be usual there is no thermodynamic gradient parallel to
the magnetic field (no grad_parallel p_i), you get

E = (M_i/Z e) (d/dt) u

Now, the difference to the usual situation is the absence of an obvious
resistivity term (eta J), but you now have the inertia (which in the
electron case you often ignore). In a steady state possibly with flow
but with no flow gradient, E has to be zero parallel to the magnetic
field (it must be completely zero if there is no magnetic field). That
by itself is like ideal MHD, so in this sense you may say the
conductivity is infinite.

In wavelike dynamics, the inertia may play the role of resistivity (as
it does for electrons in a two-component plasma [2]), so E does not have
to be zero. Nevertheless, you always have enough conductivity that E
cannot increase without bound.


[1] Tom O'Neill and collaborators at UCSD have been studying this for
decades, and there is a book about it which came out 5 or so years ago,
called Non-Neutral Plasmas (I know neither author nor publisher, but
that's the title). It is technical, but you may find it interesting to
look at.

[2] In wavelike dynamics, a phase shift between E_parallel and
J_parallel caused by instabilities in a collision free system will make
the inertia look like a complex resistance whose real part does not
vanish. Several of us in the microinstabilities and turbulence
community in fusion research have been working on this, although to my
knowledge it is all in scientific papers. See for example, Hammett and
Perkins, Phys Rev Lett 64 (1990) 3019-3022.

--
Mach's gut!
Bruce Scott The deadliest bullshit is
Max-Planck-Institut fuer Plasmaphysik odorless and transparent
bds@ipp-garching.mpg.de -- W Gibson